ALBERT

Description:    In this note I examine a number of statement made in Wadee and Yiatros (Z. Angew. Math. Phys. 61:565–577 2010 ) in relation to my paper mentioned in the title. Most of the claims by Drs. Wadee and Yiatros are re-examined here in the proper context and it is shown that the results of the title paper are free of any errors. Content Type Journal Article Pages 1-4 DOI 10.1007/s00033-011-0133-4 Authors Ciprian D. Coman, School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, Glasgow, G12 8QW UK Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    The existence of at least one mass-conserving solution for continuous coagulation-fragmentation equation has been established by Escobedo et al. (J Differ Equ 195:143–174, 2003 ) for a large class of coagulation kernels under strong binary fragmentation. In this work, uniqueness of mass-conserving solutions is demonstrated with some additional restrictions on the fragmentation kernels. Content Type Journal Article Pages 1-17 DOI 10.1007/s00033-011-0129-0 Authors Ankik Kumar Giri, Institute for Applied Mathematics, Montan University Leoben, Franz Josef Straße 18, Leoben, 8700 Austria Gerald Warnecke, Institute for Analysis and Numerics, Otto-von-Guericke University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    The initial-value problem for u t = - D 2 u - m D u - l D | Ñ u | 2 + f ( x )              ( * ) is studied under the conditions \frac ¶ ¶ n u =\frac ¶ ¶ n D u =0 on the boundary of a bounded convex domain W Ì \mathbb R n with smooth boundary. This problem arises in the modeling of the evolution of a thin surface when exposed to molecular beam epitaxy. Correspondingly the physically most relevant spatial setting is obtained when n  = 2, but previous mathematical results appear to concentrate on the case n  = 1. In this work, it is proved that when n  ≤ 3,  μ ≥ 0, λ 〉 0 and f Î L ¥ ( W ) satisfies ó õ W   f ³ 0 , for each prescribed initial distribution u 0 Î L ¥ ( W ) fulfilling ó õ W   u 0 ³ 0 , there exists at least one global weak solution u Î L 2 loc ([0, ¥ ); W 1,2 ( W )) satisfying ó õ W   u (·, t ) ³ 0 for a.e. t  〉 0, and moreover, it is shown that this solution can be obtained through a Rothe-type approximation scheme. Furthermore, under an additional smallness condition on  μ and || f || L ¥ ( W ) , it is shown that there exists a bounded set S Ì L 1 ( W ) which is absorbing for ( * ) in the sense that for any such solution, we can pick T  〉 0 such that e 2 l u (·, t ) Î S for all t  〉  T , provided that Ω is a ball and u 0 and f are radially symmetric with respect to x  = 0. This partially extends similar absorption results known in the spatially one-dimensional case. The techniques applied to derive appropriate compactness properties via a priori estimates include straightforward testing procedures which lead to integral inequalities involving, for instance, the functional ó õ W   e 2 l u dx , but also the use of a maximum principle for second-order elliptic equations. Content Type Journal Article Pages 1-34 DOI 10.1007/s00033-011-0128-1 Authors Michael Winkler, Institut für Mathematik, Universität Paderborn, 33098 Paderborn, Germany Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    The present article investigates the overall bed permeability of an assemblage of porous particles. For the bed of porous particles, the fluid-particle system is represented as an assemblage of uniform porous spheres fixed in space. Each sphere, with a surrounding envelope of fluid, is uncoupled from the system and considered separately. This model is popularly known as cell model. Stokes equations are employed inside the fluid envelope and Brinkman equations are used inside the porous region. The stress jump boundary condition is used at the porous-liquid interface together with the continuity of normal stress and continuity of velocity components. On the surface of the fluid envelope, three different possible boundary conditions are tested. The obtained expression for the drag force is used to estimate the overall bed permeability of the assemblage of porous particles and the behavior of overall bed permeability is analyzed with various parameters like modified Darcy number ( Da *), stress jump coefficient ( β ), volume fraction ( ε ), and effective viscosity. Content Type Journal Article Pages 1-20 DOI 10.1007/s00033-011-0123-6 Authors Jai Prakash, Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721 302 India G. P. Raja Sekhar, Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721 302 India Mirela Kohr, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu Str., 400084 Cluj-Napoca, Romania Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    The authors study the small oscillations of a pendulum containing an almost homogeneous, incompressible, inviscid liquid (i.e. a liquid whose density in equilibrium is practically a linear function of the height, which differs very little from a constant) and a moving gas. Using functional analysis, they prove that the spectrum is comprised of a countable set of real eigenvalues and an essential spectrum, which fills an interval, and they give an existence and uniqueness theorem for the solution of the evolution problem. Content Type Journal Article Pages 1-20 DOI 10.1007/s00033-011-0118-3 Authors H. Essaouini, Faculté des Sciences de Tétouan, Université Abdelmalek Essaâdi, Mhannech II, B.P: 2121, Tétouan, Morocco L. El Bakkali, Faculté des Sciences de Tétouan, Université Abdelmalek Essaâdi, Mhannech II, B.P: 2121, Tétouan, Morocco P. Capodanno, Université de Franche-Comté, 2B, Rue des jardins, 25000 Besançon, France Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    We show how monotonicity methods combined with infinite dimensional sandwich pairs can be used to solve very general systems of equations that are not semibounded. Content Type Journal Article Pages 1-18 DOI 10.1007/s00033-010-0108-x Authors Martin Schechter, Department of Mathematics, University of California, Irvine, CA 92697-3875, USA Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    We prove that the spherically symmetric subsonic flows in an infinitely long straight divergent nozzle with arbitrary smooth cross-section are unique for the three-dimensional steady potential flow equation. The proof depends on an extreme principle for elliptic equations in an unbounded conical domain, under the assumption that the gradient of the solution is of order O (\frac1 | x | ) as | x | ® ¥ . Similar result holds for steady subsonic Euler flows in two-dimensional infinitely long straight divergent nozzles. Content Type Journal Article Pages 1-7 DOI 10.1007/s00033-010-0107-y Authors Li Liu, Shanghai Institute of Foreign Trade, 201620 Shanghai, China Hairong Yuan, Department of Mathematics, East China Normal University, 200241 Shanghai, China Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    We produce the equations of small deformations superimposed upon large for materially uniform but inhomogeneous bodies and specialize to an isotropic material and to a homogeneous finite elastic deformation. By assuming the small deformation to be a plane wave, a set of equations for the amplitude of the wave is produced which is accompanied by an additional set of conditions. By requiring a non-trivial solution for the amplitude, we obtain the secular equation and from it a set of necessary and sufficient conditions for having a real wave speed. The second set of conditions that have to be satisfied is due to the materials inhomogeneity. Essentially, the present analysis enhances the approach of Hayes and Rivlin for materially uniform but inhomogeneous bodies. The outcome is that for such bodies the restrictions on the constitutive law for having real wave speeds for an isotropic material subjected to a pure homogeneous deformation involves the field of the inhomogeneity as well. Content Type Journal Article Pages 1-10 DOI 10.1007/s00033-011-0125-4 Authors Dimitris Sfyris, Department of Civil Engineering and Geodesy, Institute of Continuum Mechanics, Technical University of Darmstadt, Hochschulstrasse 1, 64289 Darmstadt, Germany Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    The stability of anisotropic electroactive polymers is investigated. A general criterion for the onset of instabilities under plane-strain conditions is introduced in terms of a sextic polynomial whose coefficients depend on the instantaneous electroelastic moduli. In a way of an example, the stable domains of layered neo-Hookean dielectrics are determined. It is found that depending on the direction of the electrostatic excitation field relative to the lamination direction, the critical stretch ratios at which instabilities may occur can be either larger or smaller than the ones for the purely mechanical case. Content Type Journal Article Pages 1-12 DOI 10.1007/s00033-011-0136-1 Authors Stephan Rudykh, The Pearlstone Center for Aeronautical Studies, Department of Mechanical Engineering, Ben-Gurion University, 84105 Beer-Sheva, Israel Gal deBotton, The Pearlstone Center for Aeronautical Studies, Department of Mechanical Engineering, Ben-Gurion University, 84105 Beer-Sheva, Israel Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    A new mathematical model of two-temperature magneto-thermoelasticity is constructed where the fractional order heat conduction law is considered. The state space approach is adopted for the solution of one-dimensional application for a perfect conducting half-space of elastic material with heat sources distribution in the presence of a transverse magnetic field. The Laplace-transform technique is used. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusions about the new theory are given. Some comparisons are shown in figures to estimate the effects of the temperature discrepancy and the fractional order parameter on all the studied fields. Content Type Journal Article Pages 1-16 DOI 10.1007/s00033-011-0126-3 Authors Magdy A. Ezzat, Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt Ahmed S. El Karamany, Department of Mathematical and Physical Sciences, Nizwa University, P. O. Box 1357, Nizwa, 611 Oman Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    This paper considers the effects of radiation on the flow near the two-dimensional stagnation point of a stretching sheet immersed in a viscous and incompressible electrically conducting fluid in the presence of an applied constant magnetic field. The external velocity and the stretching velocity of the sheet are assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations using a similarity transformation, before being solved numerically by the Keller-box method. The features of the heat transfer characteristics for different values of the governing parameters are analyzed and discussed. The results indicate that the heat transfer rate at the surface decreases in the presence of radiation. Content Type Journal Article Pages 1-4 DOI 10.1007/s00033-011-0131-6 Authors Ioan Pop, Faculty of Mathematics, University of Cluj, CP 253, 3400 Cluj, Romania Anuar Ishak, School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia Fazlina Aman, Faculty of Science, Arts and Heritage, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat, Johor, Malaysia Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    In the present study, we apply function transformation methods to the D -dimensional nonlinear Schrödinger (NLS) equation with damping and diffusive terms. As special cases, this method applies to the sine-Gordon, sinh-Gordon, and other equations. Also, the results show that these equations depend on only one function that can be obtained analytically by solving an ordinary differential equation. Furthermore, certain exact solutions of these three equations are shown to lead to the exact soliton solutions of a D -dimensional NLS equation with damping and diffusive terms. Finally, our results imply that the planar solitons, N multiple solitons, propagational breathers, and quadric solitons are solutions to the sine-Gordon, sinh-Gordon, and D -dimensional NLS equations. Content Type Journal Article Pages 1-9 DOI 10.1007/s00033-011-0117-4 Authors M. A. Helal, (FInstP) Mathematics Department, Faculty of Science, Cairo University, Giza, Egypt A. R. Seadawy, Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    In this paper, we consider the positive solution of the Cauchy problem for the following doubly degenerate parabolic equation u t - div ( | Ñ u | p Ñ u m )= u q with p  〉 0, q  〉 1, m  〉 1, and initial value decaying at infinity and give a new secondary critical exponent for the existence of global and nonglobal solutions. Furthermore, the large time behavior and the life spans of solutions are also studied. Content Type Journal Article Pages 1-18 DOI 10.1007/s00033-011-0130-7 Authors Yongsheng Mi, College of Mathematics and Statistics, Chongqing University, 400044 Chongqing, People’s Republic of China Chunlai Mu, College of Mathematics and Statistics, Chongqing University, 400044 Chongqing, People’s Republic of China Rong Zeng, College of Mathematics and Statistics, Chongqing University, 400044 Chongqing, People’s Republic of China Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    In this paper, we study critical points of the functional J e ( u ):=\frac e 2 2 1 ó õ 0   | u x | 2 d x + 1 ó õ 0   F ( u ) d x , u   Î W 1,2 (0,1),            (1) where F : \mathbb R ® \mathbb R is assumed to be a double-well potential. This functional represents the total free energy in models of phase transition and allows for the study of interesting phenomena such as slow dynamics . In particular, we consider a non-classical choice for F modeled on F ( u )= | 1 - u 2 | a where 1 〈  α  〈 2. The discontinuity in F ′′ at ±1 leads to the existence of multiple continua of critical points that are not present in the classical case F Î C 2 . We prove that the interior points of these continua are local minima. The energy of these local minimizers is strictly greater than the global minimum of J e . In particular, the existence of these continua leads to an alternative explanation for the slow dynamics observed in phase transition models. Content Type Journal Article Pages 1-14 DOI 10.1007/s00033-011-0124-5 Authors Pavel Drábek, Department of Mathematics and Center N.T.I.S., University of West Bohemia, P.O. Box 314, 306 14 Pilsen, Czech Republic Stephen B. Robinson, Department of Mathematics, Wake Forest University, P.O. Box 7388, Winston-Salem, NC 27109, USA Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    Building on the results of Chapman et al. (Z Angew Math Phys 47:410–431, 1996 ) on the behavior of minimizers in the Ginzburg–Landau thin-film model, we show that the vortices in the three-dimensional superconducting thin films are located in the cylinders whose cross sections coincide with the disks that contain the vortices in the two-dimensional model. To arrive at this conclusion, we prove that the three-dimensional minimizers converge to the two-dimensional counterparts in H 1 and in C α . We also give examples of regimes in which the vortex structure of the two-dimensional minimizers is well understood. Our results, in particular, provide insight into the behavior of the three-dimensional vortices in these regimes. Content Type Journal Article Pages 1-17 DOI 10.1007/s00033-011-0122-7 Authors Dmitry Glotov, Auburn University, 221 Parker Hall, Auburn, AL 36849, USA Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    This paper is concerned with the multiplicity and concentration of positive solutions for the nonlinear Schrödinger–Poisson equations $$ \left\{ {l@{\quad}l} -\varepsilon^2\triangle u+V(x)u+\phi(x) u=f(u)& {\rm in}\,{\mathbb R}^3, \\ -\varepsilon^2\triangle \phi=u^2 & {\rm in}\,{\mathbb R}^3, \\ u\in H^1({\mathbb R}^3), u(x) 〉 0,& \forall x\in{\mathbb R}^3, \\ \right. $$ where ε  〉 0 is a parameter, V : \mathbb R 3 ® \mathbb R is a continuous function and f : \mathbb R ® \mathbb R is a C 1 function having subcritical growth. The proof of the main result is based on minimax theorems and the Ljusternik–Schnirelmann theory. Content Type Journal Article Pages 1-21 DOI 10.1007/s00033-011-0120-9 Authors Xiaoming He, College of Science, Minzu University of China, Beijing, 100081 People’s Republic of China Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    We extend the study of the integrability done by Leach and Miritzis (J Nonlinear Math Phys 13:535–548, 2006 ) on the classical model of competition between three species studied by May and Leonard (SIAM J Appl Math 29:243–256, 1975 ), to all real values of the parameters. Additionally, our results provide all polynomial, rational and analytic first integrals of this extended model. We also classify all the invariant algebraic surfaces of these models. Content Type Journal Article Pages 1-17 DOI 10.1007/s00033-011-0119-2 Authors Jaume Llibre, Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain Clàudia Valls, Departamento de Matemática, Instituto Superior Técnico, 1049–001 Lisbon, Portugal Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    We discuss stress relaxation and creep experiments of fluids that are generalizations of the classical model due to Burgers by allowing the material moduli such as the viscosities and relaxation and retardation times to depend on the stress. The physical problem, which is cast within the context of one dimension, leads to an ordinary differential equation that involves nonlinear terms like product of a function with a jump discontinuity and the derivative of a function with a jump discontinuity. As the equations are nonlinear, standard techniques that are used to study problems concerning linear viscoelastic fluids such as Laplace transforms and the theory of distributions are not applicable. We find it necessary to seek the solution in a more general setting. We discuss the mathematical and physical issues concerning the jump discontinuities and nonlinearity of the governing equation, and we show that the solution to the governing equation can be found in the sense of the generalized functions introduced by Colombeau. In the framework of Colombeau algebra we, under certain assumptions, derive jump conditions that shall be used in stress relaxation and creep experiments of fluids of the Burgers type. We conclude the paper with a discussion of the physical relevance of these assumptions. Content Type Journal Article Pages 1-34 DOI 10.1007/s00033-010-0109-9 Authors Vít Průša, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, Praha 8–Karlín, CZ 186 75, Czech Republic K. R. Rajagopal, Department of Mechanical Engineering, Texas A&M University, 3123 TAMU, College Station, TX 77843-3123, United States of America Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    This paper is devoted to a study of the longtime behavior of the hyperbolic equations with an arbitrary internal damping, under sharp regularity assumptions that both the principal part coefficients and the boundary of the space domain (in which the system evolves) are continuously differentiable. For this purpose, we derive a new point-wise inequality for second differential operators with symmetric coefficients. Then, based on a global Carleman estimate, we establish an estimate on the underlying resolvent operator of the equation, via which, we show the logarithmic decay rate for solutions of the hyperbolic equations. Content Type Journal Article Pages 1-14 DOI 10.1007/s00033-010-0113-0 Authors Xiaoyu Fu, School of Mathematics, Sichuan University, Chengdu, 610064 China Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    In this paper, we prove that the C 1 planar differential systems that are integrable and non-Hamiltonian roughly speaking are C 1 equivalent to the linear differential systems × u   = u , × v   = v . Additionally, we show that these systems have always a Lie symmetry. These results are improved for the class of polynomial differential systems defined in \mathbb R 2 or \mathbb C 2 . Content Type Journal Article Pages 1-8 DOI 10.1007/s00033-011-0116-5 Authors Jaume Giné, Departament de Matemàtica, Universitat de Lleida, Av. Jaume II, 69, 25001 Lleida, Catalonia, Spain Jaume Llibre, Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    Diffusive moment equations with an arbitrary number of moments are formally derived from the semiconductor Boltzmann equation employing a moment method and a Chapman–Enskog expansion. The moment equations are closed by employing a generalized Fermi–Dirac distribution function obtained from entropy maximization. The current densities allow for a drift-diffusion-type formulation or a “symmetrized” formulation, using dual-entropy variables from nonequilibrium thermodynamics. Furthermore, drift-diffusion and new energy-transport equations based on Fermi–Dirac statistics are obtained and their degeneracy limit is studied. Content Type Journal Article Pages 1-17 DOI 10.1007/s00033-010-0106-z Authors Ansgar Jüngel, Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040 Wien, Austria Stefan Krause, Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040 Wien, Austria Paola Pietra, Istituto di Matematica Applicata e Tecnologie Informatiche, CNR, Via Ferrata 1, 27100 Pavia, Italy Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    The stress field inside a two-dimensional arbitrary-shape elastic inclusion bonded through an interphase layer to an infinite elastic matrix subjected to uniform stresses at infinity is analytically studied using the complex variable method in elasticity. Both in-plane and anti-plane shear loading cases are considered. It is shown that the stress field within the inclusion can be uniform and hydrostatic under remote constant in-plane stresses and can be uniform under remote constant anti-plane shear stresses. Both of these uniform stress states can be achieved when the shape of the inclusion, the elastic properties of each phase, and the thickness of the interphase layer are properly designed. Possible non-elliptical shapes of inclusions with uniform hydrostatic stresses induced by in-plane loading are identified and divided into three groups. For each group, two conditions that ensure a uniform hydrostatic stress state are obtained. One condition relates the thickness of the interphase layer to elastic properties of the composite phases, while the other links the remote stresses to geometrical and material parameters of the three-phase composite. Similar conditions are analytically obtained for enabling a uniform stress state inside an arbitrary-shape inclusion in a three-phase composite loaded by remote uniform anti-plane shear stresses. Content Type Journal Article Pages 1-16 DOI 10.1007/s00033-011-0134-3 Authors X. Wang, School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai, 200237 China X. -L. Gao, Department of Mechanical Engineering, Texas A&M University, 3123 TAMU, College Station, TX 77843-3123, USA Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    In this paper, we explore the wave propagation phenomenon in three-dimensional (3D) isotropic fractal media through analytical and computational means. We present the governing scalar wave equation, perform its eigenvalue decomposition, and discuss its corresponding modal solutions. The homogenization through which this fractal wave equation is derived makes its mathematical analysis and consequently the formulation of exact solutions possible if treated in the spherical coordinate system. From the computational perspective, we consider the finite element method and derive the corresponding weak formulation which can be implemented in the numerical scheme. The Newmark time-marching method solves the resulting elastodynamic system and captures the transient response. Two solvers capable of handling problems of arbitrary initial and boundary conditions for arbitrary domains are developed. They are validated in space and time, with particular problems considered on spherical shell domains. The first solver is elementary; it handles problems of purely radial dependence, effectively, 1D. However, the second one deals with general advanced 3D problems of arbitrary spatial dependence. Content Type Journal Article Pages 1-13 DOI 10.1007/s00033-011-0135-2 Authors Hady Joumaa, Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green St., Urbana, IL 61801, USA Martin Ostoja-Starzewski, Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green St., Urbana, IL 61801, USA Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description: In the future, climate models predict an increase in global surface temperature and during winter a changing of precipitation from less snowfall to more raining. Without protective snow cover, freezing can be more intensive and can enter noticeably deeper into the soil with effects on C cycling and soil organic matter (SOM) dynamics. We removed the natural snow cover in a Norway spruce forest in the Fichtelgebirge Mts. during winter from late December 2005 until middle of February 2006 on three replicate plots. Hence, we induced soil frost to 15 cm depth (at a depth of 5 cm below surface up to –5°C) from January to April 2006, while the snow-covered control plots never reached temperatures 〈 0°C. Quantity and quality of SOM was followed by total organic C and biomarker analysis. While soil frost did not influence total organic-C and lignin concentrations, the decomposition of vanillyl monomers (Ac/Ad) V and the microbial-sugar concentrations decreased at the end of the frost period, these results confirm reduced SOM mineralization under frost. Soil microbial biomass was not affected by the frost event or recovered more quickly than the accumulation of microbial residues such as microbial sugars directly after the experiment. However, in the subsequent autumn, soil microbial biomass was significantly higher at the snow-removal (SR) treatments compared to the control despite lower CO 2 respiration. In addition, the water-stress indicator (PLFA [cy17:0 + cy19:0] / [16:1ω7c + 18:1ω7c]) increased. These results suggest that soil microbial respiration and therefore the activity was not closely related to soil microbial biomass but more strongly controlled by substrate availability and quality. The PLFA pattern indicates that fungi are more susceptible to soil frost than bacteria.

Description: Intensive land use may affect soil properties ( e.g., decreased soil organic matter [SOM] content) and, consequently, reduce crop yields considerably. One way of counteracting the loss of SOM and stimulating plant productivity could be the use of organic residues from agro-industrial processes as bioactive products. The present study was focused on the possible effects of phenol-containing organic substances derived from agro-industrial by-products on maize ( Zea mays L.) metabolism in a pot experiment. Plants were grown for 12 d in a nutrient solution in the absence (control) or in the presence of either a cellulosolitic dry apple hydrolyzate (AP) or a dry blueberry cool extract (BB) applied at two rates (0.1 and 1 mL L –1 ). Both products increased root and leaf biomass and led to higher concentrations of macronutrients in the plant tissue. AP and BB also had a positive impact on nitrogen (N) metabolism stimulating the activity and gene expression of phenylalanine ammonia-lyase, a key enzyme of the phenylpropanoid pathway. Furthermore, both products increased leaf concentrations of phenols (+ 28% and 49% for AP and BB, respectively) and flavonoids (+ 22% and 25% for AP and BB, respectively). From our results it can be assumed that residues from agro-industry may be successfully used as bioactive products in agriculture to increase plant yield and resistance to stress conditions.

Description: An agricultural use of reclaimed coal-mine spoil banks is limited to nonfood crop uses and provides potential for biofuel crops. Two high-biomass crops— Galega orientalis and Helianthus tuberosus —were cultivated in a greenhouse pot experiment conducted in sterilized and nonsterile spoil bank clay. We aimed (1) to determine the possibility of reducing the applied rate of organic amendments (thus decreasing the costs of spoil-bank reclamation) and (2) to assess whether the inoculation with arbuscular mycorrhizal fungi (AMF) can improve plant growth and biomass accumulation of bioenergy crops even in nonsterile soil containing naturally occurring AMF. The spoil substrate was either unamended or treated with a mixture of composted urban waste and ligno-cellulose at a rate corresponding to 40 t ha –1 . Three native AMF isolates or three isolates from the International Bank of Glomeromycota (BEG) originating from man-made ecosystems were used for inoculation. Generally, both plant species positively responded to both mycorrhizal inoculation and organic amendment. While G. orientalis did not show any preferences towards the AMF inoculum origin in the nonsterile soil, for H. tuberosus the specific combination of organic amendment and BEG isolates resulted in highest yields of shoot biomass. The study shows that the successful planting of both tested crops requires the organic amendment. However, its dosage can be substantially reduced. The effectiveness of mycorrhizal inoculation can vary for the combination of plant species and the origin of the applied AMF.

Description: Iodine is an essential element in the human diet, and iodine deficiency is a significant health problem. No attempts to increase iodine content in plant-derived food (biofortification) have so far been particularly effective. We studied iodine uptake in tomato ( Solanum lycopersicum L.) to evaluate whether it is possible to increase the iodine concentration in its fruits. Iodine translocation and storage inside tomato tissues were studied using radioactive iodine. Potassium iodide was also supplied at different concentrations to tomato plants to evaluate the resulting iodide concentration both in the vegetative tissues and the fruits. The results indicate that iodine was taken up better when supplied to the roots using hydroponically grown plants. However, a considerable amount of iodine was also stored after leaf treatment, suggesting that iodine transport through phloem also occurred. We found that tomato plants can tolerate high levels of iodine, stored both in the vegetative tissues and fruits at concentrations that are more than sufficient for the human diet. We conclude that tomato is an excellent crop for iodine-biofortification programs.

Description: Citrus established in calcareous soils can be affected by iron (Fe)-deficiency chlorosis which limits yield and the farmers' income. The degree of deficiency depends on the rootstock, but the resistance to Fe chlorosis still requires further investigation. To study physiological parameters of citrus rootstocks that could be used to evaluate resistance to Fe deficiency, plants of Troyer citrange ( Citrus sinensis L. Osb. × Poncitrus trifoliata L. Raf.), Carrizo citrange, Volkamer lemon ( Citrus volkameriana Ten. & Pasq.), alemow ( Citrus macrophylla Wester), and sour orange ( Citrus aurantium L.) were grown in nutrient solutions with 0, 5, 10, 15, or 20 μM Fe. For each rootstock, plant height, root and shoot dry weights, and concentration of Fe in the shoots and roots were measured at the end of the experiment. Chlorophyll (CHL) concentration was estimated throughout the experimental period using a portable CHL meter (SPAD-502) calibrated for each rootstock. At the end of the experiment, CHL fluorescence parameters were measured in each rootstock with a portable fluorimeter. Maximal and variable fluorescence values indicated that the photochemistry of Troyer was more affected by a low concentration of Fe in the nutrient solution than that of other rootstocks. To compare rootstocks, the absolute CHL concentration was converted into relative yield by employing a scaling divisor based on the maximum value of total CHL in plants without Fe-deficiency symptoms. Exponential models were developed to determine the minimum Fe concentration in nutrient solution required to maintain leaf CHL at 50% of the maximum CHL concentration (IC50). Models were also developed to assess the period of time the rootstocks were able to grow under Fe-stress conditions before they reached IC50. Volkamer lemon and sour orange needed the lowest Fe concentration (between 4 and 5 μM Fe) to maintain IC50, and Troyer citrange had the highest Fe requirement (14 μM Fe). Citrus macrophylla and Carrizo citrange required 7 and 9 μM of Fe, respectively. Similarly, Volkamer lemon and sour orange rootstocks withstood more days under total Fe depletion or with a low concentration of Fe (5 μM Fe in nutrient solution) until they reached IC50, compared to the other rootstocks. The approach used led to a classification of the rootstocks into three categories, regarding their internal tolerance to Fe chlorosis: resistance (sour orange and Volkamer lemon), intermediate resistance (C . macrophylla and Carrizo citrange), and reduced resistance (Troyer citrange).

Description: Trees interact in a complex manner with soils: they recycle and redistribute nutrients via many ecological pathways. Nutrient distribution via leaf litter is assumed to be of major importance. Beech is commonly known to have lower nutrient concentrations in its litter than other hardwood tree species occurring in Central Europe. We examined the influences of distribution of beech ( Fagus sylvatica L.), ash ( Fraxinus excelsior L.), lime ( Tilia cordata Mill. and T. platyphyllos Scop.), maple ( Acer spp. L.), and clay content on small-scale variability of pH and exchangeable Ca and Mg stocks in the mineral soil and of organic-C stocks in the forest floor in a near-natural, mature mixed deciduous forest in Central Germany. The soil is a Luvisol developed in loess over limestone. We found a positive effect of the proportion of beech on the organic-C stocks in the forest floor and a negative effect on soil pH and exchangeable Ca and Mg in the upper mineral soil (0 to 10 cm). The proportion of ash had a similar effect in the opposite direction, the other species did not show any such effect. The ecological impact of beech and ash on soil properties at a sample point was explained best by their respective proportion within a radius of 9 to 11 m. The proportion of the species based on tree volume within this radius was the best proxy to explain species effects. The clay content had a significant positive influence on soil pH and exchangeable Ca and Mg with similar effect sizes. Our results indicate that beech, in comparison to other co-occurring deciduous tree species, mainly ash, increased acidification at our site. This effect occurred on a small spatial scale and was probably driven by species-related differences in nutrient cycling via leaf litter. The distribution of beech and ash resulted not only in aboveground diversity of stand structures but also induced a distinct belowground diversity of the soil habitat.

Description: Several chemical and microbial properties of mine soils need to be measured for comprehensive assessment of the reclamation success. The objective of this study was to evaluate the ability of NIR spectroscopy to predict organic C (C org ), total N (N t ), and several microbial properties of mine soils reclaimed for forestry. Soils samples ( n = 154) were collected at two reclaimed areas in central and S Poland, and their spectra in the NIR region (including the visible range, 400–2500 nm) were recorded. A half of the samples was used to develop calibration equations, and another half was used for validation. The modified partial least squares regression was applied to build calibration equations using the whole spectrum (0 to 2nd derivative). The best predictions were obtained for C org and N t (ratio of standard deviation to standard error of prediction in the validation stage [RPD] = 3.4 and 4.1; the regressions coefficients [ a ] of linear regression [measured against predicted values] = 0.94 and 0.96; correlation coefficients [ r ] = 0.96 and 0.97, respectively). Very well predictive models applicable for quantitative measurements were obtained also for microbial biomass, basal respiration, and the activities of dehydrogenase and acid phosphatase (RPD = 2.3–2.5, a = 0.90–0.99, r = 0.90–0.92). Prediction of urease activity was slightly worse (RPD = 2.1, a = 0.88, r = 0.87) but sufficient for rough estimation. The obtained results indicated the ability of NIR spectroscopy to predict complex soil microbial properties. Therefore, application of this analytical method may improve the assessment of recovery of microbial functions in reclaimed post-mining barrens.

Description: Several algorithms exist for the calibration procedures of near-infrared spectra in soil-scientific studies, but the potential of a genetic algorithm (GA) for spectral feature selection and interpretation has not yet been sufficiently explored. Objectives were (1) to test the usefulness of near-infrared spectroscopy (NIRS) for a prediction of C and N from char and forest-floor Oa material in soils using either a partial least squares (PLS) method or a GA-PLS approach and (2) to discuss the mechanisms of GA feature selection for the examined constituents. Calibration and validation were carried out for measured reflectance spectra in the visible and near-IR region (400–2500 nm) on an existing set of 432 artificial mixtures of C-free soil, char (lignite, anthracite, charcoal, or a mixture of the three coals), and forest-floor Oa material. For all constituents (total C and N, C and N from all coals and from the Oa material, C derived from mixed coal, charcoal, lignite, and anthracite), the GA-PLS approach was superior over the full-spectrum PLS method. The RPD values (ratio of standard deviation of the laboratory results to standard error of prediction) ranged from 2.4 to 5.1 in the validation and indicated a better category of prediction for three constituents: “approximate quantitative” instead of a “distinction between high and low” for C derived from mixed coal and “good” instead of “approximate quantitative” for C and N derived from all coals. Overall, this study indicates that the approach using GA may have a greater potential than the PLS method in NIRS.

Description: Several genes in the aspen genome have been modified to generate stem wood with lower lignin content and an altered lignin composition. Lower lignin in wood reduces the time and energy required for pulping. Further, this modification can also increase the allocation of photosynthate to cellulose and total biomass production, potentially increasing CO 2 -sequestration capacity. However, widespread planting of trees with altered lignin content and composition could alter soil organic-C dynamics in complex ways. To further examine the effects of altered lignin biosynthesis on plant growth and accrual of soil organic C (SOC), we conducted a repeated greenhouse study with four lines of transgenic aspen ( Populus tremuloides Michx.) and one wild-type (control) aspen. Accrual of aspen-derived SOC was quantified by growing aspen trees (C3 plants) in C4 soil and measuring changes in the natural abundance of δ 13 C. We measured plant growth, biomass, and C content and combined these data with SOC measurements to create C budgets for the plant mesocosms. Lignin modifications resulted in differences in the accrual of aspen-derived SOC and total mesocosm C, primarily due to differences in biomass between genetically modified lines of aspen. One genetic alteration (low lignin, line 23) was able to perform similarly or better than the wild-type aspen (control, line 271) without altering SOC. Alterations in lignin structure (S : G ratios) had negative effects on biomass production and SOC formation. The addition of new (aspen-derived) SOC was proportional to the loss of existing SOC, evidence for a priming effect. The pool of new SOC was related to total plant biomass, suggesting that the effects of lignin modification on SOC are driven by changes in plant growth.

Description:    In this paper, we establish existence results for positive solutions to the Lichnerowicz equations of the following type in closed manifolds - D u = A ( x ) u - p - B ( x ) u q ,    in   M , where p 〉 1, q  〉 0, and A ( x ) 〉 0, B ( x ) ≥ 0 are given smooth functions. Our analysis is based on the global existence of positive solutions to the following nonlinear heat equation { ll u t - D u = A ( x ) u - p - B ( x ) u q ,     in   M ×\mathbb R + , u ( x ,0) = u 0 ( x ),     in   M with the positive smooth initial data u 0 ( x ). Content Type Journal Article Pages 1-10 DOI 10.1007/s00033-011-0156-x Authors Li Ma, Department of Mathematics, Henan Normal University, Xinxiang, 453007 China Yuhua Sun, Department of Mathematical Sciences, Tsinghua University, Beijing, 100084 China Xiao Tang, Department of Mathematical Sciences, Tsinghua University, Beijing, 100084 China Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    In their article (Fundamental flows with nonlinear slip conditions: exact solutions, R. Ellahi, T. Hayat, F. M. Mahomed and A. Zeeshan, Z. Angew. Math. Phys. 61 ( 2010 ) 877–888.), the authors considered three simple cases of the steady flow of a third grade fluid between parallel plates with slip conditions; namely, Couette flow, Poiseuille flow, and generalized Couette flow. They obtained exact solutions, which were utilized in a way that did not lead to useful results. Their conclusion that the Couette flow cannot be obtained from the generalized Couette flow, by dropping the pressure gradient, is incorrect. Meaningful results based on their solution are herein presented. Content Type Journal Article Pages 1-6 DOI 10.1007/s00033-011-0162-z Authors Tarek M. A. El-Mistikawy, Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza, 12211 Egypt Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description: Wild barley ( Hordeum sp. ) germplasm is rich in genetic diversity and provides a treasure trove of useful genes for crop improvement. We carried out a comprehensive program combining short-term hydroponic screening via hematoxylin-staining of root-regrowth procedure and filter paper–based evaluation of diverse germplasm in response to Al/acid stress using 105 annual Tibetan wild barley and 45 cultivated barley genotypes. Root elongation among the 105 Tibetan wild barley genotypes varied significantly after Al exposure, ranging from 62.9% to 80.0% in variation coefficients and 4.35 to 4.45 in diversity index. These genotypic differences in Al resistance were fairly consistent in both the hydroponic and filter paper–based evaluations: XZ16, XZ166, and XZ113 were selected as Al-resistant genotypes, and XZ61, XZ45, and XZ98 as Al-sensitive wild genotypes. Furthermore, significantly lower Al concentrations in roots and shoots were detected in the three selected Al-resistant genotypes than in the three sensitive genotypes in the filter paper–based experiment. Meanwhile, XZ16 was the least affected by Al toxicity in regard to reduced SPAD value (chlorophyll meter readings), plant height, root length, dry biomass, tillers per plant, and chlorophyll fluorescence (Fv/Fm) in the long-term hydroponic experiment compared with the Al-resistant cultivated barley cv. Dayton, while XZ61 had the severest stress symptoms.

Description: Simplified algebraic equations are derived to calculate directly the Brooks and Corey model parameters using data obtained from one-step outflow experiments and saturated hydraulic conductivity. The suggested method has been demonstrated only for horticultural substrates and is verified experimentally for four substrates with satisfactory agreement of the results.

Description: Fine roots from the soil archive of the Swedish National Forest Soil Inventory, collected in 1964, 1972, 1985, and 1998, were analyzed for 14 C contents. Two different methods of estimating residence time were compared. Residence time of root C was estimated to be 8 y using a steady state 1-pool model.

Description: Appropriate management of P from slurry can increase crop production and decrease nutrient loss to water bodies. The present study examined how the application of different size fractions of dairy slurry influenced the quantity and composition of P leached from grassland in a temperate climate. Soil blocks were amended (day 0 = start of the experiment) with either whole slurry (WS), the 〉 425 μm fraction (coarse slurry fraction, CSF), the 〈 45 μm slurry fraction (fine liquid slurry fraction, FLF), or not amended, i.e., the control soil (CON). Deionized water was added to the soil blocks to simulate six sequential rainfall events, equivalent to 250 mm (day 0.2, 1.2, 4.2, 11.2) or 500 mm of rainfall (day 18.2 and 25.2), with leachates collected the following day. The results showed that total dissolved P (TDP), dissolved reactive P (DRP), dissolved unreactive P (DUP), orthophosphate, phosphomonoester, and pyrophosphate concentrations generally decreased with the increasing number of simulated rain events. Total dissolved P was leached in the following order WS 〉 FLF ≈ CSF 〉 CON. Dissolved organic C was correlated with TDP, DRP, and DUP in leachates of all treatments. The highest concentrations of dissolved phosphomonoesters and pyrophosphate (147 μg P L –1 and 57 μg P L –1 , respectively) were detected using solution 31 P-NMR spectroscopy in the WS leachates. Overall, there were significant differences observed between slurry treatments ( e.g., relative contributions of inorganic P vs. organic P of dissolved P in leachates). Differences were independent from the rate at which slurry P was applied, because the highest dissolved P losses per unit of slurry P applied were measured in the FLF, i.e., the treatment that received the smallest amount of P. We conclude that the specific particle-size composition of applied slurry influences dissolved P losses from grassland systems. This information should be taken in account in farm-management approaches which aim to minimizing dissolved slurry P losses from grassland systems.

Description: Several methods are used for the extraction of soil solution. The objective of this study was to find out to what extent the different extraction methods yield complementary or equivalent information. Soil solutions were sampled once at 10 different forest sites in Germany, with 4 sampling points per site, using 5 different extraction methods. Concentrations of the major ions in the 1:2 extracts and the equilibrium soil-pore solutions (obtained from percolation of field-fresh soil cores) were generally lower than in desorption solutions, suction-cup solutions, and saturation extracts. Surprisingly, the latter three methods generally yielded equivalent results. However, possible systematic differences between these methods could have been masked by the high small-scale spatial variability within the sites.

Description:    After impact of a viscous liquid drop on a dry wall surrounded by a gas, the drop surface is highly deformed, leading to the formation of an axisymmetrical lateral lamella along the wall. A local asymptotic model for the potential flow and unsteady boundary layer flow is developed to describe the lamella dynamics at early stages after impact. The second-order potential flow displaced by the unsteady boundary layer is taken into account. The lamella shape, its velocity and pressure are calculated with this model in parametrical forms. The three model parameters are evaluated here by fitting with recent experimental findings. Content Type Journal Article Pages 1-18 DOI 10.1007/s00033-011-0169-5 Authors S. Tabakova, LPCH, Institute of Mechanics, BAS, 1113 Sofia, Bulgaria F. Feuillebois, LIMSI-CNRS, UPR 3251, B.P. 133, 91403 Orsay Cedex, France A. Mongruel, PMMH, UMR 7636 CNRS-ESPCI-Paris 6-Paris 7, 10 rue Vauquelin, 75231 Paris Cedex 05, France V. Daru, LIMSI-CNRS, UPR 3251, B.P. 133, 91403 Orsay Cedex, France St. Radev, LPCH, Institute of Mechanics, BAS, 1113 Sofia, Bulgaria Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description: A standard and a high manganese (Mn) level (10 and 160 μM) were combined with a standard and a high zinc (Zn) level (4 and 64 μM) in the nutrient solution supplied to cucumber in closed-cycle hydroponic units to compensate for nutrient uptake. The concentrations of all nutrients except Mn and Zn were identical in all treatments. The objectives of the experiment were to establish critical Zn and Mn levels in both nutrient solutions and leaves of cucumber grown hydroponically, to assess the impact of gradual Zn and/or Mn accumulation in the external solution on nutrient uptake and gas exchange, and to find whether Mn and Zn have additive effects when the levels of both ions are excessively high in the root zone. The first symptoms of Mn and Zn toxicity appeared when the concentrations of Mn and Zn in the leaves of cucumber reached 900 and 450 mg kg –1 in the dry weight, respectively. Excessively high Mn or/and Zn concentrations in the leaves reduced the fruit biomass production due to decreases in the number of fruits per plant, as well as the net assimilation rate, stomatal conductance, and transpiration rate, but increased the intercellular CO 2 levels. Initially, the Mn or Zn concentrations in the recirculating nutrient solution increased rapidly but gradually stabilized to maximal levels, while the corresponding concentrations in the leaves constantly increased until the end of the experiment. The uptake of Mg, Ca, Fe, and Cu was negatively affected, while that of K and P remained unaffected by the external Mn and Zn levels. The combination of high Mn and Zn seems to have no additive effects on the parameters investigated.

Description: A pot experiment with wheat plants was carried out to study how late application of nitrogen (N) fertilizer affects the use of pre-anthesis N reserves during the grain-filling period. Increasing doses of N fertilizer were applied (0, 40, and 52 mg N plant –1 ), either in two amendments (growth stages GS20 and GS30, according to Zadoks scale) or in three amendments (GS20, GS30, and GS37). The experiment was arranged in a complete randomized three-block design with 129 plants per treatment. The plants were watered daily, harvested every 2 d between anthesis and maturity, and were separated into roots, leaf sheaths, leaf blades, and ears for further N determination. Grain N concentration improved due to a late N application in GS37 by 14% (higher N dose) and by 7% (further splitting the same N-fertilizer dose, respectively). The higher the N-fertilizer dose applied, the greater was the amount of pre-anthesis reserves in vegetative organs, these reserves became later available for remobilization. Although splitting the same N dose in three amendments did not increase the N reserves, these reserves were more efficiently remobilized allowing an improvement in grain N concentration. The fertilizer management did not change the temporary pattern of N accumulation in the ear, but did induce a change in the amount of N remobilized and in the contribution of each organ (root, leaf sheath, leaf blade) to this remobilization. Late N amendment allowed a greater N availability of leaf blades and ear N reserves (from 20% up to 26% and from 19% up to 22%, respectively) for remobilization towards the grain, decreasing the root contribution from 28% down to 15%, while the contribution of leaf sheaths was maintained around 35% irrespective of the N applied.

Description: Flooded rice ( Oryza sativa L.) may contain high arsenic (As) concentrations compared to other grain crops. For the development of measures to reduce the As concentration of rice grains, knowledge about the mobility of As within the rice plant is required. Therefore, to investigate the mobilization of As within the plant, rice was grown in nutrient solution and exposed to As either before flowering, after flowering, or continuously until maturity. Furthermore, rice was grown in four soils under greenhouse and field conditions and the time course of As accumulation in grains during the grain-filling period was investigated. When grown in nutrient solution, As removal at flowering did not reduce As concentrations in polished rice compared to plants supplied with As continuously or after flowering. Plants that received As only after flowering had the same As concentrations in shoot and bran as plants receiving As only before flowering. However, continuous As supply resulted in doubling of As concentrations in both plant parts. In contrast to grain and shoot, the As concentration in the root decreased after As removal compared to the treatments receiving As only after flowering or continuously. The observations indicate that As was mobilized from root or shoot to the grain and that it was accumulated in the grain, although it was not available in nutrient solution during the grain-filling period. In soil experiments, the 1000-grain weight increased up to 2 weeks before harvest in the field as well as in the greenhouse. The As concentration in rice grain was constant during the whole grain-filling period. It was at a similar level under field and greenhouse conditions, and its variation among soils was in the same order indicating that soil was the decisive factor for As concentration in grains. Our results suggest that temporary cultural measures during the cultivation period, for example drainage, might be ineffective because of the mobilization capacity within the rice plant. Moreover, harvest before final maturity of grains would not reduce the As concentration since it remained constant during the grain-filling period.

Description: Recent studies indicate that soil soluble organic nitrogen (SON) plays an important regulatory role in the soil–plant N cycle. The aims of this study were to identify the vertical distribution of SON and its correlation with N mineralization, nitrification, and amidohydrolase activities, in a soil repeatedly amended with cow manure or chemical fertilizer. For this purpose, soil samples were collected from 0–20, 20–40, 40–60, 60–80, and 80–100 cm depths of a calcareous soil, which has been annually amended for 5 y with cow manure (CM) at two rates of 50 (CM 50 ) and 100 (CM 100 ) Mg CM ha –1 y –1 . Treatments with chemical fertilizer (CF) and a control (CT) were also included. Soluble organic N, N mineralization, nitrification rates, as well as L-glutaminase and L-asparaginase activities were determined. Both CM 50 and CM 100 enhanced SON content throughout the soil profile. Nitrogen-mineralization rate (N m ) was increased at the 0–20 cm depth of the CM 100 treatment and remained unaffected at the deeper depths. Nitrification rate (N n ) was significantly higher at the 0–60 cm depth of CM 100 compared to CF and CT. L-glutaminase and L-asparaginase activities were significantly increased at the 0–40 cm depth in both CM 50 and CM 100 compared to CF and CT. The amidohydrolase activities could not be detected below 40 cm, regardless of the fertilizer treatments. Our results suggest that SON makes a minor contribution to N mineralization in deep soil layers. It was also concluded that changes in the SON throughout the soil profile were not associated with changes in the N-transformation rates (N m and N n ) and amidohydrolase activities. While we conclude that SON is a major N pool in the whole profile of the manure applied soil further investigation is required to characterize SON and to investigate the bioavailability of SON for microbial activity in different soil depths.

Description: Due to energy crises and stricter environmental regulations, renewable energy sources like bio-methane produced by anaerobic digestion (biogas) become increasingly important. However, the application of slurries produced by biogas fermentation to agricultural land and subsequent ammonia emission may also create environmental risks to the atmosphere and to N-limited ecosystems. Evaluating ammonia loss from agricultural land by model simulation is an important tool of agricultural-systems analysis. The objective of this study was the systematical comparison of ammonia volatilization after application of two types of biogas slurries containing high amounts of energy crops in comparison with conventional animal slurries and to investigate the relative importance of factors affecting the emission process through an empirical model. A high number of ammonia-loss field measurements were carried out in the years 2007/08 in biogas cropping systems in N Germany. The study consisted of simultaneous measurement of NH 3 losses from animal and biogas slurries in multiple-plot field experiments with different N-fertilization levels. The derived empirical model for the calculation of NH 3 losses based on explanatory variables gave good predictions of ammonia emission for both biogas and pig slurries. The root mean square error ( RMSE ) and mean bias error ( MBE ) of the empirical model for validation data were 2.19 kg N ha –1 ( rRMSE 29%) and –1.19 kg N ha –1 , respectively. Biogas slurries produced highest NH 3 emissions compared to the two animal slurries. In view of the explanatory variables included in the model, total NH application rate, slurry type, temperature, precipitation, crop type, and leaf-area index were important for ammonia-volatilization losses.

Description:    We consider the stationary nonlinear magnetic Choquard equation ( - i Ñ + A ( x )) 2 u + V ( x ) u = (\frac1 | x | a * | u | p ) | u | p - 2 u ,    x Î \mathbb R N where A is a real-valued vector potential, V is a real-valued scalar potential, N ≥ 3, a Î (0, N ) and 2 − ( α / N ) 〈  p 〈 (2 N − α )/( N −2). We assume that both A and V are compatible with the action of some group G of linear isometries of \mathbb R N . We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition u ( gx ) = t ( g ) u ( x )    for   all   g Î G ,   x Î \mathbb R N , where t : G ® \mathbb S 1 is a given group homomorphism into the unit complex numbers. Content Type Journal Article Pages 1-16 DOI 10.1007/s00033-011-0166-8 Authors Silvia Cingolani, Dipartimento di Matematica, Politecnico di Bari, via Orabona 4, 70125 Bari, Italy Mónica Clapp, Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., 04510 México D.F., Mexico Simone Secchi, Dipartimento di Matematica ed Applicazioni, Università di Milano-Bicocca, via Cozzi 53, 20125 Milano, Italy Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    This paper is concerned with the homogenization of the equations describing a magnetohydrodynamic boundary layer flow past a flat plate, the flow being subjected to velocities caused by injection and suction. The fluid is assumed incompressible, viscous and electrically conducting with a magnetic field applied transversally to the direction of the flow. The velocities of injection and suction and the applied magnetic field are represented by rapidly oscillating functions according to several scales. We derive the homogenized equations, prove convergence results and establish error estimates in a weighted Sobolev norm and in C 0 -norm. We also examine the asymptotic behavior of the solutions of the equations governing a boundary layer flow past a rough plate with a locally periodic oscillating structure. Content Type Journal Article Pages 1-28 DOI 10.1007/s00033-011-0167-7 Authors Youcef Amirat, Laboratoire de Mathématiques, CNRS UMR 6620, Université Blaise Pascal (Clermont-Ferrand 2), 63177 Aubière cedex, France Gregory A. Chechkin, Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow, 119991 Russia Maxim Romanov, Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow, 119991 Russia Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description: Soil sulfur (S) partitioning among the various pools and changes in tropical pasture ecosystems remain poorly understood. Our study aimed to investigate the dynamics and distribution of soil S fractions in an 8-year-old signal grass ( Brachiaria decumbens Stapf.) pasture fertilized with nitrogen (N) and S. A factorial combination of two N rates (0 and 600 kg N ha –1 y –1 , as NH 4 NO 3 ) and two S rates (0 and 60 kg S ha –1 y –1 , as gypsum) were applied to signal grass pastures during 2 y. Cattle grazing was controlled during the experimental period. Organic S was the major S pool found in the tropical pasture soil, and represented 97% to 99% of total S content. Among the organic S fractions, residual S was the most abundant (42% to 67% of total S), followed by ester-bonded S (19% to 42%), and C-bonded S (11% to 19%). Plant-available inorganic SO 4 -S concentrations were very low, even for the treatments receiving S fertilizers. Low inorganic SO 4 -S stocks suggest that S losses may play a major role in S dynamics of sandy tropical soils. Nitrogen and S additions affected forage yield, S plant uptake, and organic S fractions in the soil. Among the various soil fractions, residual S showed the greatest changes in response to N and S fertilization. Soil organic S increased in plots fertilized with S following the residual S fraction increment (16.6% to 34.8%). Soils cultivated without N and S fertilization showed a decrease in all soil organic S fractions.

Description: A greenhouse pot experiment was carried out to investigate the effects of different P-fertilizer application forms (triple superphosphate [TSP], compost + TSP, TSP-enriched compost) on the growth of ryegrass and the soil microbial biomass. The fertilizers were applied at equivalent doses for all nutrients to a neutral Luvisol in comparison with an acidic Ferralsol. Fertilizer application led to significantly increased contents of microbial biomass C, N, and P. Furthermore, yields of shoot C and root C, and concentrations of P, Ca, Mg, K, Fe, and Mn in shoots and roots were significantly increased. These increases always followed the order TSP 〈 compost + TSP 〈 TSP-enriched compost. Sole TSP application led only to maximum concentrations of N and S. In the Ferralsol, TSP had only minimal positive effect on the P concentration of the grass shoots. The positive effect of TSP-enriched compost, i.e., incubating TSP together with compost for 24 h, did not differ between the neutral Luvisol and the acidic Ferralsol, i.e., the effect is independent of the soil type. Consequently, soluble inorganic P fertilizer should generally be mixed into an organic fertilizer before application to soil.

Description: The physical properties of a Luvisol derived from loess near Bonn, Germany, under different long-term fertilization treatments were examined. For the investigation of the impact of farmyard manure (FYM) on soil strength at the mesoscale (100 to 300 cm 3 soil cores), undisturbed samples were taken from two different depths (10 and 40 cm), either with no fertilization at all, with full mineral fertilization, with FYM only, and with both mineral and organic fertilization. We investigated hydraulic and mechanical parameters, namely precompression stress, pore-size distribution, saturated hydraulic and air conductivity, and calculated pore connectivity. Long-term organic fertilization resulted in significantly more and coarser pores which in addition were more conductant and mechanically stronger by trend. Mineral fertilization also increased pore volume by trend but not pore functionality. Mechanical strength generally increased with fertilization by trend, however, was reduced again when organic and mineral fertilization were combined. Nonetheless, FYM led to relatively higher soil strength as the FYM-treated plots with lower bulk density attained similar soil strength as the unfertilized but denser plots and thus supported the soil-improving impact of organic amendments. The subsoil physical properties were rather unaffected by fertilization, but were dominated by texture.

Description: Little is known about nutrient fluxes and nutrient-use efficiencies in urban and peri-urban agriculture (UPA) of rapidly expanding cities in developing countries. Therefore, horizontal flows of carbon (C), nitrogen (N), phosphorus (P), and potassium (K) as well as leaching losses of mineral N and P were measured over 2 years in three representative agricultural production systems of Kabul. These comprised 21 gardens and 18 fields dedicated to vegetable farming, cereal farming, and table-grape production (vineyards). Across sites (fields and gardens) biennial inputs averaged 375 kg N ha –1 , 155 kg P ha –1 , 145 kg K ha –1 , and 15 kg C ha –1 while with harvests 305 kg N ha –1 , 40 kg P ha –1 , 330 kg K ha –1 , and 7 kg C ha –1 were removed. In vegetable gardens, biennial net balances were 80 kg N ha –1 , 75 kg P ha –1 , –205 kg K ha –1 , and 4 kg C ha –1 , whereas in cereal farming biennial horizontal balances amounted to –155 kg N ha –1 , 20 kg P ha –1 , –355 kg K ha –1 , and 5 kg C ha –1 . In vineyards, corresponding values were 295 kg N ha –1 , 235 kg P ha –1 , 5 kg K ha –1 , and 3 kg C ha –1 . Annual leaching losses in two selected vegetable gardens varied from 70 to 205 kg N ha –1 and from 5 to 10 kg P ha –1 . Night soil and irrigation water were the major sources among the applied nutrient inputs in all studied farming systems, contributing on average 12% and 25% to total N, 22% and 12% to total P, 41% and 53% to total K, and 79% and 10% to total C, respectively. The results suggest that soils in extensive cereal fields are at risk of N and K depletion and in vegetable gardens of K depletion, while vineyards may be oversupplied with nutrients possibly contributing to groundwater contamination. This merits verification.

Description: Residues from biogas production contain essential plant nutrients such as nitrogen (N), phosphorus (P), and potassium (K) but also organic matter, and should be recycled in crop production. For efficient re-use as fertilizers, the availability of nutrients for crops and the effect of the residues on soil fertility need to be evaluated. Focusing on the element P, we compared effects of codigested slurry with dairy slurry, highly soluble mineral NPK fertilizer, and a control without any P supply (NK). Codigested slurry used in this experiment was based on anaerobic digestion of dairy slurry, maize silage, and wheat grain. The fertilizing effects were tested in an 8-week pot experiment on a sandy and a loamy soil using two crop species ( Zea mays L., Amaranthus cruentus L.). The plant P uptake was up to 64% greater in the slurry treatments than in the treatment without P. The effect of codigested slurry on P uptake was comparable to that of dairy slurry and mineral P. Plant N uptake from codigested slurry was lower than that from mineral N (NK, NPK), but tended to be higher than from dairy slurry. The water-soluble and double lactate–soluble P content of the soil was lower in the slurry treatments than in the mineral-P treatments and accompanied by higher contents of microbial-bound P. Differences between both organic fertilizers were detected for dehydrogenase activity which was up to 32% lower in soils fertilized with codigested slurry than it was in soils fertilized with dairy slurry. Our results indicate that codigestion of slurries in biogas plants does not substantially alter their fertilizer value as P and N sources for crops.

Description: The effect of different deficit-irrigation treatments on the dynamics of mineral nutrients in leaves of peach trees growing under Mediterranean conditions was studied. Treatments consisted of a control, continuous deficit irrigation, regulated deficit irrigation, and partial root drying. The dynamics of nutrients were unchanged by the water deficits, though the amount absorbed was slightly modified. The advantages of deficit-irrigation strategies with regard to water-use efficiency were accompanied by the absence of any harmful effect on leaf mineral nutrition.

Description: It has been suggested that short-term field experiments are not suitable for the quantitative assessment of cropping-systems impact on soil organic matter (SOM) levels in arable soils, as expectable temporal changes are very small compared to a large spatial variation of SOM background levels. However, applying an optimized sampling design based on repeated sampling in small plots, we were able to detect soil total carbon (STC) and nitrogen (STN) changes in the magnitude of ≈ 1% (STC) and ≈ 2% (STN) of background levels with only four replications, respectively. Gradually enlarging the sample size up to n = 24 did not considerably improve change detectability with STC, but with STN ( n = 15 allowing for the dection of ≈ 1% change of background levels). The common calculation of minimum detectable differences (MDD) based on a state analysis of SOM levels instead of repeated measurements considerably underestimated change detectability.

Description: Two experiments were conducted to study the effect of grafting on nitrogen-use efficiency (NUE) in mini-watermelon plants. In the first study, mini-watermelon plants ( Citrullus lanatus [Thumb.] Matsum. and Nakai cv. Minirossa) either ungrafted or grafted onto Macis, Vita ( Lagenaria siceraria [Mol.] Standl.), PS1313, and RP15 ( Cucurbita maxima Duchesne × Cucurbita moschata Duchesne) rootstocks grown in hydroponics were compared in terms of shoot dry biomass, leaf area, root-to-shoot ratio, SPAD index, shoot N uptake, and nitrate reductase (NR) activity 40 d after transplantation in response to nitrate concentration in the nutrient solution (0.5, 2.5, 5, 10, 15, or 20 mM of NO ). In the second experiment, the suitability of a selected rootstock with high NUE (Vita) to improve crop performance and NUE of grafted mini-watermelon plants was evaluated under field conditions. In the hydroponic experiment mini-watermelon grafted onto Vita rootstock needed the lowest nitrate concentration (1.31 mM of NO 3 ) in the nutrient solution to reach half maximum shoot dry weight. Total leaf area, SPAD index, and shoot N uptake increased in response to an increase of N concentration in the nutrient solution. At 2.5 mM NO , mini-watermelon grafted on either Vita or RP15 had the highest NR activity whereas no significant difference was observed at 10 mM NO . The open-field study indicated that increasing N-fertilization rates from 0 to 100 kg ha –1 improved total and marketable yields of mini-watermelon plants while decreasing NUE. When averaged over N levels, the marketable yield, NUE, N-uptake efficiency, and N-utilization efficiency were significantly higher by 39%, 38%, 21%, and 17%, respectively, in Minirossa grafted onto Vita compared to ungrafted Minirossa plants. Therefore, grafting mini-watermelon plants onto selected rootstocks can be used as a quick and effective method for improving productivity and NUE.

Description:    We consider the stability of a cylindrically layered smectic A liquid crystal sample under a sinusoidal perturbation where we allow for the decoupling between the layer normal and the director. Two forms of general anstazes are proposed: one provides exact solutions for the flow and layer undulations while the other provides series solutions for the hydrodynamic variables. Both cases provide an estimate for a stability parameter. Plots of the flow, layer undulations and pressure are provided. Content Type Journal Article Pages 1-15 DOI 10.1007/s00033-011-0155-y Authors A. J. Walker, Department of Computing and Mathematics, University of Glamorgan, CF37 1DL Pontypridd, UK I. W. Stewart, Department of Mathematics and Statistics, University of Strathclyde, G1 1XH Glasgow, UK Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    We study the eigenpairs of a model Schrödinger operator with a quadratic potential and Neumann boundary conditions on a half-plane. The potential is degenerate in the sense that it reaches its minimum all along a line that makes the angle θ with the boundary of the half-plane. We show that the first eigenfunctions satisfy localization properties related to the distance to the minimum line of the potential. We investigate the densification of the eigenvalues below the essential spectrum in the limit θ → 0, and we prove a full asymptotic expansion for these eigenvalues and their associated eigenvectors. We conclude the paper by numerical experiments obtained by a finite element method. The numerical results confirm and enlighten the theoretical approach. Content Type Journal Article Pages 1-29 DOI 10.1007/s00033-011-0163-y Authors Virginie Bonnaillie-Noël, IRMAR, ENS Cachan Bretagne, Université de Rennes 1, CNRS, UEB, av. Robert Schuman, 35170 Bruz, France Monique Dauge, IRMAR, Université de Rennes 1, CNRS, Campus de Beaulieu, 35042 Rennes cedex, France Nicolas Popoff, IRMAR, Université de Rennes 1, CNRS, Campus de Beaulieu, 35042 Rennes cedex, France Nicolas Raymond, IRMAR, Université de Rennes 1, CNRS, Campus de Beaulieu, 35042 Rennes cedex, France Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    We prove the uniqueness for weak solutions of the time-dependent 2-D Ginzburg-Landau model for superconductivity with L 2 initial data in the case of Coulomb gauge. This question was left open in Tang and Wang (Physica D, 88:139–166, 1995 ). We also prove the uniqueness of the 3-D radially symmetric solution in bounded annular domain with the choice of Lorentz gauge and L 2 initial data. Content Type Journal Article Pages 1-7 DOI 10.1007/s00033-011-0164-x Authors Jishan Fan, Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037 People’s Republic of China Tohru Ozawa, Department of Applied Physics, Waseda University, Tokyo, 169-8555 Japan Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    In this paper, we consider a class of nonlinear higher-order wave equation with nonlinear damping u tt +( - D ) m u + a | u t | p - 2 u t = b | u | q - 2 u in a bounded domain W Ì \mathbb R N ( N  ≥ 1 is a natural number). We show that the solution is global in time under some conditions without the relation between p and q and we also show that the local solution blows up in finite time if q  〉  p with some assumptions on initial energy. The decay estimate of the energy function for the global solution and the lifespan for the blow-up solution are given. This extend the recent results of Ye (J Ineq Appl, 2010 ). Content Type Journal Article Pages 1-13 DOI 10.1007/s00033-011-0165-9 Authors Jun Zhou, School of Mathematics and Statistics, Southwest University, Chongqing, 400715 People’s Republic of China Xiongrui Wang, Department of Mathematics, Yibin College, Yibin, 644007 People’s Republic of China Xiaojun Song, Department of Mathematics, China West Normal University, Nanchong, 637002 People’s Republic of China Chunlai Mu, School of Mathematics and Statistics, Chongqing University, Chongqing, 400044 People’s Republic of China Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    This paper deals with a doubly degenerate parabolic system multi-coupled by inner and boundary sources. The necessary-sufficient conditions for global weak solutions are determined, which involve a complete classification for all the eight nonlinear parameters of the model and cover all possible blowing up mechanisms of solutions. The results of the paper are mainly rely on the comparison principle and the energy method. Content Type Journal Article Pages 1-17 DOI 10.1007/s00033-011-0146-z Authors Zhaoxin Jiang, School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024 People’s Republic of China Sining Zheng, School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024 People’s Republic of China Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    In this paper, we consider the viscoelastic wave equation with a delay term in internal feedbacks; namely, we investigate the following problem u tt ( x , t ) - D u ( x , t )+ t ó õ 0   g ( t - s ) D u ( x , s ) d s + m 1 u t ( x , t )+ m 2 u t ( x , t - t )=0 together with initial conditions and boundary conditions of Dirichlet type. Here ( x , t ) Î W ×(0, ¥ ), g is a positive real valued decreasing function and  μ 1 , μ 2 are positive constants. Under an hypothesis between the weight of the delay term in the feedback and the weight of the term without delay, using the Faedo–Galerkin approximations together with some energy estimates, we prove the global existence of the solutions. Under the same assumptions, general decay results of the energy are established via suitable Lyapunov functionals. Content Type Journal Article Pages 1-18 DOI 10.1007/s00033-011-0145-0 Authors Mokhtar Kirane, Mathématiques, Image et Applications Pole Sciences et Technologie, Université de la Rochelle, La Rochelle, France Belkacem Said-Houari, Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz, Germany Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description: An evaluation of the factors determining the occurrence and the properties of soils with low permeability occurring in vast areas in S Portugal was carried out taking into account the terrain morphology and the geology of the region. This paper deals with the variation patterns of the physical and chemical characteristics of soils from several soil toposequences that occur under different gradient slopes and on different parent rocks. Spatial variation of soil properties mainly depends on the composition of their cation-exchange complex, as the role of other factors, such as the mineralogy of the clay fraction, were of minor importance. There is often a stronger increment of Na and/or Mg than of Ca with depth, causing a variable degree of sodicity in some of these soils, to which waterlogging tendency of their upper horizons is related. Though the occurrence of these features is determined by the nature of the parent rock, their degree of expression varies primarily according to the topographic position of soils. Therefore, a catenary distribution including nonsodic Cambisols or Luvisols in the hillcrests and Stagnic Solonetz or Sodic Luvisols or Sodic Stagnosols in the topographic lows is common. Such soil characteristics are of utmost importance for irrigation suitability and management of these soils, and for environmental impacts assessment, as the region is vulnerable to desertification.

Description: Oxisols cover ≈ 23% of the land surface in the tropics and are utilized extensively for agricultural purposes in the tropical countries. Under the variable input types of agricultural systems practiced locally, some of these soils still appear to have problems in terms of proper soil classification and subsequently hinder attempts to implement sustainable agro-management protocols. The definition for Oxisols in Soil Survey Staff (1999) indicates that additional input is still required to refine the definition in order to resolve some of the outstanding classification problems. Therefore, the objective of this study is to examine the properties of some Oxisols and closely related soils in order to evaluate the classification of these soils. Soils from Brazil, several countries in Africa, and Malaysia were used in this study. Field observations provided the first indication that some of the presently classified kandi-Alfisols and kandi-Ultisols were closer to Oxisols in terms of their properties. Water-retention differences and apparent CEC of the subsurface horizons also supported this idea. The types of extractable Fe oxides and external specific surface areas of the clay fractions showed that many kandic horizons have surface properties that are similar to the oxic horizons. Micromorphology indicated that the genetic transition from the argillic to the oxic involves a diminishing expression of the argillic. Properties, such as CEC, become dominant. The kandic horizon is therefore inferred as a transition to the oxic horizon. It is proposed that the Oxisols be keyed out based only on the presence of an oxic horizon and an iso–soil temperature regime. The presence of a kandic horizon will be reflected at lower levels in Oxisols. The Oxisols will now be exclusive to the intertropical belt with an iso–soil temperature regime. The geographic extend of the Oxisols would increase and that of kandi-Alfisols and Ultisols would decrease. A few kandi-Alfisols and Ultisols in the intertropical area will have low CEC which would fail the weatherable mineral contents. The kandic subgroups of some Alfisols and Ultisols will be transitional between the low (〈 16 cmol c [kg clay] –1 )- and high (〉 24 cmol c [kg clay] –1 )-activity clay soils. The proposed changes to classification will contribute to a better differentiation of the landscape units in the field. Testing of the proposed classification on some Malaysian soils showed that the new definition for Oxisols provides a better basis for the classification of the local soils and the development of meaningful soil-management groups for plantations.

Description: Variability in soil properties is a complication for fertilization, irrigation, and amendment application. However, only limited progress has been made in managing soil variability for uniform productivity and increased water-use efficiency. This study was designed to ameliorate the poor-productivity areas of the variable sandy soils in Florida citrus groves by using frequent small irrigations and applying organic and inorganic soil amendments. Two greenhouse experiments were set up with sorghum and radish as bioassay crops in a randomized complete block design (RCBD). The factors studied were two soil-productivity classes (very poor and very good), two water contents (50% and 100% of field capacity), two amendments (phosphatic clay and Fe humate), and two amendment rates (10 and 25 g kg –1 for sorghum and 50 and 100 g kg –1 for radish). Amendments applied at 50 and 100 g kg –1 increased the water-holding capacity (WHC) of poor soil by 2- to 6-fold, respectively. The lower rates (10 and 25 g kg –1 ) of amendments were not effective in enhancing sorghum growth. The higher rates (50 and 100 g kg –1 ) doubled the radish growth as compared to the control. The results indicate that rates greater than 50 g kg –1 of both amendments were effective in improving water retention and increasing productivity. Irrigation treatment of 100% of field capacity (FC) increased the sorghum and radish growth by about 2-fold as compared with the 50%–water content treatment. The results suggest that the root-zone water content should be maintained near FC by frequent small irrigations to enhance water availability in excessively drained sandy soils. In addition, application of soil amendments in the root zone can enhance the water retention of these soils. Furthermore, managing variable sandy soils with WHC-based irrigation can increase water uptake and crop production in the poor areas of the grove.

Description: A greenhouse experiment was conducted to evaluate the effects of humic substances extracted from composted sewage sludge on growth, phenological development, and photosynthetic activity of pepper ( Capsicum annuum L. cv. Piquillo) plants. Humic substances derived from composted sludge (HSS) were compared with those derived from leonardite (HSL). Two doses of both humic substances were assayed (200 and 500 mg C [L substrate] –1 ) and compared with a control (C). HSS showed higher nitrogen content and a higher percentage of aliphatic carbon, as well as a lower content of aromatic and phenolic carbon than HSL. HSS significantly increased plant dry-matter production (up to 560%), plant height (86%–151%), and leaf area (436%–1397%) during the early stages of pepper development. Net photosynthesis and stomatal conductance increased in the treatments with HSS (up to 48% and 63%, respectively) at the vegetative stage. In addition, HSS accelerated the phenological development of pepper plants, reducing significantly the number of days to flowering and ripening, which occurred 12 and 14 d earlier than in control plants, respectively. In general, the treatments with HSS and HSL did not markedly affect chlorophyll and nutrient concentrations in the leaves. At maturity, only small differences in total fruit yield, number of fruits per plant, and fruit size were observed between amended and control plants. The results suggest that the mechanisms through which HSS affected plant growth and development were not associated with an improved nutrient uptake. Although the identity of the growth-promoting factors remains to be found, the results suggest that they may be linked to the chemical structure of the humic substances.

Description:    An accurate quantification of negative pore pressure (commonly referred to as ‘suction’) in the pore network is necessary for modeling the mechanical response of unsaturated geomaterials. Traditional definitions and formulations of total, matric, and osmotic suction suggest incorrect pore fluid pressures under certain conditions. In this paper, the notion of suction is revisited by deriving an expression for pore fluid pressure in a simple osmotic, capillary tube using the framework of mixture theory in conjunction with the fundamental laws of thermodynamics. Based on the derived expression for the tube, expressions are derived for total, matric, and osmotic suction for partially saturated geomaterials. Particular attention is given to osmotic suction since confusion regarding its mechanisms has apparently contributed to its misapplication in geomechanics. The new expressions derived herein adequately explain behavior that is incorrectly explained by the traditional formulations and unifies two approaches to modeling osmotic suction previously considered to be in contradiction. Content Type Journal Article Pages 1-22 DOI 10.1007/s00033-011-0168-6 Authors Zachary C. Grasley, College Station, TX, USA Kumbakonam R. Rajagopal, College Station, TX, USA Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description: An accurate assessment of soil respiration is critical for understanding and predicting ecosystem responses to anthropogenic perturbation such as climate change, pollution, and agriculture. Infra-red gas analyzer (IRGA)–based field measurement is the most widely used technique for assessing soil-respiration flux rates. In this study, respiration rates obtained with two common IRGA systems (LI-COR 8100 and PP Systems EGM-4) were compared across three ecosystem types. Our results showed that both methods were highly comparable in their flux estimates, but the associated methodology used (notably the use or absence of a soil collar) resulted in greater uncertainty in flux rates and a greater degree of intrasite variation. Specifically, the use of collars significantly decreased the flux estimate for both IRGAs compared to the no-collar estimate. The disturbance caused by collar insertion was assumed to be a major factor in causing the differing flux estimates, with root and mycorrhizal severance likely being the main contributor. We conclude that the two IRGAs used in this study can be reliably compared for overall flux estimates but emphasis is needed to validate a common measurement methodology.

Description: Provision of appropriate fertilizer recommendations to smallholder farmers is becoming increasingly important, for reasons of food security, economic viability, and the need to maintain soil fertility. Oil palm is one of the most important crops in the humid tropics, but smallholder growers (〈 10 ha) typically have low yields, largely due to inadequate fertilizer inputs and/or incomplete harvesting. It is difficult to produce appropriate fertilizer recommendations for the smallholder growers, due to their large numbers and small farm sizes. In this work, we developed a way of transferring to smallholder growers the fertilizer recommendations that have been developed for nearby plantation fields using large fertilizer trials. The study site was in West New Britain Province, Papua New Guinea, and transfer of information was done using a geographic information system and maps of plantation fields, smallholder blocks, and soil types. The soil-map-unit descriptions were interpreted, and a unified classification system was derived. Then, fertilizer recommendations that had been made on a field-specific basis for the large plantations were allocated to soil types and thereby to individual smallholder blocks. In this way, block-specific fertilizer recommendations were made for more than 4000 individual smallholders. The procedures used were developed into a conceptual framework which is transferable to other regions. Recommendations can be updated as new information becomes available on smallholder block locations or plantation fertilizer recommendations.

Description: The efficacy of arbuscular mycorrhizae (AM) on nutrients, organic solutes, and antioxidant enzymes of wheat under salt stress was investigated and related to root colonization and plant productivity. The mycorrhizal inoculation increased N, P, K, Ca, and Mg uptake, soluble sugars, free amino acids, and proline accumulation, as well as peroxidase and catalase activities under saline conditions as compared to nonmycorrhizal plants. On the other hand, Na concentration was lower in mycorrhizal than in nonmycorrhizal plants grown under saline conditions. Arbuscular mycorrhizae protected wheat against the detrimental effects of salinity and stimulated its productivity. Hence, mycorrhizal colonization can play a vital role in the mitigation of the adverse effects of salinity by improving the wheat osmotic adjustment response, enhancing its defense system, and alleviating oxidative damage to cells. Arbuscular mycorrhizae are able to alter plant physiology in a way that empowers the plant to grow more efficiently on salt-affected lands.

Description:    The authors study the small oscillations of a pendulum containing an almost homogeneous, incompressible, inviscid liquid (i.e. a liquid whose density in equilibrium is practically a linear function of the height, which differs very little from a constant) and a moving gas. Using functional analysis, they prove that the spectrum is comprised of a countable set of real eigenvalues and an essential spectrum, which fills an interval, and they give an existence and uniqueness theorem for the solution of the evolution problem. Content Type Journal Article Pages 1-20 DOI 10.1007/s00033-011-0118-3 Authors H. Essaouini, Faculté des Sciences de Tétouan, Université Abdelmalek Essaâdi, Mhannech II, B.P: 2121, Tétouan, Morocco L. El Bakkali, Faculté des Sciences de Tétouan, Université Abdelmalek Essaâdi, Mhannech II, B.P: 2121, Tétouan, Morocco P. Capodanno, Université de Franche-Comté, 2B, Rue des jardins, 25000 Besançon, France Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    We extend the study of the integrability done by Leach and Miritzis (J Nonlinear Math Phys 13:535–548, 2006 ) on the classical model of competition between three species studied by May and Leonard (SIAM J Appl Math 29:243–256, 1975 ), to all real values of the parameters. Additionally, our results provide all polynomial, rational and analytic first integrals of this extended model. We also classify all the invariant algebraic surfaces of these models. Content Type Journal Article Pages 1-17 DOI 10.1007/s00033-011-0119-2 Authors Jaume Llibre, Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain Clàudia Valls, Departamento de Matemática, Instituto Superior Técnico, 1049–001 Lisbon, Portugal Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    This paper is concerned with the multiplicity and concentration of positive solutions for the nonlinear Schrödinger–Poisson equations $$ \left\{ {l@{\quad}l} -\varepsilon^2\triangle u+V(x)u+\phi(x) u=f(u)& {\rm in}\,{\mathbb R}^3, \\ -\varepsilon^2\triangle \phi=u^2 & {\rm in}\,{\mathbb R}^3, \\ u\in H^1({\mathbb R}^3), u(x) 〉 0,& \forall x\in{\mathbb R}^3, \\ \right. $$ where ε  〉 0 is a parameter, V : \mathbb R 3 ® \mathbb R is a continuous function and f : \mathbb R ® \mathbb R is a C 1 function having subcritical growth. The proof of the main result is based on minimax theorems and the Ljusternik–Schnirelmann theory. Content Type Journal Article Pages 1-21 DOI 10.1007/s00033-011-0120-9 Authors Xiaoming He, College of Science, Minzu University of China, Beijing, 100081 People’s Republic of China Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    Building on the results of Chapman et al. (Z Angew Math Phys 47:410–431, 1996 ) on the behavior of minimizers in the Ginzburg–Landau thin-film model, we show that the vortices in the three-dimensional superconducting thin films are located in the cylinders whose cross sections coincide with the disks that contain the vortices in the two-dimensional model. To arrive at this conclusion, we prove that the three-dimensional minimizers converge to the two-dimensional counterparts in H 1 and in C α . We also give examples of regimes in which the vortex structure of the two-dimensional minimizers is well understood. Our results, in particular, provide insight into the behavior of the three-dimensional vortices in these regimes. Content Type Journal Article Pages 1-17 DOI 10.1007/s00033-011-0122-7 Authors Dmitry Glotov, Auburn University, 221 Parker Hall, Auburn, AL 36849, USA Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    The present article investigates the overall bed permeability of an assemblage of porous particles. For the bed of porous particles, the fluid-particle system is represented as an assemblage of uniform porous spheres fixed in space. Each sphere, with a surrounding envelope of fluid, is uncoupled from the system and considered separately. This model is popularly known as cell model. Stokes equations are employed inside the fluid envelope and Brinkman equations are used inside the porous region. The stress jump boundary condition is used at the porous-liquid interface together with the continuity of normal stress and continuity of velocity components. On the surface of the fluid envelope, three different possible boundary conditions are tested. The obtained expression for the drag force is used to estimate the overall bed permeability of the assemblage of porous particles and the behavior of overall bed permeability is analyzed with various parameters like modified Darcy number ( Da *), stress jump coefficient ( β ), volume fraction ( ε ), and effective viscosity. Content Type Journal Article Pages 1-20 DOI 10.1007/s00033-011-0123-6 Authors Jai Prakash, Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721 302 India G. P. Raja Sekhar, Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721 302 India Mirela Kohr, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu Str., 400084 Cluj-Napoca, Romania Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    In this paper, we study critical points of the functional J e ( u ):=\frac e 2 2 1 ó õ 0   | u x | 2 d x + 1 ó õ 0   F ( u ) d x , u   Î W 1,2 (0,1),            (1) where F : \mathbb R ® \mathbb R is assumed to be a double-well potential. This functional represents the total free energy in models of phase transition and allows for the study of interesting phenomena such as slow dynamics . In particular, we consider a non-classical choice for F modeled on F ( u )= | 1 - u 2 | a where 1 〈  α  〈 2. The discontinuity in F ′′ at ±1 leads to the existence of multiple continua of critical points that are not present in the classical case F Î C 2 . We prove that the interior points of these continua are local minima. The energy of these local minimizers is strictly greater than the global minimum of J e . In particular, the existence of these continua leads to an alternative explanation for the slow dynamics observed in phase transition models. Content Type Journal Article Pages 1-14 DOI 10.1007/s00033-011-0124-5 Authors Pavel Drábek, Department of Mathematics and Center N.T.I.S., University of West Bohemia, P.O. Box 314, 306 14 Pilsen, Czech Republic Stephen B. Robinson, Department of Mathematics, Wake Forest University, P.O. Box 7388, Winston-Salem, NC 27109, USA Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description: Different procedures to investigate dissolved trace element concentration at the transition from unsaturated to saturated zone in soils were compared by concurrent sampling of soil solution and solid soil material in this zone. The in situ sampled soil solution from the percolated water was used to measure in situ concentrations, while solid soil material was used to measure concentrations at two liquid–solid ratios using batch experiments on 250 sample pairs. The liquid–solid ratios were 2 L kg –1 and 5 L kg –1 . At 5 L kg –1 , the ionic strength was adjusted with Ca(NO 3 ) 2 to a sample-specific value similar to in situ , while at 2 L kg –1 , the ionic strength was not adjusted. The extracted concentrations of most trace elements exhibited a statistically significant but weak correlation ( p value 〈 0.01) to the corresponding in situ concentrations. In the liquid–solid ratio of 2 L kg –1 extracts, Pb and Cr showed very poor comparability with the in situ equivalent. A likely cause was the enhanced dissolved-organic-C release in the extract due to the lower ionic strength compared to in situ conditions in combination with effects from drying and moistening soil samples. For the other elements, correlation increased in the order As 〈 Cu, Zn, Sb, Mo, V 〈 Cd, Ni, Co where adjustment of the ionic strength led to slightly better results. In addition to the element-specific shortcomings, it appeared that low concentration levels of in situ concentrations were generally underestimated by batch extraction methods. The liquid–solid ratio of 2 L kg –1 extracts could only be used as a method to predict exceedance of thresholds if a safety margin of approximately one order of magnitude higher than the thresholds was adopted. The ability of the batch-extraction methods to estimate in situ concentrations was equally limited.

Description: Tonoplast Na + /H + antiporters increase the salt resistance of various plant species, but very little is known about the role of these antiporters in the salt resistance of trees. Understanding the physiological responses of plants to salinity stress is of paramount importance in examining the salt resistance of transgenic plants. In this study, the wild-type poplar (WT; Populus × euramericana var. Neva) and its transgenic varieties (TR) that overexpress the AtNHX1 gene were exposed to various seawater concentrations (0%, 10%, 20%, and 30%) for 30 d to determine the effects of seawater on seedling growth, ion content, and photosynthetic productivity. Results show that TR plants grew much better than WT under saline conditions. Differences between WT and TR in most parameters were significant after 30 d exposure to 20% and 30% seawater concentrations. The dry weight of TR was higher than that of WT for each seawater treatment. Transgenic variety was able to maintain higher photosynthetic ability than WT upon exposure to salinity and maintained higher K + concentrations and K + : Na + ratio but had less Cl – compared with WT. This suggests that AtNHX1 has a critical role in the regulation of K + homeostasis, which in turn affects plant K + nutrition and salt resistance.

Description: Recent studies have documented adverse affects of urea on the establishment and growth of aerobic rice when applied at seeding. The following experiments were conducted to examine the relative importance of ammonia and nitrite (NO ) toxicities as mechanisms contributing to poor germination and early growth of aerobic rice. Soil was collected from an experiment in the Philippines where aerobic rice was grown continuously for 7 years. Subsamples of the soil were: (1) pretreated with sulfuric acid (0.5 M H 2 SO 4 added at 75 mL kg –1 ), (2) oven-heated at 120°C for 12 h, or (3) left untreated. In a greenhouse study N was applied to the untreated, acidified, and oven-heated soils as either urea or ammonium sulfate (0.0 or 0.3 g N kg –1 ). Plant height, root length, total biomass, and number of seminal roots were evaluated after 10 d. Microdiffusion incubations were used to assess the effects of soil pretreatment, N source, and N rate (0, 0.5, 1.0, 1.5 g N kg –1 ) on ammonia (NH 3 ) volatilization and germination. Nitrite incubations were conducted to establish a critical level for NO toxicity and measure the extractable NO and germination trends as affected by soil pretreatment, N source, and N rate. On untreated soil, urea reduced early growth and germination while ammonium sulfate caused no adverse effects. Progressively higher rates of urea increased NH 3 volatilization and inhibited germination, while oven-heating and acidification minimized the adverse effects. All treatment combinations (soil pretreatment, N source, N rate) had extractable NO levels below the critical level of 0.2 g N kg –1 , suggesting that ammonia and not NO toxicity was the principal cause of inhibition. Since the risk of NH 3 toxicity is highest just following urea hydrolysis, strategies to optimize the timing and placement of urea should be considered.

Description: Soil structure affects all soil functions especially those related to physical and biological processes. On the other hand, soil structure itself is directly affected by these agents. Hence, soil structure—from single pores to the pedon scale—is expected to reflect the capacity of soil to deliver ecosystem functions. We analyzed soil structure including its seasonal dynamics for two plots within the long-term fertilization experiment in Bad Lauchstädt (Germany). The different plots received very different amounts of mineral and organic fertilizers over a period of 106 y. The quantification of structural properties includes pore-size distribution and pore connectivity obtained by X-ray microtomography. We present a methodological approach for image analysis that allows to combine samples of different size and resolution to cover pores within one order of magnitude in diameter. The results for the different plots obtained in spring and summer are compared. We found that the enormous difference in energy input only affects the structure of the topsoil (Ap horizon) towards a higher porosity and pore-network connectivity and in terms of an increased resilience after tillage. However, the structural properties of the subsoil below the plowed horizon (Ah horizon) are not affected. We hypothesize that the structure of the subsoil reflects soil formation over much longer time scales, it allows for an increased turnover of soil organic matter, and it is rather stable at the time scale of the fertilization experiment.

Description: The organic matter supply can promote the dispersal and activity of applied plant growth–promoting rhizobacteria (PGPR), but the complementary effect of organic fertilization and PGPR application on the turnover of P is scarcely known. The effects of the application of two PGPR strains ( Pseudomonas fluorescens strain DR54 and Enterobacter radicincitans sp. nov. strain DSM 16656) alone and in combination with organic fertilization (cattle manure and biowaste compost) on growth and P uptake of maize ( Zea mays L.) and oilseed rape ( Brassica napus L.) were investigated under semi–field conditions. Furthermore, P pools and phosphatase activities in soil and the arbuscular mycorrhizal–fungi colonization of maize roots were examined. The organic-fertilizer amendments increased the growth and P uptake of both plant species and the soil P pools. The application of the E. radicincitans strain increased P uptake of oilseed rape when no organic fertilizer was added. Furthermore, the application of both bacterial strains increased the activities of phosphatases under both plant species. Here, the effect of the PGPR application even exceeded the effect of organic fertilization. The magnitude of this effect varied between the different fertilizing treatments and between the two bacterial strains. Phosphatase activities were increased to the greatest extent after application of P. fluorescens in the unfertilized soil. Under rape increases of 52% for acid phosphatase activities (ACP), 103% for alkaline phosphatase activities (ALP), and 133% for phosphodiesterase (PDE) were observed therewith. In the unfertilized soil, the application of P. fluorescens also resulted in a strong increase of the arbuscular mycorrhizal colonization of maize. We conclude that application of PGPR can promote the P mobilization and supply of crops in P-deficient soils, however, in combination with organic fertilization these effects might be masked by a general improved P supply of the crops. Interactive effects of applied bacterial strains and organic fertilization depend on the sort of organic fertilizer and crop species used.

Description: To ensure high yield and quality in organic vegetable production, crops often require additional fertilizer applied during the season. Due to the risk of contamination of edible plant products from slurry, plant-based fertilizers may be used as an alternative. The purpose of our work was to develop mobile green manures with specific high nutrient concentrations ( e.g., nitrogen [N], sulfur [S], and phosphorus [P]) that are released quickly after soil incorporation and that are easy to handle during storage and application. To distinguish from traditional green manures that are grown to improve soil fertility, the term “mobile green manures” is used for green-manure crops that are harvested in one field and then moved as a whole and used as fertilizer in other fields. To further investigate mobile-green-manure crops for use as efficient fertilizers, pot and field experiments were conducted with cauliflower ( Brassica oleracea botrytis ) and kale ( Brassica oleracea sabellica ) supplied with organic matter consisting of a wide range of plant species with varying nutrient concentrations. Further, field experiments were conducted with leek ( Allium porrum ) and celery ( Apium graveolens dulce ) supplied with increasing amounts of organic matter consisting of fresh, ensiled, or dried green manures. Results show that garden sorrel ( Rumex acetosa ), dyer's woad ( Isatis tinctoria ), and fodder radish ( Raphanus sativus ) harvested with a high leaf-to-stem ratio resulted in high P concentration, and cruciferous crops in high S concentration. Dyer's woad, salad burnet ( Sanguisorba minor ), and stinging nettle ( Urtica dioica ) showed high boron (B) concentration, whereas species such as dandelion ( Taraxacum officinale ), chicory ( Cichorium intybus ), and garden sorrel showed high potassium (K) concentration. Green manures with high P and S concentrations increased the nutrient uptake and yield of pot-grown cauliflower and kale. Field experiments showed that the production of cauliflower and kale decreased when the carbon-to-nitrogen (C : N) ratio of applied green manure increased. In kale, for example, application of 160 kg N ha –1 in early harvested lucerne ( Medicago sativa ) with a C : N ratio of 10 resulted in the highest kale production whereas application of an equal amount of N in late harvested lucerne with a C : N ratio of 20 produced 34% less. Differences in vegetable production were not due to the amount of N applied, but to the N availability. Field experiments with fresh, ensiled, or dry green manure applied to leek and celery showed that the C : N ratio has to be low to get a fast response. Further, these field experiments demonstrate the importance of green manures, which can be stored and are easy to handle during transport, crop application, and soil incorporation. It is concluded that it is possible to produce green manures with high concentrations of S, P, K, and B, and low C : N ratios and that these properties have a great impact on the value of the green manure for vegetable production.

Description:    In the present study, we apply function transformation methods to the D -dimensional nonlinear Schrödinger (NLS) equation with damping and diffusive terms. As special cases, this method applies to the sine-Gordon, sinh-Gordon, and other equations. Also, the results show that these equations depend on only one function that can be obtained analytically by solving an ordinary differential equation. Furthermore, certain exact solutions of these three equations are shown to lead to the exact soliton solutions of a D -dimensional NLS equation with damping and diffusive terms. Finally, our results imply that the planar solitons, N multiple solitons, propagational breathers, and quadric solitons are solutions to the sine-Gordon, sinh-Gordon, and D -dimensional NLS equations. Content Type Journal Article Pages 1-9 DOI 10.1007/s00033-011-0117-4 Authors M. A. Helal, (FInstP) Mathematics Department, Faculty of Science, Cairo University, Giza, Egypt A. R. Seadawy, Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description: Splash cups have long been successfully used for both the quantification of kinetic energy of rainfall and the detachability of soil particles by rainfall impact, the so-called “splash erosion”. Measurements of kinetic energy, however, have been difficult to operate in the field especially in remote areas, on steep slopes, and in forests since boundary conditions need to be controlled precisely. This paper introduces a new splash cup based on Ellison's archetype that reliably and accurately measures kinetic energy as a function of sand loss under a large variety of conditions. The Tübingen splash cup (T splash cup) is relatively easy to operate under harsh field conditions, and it can be used in experimental designs with a large number of plots and replications at reasonably low costs. The cup is constructed from plastic laboratory flasks and plastic pipes from water-supply equipments. The unit sand is held by a removable carrier system that can easily be replaced in the field. The splash cups have been calibrated in combination with a laser distrometer using a linear regression function with r 2 = 0.98. They measure kinetic energy over a wide range of rainfall intensities from 0.6 to 40 L m –2 h –1 . Kinetic energy per area varies between 10 and 250 J m –2 . Two years of field test measurements in a subtropical forest ecosystem in China proved the reliability, durability, and usability of our new splash cups and allowed detecting differences in kinetic energy between different tree species and biodiversity levels.

Description: A multivariate statistical approach based on a large data set of abiotic and biotic variables was used to classify four contrasting-land-use soils. Soil samples were collected at increasing depth from a calcareous agricultural soil, a temperate upland grassland soil, a moderately acidic agricultural soil, and an acidic pine forest soil. Analytical investigations were carried out by using a combination of conventional physical, chemical, and biochemical methods coupled with denaturing gradient gel electrophoresis (DGGE) community fingerprinting of PCR-amplified 16S rRNA gene-coding fragments from soil-extracted total-community DNA. The data set of soil physical, chemical, and biochemical variables was reduced in dimensionality by means of a principal-component-analysis (PCA) procedure. Compositional shifts in soil bacterial-community structure were analyzed through a clustering algorithm that allowed identifying six main bacterial-community clusters. DGGE fingerprinting clusters were further analyzed by discriminant analysis (DA) using extracted PCA components as explanatory variables. Soil organic matter–related pools (TOC, TN) and functionally related active pools (microbial biomass C and N, K 2 SO 4 -extractable C) significantly decreased with soil depth, and resulted statistically linked to one other and positively related to enzymatic activities (acid phosphatase, arylsulfatase, β-glucosidase, dehydrogenase, hydrolysis of fluorescein diacetate) and silt content. Besides organic-C gradients, pedogenetic-driven physico-chemical properties, and possibly soil thermal and moisture regimes seemed to play a key role in regulating size and energetic ecophysiological status of soil microbial communities. DGGE analysis showed that contrasting horizons were conducive to the dominance of particular bacterial ribotypes. DA revealed that the bacterial-community structure was mainly influenced by organic matter–related variables (TOC, TN, CEC, C flush , N flush , Extr-C), chemical properties such as pH, CaCO 3 , and EC, together with textural properties. Results indicate that, beyond land use or plant cover, pedogenetic-driven physico-chemical conditions changing with soil type and depth are the key factors regulating microbial size and activity, and determining the genetic structure of bacterial community.

Description: Sulfonamides are the second most used antibiotic class in veterinary medicine and applied to livestock to treat bacterial infections. Subsequently, they are spread onto agricultural soils together with the contaminated manure used as fertilizer. Both manure and antibiotics affect the soil microbial community. However, the influence of different liquid manure loads on effects of antibiotics to soil microorganisms is not well understood. Therefore, we performed a microcosm experiment for up to 32 d to clarify whether the function and structure of the soil microbial community is differently affected by interactions of manure and the antibiotic sulfadiazine (SDZ). To this end selected concentrations of pig liquid manure (0, 20, 40, 80 g kg –1 ) and SDZ (0, 10, 100 mg kg –1 ) were combined. We hypothesized that incremental manure amendment might reduce the effect of SDZ in soils, due to an increasing sorption capacity of SDZ to organic compounds. Clear dose-dependent effects of SDZ on microbial biomass and PLFA pattern were determined, and SDZ effects interacted with the liquid manure application rate. Soil microbial biomass increased with incremental liquid manure addition, whereas this effect was absent in the presence of additional SDZ. However, activities of enzymes such as urease and protease were only slightly affected and basal respiration was not affected by SDZ application, while differences mostly depended on the concentration of liquid manure. These results illustrated that the microbial biomass and structural composition react more sensitive to SDZ contamination than functional processes. Furthermore, effects disproportionally increased with incremental liquid manure addition, although extractable amounts of SDZ declined with increasing liquid manure application.

Description: The present investigation was aimed to analyze influence of earthworm culture on nutritive status, microbial population, and enzymatic activities of composts prepared by utilizing different plant wastes. Vermicomposts were prepared from different types of leaves litter of horticulture and forest plant species by modified vermicomposting process at a farm unit. Initial thermophilic decomposition of waste load using cow-dung slurry was done in the separate beds. The culture of Eisenia fetida was used for vermicomposting in specially designed vermibeds at the farm unit. The physico-chemical characteristics, enzyme activities (oxido-reductases and hydrolases), and microbial population (bacteria, fungi, free-living nitrogen-fixing bacteria, actinomycetes, Bacillus, Pseudomonas , phosphate-solubilizing bacteria and fungi) of vermicomposts were found significantly higher ( p 〈 0.05) than those of control (without earthworm inoculum). The study quantified significant contributions of earthworm culture to physico-chemical, enzymatic, and microbiological properties of vermicompost and confirmed superior fertilization potential of vermicompost for organic farming. The agronomic utility of vermicompost was assessed on yellow mustard plant in a pot experiment. Pot soil was amended with different ratios (5%, 10%, 20%) of vermicompost and normal compost (without earthworm inoculum). Effects of these amendments on the growth of Brassica comprestis L. were studied. The significant differences ( p 〈 0.05) in the growth of plant were observed among vermicompost-, compost-amended soil, and control. Vermicompost increased the root and shoot lengths, numbers of branches and leaves per plant, fresh and dry weights per plant, numbers of pods and flowers, and biochemical properties of plant leaf significantly, especially in 20% amendment. These results proved better fertilization potential of vermicompost over non-earthworm-inoculated compost.

Description: Experiments to evaluate the effect of in-season calcium (Ca) sprays on late-season peach ( Prunus persica L. Batsch cv. Calrico) were carried out for a 2-year period. Calcium formulations (0.5% and 1.0% in 2008 and only 0.5% tested in 2009) supplied either as CaCl 2 or Ca propionate in combination with two or three adjuvants (0.05% of the nonionic surfactants Tween 20 and Break Thru, and 0.5% carboxymethylcellulose, CMC) were sprayed four to five times over the growing season. Peach mesocarp and endocarp Ca concentrations were determined on a 15-day basis from the beginning of May until the end of June. Further tissue analyses were performed at harvest. A decreasing trend in fruit Ca concentrations over the growing season was always observed regardless of the Ca treatments. Both in 2008 and 2009, significant tissue Ca increments associated with the application of Ca-containing sprays in combination with adjuvants were only observed in June, which may be coincident with the period of pit hardening. In 2008, both at harvest and after cold storage, the total soluble-solids concentration (° Brix) of fruits supplied with Ca propionate (0.5% and 1.0% Ca) was always lower as compared to the rest of treatments. The application of multiple Ca-containing sprays increased firmness at harvest and after cold storage, especially when CaCl 2 was the active ingredient used. Supplying the adjuvants Tween 20 and CMC increased fruit acidity both at harvest and after cold storage. Evaluation of the development of physiological disorders after cold storage (2 weeks at 0°C) indicated a lower susceptibility of Ca-treated fruits to internal browning. Fruits treated with multiple CaCl 2 -, CMC-, and Break Thru®-containing sprays during the growing season were significantly less prone to the development of chilling injuries as compared to untreated peaches.

Description: Recent literature confirmed that P fractions in soil are controlled by land use. However, differences in intensity of the same type of land use have received less attention although management intensity plays a crucial role in determining nutrient supply in soil. The objective of our work was to assess the influence of land-use intensity (LUI) on P fractions in soil. In the “Biodiversity Exploratories”, grassland and forest sites in Germany were selected in three regions (Schorfheide-Chorin, Hainich-Dün, Schwäbische Alb). In spring 2008, we sampled topsoil of 241 experimental plots. The plots included unfertilized and fertilized meadows, pastures, and mown pastures and near-natural to intensively used forests. Land-use intensity was classified according to the extent of annual biomass removal. We used the sequential extraction method of Hedley et al. (1982) to characterize P partitioning in soil. In summary, total P (TP) concentrations in soil were lowest at Schorfheide-Chorin (62–952 mg kg –1 ) followed by the Hainich-Dün (230–1631 mg kg –1 ) and the Schwäbische Alb (205–1838 mg kg –1 ). Differences between grassland and forest sites were mainly attributable to pH. The pH value was the most important factor among several soil properties explaining P partitioning in soil. For grassland, at pH values ≈ 6.5, the application of lime-containing fertilizer increased P availability in soil while effects of organic or mineral P fertilizers were negligible and related to the low application rates (〈 12 kg ha –1 ). Land-use intensity contributed up to 10% of the variation in the contribution of NaOH-P i to TP concentrations (ANOVA, Type I). In the Schwäbische Alb grassland soils, elevated LUI resulted in low NaOH-P i concentrations in soil which was probably caused by reduced sorption. Our findings highlight the importance of LUI as a control of P fractions in soil.

Description: This study explored the influence of 10 annual forage legumes belonging to the Lathyrus and Vicia genera on wet aggregate stability (WAS) and dispersion ratio (DR) indices of a clay soil. Five Lathyrus and five Vicia species were sown in autumn. Seed-to-seed and row-to-row distance was maintained at 5 cm and 20 cm, respectively. The experiment was planned in a randomized block design with three replications. After 90 d following seed harvest, soil cores were collected from two depths (0–15, 15–30 cm) in each plot and WAS and DR were determined. Annual forage legumes increased WAS of the soil but decreased the DR index. The WAS and DR values were affected at level of p 〈 0.001 by genus, species, and soil depth. Values of WAS and DR of the control plots without plant on the average were found to be 44.5% and 9.3% for 0–15 cm, and 41.2% and 10.1% for 15–30 cm, respectively. For 0–15 cm depth, the highest WAS (77.7%) and the lowest DR (6.4%) values were found in L. sphaericus L. (wild) plots. For 15–30 cm depth, the highest WAS value (62.6%) was obtained in L. annuus L. (wild) plots and the lowest DR value (6.7%) was in L. sativus L. (Gurbuz-2001) plots.

Description: A major challenge in sustainable crop management is to ensure adequate P supply for crops, while minimizing losses of P that could negatively impact water quality. The objective of the present study was to investigate the effects of long-term applications of different levels of mineral fertilizers and farmyard manure on (1) the availability of P, (2) the relationship between soil C, N, and P, and (3) the distribution of inorganic and organic P in size fractions obtained by wet sieving. Soil samples were taken from the top 20 cm of a long-term (29 y) fertilization trial on a sandy Cambisol near Darmstadt, SW Germany. Plant-available P, determined with the CAL method, was little affected by fertilization treatment ( p 〈 0.05) and was low to optimal. The concentration of inorganic and organic P extracted with a NaOH-EDTA solution (P NaOH-EDTA ) averaged about 350 mg (kg dry soil) –1 , with 42% being in the organic form (P o ). Manure application tended to increase soil C, N, and P o concentrations by 8%, 9%, and 5.6%, respectively. Across all treatments, the C : N : P o ratio was 100 : 9.5 : 2 and was not significantly affected by the fertilization treatments. Aggregate formation was weak due to the low clay and organic-matter content of the soil, and the fractions 〉 53 μm consisted predominantly of sand grains. The different fertilization treatments had little effect on the distribution of size fractions and their C, N, and P contents. In the fractions 〉 53 μm, P NaOH-EDTA ranged between 200 and 300 mg kg –1 , while it reached 1260 mg kg –1 in the fraction 〈 53 μm. Less than one third of P NaOH-EDTA was present as P o in the fractions 〉 53 μm, while P o accounted for 70% of P NaOH-EDTA in the smallest fraction (〈 53 μm). Therefore, 16% and 28% of P NaOH-EDTA and P o , respectively, were associated with the smallest fraction, even though this fraction accounted for 〈 5% of the soil mass. Therefore, runoff may cause higher P losses than the soil P content suggests in this sandy soil with a weak aggregate formation. Overall, the results indicate that manure and mineral fertilizer had similar effects on soil P fractions.

Description:    In this paper, we investigate the trajectory of the passive tracer model governed by the ordinary differential equation \frac d x ( t ) d t = F ( x ( t )),     x (0) = x 0 , where F ( x ) is a zero mean, homogeneous, isotropic Poisson shot noise random field. We prove the superdiffusive character of the trajectories under certain conditions on the energy spectrum of the velocity field. Content Type Journal Article Pages 1-9 DOI 10.1007/s00033-010-0110-3 Authors Ernest Nieznaj, Department of Mathematics, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, Nadbystrzycka 38A, 20-618 Lublin, Poland Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275