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  • Articles  (531)
  • rice  (281)
  • stability  (251)
  • Springer  (531)
  • Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition  (308)
  • Mathematics  (222)
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  • 1
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    The journal of Fourier analysis and applications 5 (1999), S. 105-125 
    ISSN: 1531-5851
    Keywords: 26B05 ; 42B10 ; 42C99 ; frame ; Gabor system ; Riesz basis ; stability ; wavelet
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract If the sequence of functions ϕj, k is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system ψj,k which is still a frame (Riesz basis) under very mild conditions. For example, we do not need to know that the support of ϕ or ψ $$(\hat \phi or\hat \psi )$$ is compact as in [14]. We also discuss the stability of irregular sampling problems. In order to arrive at some of our results, we set up a general multivariate version of Littlewood-Paley type inequality which was originally considered by Lemarié and Meyer [17], then by Chui and Shi [9], and Long [16].
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    European journal of nutrition 29 (1990), S. 219-228 
    ISSN: 1436-6215
    Keywords: Vitamin K ; Menadion ; Menadiol ; Bioverfügbarkeit ; Stabilität ; Geflügel ; vitamin K ; menadione ; menadiol ; bioavailability ; stability ; poultry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary A bioassay of vitamin K is described, based on the prothrombin clotting time of 3-week-old, vitamin-K-depleted, and cumatetralyl-sensitized male broiler chicks, using a homologous thrombokinase preparation. With this test it could be shown that the diacetate and dibutyrate esters of menadiol are vitamin-K-active. The bioactivity of menadione from these menadiolesters amounted to about 70 % of the standard menadione from a coated menadione sodium bisulfite (Dohyfral). Menadiol seems to be temperature-resistant under such conditions, whereby two uncoated MSB preparations lost about 60 % of their activity.
    Notes: Zusammenfassung In einem biologischen Testverfahren an Cumatetralyl sensibilisierten Küken konnte in 3 Versuchen anhand des Parameters Thromboplastinzeit mit homologer Thrombokinase gezeigt werden, da\ Menadioldiacetat und Menadioldibutyrat Vitamin-K-wirksam sind. Die biologische Wirksamkeit von Menadion aus diesen Menadiolestern betrug ca. 70 % der Menadionaktivität aus gecoatetem Menadionbisulfit (Dohyfral®). Im Gegensatz zu 2 ungeschützten MSB-Präparationen, welche bei Wärmebelastung ca. 60 % ihrer ursprünglichen Wirkung verloren, waren die Menadiolester temperaturstabil.
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  • 3
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    OR spectrum 20 (1998), S. 101-107 
    ISSN: 1436-6304
    Keywords: Competitive location model ; Nash equilibria ; stability ; reachability ; Wettbewerbsmodelle in der Standorttheorie ; Nash Gleichgewicht ; Stabilität ; Erreichbarkeit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In der Arbeit werden die Standorte von Duopolisten in einem Baum untersucht. Unter der Annahme festgesetzter Preise werden notwendige und hinreichende Bedingungen für Nash Gleichgewichte für Standorte auf Bäumen hergeleitet. Unter Verwendung dieser Bedingungen wird dann gezeigt, daß — angenommen Nash Gleichgewichte existieren — diese in einem wiederholt angewandten sequentiellen Standortfindungsprozeß, in dem beide Duopolisten als Zielfunktion kurzfristige Gewinnmaximierung haben, auch erreicht werden.
    Notes: Abstract This paper examines the location of duopolists on a tree. Given parametric prices, we first delineate necessary and sufficient conditions for locational Nash equilibria on trees. Given these conditions, we then show that Nash equilibria, provided they exist, can be reached in a repeated sequential relocation process in which both facilities follow short-term profit maximization objectives.
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    OR spectrum 20 (1998), S. 101-107 
    ISSN: 1436-6304
    Keywords: Key words: Competitive location model ; Nash equilibria ; stability ; reachability ; Schlüsselwörter: Wettbewerbsmodelle in der Standorttheorie ; Nash Gleichgewicht ; Stabilität ; Erreichbarkeit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. In der Arbeit werden die Standorte von Duopolisten in einem Baum untersucht. Unter der Annahme festgesetzter Preise werden notwendige und hinreichende Bedingungen für Nash Gleichgewichte für Standorte auf Bäumen hergeleitet. Unter Verwendung dieser Bedingungen wird dann gezeigt, daß– angenommen Nash Gleichgewichte existieren – diese in einem wiederholt angewandten sequentiellen Standortfindungsprozeß, in dem beide Duopolisten als Zielfunktion kurzfristige Gewinnmaximierung haben, auch erreicht werden. “Equilibrium is a place in heaven, but how do we get there from here?”
    Notes: Abstract. This paper examines the location of duopolists on a tree. Given parametric prices, we first delineate necessary and sufficient conditions for locational Nash equilibria on trees. Given these conditions, we then show that Nash equilibria, provided they exist, can be reached in a repeated sequential relocation process in which both facilities follow short-term profit maximization objectives.
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    OR spectrum 16 (1994), S. 47-52 
    ISSN: 1436-6304
    Keywords: Vector optimization ; approximately efficient solutions ; stability ; Vektoroptimierung ; Näherungslösungen ; Stabilität
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Wir führen ein Konzept für Näherungslösungen in der Vektoroptimierung ein und vergleichen dieses mit einem neuen Konzept aus [8]. Weiterhin untersuchen wir Beziehungen zwischen der Menge der Näherungslösungen eines Vektoroptimierungsproblems und den Näherungslösungen eines entsprechenden parametrischen Ersatzproblems. Schließlich beweisen wir Stabilitätseigenschaften des skalaren Ersatzproblems.
    Notes: Abstract We introduce a concept for approximately efficient solutions in vector optimization and compare it with another recent concept given in [8]. Further, we study relations between the set of approximately efficient solutions of a vector optimization problem and the approximate solutions of a corresponding parametric surrogate optimization problem. Finally, we prove stability properties for the scalar surrogate problem.
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  • 6
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    OR spectrum 18 (1996), S. 231-239 
    ISSN: 1436-6304
    Keywords: Generalized polymatrix games ; generalized linear complementarity problem ; stability ; degree theory ; Verallgemeinerte Polymatrix-Spiele ; verallgemeinertes lineares Komplementaritätsproblem ; Stabilität ; Grad-Theorie
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In dieser Arbeit führen wir eine Verallgemeinerung des Polymatrix-Spiels (eines Nicht-Nullsummen- und nicht-kooperativenn-Personen-Spiels), das von Howson betrachtet wurde, ein und führen das Problem, eine Gleichgewichtsmenge von Strategien für ein solches Spiel zu berechnen, auf das verallgemeinerte lineare Komplementaritätsproblem von Cottle und Dantzig zurück. Für eine noch allgemeinere Version des Spiels beweisen wir die Existenz einerε-Gleichgewichtsmenge von Strategien. Wir präsentieren auch ein Ergebnis über die Stabilität der Gleichgewichte, das auf der Grad-Theorie beruht.
    Notes: Abstract In this paper, we introduce a generalization of the polymatrix game (a nonzero sum noncooperativen-person game) considered by Howson and relate the problem of computing an equilibrium set of strategies for such a game to the generalized linear complementarity problem of Cottle and Dantzig. For an even more general version of the game we prove the existence of anε-equilibrium set of strategies. We also present a result on the stability of the equilibria based on degree theory.
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    Mathematical programming 47 (1990), S. 117-141 
    ISSN: 1436-4646
    Keywords: Bifurcation ; singularity ; parametric programming ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The structure of solutions to the nonlinear parametric programming problem with a one dimensional parameter is analyzed in terms of the bifurcation behavior of the curves of critical points and the persistence of minima along these curves. Changes in the structure of the solution occur at singularities of a nonlinear system of equations motivated by the Fritz John first-order necessary conditions. It has been shown that these singularities may be completely partitioned into seven distinct classes based upon the violation of one or more of the following: a complementarity condition, a constraint qualification, and the nonsingularity of the Hessian of the Lagrangian on a tangent space. To apply classical bifurcation techniques to these singularities, a further subdivision of each case is necessary. The structure of curves of critical points near singularities of lowest (zero) codimension within each case is analyzed, as well as the persistence of minima along curves emanating from these singularities. Bifurcation behavior is also investigated or discussed for many of the subcases giving rise to a codimension one singularity.
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  • 8
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    Mathematical programming 54 (1992), S. 57-67 
    ISSN: 1436-4646
    Keywords: Matchings ; stability ; extreme points ; polytope
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The purpose of this paper is to extend a modified version of a recent result of Vande Vate (1989) which characterizes stable matchings as the extreme points of a certain polytope. Our proofs are simpler and more transparent than those of Vande Vate.
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  • 9
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    Mathematical programming 61 (1993), S. 197-214 
    ISSN: 1436-4646
    Keywords: Epi-convergence ; epi-distance ; stability ; convex optimization ; approximate solutions ; subgradients ; level sets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We prove that theε-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar property is obtained for the distance between the level sets of extended real valued functions. We also show that these properties imply that theε-subgradient mapping is Lipschitz continuous.
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    Journal of dynamics and differential equations 1 (1989), S. 269-298 
    ISSN: 1572-9222
    Keywords: Geometric mechanics ; reduction ; stability ; chaos ; rigid body dynamics ; periodic orbits ; 58F
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    Topics: Mathematics
    Notes: Abstract We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincaré-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden.
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    Journal of dynamics and differential equations 10 (1998), S. 151-188 
    ISSN: 1572-9222
    Keywords: Fourth-order solitary waves ; stability ; instability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study ground-state traveling wave solutions of a fourth-order wave equation. We find conditions on the speed of the waves which imply stability and instability of the solitary waves. The analysis depends on the variational characterization of the ground states rather than information about the linearized operator.
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    Journal of dynamics and differential equations 6 (1994), S. 37-51 
    ISSN: 1572-9222
    Keywords: Celestial mechanics ; relative equilibria ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A criterion for the linear stability of relative equilibria of the Newtoniann-body problem is found in the case whenn−1 of the masses are small. Several stable periodic orbits of the problem are presented as examples.
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    Order 9 (1992), S. 163-175 
    ISSN: 1572-9273
    Keywords: Primary 06A07 ; secondary 05C70 ; Partial order ; interval ; stability ; covering ; Sperner property ; symmetric chains ; NP-completeness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Given a finite ranked posetP, let α(P) be the maximum size of a subset ofP such that no two elements of it belong simultaneously to some interval ofP and let ϱ(P) be the minimum number of intervals covering all elements ofP. We say thatP has the strong interval stability property (resp. the strong interval covering property) if for each subposetP′ induced by consecutive levels ofP, i.e.,P′=P (l)∪...∪P (u), one has α(P′)=max{|P (l)|, |P (u)|} (resp. ϱ(P′)=max{|P (l)|, |P (u)|}). We prove these properties for several classes of posets and discuss some general facts concerning the numbers α(P) and ϱ(P), e.g., NP-completeness and min-max relations.
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    Positivity 1 (1997), S. 319-330 
    ISSN: 1572-9281
    Keywords: delay equations ; stability ; positive solutions ; spectral growth condition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove stability for a semilinear delay equation, whose nonlinearity is majorized by a linear positive operator. The key ingredients are a spectral condition, positivity of solutions to the linear problem, and lattice properties of the Banach space.
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  • 15
    ISSN: 1572-9281
    Keywords: asymptotic stability ; dichotomic maps ; retarded functional differential equation ; stability
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    Topics: Mathematics
    Notes: Abstract This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation $$x'(t) = - b(t)x(t - r)$$ and of itsnonlinear generalization $$x'(t) = b(t)f(x(t - r))$$ are established.
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    Journal of computational analysis and applications 2 (2000), S. 293-308 
    ISSN: 1572-9206
    Keywords: parabolic equations ; ADI scheme ; stability
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    Topics: Mathematics
    Notes: Abstract An ADI scheme for solving three-dimensional parabolic equations withfirst-order derivatives and variable coefficients has been developed basedon our previous papers and the idea of the modified upwind differencescheme. This ADI scheme is second-order accurate and unconditionallystable. Further, a small parameter can be chosen which makes it suitablefor simulating fast-transient phenomena or for computations on fine spatialmeshes. The method is illustrated with numerical examples.
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    Journal of dynamics and differential equations 5 (1993), S. 625-671 
    ISSN: 1572-9222
    Keywords: Scalar reaction-diffusion equation ; singular perturbation methods ; internal layer ; Neumann layer ; stability ; 35K57 ; 35B25 ; 35B35
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    Topics: Mathematics
    Notes: Abstract The multiple existences and their stability properties of stationary solutions with a single transition layer in some scalar reaction-diffusion equation are shown. Each solution is constructed by using classical singular perturbation methods and its stability property is determined by a simple algebraic quantity, say index, appearing in the construction of a solution.
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    Journal of dynamics and differential equations 6 (1994), S. 639-658 
    ISSN: 1572-9222
    Keywords: Symmetry ; parabolic equations ; positive solutions ; stability
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    Topics: Mathematics
    Notes: Abstract Symmetry properties of positive solutions of a Dirichlet problem for a strongly nonlinear parabolic partial differential equation in a symmetric domainD ⊂ R n are considered. It is assumed that the domainD and the equation are invariant with respect to a group {Q} of transformations ofD. In examples {Q} consists of reflections or rotations. The main result of the paper is the theorem which states that any compact inC(D) negatively invariant set which consists of positive functions consists ofQ-symmetric functions. Examples of negatively invariant sets are (in autonomous case) equilibrium points, omega-limit sets, alpha-limit sets, unstable sets of invariant sets, and global attractors. Application of the main theorem to equilibrium points gives the Gidas-Ni-Nirenberg theorem. Applying the theorem to omega-limit sets, we obtain the asymptotical symmetrization property. That means that a bounded solutionu(t) asr→∞ approaches subspace of symmetric functions. One more result concerns properties of eigenfunctions of linearizations of the equations at positive equilibrium points. It is proved that all unstable eigenfunctions are symmetric.
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    Set-valued analysis 5 (1997), S. 73-88 
    ISSN: 1572-932X
    Keywords: differential inclusion ; invariance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The properties of invariance, stability, asymptotic stability and attainability of a given compact set $$K \subset \mathbb{R}^n $$ with respect to a differential inclusion, have weak and strong versions: the weak version requires existence of a trajectory with the corresponding property, while the strong one requires this property for all trajectories. The following statement is proven in the paper (under slight restrictions) for each of the above-mentioned properties: if K has the weak property with respect to $$\dot x \in F(x) $$ , then there is a (regulation) mapping G such that G(x) ⊂ F(x) ∀ x and G has the strong property with respect to $${\dot x}$$ ε G(x). In addition, certain regularity of the set of solutions of the last inclusion is claimed.
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    Set-valued analysis 5 (1997), S. 365-375 
    ISSN: 1572-932X
    Keywords: set-valued mappings ; vector optimization ; stability
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    Topics: Mathematics
    Notes: Abstract We establish optimization results for set-valued mappings, with the image space given by a topological vector space partially ordered by a cone. Moreover, we obtain stability results relative to parametrized optimization problems. We use a weak semicontinuity concept related to the order structure of the image space and show how compactness assumptions used in previous papers can be lightened.
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    Annals of operations research 27 (1990), S. 343-369 
    ISSN: 1572-9338
    Keywords: Bifurcation ; singularities ; continuation ; parametric nonlinear programming ; stability
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    Topics: Mathematics , Economics
    Notes: Abstract Bifurcation and continuation techniques are introduced as a class of methods for investigating the parametric nonlinear programming problem. Motivated by the Fritz John first-order necessary conditions, the parametric programming problem is first reformulated as a closed system of nonlinear equations which contains all Karush-Kuhn-Tucker and Fritz John points, both feasible and infeasible solutions, and relative minima, maxima, and saddle points. Since changes in the structure of the solution set and critical point type can occur only at singularities, necessary and sufficient conditions for the existence of a singularity are developed in terms of the loss of a complementarity condition, the linear dependence constraint qualification, and the singularity of the Hessian of the Lagrangian on a tangent space. After a brief introduction to elementary bifurcation theory, some simple singularities in this parametric problem are analyzed for both branching and persistence of local minima. Finally, a brief introduction to numerical continuation and bifurcation procedures is given to indicate how these facts can be used in a numerical investigation of the problem.
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    Annals of operations research 56 (1995), S. 79-93 
    ISSN: 1572-9338
    Keywords: Multistage stochastic programs ; optimization in Banach spaces ; stability ; approximation
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    Topics: Mathematics , Economics
    Notes: Abstract Multistage stochastic programs are regarded as mathematical programs in a Banach spaceX of summable functions. Relying on a result for parametric programs in Banach spaces, the paper presents conditions under which linearly constrained convex multistage problems behave stably when the (input) data process is subjected to (small) perturbations. In particular, we show the persistence of optimal solutions, the local Lipschitz continuity of the optimal value and the upper semicontinuity of optimal sets with respect to the weak topology inX. The linear case with deterministic first-stage decisions is studied in more detail.
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    Computational & mathematical organization theory 5 (1999), S. 5-30 
    ISSN: 1572-9346
    Keywords: network models ; organization theory ; rule following ; self organized ; stability ; work teams ; work routine
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Self-organized rule-following systems are increasingly relevant objects of study in organization theory due to such systems&2018; capacity to maintain control while enabling decentralization of authority. This paper proposes a network model for such systems and examines the stability of the networks&2018; repetitive behavior. The networks examined are Ashby nets, a fundamental class of binary systems: connected aggregates of nodes that individually compute an interaction rule, a binary function of their three inputs. The nodes, which we interpret as workers in a work team, have two network inputs and one self-input. All workers in a given team follow the same interaction rule. We operationalize the notion of stability of the team&2018;s work routine and determine stability under small perturbations for all possible rules these teams can follow. To study the organizational concomitants of stability, we characterize the rules by their memory, fluency, homogeneity, and autonomy. We relate these measures to work routine stability, and find that stability in ten member teams is enhanced by rules that have low memory, high homogeneity, and low autonomy.
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    Journal of dynamics and differential equations 12 (2000), S. 117-167 
    ISSN: 1572-9222
    Keywords: singular perturbation ; standing pulses ; stability ; Hopf bifurcation ; reaction-diffusion system
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    Topics: Mathematics
    Notes: Abstract Bifurcation phenomena from standing pulse solutions of the problem $$\varepsilon \tau u_t = \varepsilon ^2 u_{xx} + f(u,v),{\text{ }}v_t = v_{xx} + g(u,v)$$ is considered. ε(〉0) is a sufficiently small parameter and τ is a positive one. It is shown that there exist two types of destabilization of standing pulse solutions when τ decreases. One is the appearance of travelling pulse solutions via the static bifurcation and the other is that of in-phase breathers via the Hopf bifurcation. Furthermore which type of destabilization occurs first with decreasing τ is discussed for the piecewise linear nonlinearities f and g.
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    Journal of dynamics and differential equations 5 (1993), S. 189-218 
    ISSN: 1572-9222
    Keywords: Equivariant bifurcation ; symmetry ; singularity ; equivariant jets and transversality ; normal forms ; universal unfolding ; stability ; structural stability ; 58F14 ; 58E07 ; 58C27
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    Topics: Mathematics
    Notes: Abstract The theoretical machinery from singularity theory introduced by Golubitsky, Stewart, and Schaeffer, to study equivariant bifurcation problems, is completed and expanded while generalized to the multiple parameter context. In this setting the finite determinacy theorems or normal forms, the stability of equivariant bifurcation problems, and the structural stability of the universal unfolding are discussed.
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    Journal of dynamics and differential equations 6 (1994), S. 447-486 
    ISSN: 1572-9222
    Keywords: Free boundary problems ; gasless combustion ; stability ; Hopf bifurcation ; 35R35 ; 35B40 ; 80A25
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    Topics: Mathematics
    Notes: Abstract In this paper, we analyze a simple free boundary model associated with solid combustion and some phase transition processes. There is strong evidence that this “one-phase” model captures all major features of dynamical behavior of more realistic (and complicated) combustion and phase transition models. The principal results concern the dynamical behavior of the model as a bifurcation parameter (which is related to the activation energy in the case of combustion) varies. We prove that the basic uniform front propagation is asymptotically stable against perturbations for the bifurcation parameter above the instability threshold and that a Hopf bifurcation takes place at the threshold value. Results of numerical simulations are presented which confirm that both supercritical and subcritical Hofp bifurcation may occur for physically reasonable nonlinear kinetic functions.
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    Journal of dynamics and differential equations 9 (1997), S. 463-505 
    ISSN: 1572-9222
    Keywords: Difference equations ; random perturbation ; averaging ; diffusion approximation ; randomly perturbed iterations ; stability ; 3SR60 ; 60H15 ; 60J99
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    Topics: Mathematics
    Notes: Abstract Let (X, ℬ) and (Y,C) be two measurable spaces withX being a linear space. A system is determined by two functionsf(X): X→ X andϕ:X×Y→X, a (small) positive parameterε and a homogeneous Markov chain {y n } in (Y,C) which describes random perturbations. States of the system, say {x n ɛ ∈X, n=0, 1,⋯}, are determined by the iteration relations:x n+1 ɛ =f(x n ɛ )+ɛϕ(x n ɛ ,Yn+1) forn≥0, wherex 0 ɛ =x 0 is given. Here we study the asymptotic behavior of the solutionx n ɛ asε → 0 andn → ∞ under various assumptions on the data. General results are applied to some problems in epidemics, genetics and demographics.
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    Set-valued analysis 5 (1997), S. 377-390 
    ISSN: 1572-932X
    Keywords: differential inclusions ; stability ; boundedness of solutions ; Lyapunov functions
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    Topics: Mathematics
    Notes: Abstract For Lipschitzian differential inclusions, we prove that the existence of suitable Lyapunov functions is necessary for uniform stability and uniform boundedness of solutions.
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    Set-valued analysis 4 (1996), S. 361-374 
    ISSN: 1572-932X
    Keywords: 34A60 ; 34E15 ; 34C29 ; differential inclusion ; singular perturbation ; averaging method ; controlability ; stability
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    Topics: Mathematics
    Notes: Abstract We consider nonlinear, singularly perturbed differential inclusions and apply the averaging method in order to construct a limit differential inclusion for slow motion. The main approximation result states that the existence and regularity of the limit differential inclusion suffice to describe the limit behavior of the slow motion. We give explicit approximation rates for the uniform convergence on compact time intervals. The approach works under controllability or stability properties of fast motion.
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    Set-valued analysis 7 (1999), S. 209-238 
    ISSN: 1572-932X
    Keywords: nonsmooth analysis ; subdifferentials ; coderivatives ; implicit function theorem ; solvability ; stability ; open mapping theorem ; metric regularity ; multidirectional mean value inequality
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    Topics: Mathematics
    Notes: Abstract We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunction theorem by reducing it to an implicit function/solvability theorem for functions. This approach can also be used to prove the Robinson–Ursescu open mapping theorem. As a tool for this alternative proof of the Robinson–Ursescu theorem, we also establish a refined version of the multidirectional mean value inequality which is of independent interest.
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    Set-valued analysis 1 (1993), S. 393-402 
    ISSN: 1572-932X
    Keywords: Primary: 49J40, 65K10, 47A55, 47H05, 65L20 ; Variational inequality ; perturbation ; unbounded and nonsmooth operators ; convex sets ; Hausdorff distance ; regularization ; monotonicity ; convergence ; stability
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    Topics: Mathematics
    Notes: Abstract The stability and convergence of the solutions of perturbed and regularized variational inequality to the solutions of the primary (unstable a priori) variational inequality with proper monotone operator are investigated. All the objects of inequality: the operatorA, the right-hand partf and the set of constrains Ω are to be perturbed. At the same time no assumptions of boundedness and smoothness of the operatorA are used. The connection between the parameters of perturbations, which guarantees strong convergence of approximate solutions, is established. It is proved that the existence of the solution to the unperturbed variational inequality is necessary and sufficient condition for convergence of the regularized perturbed inequality solutions.
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    Journal of dynamics and differential equations 1 (1989), S. 299-325 
    ISSN: 1572-9222
    Keywords: Commodity markets ; time delays ; stability ; Hopf bifurcation ; 34K15 ; 45J05 ; 90A16
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    Topics: Mathematics
    Notes: Abstract A model for the dynamics of price adjustment in a single commodity market is developed. Nonlinearities in both supply and demand functions are considered explicitly, as are delays due to production lags and storage policies, to yield a nonlinear integrodifferential equation. Conditions for the local stability of the equilibrium price are derived in terms of the elasticities of supply and demand, the supply and demand relaxation times, and the equilibrium production-storage delay. The destabilizing effect of consumer memory on the equilibrium price is analyzed, and the ensuing Hopf bifurcations are described.
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    Journal of dynamics and differential equations 4 (1992), S. 161-190 
    ISSN: 1572-9222
    Keywords: Delay differential equations ; equilibrium ; stability ; limiting equations ; population dynamics ; 34K20 ; 34K25 ; 92A15
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    Topics: Mathematics
    Notes: Abstract Applying an analytical method and several limiting equations arguments, some sufficient conditions are provided for the existence of a unique positive equilibriumK for the delay differential equationx=−γx+D(x t ), which is the general form of many population models. The results are concerned with the global attractivity, uniform stability, and uniform asymptotic stability ofK. Application of the results to some known population models, which shows the effectiveness of the methods applied here, is also presented.
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    Journal of dynamics and differential equations 5 (1993), S. 105-128 
    ISSN: 1572-9222
    Keywords: Delay system ; stability ; relative variance ; dynamical disease
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    Topics: Mathematics
    Notes: Abstract A new approach to the study of delay systems, applicable to physiological control systems and other systems where little information about the time delays is available, is examined. The method is based on the fact that stability information can be deduced from the statistical properties of the probability distribution that encodes the structure of the time delay. The main statistical variables used are the usual expectation parameter,E, and a modified variance, calledrelative variance and denotedR, that is invariant under time scale changes. Recent work of the author has shown that stability often improves asR increases whileE remains fixed. A four-parameter family of delay models is analysed in this paper, and the (E, R) pair is found to be a reliable indicator of stability over the global parameter domain of the family.
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    Journal of dynamics and differential equations 6 (1994), S. 325-334 
    ISSN: 1572-9222
    Keywords: Nonlinear Schrödinger equations ; anisotropic standing waves ; stability ; concentration compactness principle ; Davey-Stewartson system ; 35Q35 ; 35B35
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    Topics: Mathematics
    Notes: Abstract We study the stability of standing waves for a nonlinear Schrödinger equation, which derives from the generalized Davey-Stewartson system in the elliptic-elliptic case. We prove the existence of stable standing waves under certain conditions.
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    Journal of dynamics and differential equations 6 (1994), S. 631-637 
    ISSN: 1572-9222
    Keywords: stability ; fixed point index ; periodic solutions
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    Topics: Mathematics
    Notes: Abstract In this paper, we prove that a stable isolated fixed point of an orientation preserving local homeomorphism onR 2 has fixed point index 1. We also give a number of applications to differential equations. In particular, we deduce that a number of existence methods for producing periodic solutions of differential equations in the plane always produce unstable solutions.
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    Set-valued analysis 8 (2000), S. 253-266 
    ISSN: 1572-932X
    Keywords: Hausdorff metric ; linear inequality systems ; stability
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    Topics: Mathematics
    Notes: Abstract In this paper, we propose a Hausdorff metric to measure the “distance” between two linear inequality systems on a real normed space X. For this topology, which comes through a pseudo-metric in the set Σ of linear inequality systems, the closedness of the feasible set mapping is studied, and at the same time a characterization of the stability of the subset Σ c of consistent sytems is given.
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    Annals of operations research 99 (2000), S. 251-265 
    ISSN: 1572-9338
    Keywords: stochastic programming ; bond portfolio management ; interest ratescenarios ; stability ; sensitivity
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    Topics: Mathematics , Economics
    Notes: Abstract The bond portfolio management problem is formulated as a multiperiod two-stage or multistage stochastic program based on interest rate scenarios. These scenarios depend on the available market data, on the applied estimation and sampling techniques, etc., and are used to evaluate coefficients of the resulting large scale mathematical program. The aim of the contribution is to analyze stability and sensitivity of this program on small changes of the coefficients – the (scenario dependent) values of future interest rates and prices. We shall prove that under sensible assumptions, the scenario subproblems are stable linear programs and that also the optimal first-stage decisions and the optimal value of the considered stochastic program possess acceptable continuity properties.
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    Acta applicandae mathematicae 28 (1992), S. 1-42 
    ISSN: 1572-9036
    Keywords: 35R30 ; Inverse scattering ; stability ; noisy data
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    Topics: Mathematics
    Notes: Abstract An algorithm is given for calculating the solution to the 3D inverse scattering problem with noisy discrete fixed energy data. The error estimates for the calculated solution are derived. The methods developed are of a general nature and can be used in many applications: in nondestructive evaluation and remote sensing, in geophysical exploration, medical diagnostics, and technology.
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    Advances in computational mathematics 10 (1999), S. 271-289 
    ISSN: 1572-9044
    Keywords: delay differential equations ; steady state solutions ; stability ; 34K20 ; 65J10
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    Topics: Mathematics
    Notes: Abstract The characteristic equation of a system of delay differential equations (DDEs) is a nonlinear equation with infinitely many zeros. The stability of a steady state solution of such a DDE system is determined by the number of zeros of this equation with positive real part. We present a numerical algorithm to compute the rightmost, i.e., stability determining, zeros of the characteristic equation. The algorithm is based on the application of subspace iteration on the time integration operator of the system or its variational equations. The computed zeros provide insight into the system’s behaviour, can be used for robust bifurcation detection and for efficient indirect calculation of bifurcation points.
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    Annals of global analysis and geometry 11 (1993), S. 387-395 
    ISSN: 1572-9060
    Keywords: Curvatures of hypersurfaces ; Reilly's inequality ; stability ; 53 A 10 ; 53 C 42
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    Topics: Mathematics
    Notes: Abstract We generalize Reilly's inequality for the first eigenvalue of immersed submanifolds ofIR m +1 and the total (squared) mean curvature, to hypersurfaces ofIR m +1 and the first eigenvalue of the higher order curvatures. We apply this to stability problems. We also consider hypersurfaces in hyperbolic space.
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    Applications of mathematics 45 (2000), S. 161-176 
    ISSN: 1572-9109
    Keywords: reaction-diffusion system ; unilateral conditions ; quasivariational inequality ; Leray-Schauder degree ; eigenvalue ; stability
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    Topics: Mathematics
    Notes: Abstract We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.
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    BIT 17 (1977), S. 321-328 
    ISSN: 1572-9125
    Keywords: 5.15 ; nonlinear equation ; root finding ; multiple root ; secant method ; Steffensen procedure ; order of convergence ; efficiency ; stability
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    Notes: Abstract A superlinear procedure for finding a multiple root is presented. In it the secant method is applied to the given function divided by a divided difference whose increment shrinks toward zero as the root is approached. Two function evaluations per step are required, but no derivatives need be calculated.
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    BIT 33 (1993), S. 332-350 
    ISSN: 1572-9125
    Keywords: AMS(MOS): 65L06 ; Multistep collocation method ; continuous solution ; stability
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    Topics: Mathematics
    Notes: Abstract This paper describes an implementation of multistep collocation methods, which are applicable to stiff differential problems, singular perturbation problems, and D.A.E.s of index 1 and 2. These methods generalize one-step implicit Runge-Kutta methods as well as multistep one-stage BDF methods. We give numerical comparisons of our code with two representative codes for these methods, RADAU5 and LSODE.
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    BIT 36 (1996), S. 531-541 
    ISSN: 1572-9125
    Keywords: Meromorphic resolvent ; stability ; power bounded
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    Topics: Mathematics
    Notes: Abstract Tools to estimate resolvents are developed and a model result is given for power bounded operators: the dimension showing up in the Kreiss matrix theorem can be replaced by the trace norm.
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    BIT 39 (1999), S. 385-402 
    ISSN: 1572-9125
    Keywords: Gaussian elimination ; stability ; backward error analysis ; growth factor
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    Notes: Abstract A new backward error analysis of LU factorization is presented. It allows to obtain a sharper upper bound for the forward error and a new definition of the growth factor that we compare with the well known Wilkinson growth factor for some classes of matrices. Numerical experiments show that the new growth factor is often of order approximately log2 n whereas Wilkinson's growth factor is of order n or $$\sqrt n$$ .
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    BIT 7 (1967), S. 65-70 
    ISSN: 1572-9125
    Keywords: Differential equations ; multistep methods ; stability
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    Notes: Abstract It has been shown by Dahlquist [3] that the trapezoidal formula has the smallest truncation error among all linear multistep methods with a certain stability property. It is the purpose of this note to show that a slightly different stability requirement permits methods of higher accuracy.
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    Advances in computational mathematics 9 (1998), S. 145-171 
    ISSN: 1572-9044
    Keywords: periodic pseudodifferential equations ; multiwavelets ; splines with multiple knots ; generalized Galerkin–Petrov schemes ; boundary element methods ; error analysis ; stability ; Strang–Fix condition ; 65J10 ; 65N30 ; 65N35 ; 65R20 ; 47G30 ; 45P05 ; 41A25 ; 41A30 ; 41A15
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    Notes: Abstract We develop a stability and convergence analysis of Galerkin–Petrov schemes based on a general setting of multiresolution generated by several refinable functions for the numerical solution of pseudodifferential equations on smooth closed curves. Particular realizations of such a multiresolution analysis are trial spaces generated by biorthogonal wavelets or by splines with multiple knots. The main result presents necessary and sufficient conditions for the stability of the numerical method in terms of the principal symbol of the pseudodifferential operator and the Fourier transforms of the generating multiscaling functions as well as of the test functionals. Moreover, optimal convergence rates for the approximate solutions in a range of Sobolev spaces are established.
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    Advances in computational mathematics 12 (2000), S. 229-250 
    ISSN: 1572-9044
    Keywords: numerical analysis ; shallow water problems ; DIRK methods ; stability ; 65L06 ; 65L20 ; 65M12 ; 65M20
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    Topics: Mathematics
    Notes: Abstract We construct A‐stable and L‐stable diagonally implicit Runge–Kutta methods of which the diagonal vector in the Butcher matrix has a minimal maximum norm. If the implicit Runge–Kutta relations are iteratively solved by means of the approximately factorized Newton process, then such iterated Runge–Kutta methods are suitable methods for integrating shallow water problems in the sense that the stability boundary is relatively large and that the usually quite fine vertical resolution of the discretized spatial domain is not involved in the stability condition.
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    Advances in computational mathematics 4 (1995), S. 1-26 
    ISSN: 1572-9044
    Keywords: Wavelets ; biorthogonal wavelets ; stability ; primary 15A12 ; 65F35 ; secondary 42C15
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    Topics: Mathematics
    Notes: Abstract For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including efficient numerical estimates if the numberL of decomposition levels is small, as well as growth estimates forL → ∞. These estimates allow easy determination of numerical stability directly from the wavelet coefficients. Examples show that many biorthogonal wavelets are in fact numerically well behaved.
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    Annals of global analysis and geometry 11 (1993), S. 221-235 
    ISSN: 1572-9060
    Keywords: Second variation formula ; Morse index ; stability ; 53C
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    Topics: Mathematics
    Notes: Abstract Iff is a minimal, isometric immersion of the Riemannian manifoldM of dimensionn in a Riemannian manifold $$\overline M$$ of dimensionm and ifI N is the „differential Jacobi operator” acting on the cross sections of the normal bundleN(M), we obtain some information on the Morse index and on the stability ofM through a detailed geometric analysis of the immersionf obtained when considering the higher fundamental forms off.
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    Annals of global analysis and geometry 13 (1995), S. 141-148 
    ISSN: 1572-9060
    Keywords: Gauss curvature ; stability ; 53
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    Topics: Mathematics
    Notes: Abstract We prove that a domain on a surface of constant curvature is stable provided the integral of the mean curvature is small enough.
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    Annals of global analysis and geometry 15 (1997), S. 277-297 
    ISSN: 1572-9060
    Keywords: mean curvature ; $$r$$ -mean curvature ; sphere ; stability ; stable
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    Topics: Mathematics
    Notes: Abstract We deal with compact hypersurfaces immersed in space forms with constant $$r$$ -mean curvature. They are critical points for a variational problem. We show they are stable if and only if they are geodesic spheres, generalizing results on constant curvature hypersurfaces.
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    ISSN: 1572-9125
    Keywords: finite difference methods ; wave equation ; accuracy ; stability ; Padé approximants ; order stars ; Riemann surface
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    Notes: Abstract We consider three time-level difference schemes, symmetric in time and space, for the solution of the wave equation,u tt =c 2 u xx , given by $$\sum\limits_{j = - S}^S {b_j U_{n + 1,m + j} + } \sum\limits_{j = - S}^S {a_j U_{n,m + j} + } \sum\limits_{j = - S}^S {b_j U_{n - 1,m + j} } = 0.$$ It has already been proved that the maximal order of accuracyp of such schemes is given byp ≤ 2(s + S). In this paper we show that the requirement of stability does not reduce this maximal order for any choice of the pair (s, S). The result is proved by introducing an order star on the Riemann surface of the algebraic function associated with the scheme. Furthermore, Padé schemes, withS = 0,s 〉 0, ands = 0,S 〉 0, are proved to be stable for 0 〈 μ 〈 1, where μ is the Courant number. These schemes can be implemented with high-order absorbing boundary conditions without reducing the range of μ for which stable solutions are obtained.
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    BIT 26 (1986), S. 93-99 
    ISSN: 1572-9125
    Keywords: Primary 65HO5 ; nonlinear equation ; multiple roots ; multipoint iterative methods ; error constant ; stability ; efficiency
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    Topics: Mathematics
    Notes: Abstract A one-parameter family of derivative free multipoint iterative methods of orders three and four are derived for finding the simple and multiple roots off(x)=0. For simple roots, the third order methods require three function evaluations while the fourth order methods require four function evaluations. For multiple roots, the third order methods require six function evaluations while the fourth order methods require eight function evaluations. Numerical results show the robustness of these methods.
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    BIT 27 (1987), S. 424-437 
    ISSN: 1572-9125
    Keywords: 65 L 05 ; 65 L 20 ; stability ; contractivity ; numerical solution of stiff initial value problems in ordinary differential equations ; Runge-Kutta methods ; Rosenbrock methods ; rational Runge-Kutta methods
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    Topics: Mathematics
    Notes: Abstract This paper concerns the stability analysis of numerical methods for approximating the solutions to (stiff) initial value problems. Our analysis includes the case of (nonlinear) systems of differential equations that are essentially more general than the classical test equationU′=λU, with λ a complex constant. We explore the relation between two stability concepts, viz. the concepts of contractivity and weak contractivity. General Runge-Kutta methods, one-stage Rosenbrock methods and a notable rational Runge-Kutta method are analysed in some detail.
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    BIT 30 (1990), S. 332-346 
    ISSN: 1572-9125
    Keywords: 65D05 ; polynomial interpolaton ; Newton form ; stability ; Leja points ; ordering of interpolation points
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    Topics: Mathematics
    Notes: Abstract The Newton form is a convenient representation for interpolation polynomials. Its sensitivity to perturbations depends on the distribution and ordering of the interpolation points. The present paper bounds the growth of the condition number of the Newton form when the interpolation points are Leja points for fairly general compact sets K in the complex plane. Because the Leja points are defined recursively, they are attractive to use with the Newton form. If K is an interval, then the Leja points are distributed roughly like Chebyshev points. Our investigation of the Newton form defined by interpolation at Leja points suggests an ordering scheme for arbitrary interpolation points.
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    Acta applicandae mathematicae 49 (1997), S. 35-54 
    ISSN: 1572-9036
    Keywords: dynamical systems ; stability ; pseudo orbit tracing property ; nonstandard analysis
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    Topics: Mathematics
    Notes: Abstract It is known that it is not possible to introduce C0 -structural stability for whole systems in topological dynamics. Using the methods of Nonstandard Analysis, we suggest four different purely topological stability concepts for dynamical systems on compact subsets of Rn. Classically these amount to considering the space of all systems on a given subset of Rn as the fundamental entity when deforming a continuous system (instead of the space of all continuous systems as is normally done in topological dynamics). For two of the introduced stability concepts, we will show that all minimal flows are stable in this sense. Besides this, we will show that one of our stability concepts is related to what is called the pseudo orbit tracing property in a recently published book by Aoki and Hiraide and compare some of our results to the theory of dynamical systems as presented there.
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    BIT 32 (1992), S. 634-649 
    ISSN: 1572-9125
    Keywords: AMS(MOS): 65L20 ; CR: 5.17 ; delay differential equations ; numerical solution ; Runge-Kutta methods ; interpolation procedures ; stability
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    Topics: Mathematics
    Notes: Abstract This paper deals with adapting Runge-Kutta methods to differential equations with a lagging argument. A new interpolation procedure is introduced which leads to numerical processes that satisfy an important asymptotic stability condition related to the class of testproblemsU′(t)=λU(t)+μU(t−τ) with λ, μ ε C, Re(λ)〈−|μ|, and τ〉0. Ifc i denotes theith abscissa of a given Runge-Kutta method, then in thenth stept n−1→t n :=t n−1+h of the numerical process our interpolation procedure computes an approximation toU(t n−1+c i h−τ) from approximations that have already been generated by the process at pointst j−1+c i h(j=1,2,3,...). For two of these new processes and a standard process we shall consider the convergence behaviour in an actual application to a given, stiff problem.
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    BIT 40 (2000), S. 62-73 
    ISSN: 1572-9125
    Keywords: Gaussian elimination ; stability ; pivoting
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    Notes: Abstract It has been recently shown that large growth factors might occur in Gaussian Elimination with Partial Pivoting (GEPP) also when solving some plausibly natural systems. In this note we argue that this potential problem could be easily solved, with much smaller risk of failure, by very small (and low cost) modifications of the basic algorithm, thus confirming its inherent robustness. To this end, we first propose an informal model with the goal of providing further support to the comprehension of the stability properties of GEPP. We then report the results of numerical experiments that confirm the viewpoint embedded in the model. Basing on the previous observations, we finally propose a simple scheme that could be turned into (even more) accurate software for the solution of linear systems.
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    BIT 40 (2000), S. 611-639 
    ISSN: 1572-9125
    Keywords: Runge-Kutta methods ; stability ; convergence ; stiff problems
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    Notes: Abstract This paper studies the stability and convergence properties of general Runge-Kutta methods when they are applied to stiff semilinear systems y′(t) = J(t)y(t) + g(t, y(t)) with the stiffness contained in the variable coefficient linear part. We consider two assumptions on the relative variation of the matrix J(t) and show that for each of them there is a family of implicit Runge-Kutta methods that is suitable for the numerical integration of the corresponding stiff semilinear systems, i.e. the methods of the family are stable, convergent and the stage equations possess a unique solution. The conditions on the coefficients of a method to belong to these families turn out to be essentially weaker than the usual algebraic stability condition which appears in connection with the B-stability and convergence for stiff nonlinear systems. Thus there are important RK methods which are not algebraically stable but, according to our theory, they are suitable for the numerical integration of semilinear problems. This paper also extends previous results of Burrage, Hundsdorfer and Verwer on the optimal convergence of implicit Runge-Kutta methods for stiff semilinear systems with a constant coefficients linear part.
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    Geometriae dedicata 62 (1996), S. 281-298 
    ISSN: 1572-9168
    Keywords: 53C23 ; Hyperbolicity ; stability ; quasi-geodesics
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    Topics: Mathematics
    Notes: Abstract It is known that for a geodesic metric space hyperbolicity in the sense of Gromov implies geodesic stability. In this paper it is shown that the converse is also true. So Gromov hyperbolicity and geodesic stability are equialent for geodesic metric spaces.
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    Acta applicandae mathematicae 37 (1994), S. 129-136 
    ISSN: 1572-9036
    Keywords: 35B35 ; 35Q30 ; 76N10 ; stability ; Navier-Stokes equations ; compressible fluids
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    Topics: Mathematics
    Notes: Abstract We prove that the uniform stability at permanently acting disturbances of a given solution of the Navier-Stokes equations for viscous compressible isothermic fluid is a consequence of the uniform exponential stability of the zero solution of so-called linearized equations.
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    Acta applicandae mathematicae 9 (1987), S. 219-237 
    ISSN: 1572-9036
    Keywords: 34A34 ; 34D99 ; 90A16 ; Nonlinear differential equations ; stability ; growth ; economic dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.
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    Advances in computational mathematics 10 (1999), S. 115-133 
    ISSN: 1572-9044
    Keywords: Runge–Kutta–Nyström methods ; predictor–corrector methods ; stability ; parallelism ; 65M12 ; 65M20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes the construction of block predictor–corrector methods based on Runge–Kutta–Nyström correctors. Our approach is to apply the predictor–corrector method not only with stepsize h, but, in addition (and simultaneously) with stepsizes a i h, i = 1 ...,r. In this way, at each step, a whole block of approximations to the exact solution at off‐step points is computed. In the next step, these approximations are used to obtain a high‐order predictor formula using Lagrange or Hermite interpolation. Since the block approximations at the off‐step points can be computed in parallel, the sequential costs of these block predictor–corrector methods are comparable with those of a conventional predictor–corrector method. Furthermore, by using Runge–Kutta–Nyström corrector methods, the computation of the approximation at each off‐step point is also highly parallel. Numerical comparisons on a shared memory computer show the efficiency of the methods for problems with expensive function evaluations.
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    BIT 33 (1993), S. 74-84 
    ISSN: 1572-9125
    Keywords: 65J10 ; 65M12 ; Analytic semigroup ; Banach space ; rational approximation ; A-acceptable ; A(θ)-acceptable ; stability ; Crank-Nicolson method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is shown thatA-acceptable and, more generally,A(θ)-arational approximations of bounded analytic semigroups in Banach space are stable. The result applies, in particular, to the Crank-Nicolson method.
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    BIT 33 (1993), S. 285-303 
    ISSN: 1572-9125
    Keywords: 65L05 ; stiffness ; stability ; pseudospectra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is argued that even for a linear system of ODEs with constant coefficients, stiffness cannot properly be characterized in terms of the eigenvalues of the Jacobian, because stiffness is a transient phenomenon whereas the significance of eigenvalues is asymptotic. Recent theory from the numerical solution of PDEs is adapted to show that a more appropriate characterization can be based upon pseudospectra instead of spectra. Numerical experiments with an adaptive ODE solver illustrate these findings.
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    BIT 39 (1999), S. 620-645 
    ISSN: 1572-9125
    Keywords: Numerical integrator ; oscillatory solutions ; Schrödinger equation ; quantum-classical coupling ; error bounds ; stability
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    Topics: Mathematics
    Notes: Abstract We study time integration methods for equations of mixed quantum-classical molecular dynamics in which Newtonian equations of motion and Schrödinger equations are nonlinearly coupled. Such systems exhibit different time scales in the classical and the quantum evolution, and the solutions are typically highly oscillatory. The numerical methods use the exponential of the quantum Hamiltonian whose product with a state vector is approximated using Lanczos' method. This allows time steps that are much larger than the inverse of the highest frequencies. We describe various integration schemes and analyze their error behaviour, without assuming smoothness of the solution. As preparation and as a problem of independent interest, we study also integration methods for Schrödinger equations with time-dependent Hamiltonian.
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    BIT 40 (2000), S. 226-240 
    ISSN: 1572-9125
    Keywords: Stochastic differential equations ; regularisation ; stability
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    Topics: Mathematics
    Notes: Abstract This paper is devoted to the numerical analysis of ill-posed problems of evolution equations in Banach spaces using certain classes of stochastic one-step methods. The linear stability properties of these methods are studied. Regularisation is given by the choice of the regularisation parameter as α = $$\sqrt {\tau _n }$$ , where τ n is the stepsize and provides the convergence on smooth initial data. The case of the approximation of well-posed problems is also considered.
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    BIT 34 (1994), S. 62-79 
    ISSN: 1572-9125
    Keywords: AMS(MOS) 65D30 ; 65B05 ; adaptive ; cubature ; singularity ; extrapolation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new approach to the integration of vertex singularities is described. This approach is based on a non-uniform subdivision of the region of integration and the technique fits well to the subdivision strategy used in many adaptive algorithms. A nice feature with this approach is that it can be used in any dimension and on any region of integration which can be subdivided into subregions of the same form. The strategy can be applied both to vertex singularities and internal point singularities. In the latter case this can be done without an initial subdivision of the region in order to put the singular point in a vertex. It turns out that the technique has excellent numerical stability properties.
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    Zeitschrift für angewandte Mathematik und Physik 47 (1996), S. 809-816 
    ISSN: 1420-9039
    Keywords: 34D20 ; 34D35 ; 35Q72 ; 73H10 ; 73K03 ; Elastic string ; stability ; energy-momentum ; axial motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We establish the stability of axial motions (steady motions along the lengthwise direction) of nonlinearly elastic loops of string. A key observation here is that a linear combination of the total energy and the total circulation of the string, both of which are conserved quantities, yields an appropriate Liapunov function. From our previous work [5], we know that there are uncountably many shapes corresponding to a given axial speed. Accordingly, we establish “orbitai” stability (modulo this collection of relative equilibria). For a well-defined class of “soft” materials, there is an upper bound on the axial speed sufficient for stability; “stiff” materials are shown to be orbitally stable at any axial speed.
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    Monatshefte für Mathematik 126 (1998), S. 117-124 
    ISSN: 1436-5081
    Keywords: 52A20 ; 52A22 ; star bodies ; spherical integral transformations ; convex bodies ; stability
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    Topics: Mathematics
    Notes: Abstract LetK be ad-dimensional star body (with respect to the origino). It is known that the (d−1)-dimensional volume of the intersections ofK with the hyperplanes througho does not uniquely determineK. Uniqueness can only be achieved under additional assumptions, such as central symmetry. Here it is pointed out that if one uses, instead of intersections by hyperplanes, intersections by half-planes that containo on the boundary, then, without any additional assumptions, the volume of these intersections determinesK uniquely. This assertion, and more general results of this kind, together with stability estimates, are obtained from uniqueness results and estimates concerning a particular spherical integral transformation.
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    Archive for rational mechanics and analysis 72 (1980), S. 203-218 
    ISSN: 1432-0673
    Keywords: simple fluid ; viscoelastic ; fading memory ; stability ; Liapunov function ; dynamical system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The nonlinear equations of motion for an incompressible simple fluid, occupying a fixed bounded container, are formulated on the basis of the “finitelinear” viscoelasticity theory for materials with fading memory; this formal boundary-initial value problem is then viewed as a nonlinear abstract evolution equation on a certain Hilbert space. It is shown that a linearized version of this evolution equation is associated with a linear dynamical system on this Hilbert space, and several results for stability and asymptotic behavior for this linearized problem are proved through the use of Liapunov stability methods. On the assumption that the original nonlinear evolution equation also is associated with some dynamical system on the same space, it is shown that the rest condition of the fluid is stable and all motions are bounded. The Liapunov function employed for this purpose can be interpreted as a mechanical energy function for the fluid.
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    OR spectrum 15 (1994), S. 197-203 
    ISSN: 1436-6304
    Keywords: Inventory ; dynamic programming ; stability ; Lagerhaltung ; Dynamische Optimierung ; Stabilität
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Die Menge der Kostenparameter, für die eine optimale Lösung des dynamischen Losgrößenmodells optimal bleibt wird hier Stabilitätsregion genannt. Die Größe einer solchen Menge kann als Maß der Robustheit einer Lösung angesehen werden. Es ist zu erwarten, daß die Stabilitätsregionen mit wachsendem Zeithorizont schrumpfen und daß sie in diesem Sinne monoton sind. In der vorliegenden Arbeit werden verschiedene hinreichende Bedingungen für diese Monotonie untersucht. Die Bedingungen setzen unter anderem die Existenz von Planungs- und Vorhersage-Horizonten voraus und verallgemeinern so Ergebnisse einer früheren Arbeit, in der Aussagen für gewöhnliche Planungs-Horizonte vorgestellt wurden.
    Notes: Abstract The set of cost inputs for which an optimal solution of the dynamic lot size model remains valid is called stability region. The size of this region may be viewed as a measure of robustness of a solution. It is an expectation that the stability regions shrink with growing time horizons and that they are monotonous in this sense. In the present paper several sufficient conditions implying monotonicity will be studied. The conditions cover the existence of planning and forecast horizons and generalize the results of a previous paper in wich monotonicity results were presented for the case of ordinary planning horizons.
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    K-Theory 1 (1987), S. 185-196 
    ISSN: 1573-0514
    Keywords: Quadratic space ; patching diagram ; projective module ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove that every quadratic space of sufficiently large index contains a hyperbolic orthogonal summand.
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    K-Theory 10 (1996), S. 491-516 
    ISSN: 1573-0514
    Keywords: 57M60 ; 57N13 ; 57R91 ; 19G38 ; topological 4-manifold ; pseudofree action ; equivariant intersection form ; stability ; topological rigidity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the algebraic aspects of the classification of pseudofree, locally linear group actions on a simply connected 4-manifold, particularly with the splitting and stability properties of the associated Hermitian intersection module and its isometry group. Our main result is the proof of stability of the equivariant intersection form for a large class of pseudofree actions. We also prove a topological rigidity theorem stating that two locally linear, pseudofree actions on a closed, oriented, simply connected 4-manifold, with the equivariant intersection forms indefinite and of rank at least 3 at each irreducible character, are topologically conjugate by an orientation preserving homeomorphism if and only if their oriented local representations at the corresponding fixed points are linearly equivalent.
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    K-Theory 2 (1988), S. 1-355 
    ISSN: 1573-0514
    Keywords: Pseudoisotopy ; stability ; Morse theory
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    Topics: Mathematics
    Notes: Abstract The stability theorem states that the suspension map C(M) → C(M X I) defined on the pseudoisotopy space C(M)=Diff(M X I rel M X O U ∂M X I) of a compact smooth n-manifold M is ∼ n/3-connected. This implies that C(M) has the R~ n/3-homotopy type of the stable pseudoisotopy space P(M) which is related to Waldhausen's algebraic K-theory of spaces by Waldhausen's formula A(X) Ω∞S∞(X+) X B2P(X). This paper gives a detailed proof of the smooth stability theorem following ideas by Hatcher for the proof of a PL stability theorem.
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    K-Theory 4 (1991), S. 363-397 
    ISSN: 1573-0514
    Keywords: Nonabelian K 1 ; noncommutative homotopy ; general linear group ; superspecial linear groups ; descending central series ; stability ; relative normal subgroups ; nilpotent sandwich classifications ; quasi-finite algebras
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    Topics: Mathematics
    Notes: Abstract A functorial filtration GL n =S−1L n $$ \supseteq$$ S0L n $$ \supseteq$$ ⋯ $$ \supseteq$$ S i L n $$ \supseteq$$ ⋯ $$ \supseteq$$ E n of the general linear group GL n, n ⩾ 3, is defined and it is shown for any algebra A, which is a direct limit of module finite algebras, that S−1 L n (A)/S0L n (A) is abelian, that S0L n (A) $$ \supseteq$$ S1L n (A) $$ \supseteq$$ ⋯ is a descending central series, and that S i L n (A) = E n(A) whenever i ⩾ the Bass-Serre dimension of A. In particular, the K-functors k 1 S i L n =S i L n /E n are nilpotent for all i ⩾ 0 over algebras of finite Bass-Serre dimension. Furthermore, without dimension assumptions, the canonical homomorphism S i L n (A)/S i+1 L n (A)→S i L n+ 1(A)/S i+1 L n + 1 (A) is injective whenever n ⩾ i + 3, so that one has stability results without stability conditions, and if A is commutative then S0L n (A) agrees with the special linear group SL n (A), so that the functor S0L n generalizes the functor SL n to noncommutative rings. Applying the above to subgroups H of GL n (A), which are normalized by E n(A), one obtains that each is contained in a sandwich GL′ n (A, ρ) $$ \supseteq$$ H $$ \supseteq$$ E n(A, ρ) for a unique two-sided ideal ρ of A and there is a descending S0L n (A)-central series GL′ n (A, ρ) $$ \supseteq$$ S0L n (A, ρ) $$ \supseteq$$ S1L n (A, ρ) $$ \supseteq$$ ⋯ $$ \supseteq$$ S i L n (A, ρ) $$ \supseteq$$ ⋯ $$ \supseteq$$ E n(A, ρ) such that S i L n (A, ρ)=E n(A, ρ) whenever i ⩾ Bass-Serre dimension of A.
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    K-Theory 7 (1993), S. 333-367 
    ISSN: 1573-0514
    Keywords: Locally flat embedding ; pointed Hermitian module ; splitting ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove an existence result for topologically locally flat embeddings of 2-spheres in simply connected 4-manifolds. This topological result is deduced from a splitting theorem for pointed Hermitian modules over a cyclic group ring. A stability result for such modules is also proved. This applies to the isotopy classification of locally flat embeddings.
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    Letters in mathematical physics 53 (2000), S. 313-320 
    ISSN: 1573-0530
    Keywords: partial differential equations ; nonlinearities ; symmetries ; stability ; minimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We suggest a simple but general method of establishing symmetry properties of stable solutions of nonlinear elliptic equations. The method relies on characterization of symmetry breaking with a help of zero modes and on a generalization of the Perron–Frobenius theory.
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    Nutrient cycling in agroecosystems 16 (1988), S. 257-272 
    ISSN: 1573-0867
    Keywords: NH3-volatilization ; nitrogen-transformations ; denitrification ; nitrogen leaching ; nitrogen-application time ; rice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Ammonia volatilization losses and other N transformations were studied in drill sown rice bays fertilized with urea at various times between permanent flooding (PF) and panicle initiation (PI). Ammonia loss was measured directly with flow chambers and indirectly through application of Freney et al.'s (1985) model. Both techniques indicated that ammonia volatilization was negligible from fields fertilized immediately before PF. Applying 100 kg urea-N ha−1 to floodwater one day after flooding significantly increased floodwater ammoniacal-N and urea-N content, however the concentrations fell rapidly over the following five days. Fertilizer-N dissolved in the floodwater was in the urea rather than the ammoniacal-N form, indicating slow hydrolysis until it moved into the soil. Floodwater on plots receiving urea one day after PF frequently had more than double the NO3-N concentration of plots fertilized before flooding. Applying up to 140 kg urea-N ha−1 at PI increased floodwater ammoniacal-N concentrations from almost zero to over 27 g m−3, but three days after fertilization there was less than 3 g m−3 present. Fertilization also increased NH4-N concentration in the top 40 mm of soil. Higher ammoniacal-N concentration at PI suggests higher urease activity. Floodwater pH at PI was low, with a mean daily maximum of 7.8 and this reduced ammonia loss to less than 1% of the applied N. The results indicate that volatilization from fields fertilized prior to PF is minimal because of the low floodwater pH and ammoniacal-N concentration, while low floodwater pH restricts volatilization from fields topdressed at PI.
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    Nutrient cycling in agroecosystems 17 (1988), S. 47-59 
    ISSN: 1573-0867
    Keywords: Azolla pinnata (Bangkok) ; blue-green algae (BGA) ; N accumulation ; nitrogen fertilizer ; rice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Application of higher levels (60 and 90 kg N ha−1) of nitrogen fertilizer (Urea) inhibited the growth ofAzolla pinnata (Bangkok) and blue-green algae (BGA) though the reduction was more in BGA thanAzolla. Inoculation of 500 kg ha−1 of freshAzolla 10 days after transplanting (DAT) in the rice fields receiving 30, 60 and 90 kg N ha−1 as urea produced an average of 16.5, 15.0 and 13.0 t ha−1 fresh biomass ofAzolla at 30 DAT, which contained 31, 31 and 27 kg N ha−1, respectively. The dry mixture of BGA (60%Aulosira, 35%Gloeotrichia and 5% other BGA on fresh weight basis) inoculated in rice field 3 DAT at a rate of 10 kg ha−1 showed a mat formation at 80 DAT with an average fresh biomass of 8.0, 5.8 and 4.2 t ha−1 containing 22, 17 and 12 kg N ha−1, respectively with those N fertilizer doses. Application ofAzolla showed positive responses to rice crop by increasing the panicle number and weight, grain and straw yields and nitrogen uptake in rice significantly at all the levels of chemical nitrogen. But, the BGA inoculation had a significant effect on the grain and straw yields only during the dry season in the treatment where 30 kg N was applied. During the wet season and in the other treatments performed during the dry season no significant increase in yields, yield components and N uptake were observed with BGA. The intercropping ofAzolla and rice in combination with 30, 60 and 90 kg N ha−1 as urea showed the yields, yield attributes and nitrogen uptake in rice at par with those obtained by applying 60, 90 and 120 kg N ha−1 as urea, respectively but, the BGA did not. The analysis of soil from rice field after harvest showed thatAzolla and BGA intercropping with rice in combination with chemical fertilizer significantly increased the organic carbon, available phosphorus and total nitrogen of soil.
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    ISSN: 1573-0867
    Keywords: farmyard manure ; maize ; nitrogen ; phosphorus ; rice ; wheat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Field experiments with rice-wheat rotation were conducted during five consecutive years on a coarse-textured low organic matter soil. By amending the soil with 12t FYM ha−1, the yield of wetland rice in the absence of fertilizers was increased by 32 per cent. Application of 80 kg N ha−1 as urea could increase the grain yield of rice equivalent to 120 kg N ha−1 on the unamended soil. Although the soil under test was low in Olsen's P, rice did not respond to the application of phosphorus on both amended and unamended soils. For producing equivalent grain yield, fertilizer requirement of maize grown on soils amended with 6 and 12 t FYM ha−1 could be reduced, respectively to 50 and 25 per cent of the dose recommended for unamended soil (120 kg N + 26.2 kg P + 25 kg K ha−1). Grain yield of wheat grown after rice on soils amended with FYM was significantly higher than that obtained on unamended soil. In contrast, grain yield of wheat which followed maize did not differ significantly on amended or unamended soils.
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    Nutrient cycling in agroecosystems 20 (1989), S. 27-32 
    ISSN: 1573-0867
    Keywords: Cropping system ; phosphorus ; rice ; wheat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract A long term field experiment was conducted on a sandy loam soil from 1983 to 1987 to determine how to best apply phosphorus fertilizer in a rice-wheat cropping system. The treatments included 9 combinations of phosphorus application either to both rice and wheat or to rice or wheat alone. Direct application of phosphorus at 13 kg/ha to both the crops resulted in significantly higher total productivity of the rice-wheat cropping system as compared with 26 kg P/ha applied either to rice or wheat alone. Phosphorus at 13 kg/ha for rice and 26 kg/ha for wheat was as efficient as 13 kg P/ha for rice and 13 kg P/ha for wheat. The higher rate of P (26 kg/ha) applied to both rice and wheat resulted a decline in the total productivity. The residual effects of phosphorus applied to either rice or wheat were significant to the succeeding crop but was inferior to its direct application. Phosphorus increased the leaf area index, chlorophyll content of leaves, and interception of more photosynthetically active radiation (PAR) which resulted in increased grain yield of rice and wheat. Phosphorus status of the surface soil declined markedly, in the absence of P application from 15.4 to 6.4 kg P/ha. Phosphorus applied at 26 kg P/ha to both the crops resulted a build up of the available P status of soil. Phosphorus application at 13 kg/ha to both rice and wheat maintained the phosphorus status of the soil at original level.
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    Nutrient cycling in agroecosystems 21 (1989), S. 113-123 
    ISSN: 1573-0867
    Keywords: Nitrogen use ; farmer risk aversion ; rice ; Asia
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Year to year variability in nitrogen response is widely believed to be responsible for low levels of fertilizer application by risk averse farmers. Certain authors have claimed that production risk is not responsible for sub-optimal applications of fertilizer. Since these studies estimated fertilizer response in irrigated areas or in simulated rainfed areas in experiment stations they may have underestimated the degree of risk faced by the majority of farmers. This study seeks to address this issue of risk under farmers' conditions by using data from rainfed farmers fields in a risky rice growing area of the Philippines. Long term distributions of factors responsible for temporal variability in N-response, such as moisture stress and typhoons, are derived by using a rainfall simulator and a water balance model. These distributions are combined with a hetereoscedastic nitrogen response function to simulate long term yield distributions at different N-rates. The application of risk averse and risk neutral decision making models shows that risk aversion reduces fertilizer application by only 7–9%. These results occur because as N-rates increase, the benefits from increased average profits outweigh the disadvantages of increased variability in profits. These findings provide additional evidence to support the emerging consensus that the impact of risk aversion on fertilizer use is much smaller than previously believed.
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    Nutrient cycling in agroecosystems 41 (1995), S. 67-75 
    ISSN: 1573-0867
    Keywords: additives ; agronomic efficiency ; P availability ; phosphate rocks ; rice ; (Oryza sativa L.) ; thermally altered rock P
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract The P availability in soil and agronomic efficiency of the products of non-premium grade, unreactive Purulia phosphate rock (PPR) heated alone or with Na2CO3 or KCl at different temperatures were investigated in two P deficient soils. The heated products of PPR alone did not improve the P availability in soil or P utilisation by rice over the original PPR. The products of PPR-KCl mixtures heated at 300-900°C were not effective at all. Out of several products of PPR with Na2CO3, the product prepared from PPR and Na2CO3 mixture in the weight ratio 2:1 heated at 900°C was comparable to superphosphate (SP) with respect to P availability in soil, straw and grain yield and P uptake by rice. The effectiveness of the products of PPR-Na2CO3 mixtures heated at 700°C though inferior to SP were superior to that of the original PPR in the highly acidic P deficient soil from Choudwar. However, products of another phosphate rock (PR) from Jordan and NA2CO3 mixtures heated at 900°C were less effective in comparison to SP. The amount of inherent silica present in Jordan PR was inadequate to promote the apatite-NA2CO3-SiO2 reaction towards completion thus leading to an inferior product. On the other hand, similar products of non-premium grade Kasipatnam and Mussoorie PRs which are not suitable for direct application were comparable to SP in their effectiveness when these PRs were fused with Na2CO3 in the weight ratio 2:1 at 900°C. X-ray diffraction studies indicated presence of water and citrate soluble phosphate phases viz., Na3PO4, NaCaPO4 and possibly Ca7 (PO4)2 (S104)2 in these products of PR-Na2CO3 mixture heated at 900°C. The water and citrate soluble phases of these products could release adequate P for absorption by crop.
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    Nutrient cycling in agroecosystems 42 (1995), S. 261-276 
    ISSN: 1573-0867
    Keywords: Azolla ; BNF ; cyanobacteria ; green manure ; heterotrophic bacteria ; legume ; rice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract The review summarizes the current status of the utilization of N2-fixing organisms as biofertilizer in rice cultivation. Heterotrophic bacteria, free-living cyanobacteria,Azolla, and legume green manures are considered with regard to their potential for increasing yield, their current use and the prospects for their use with regard to the identified limiting factors. Biological N2 fixation has been the most effective system for sustaining production in low-input traditional rice cultivation. On the other hand, the utilisation of N2-fixing organisms in intensified rice production encounters serious limitations. The utilization of free-living bacteria and cyanobacteria is refrained by their modest potential and the non establishment of inoculated strains.Azolla and legumes used as green manures have a high potential as N source, but their utilization is severely limited by socio-economic factors.
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    Nutrient cycling in agroecosystems 43 (1995), S. 143-148 
    ISSN: 1573-0867
    Keywords: method of nitrogen application ; modified urea ; N-15 recovery ; rice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Rice is a very responsive crop to nitrogen, but the efficiency of the N-fertilizer is low. Greenhouse experiment has been conducted to evaluate several methods to improve fertilizer efficiency and reduce N-losses in rice fields. N-15 labelled urea was applied to 10 kg soils in pots, urea was applied alone, addition of two urease inhibitors N-(n-butyle) thiosphosphoric triamide (NBPT) and hydroquinone (HQ), with addition of nitrification inhibitor Dicyandimide (DCD), or with the combination of both inhibitors. The fertilizer was applied either broadcast on soil surface or at depth of 8 cm below the surface. At maturity, plants were separated into grain and straw, dried and weighted. Soil and plant samples were analyzed for total N and N-15 excess. Both fertilizer placement and inhibitor application significantly increased straw and grain yield, as well as N- uptake. Nitrogen derived from fertilizer (% Ndff) was more than doubled, when urea was applied deep and in combination with inhibitors. Total plant recovery of N-15 labelled urea ranged from 17% to 75% according to treatment. Regardless of inhibitors application, plant recovery was increased from 39% to 65% when urea was applied at depth of 8 cm. Approximately, 2/3 of the applied urea (64%) was lost, when urea was applied alone. Those losses were reduced down to 12% with deep placement and inhibitor application. The two management practices show significant effect on minimizing N-losses and increasing plant recovery.
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    Nutrient cycling in agroecosystems 32 (1992), S. 55-59 
    ISSN: 1573-0867
    Keywords: 15N ; nitrogen ; rice ; soil N ; N fertilizer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract In the southern U.S. rice belt it is recommended that rice (Oryza sativa L.) grown in the dry-seeded, delayed flood cultural system have the preflood N fertilizer applied and the field flooded at the fourth to fifth leaf stage of plant development. The objective of this field study was to determine if delaying the flood and preflood N application past the fifth leaf stage was detrimental to rice total N and fertilizer15N uptake, total dry matter, and grain yield. This study was conducted on a Crowley silt loam (Typic Albaqualfs) and a Perry clay (Vertic Haplaquepts). The preflood N fertilizer and flood were delayed 0, 7, 14, or 21 d past the fourth to fifth leaf stage, after which time a permanent flood was established and maintained until maturity. All treatments received 20.5 g N m−2 as15N-labeled urea in three topdress applications. All plant and soil samples were taken at maturity. Harvest index increased as the preflood N and flood were delayed past the 4 to 5 leaf stage. Total N in the grain + straw either decreased or showed a decreasing trend as the N and flood were delayed. Similarly, uptake of native soil N decreased as flood was delayed. Conversely, percent recovery of fertilizer N in the rice plant and the plant-soil system increased as the preflood N and flood were delayed. Rice grain yield was not significantly affected by delaying the preflood N and flood up to 21 d.
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  • 90
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    Nutrient cycling in agroecosystems 32 (1992), S. 83-90 
    ISSN: 1573-0867
    Keywords: Fertilizer ; slow-release ; rubber matrix ; urea ; rice ; ammonia volatilization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract The efficacy of a prototype slow-release fertilizer, urea-rubber matrix (URM) was assessed under flooded rice conditions. URM cuboids of size 0.5 × 1.0 × 0.4 cm were applied in comparison with prilled urea at levels of 50, 130 and 200 kg N ha−1. URM was placed at the soil/solution interface in intimate association with rice seedlings whereas prilled urea was broadcast into the floodwater to simulate the normal application method of South East Asian farmers. URM cuboid sizes of 0.25 × 0.5 × 0.4 cm, 0.5 × 0.5 × 0.4 cm and 1.0 × 1.0 × 0.4 cm were similarly evaluated at a single rate of 130 kg N ha−1; a broadcast URM treatment was also included. Different methods of prilled urea application including deep placement and split application were also studied at a single rate of 130 kg N ha−1. It was found that the build-up of floodwater N (urea + NH 4 + ) from URM during the 13 days following application was almost negligible irrespective of level or method of application. This was thought to result in low losses of N through ammonia volatilization as shown by higher rice grain yields in comparison with prilled urea at all levels of application. Deep-placed urea gave a comparable grain yield to that of broadcast URM. There was no significant difference in grain yield between URM applied by placement and by broadcast, suggesting that URM can be effectively applied either in intimate association with rice seedlings or by broadcasting to the rice field before, or after, planting. An attempt to predict the release of urea from URM was made using a diffusion-based simulation model. It was found that the model underestimated the actual release of urea from URM within the rhizosphere, probably due to the extensive penetration by rice roots of the URM cuboids.
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  • 91
    ISSN: 1573-0867
    Keywords: long-term experiments ; potassium ; rice ; soil testing ; ion-exchange resin ; potassium-supplying capacity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Based on the analysis of soil K status in 11 long-term fertility experiments in Asia, two approaches for assessing the K-supplying power of lowland paddy soils were evaluated to predict total K uptake by irrigated rice. A regression model combining commonly used static soil test parameters that appeared to integrate measures of K release from nonexchangeable forms as well as chemical factors affecting K activity in soil solution explained 72% of the crop K uptake in NP and NPK treatments. However, this approach would require determination of six soil properties and it does not provide a direct measure of K release dynamics. The second approach used mixed-bed ion exchange resin capsules to measure K release during 2-wk anaerobic incubation. The resin method provided an integrative measure of soil K status and the factors controlling K transformation and diffusion rates, which are embodied in two kinetic parameters describing the dynamics of rapid- and slow-phase K release. The resin method was sensitive to past fertilizer history and the resulting buildup or depletion of soil K reserves and it was a better predictor of total K uptake in the NP and NPK plots (r2=0.82) than static soil tests. The results also indicated that high (Ca+Mg)/K ratios may contribute to K deficiency in rice soils.
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  • 92
    ISSN: 1573-0867
    Keywords: long-term experiments ; phosphorus ; rice ; nutrient balance ; phosphorus uptake ; fertilizer P response ; soil testing ; ion-exchange resin ; phosphorus supplying capacity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Data from long-term experiments at 11 sites in Asia with a wide range of nutrient input treatments and yield levels were used to quantify crop P requirements of rice (Oryza sativa L.) and the P balance in intensive, irrigated rice systems. Uptake of 1.8–4.2 kg P was required to produce one ton of grain yield. Physiological P use efficiency varied between 220 to 900 kg grain kg P-1. Without added P, there was a net loss of 7 to 8 kg P ha-1 per crop; with added P there was a net gain of 4 to 5 kg P ha-1 per crop. Phosphorus adsorption kinetics on mixed-bed ion-exchange resin capsules provided an integrative measure of soil P status, P diffusion, and acid-induced P solubilization. The resin capsule was a sensitive tool to characterize buildup or depletion of soil P as a result of different P balances. Both Olsen-P and the resin capsule were suitable methods to predict P uptake of tropical lowland rice. It is hypothesized that both methods measure a similar soil P pool which is soluble under alkaline, aerobic conditions but transformed into acid-soluble P froms as a result of submergence and reduction. Present recommendations for P fertilizer use on rice of 20–25 kg P ha-1 are adequate to maintain yields of 5–6 t ha-1, but sustaining higher yields of 7–8 t ha-1 will require farm-specific management strategies based on knowledge of the long-term P balance and soil P-supplying capacity.
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  • 93
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    Nutrient cycling in agroecosystems 46 (1996), S. 189-193 
    ISSN: 1573-0867
    Keywords: available P ; green manure ; P source ; P uptake ; residual effect ; rice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract To evaluate residual recoveries of fertilizer phosphorus (P) two field experiments were conducted in Quezon Province, Philippines during 1991 dry season, under irrigated condition. Average grain yield increase was 0.50–0.9 t/ha due to residual effects of inorganic fertilizer P, regardless of source. Residual effects of fertilizer P with Sesbania rostrata or alone increased grain yield by 0.3–1.0 t/ha over control. Significantly higher yields were obtained with S. rostrata fertilized with Morocco phospate Rock (MPR) and S. rostrata + MPR applied on rice than the control. Results revealed that there is a promising effect of residual P from the applied P sources in increasing rice grain yield. Total P uptake increased due to residual P from fertilizer P applied. Results suggest that increased P uptake increased dry matter and grain yield.
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  • 94
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    Nutrient cycling in agroecosystems 46 (1996), S. 195-203 
    ISSN: 1573-0867
    Keywords: available phosphorus ; green manure ; phosphorus source ; phosphorus uptake ; relative effectiveness ; rice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract To evaluate alternative fertilizer phosphorus (P) sources in lowland rice, two field experiments were conducted under irrigated conditions in Quezon Province, Philippines during 1990–1991 crop year. In another field experiment fertilizer P recycling through a green manure crop applied in the succeeding rice, was studied. Addition of fertilizer P increased grain yield by 1.5–2.0 t/ha (46%) in 1990 wet season (WS) and by 1.6–2.1 t/ha (56%) in 1991 dry season (DS). However, fertilizer P source and application level did not effect grain yield significantly. Results indicated that the less water-soluble and less expensive partially acidulated phosphate rock (PAPR), phosphate rock (PR) and less reactive PR were as effective as the more soluble but more expensive triple superphosphate (TSP). The relative effectiveness (RE) of local guano was significantly lower than that of other sources of fertilizer P. Fertilizer P applied to a pre-rice Sesbania rostrata green manure increased rice grain yield by 1.5–1.9 t/ha during 1991 DS. Further, S. rostrata fertilized with Morocco phosphate rock (MPR) gave significantly higher rice grain yield than did rice fertilized with MPR applied alone. In the P source experiments Olsen method and Pi correlated better with growth attributes than Bray 2 P. Phoshours uptake did not differ significantly among P sources and levels. Results suggest that P uptake was improved with green manuring. Correlation analyses revealed a close correlation between P uptake and dry matter yield and P uptake and grain yield.
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  • 95
    ISSN: 1573-0867
    Keywords: long-term experiments ; nutrient balance ; potassium ; rice ; potassium use efficiency ; potassium uptake ; potassium response
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Research in many countries indicates a negative K balance in intensive, irrigated rice systems but comparative studies across different environments are few. Using a uniform sampling methodology, we measured K uptake, K use efficiency, and K balance in six different fertilizer treatments of long-term fertility experiments with rice at 11 sites in five Asian countries. Depending on the absolute yield level, K uptake requirements of rice ranged from 17 to 30 kg K per ton of grain. For yields greater than 8 t ha-1, total K uptake exceeded 200 kg ha-1. The K balance at most experimental sites was negative, with an average net removal of 34–63 kg K season-1. There was significant depletion of soil K reserves at many sites. Based on these data, we estimated that the amount of K cycled annually from the soil into rice plants is 7–10 million t in irrigated rice systems of Asia. About 1 million t of this total amount is removed with the harvested grain. Present recommendations for K addition in most intensive irrigated rice domains are insufficient to replace K removal. However, response to K can only be expected on soils with deficient supply capacity and where other nutrients, particularly N and P, are not limiting. Efficient K management for rice must therefore be based on the K input/output balance, the achievable yield target, and the effective K-supplying power of the soil.
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  • 96
    ISSN: 1573-0867
    Keywords: millet ; sorghum ; rice ; maize ; wheat ; nutrient harvest index ; post-anthesis nutrient uptake ; recovery fraction ; simulation modelling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract In land use plans, fertilizer recommendations are indispensable to avoid soil nutrient depletion or soil water pollution. Nutrient relations of five cereals have been evaluated on the basis of a literature review with the aim of arriving at such fertilizer recommendations at regional level. Nutrients considered were nitrogen, phosphorus and potassium for millet, sorghum, maize, rice and wheat. The relevant nutrient relations are fertilizer nutrient application to nutrient uptake, and nutrient uptake to crop yield. In addition, post-anthesis nutrient uptake is considered. Subsequently, obtained results are used in simulation modelling exercises to calculate the time required to attain an equilibrium nutrient balance and to investigate the effect of erosion control and straw recycling. Although fertilizer requirements could be assessed for each of the five cereals, monitoring of nutrient supply from natural sources remains necessary. Moreover, research on fertilizer use should focus on improvement of fertilizer recoveries and multiperiod models for both N and P uptakes by crops to allow quantitative land use planning where the time scale is included.
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  • 97
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    Nutrient cycling in agroecosystems 46 (1996), S. 29-39 
    ISSN: 1573-0867
    Keywords: Côte d'Ivoire ; rice ; fertilizers ; adoption ; gender ; socioeconomic factors ; field factors ; markets ; population pressure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract This paper analyzed the factors that affect the adoption of chemical fertilizers by rice farmers in Côte d'Ivoire using a Tobit model. The results show that the major factors that positively influence farmers' use of fertilizers in rice fields are cultivation of lowlands, use of mechanization, farm size, land pressure and availability of non-farm income. Factors found to negatively affect the use of fertilizer in rice fields are the distance of the field to the village, distance of the village to the major market, and if the cultivator is a female. The paper concludes with strategies for targeting soil fertility interventions on farmers' rice fields.
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  • 98
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    Nutrient cycling in agroecosystems 51 (1998), S. 269-279 
    ISSN: 1573-0867
    Keywords: denitrification ; gas entrapment ; nitrification inhibitors ; 15N ; rice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Denitrification rates (d) in a flooded alkaline clay were measured following addition of either $$^{15} NO_3^ - or^{15} NH_4^ + $$ to the floodwater, by collecting evolved N2 + N2O in an enclosure in the absence or presence of rice plants. Similar estimates of d were obtained in the $$^{15} NO_3^ - $$ treatment when the isotopic composition of the enclosed atmosphere was determined using arc redistribution or direct mass spectrometric analysis. Approximately 90% of the gaseous products of denitrification were physically trapped in the soil five days after $$^{15} NO_3^ - $$ addition. Mechanical shaking of the soil-water system was an effective method for releasing entrapped gas. Denitrification showed a marked diurnal variation in both $$^{15} NO_3^ - $$ and $$^{15} NH_4^ + $$ treatments planted to rice, with higher rates during the day than at night. Measured rates of denitrification were higher in planted than in unplanted pots for both $$^{15} NO_3^ - $$ and $$^{15} NH_4^ + $$ treatments for normal gas sampling. However, evidence was obtained that this was not a real effect, but was due to release of entrapped gas. Denitrification losses corrected for gas entrapment were estimated at 〈5% of applied $$^{15} NH_4^ + $$ . The 15N mass balance indicated that a much larger amount of applied ammonium (15–25%) was lost by NH3 volatilisation. The rate of denitrification corrected for gas entrapment was similar to the rate of nitrification estimated by inhibition of ammonium oxidation. Although the inhibitors 2-ethynylpyridine and acetylene prevented denitrification by effectively inhibiting nitrification of $$^{15} NH_4^ + $$ , the total recovery of 15N in the soil-plant system did not increase. The total recovery of $$^{15} NH_4^ + $$ was 7–9% higher in the presence than in the absence of rice.
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  • 99
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    Nutrient cycling in agroecosystems 51 (1998), S. 259-267 
    ISSN: 1573-0867
    Keywords: nitrification ; nitrification inhibitors ; 15N-dilution ; rice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Nitrification rates (n) in the floodwater of an alkaline clay were measured in the absence or presence of rice plants by inhibition of ammonium oxidation and 15N-dilution techniques. Floodwater nitrate concentrations in control treatments showed a marked diurnal variation, and were higher than in the inhibitor treatments after the first day. Ammonium concentrations in floodwater declined exponentially in all treatments, being markedly affected by diffusion and NH3 volatilization but little affected by nitrification and plant uptake. Nitrification rates in floodwater estimated by 15N-dilution were generally higher than the rates estimated by the inhibitor method. Estimates of n were generally higher during daylight hours than at night, and did not differ significantly between planted and unplanted pots. Microbial immobilisation of labelled ammonium and gross N immobilisation were not affected by addition of the nitrification inhibitor 2-ethynylpyridine.
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  • 100
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    Nutrient cycling in agroecosystems 53 (1998), S. 71-81 
    ISSN: 1573-0867
    Keywords: fallow ; legumes ; nitrogen fixation ; rice ; weeds ; West Africa
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Traditional upland rice-based cropping systems in West Africa rely on periods of fallow to restore soil fertility and prevent the build-up of insect pests and weeds. Demographic growth and increased demand for land is forcing many farmers to intensify their rice production systems. Declining fallow length and increasing number of crops before leaving the land to extended fallow result in a significant yield reduction. Promising cropping system alternatives include the use of site specific, weed-suppressing, multi-purpose cover legumes as short duration fallows. Constraints to rice production related to intensification were determined in 209 farmers' fields in four agro-ecological zones during 1994 and 1995. Nitrogen accumulation and weed suppression were evaluated in 54 legume accessions, grown for six months during the dry season, under a range of hydrological and soil conditions in 1994/95. Their effect on the yield of upland rice was determined in 1995. To increase benefits from improved fallow technology, the timing of legume establishment in relation to rice and the effect on crop and weed growth of removing, burning, mulching, or incorporating fallow residues prior to the rice crop were determined. Intensified land use resulted in a significant plot-level yield reduction that was highest in the derived savanna and the bimodal forest zones where it was associated with a doubling of the weed biomass in rice and a significant reduction in soil N supply. Legume fallows appear to offer the potential to sustain rice yields under intensified cropping. Legume biomass was in most instances significantly greater than in the weedy fallow control and several legume species suppressed weed growth. Nitrogen accumulation by legumes varied between 1–200 kg N ha-1 with 30–90% Ndfa. Rice grain yield following legume fallows increased by an average of 0.2 mg ha-1 or 29% above the weedy fallow control. Relay establishment substantially increased legume biomass. However, seeding of the legume at 28 days or earlier significantly reduced grain yield due to interspecific competition. Incorporating or mulching of fallow residues provided no significant yield advantage as compared to burning. Absolute effects varied as a function of site, legume species, and management practice.
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