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  • CR: 5.17  (143)
  • phosphorus
  • Springer  (209)
  • American Chemical Society
  • American Meteorological Society (AMS)
  • 1980-1984  (156)
  • 1975-1979  (53)
Collection
Publisher
  • Springer  (209)
  • American Chemical Society
  • American Meteorological Society (AMS)
Years
Year
  • 1
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    Numerische Mathematik 43 (1984), S. 105-119 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A new formulation of the Dirichlet problem for the biharmonic operator is presented. This gives rise to a simple numerical method to solve the above problem. Convergence is proved in the unidimensional case. Numerical results in one and two dimensional test problems are presented.
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  • 2
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    Numerische Mathematik 43 (1984), S. 175-198 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 L 10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present a difference scheme for solving a semilinear singular perturbation problem with any number of turning points of arbitrary orders. It is shown that a solution of the scheme converges, uniformly in a perturbation parameter, to that of the continuous problem.
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  • 3
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65 N 30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary This paper uses Augmented Lagrangian techniques for the numerical solution of equilibrium problems of compressible hyperelastic bodies subjected to large deformations. The resulting method is illustrated by several numerical examples.
    Notes: Résumé Cet article applique les techniques de Lagrangien Augmenté à la résolution numérique des problèmes d'équilibre de corps hyperélastiques compressibles soumis à de grandes déformations. La méthode obtenue est illustrée par plusieurs exemples numériques.
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  • 4
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    Nutrient cycling in agroecosystems 5 (1984), S. 371-382 
    ISSN: 1573-0867
    Keywords: nitrogen ; phosphorus ; dry areas ; apparent recovery fraction ; fertilizer management
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Agronomic efficiency (AE) is defined as the increase in economic yield of a crop per unit fertilizer applied. Components of AE are physiological efficiency and apparent recovery fraction. The latter can be further separated into uptake efficiency and availability index. Ways to increase the nitrogen fertilizer use efficiency in rainfed agriculture through fertilizer management are discussed.
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  • 5
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    Numerische Mathematik 45 (1984), S. 105-116 
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65 N 30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study a superconvergence phenomenon which can be obtained when solving a 2nd order elliptic problem by the usual linear elements. The averaged gradient is a piecewise linear continuous vector field, the value of which at any nodal point is an average of gradients of linear elements on triangles incident with this nodal point. The convergence rate of the averaged gradient to an exact gradient in theL 2-norm can locally be higher even by one than that of the original piecewise constant discrete gradient.
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  • 6
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    Numerische Mathematik 45 (1984), S. 201-206 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Bulirsch and Stoer have shown how to construct asymptotic upper and lower bounds on the true (global) errors resulting from the solution by extrapolation of the initial value problem for a system of ordinary differential equations. It is shown here how to do this for any one-step method endowed with an asymptotically correct local error estimator. The one-step method can be changed at every step.
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  • 7
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    Numerische Mathematik 44 (1984), S. 191-200 
    ISSN: 0945-3245
    Keywords: AMS (MOS): Primary 65M05, 65M10, 65M15 ; Secondary: 35M05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider the numerical solution of the boundary value problem (1) $$(1) Lu = k(y)u_{xx} + u_{yy} - c(x,y)u = f, u|_{\Gamma _0 \cup \Gamma _1 } = 0,$$ where $$k(y) \gtreqless 0$$ for $$y \gtreqless 0$$ Г 0 andГ 1 are parts of the boundary of a bounded simply connected regionG inR 2.G is bounded fory〉0 by a piecewise smooth curveГ 0 which intersects the liney=0 at the pointsA(−1,0) andB(0, 0). Fory〈0,G is bounded by a piecewise smooth curveГ 1 throughA, which meets the characteristic of (1) issued fromB at pointC, and by the curveГ 2 which consists of the portionCB of the characteristic throughB. Using a weak formulation based on different spaces of test and trial functions, we construct a Galerkin procedure for the above boundary value problem. Existence, uniqueness and uniform stability of an approximate solution is proven and a priori error bounds are given.
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  • 8
    ISSN: 0945-3245
    Keywords: AMS: 65N10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper deals with such estimates of the rate of convergence of difference methods, which are compatible with the smoothness of the exact solutionu ∈ W 2 m (Ω),m〉0.5, of elliptic equations with mixed derivatives: The error in the norm of the discrete Sobolev spaceW 2 s (ω), ω denoting the set of grid points, is shown to be of the orderO(|h| m−s), 0≦s〈m.
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  • 9
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    Numerische Mathematik 44 (1984), S. 247-259 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L05 ; 65M05 ; 65M20 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The aim of this paper is to study contractivity properties of two locally one-dimensional splitting methods for non-linear, multi-space dimensional parabolic partial differential equations. The term contractivity means that perturbations shall not propagate in the course of the time integration process. By relating the locally one-dimensional methods with contractive integration formulas for ordinary differential systems it can be shown that the splitting methods define contractive numerical solutions for a large class of non-linear parabolic problems without restrictions on the size of the time step.
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  • 10
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    Numerische Mathematik 43 (1984), S. 419-437 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, we consider monotone explicit iterations of the finite element schemes for the nonlinear equations associated with the boundary value problem Δu=bu 2, based on piecewise linear polynomials and the lumping operator. These iterations construct the monotonically decreasing and increasing sequences, and convergence proofs are given. Finally, we present some numerical examples verifying the effectiveness of the theory.
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  • 11
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    Numerische Mathematik 43 (1984), S. 463-483 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The method of lines is used to semi-discretize the non-linear Poisson equation over a domain with a free boundary. The resulting multipoint free boundary problem is solved with a line Gauss-Seidel method which is shown to converge monotonically. The method of lines solution is then shown to converge to the continuous solution of the variational inequality form of the obstacle problem. Some numerical results for the diffusion-reaction equation indicate that the method is applicable to more general free boundary problems for nonlinear elliptic equations.
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  • 12
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    Numerische Mathematik 43 (1984), S. 309-327 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 N 30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Diffusion problems occuring in practice often involve irregularities in the initial or boundary data resulting in a local break-down of the solution's regularity. This may drastically reduce the accuracy of discretization schemes over the whole interval of integration, unless certain precautions are taken. The diagonal Padé schemes of order 2μ, combined with a standard finite element discretization, usually require an unnatural step size restriction in order to achieve even locally optimal accuracy. It is shown here that this restriction can be avoided by means of a sample damping procedure which preserves the order of the discretization and, in the case μ=1, does not increase the costs.
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  • 13
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    Numerische Mathematik 43 (1984), S. 343-360 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Retarded initial value problems are routinely replaced by an initial value problem of ordinary differential equations along with an appropriate interpolation scheme. Hence one can control the global error of the modified problem but not directly the actual global error of the original problem. In this paper we give an estimate for the actual global error in terms of controllable quantities. Further we show that the notion of local error as inherited from the theory of ordinary differential equations must be generalized for retarded problems. Along with the new definition we are led to developing a reliable basis for a step selection scheme.
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  • 14
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    Numerische Mathematik 43 (1984), S. 389-396 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L20 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Stability analysis of θ-methods for functional differential equations based on the test equation $$\begin{gathered} y'(t) = ay(t - \lambda ) + by(t),t 〉 0 \hfill \\ y(t) = \psi (t),t \in \left[ { - \lambda ,0} \right] \hfill \\ \end{gathered} $$ λ〉0, is presented. It is known thaty(t)→0 ast→∞ if and only if |b|〈−a and we investigate whether this property is inherited by the numerical solution approximatingy.
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  • 15
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    Numerische Mathematik 44 (1984), S. 75-102 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper examines the concepts of feedback and adaptivity for the Finite Element Method. The model problem concernsC 0 elements of arbitrary, fixed degree for a one-dimensional two-point boundary value problem. Three different feedback methods are introduced and a detailed analysis of their adaptivity is given.
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  • 16
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    Numerische Mathematik 44 (1984), S. 201-217 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Resumé On présente une méthode d'approximation numérique des équations de Navier-Stokes possédant une direction de périodicité. Dans cette direction une méthode pseudospectrale basée sur des développements en série de Fourier est utilisée, dans les deux autres on applique une méthode d'éléments finis standard. On montre que la convergence est optimale et que les deux paramètres de discrétisation peuvent être choisis de façon indépendante.
    Notes: Summary We present a method for the numerical approximation of Navier-Stokes equations with one direction of periodicity. In this direction a Fourier pseudospectral method is used, in the two others a standard F.E.M. is applied. We prove optimal rate of convergence where the two parameters of discretization intervene independently.
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  • 17
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    Numerische Mathematik 44 (1984), S. 219-222 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An analysis of the Babuška stability of bilinear/constant finite element pairs for viscous flow calculations is given. An unstable mode not of the checkerboard type is given for which the stability constant turns out to beO(h). Thus, the indicated spaces are not stable in general for numerical calculation.
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  • 18
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    Numerische Mathematik 44 (1984), S. 285-300 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, we investigate the numerical asymptotic behavior of the finite element solutions for linear parabolic equations under some appropriate conditions. We also give some results of numerical experiments in the two dimensional problems to indicate the effectiveness of our results.
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  • 19
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    Numerische Mathematik 45 (1984), S. 283-300 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper deals with the solution of partitioned systems of nonlinear stiff differential equations. Given a differential system, the user may specify some equations to be stiff and others to be nonstiff. For the numerical solution of such a system partitioned adaptive Runge-Kutta methods are studied. Nonstiff equations are integrated by an explicit Runge-Kutta method while an adaptive Runge-Kutta method is used for the stiff part of the system. The paper discusses numerical stability and contractivity as well as the implementation and usage of such compound methods. Test results for three partitioned stiff initial value problems for different tolerances are presented.
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    Numerische Mathematik 45 (1984), S. 51-74 
    ISSN: 0945-3245
    Keywords: MR65 M15 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The error of the approximate solution obtained by discretising a functional equation can be shown under certain conditions to possess an asymptotic expansion in terms of some parameter which is usually a representative step-length. We consider the case of two-parameter expansions, which is particularly relevant to parabolic equations. We derive results for the existence of the expansion and for the application of the classical difference correction and of defect correction. The theory is illustrated by the discussion of a simple parabolic problem
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  • 21
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    Hydrobiologia 111 (1984), S. 49-56 
    ISSN: 1573-5117
    Keywords: nutrient enrichment ; yield coefficient ; nitrogen ; phosphorus ; mass culturing ; phytoplankton ; sea water
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Natural phytoplankton of Cabo Frio area was grown in 42 m-deep artificially upwelled seawater enriched with increasing concentrations of nitrogen or phosphorus. Respective values allowing maximum biomass, maximum uptake of initial reserve and maximum yield coefficient are rather conflicting. Notwithstanding, respective values of 75 µg at 1−1 nitrogen and 5 µg at 1−1 phosphorus, and therefore N:P = 15, appeared to be the best compromise for initial nutrient levels.
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  • 22
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    Hydrobiologia 112 (1984), S. 131-136 
    ISSN: 1573-5117
    Keywords: reed ; harvest ; nitrogen ; phosphorus ; redox potential ; oxygen
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract An investigation of the effects of repeated winter harvest and removal of dry reed culms on water and sediment chemistry was made in a shallow lake dominated by closed, monospecific reed stands. The oxygen concentration and redox potential in the water, as well as temperature, showed regular diurnal fluctuations inside the reed stands. Ammonium and nitrate + nitrite did not exhibit diurnal fluctuations and differences between a harvested and an unharvested reed area were small. Molybdate reactive phosphorus (MRP) concentration was higher in the unharvested area. Because the winter harvest caused an almost doubling of shoot production compared to the unharvested area, net addition of reed litter (leaves, stubble and culms) to the sediment of the harvested area was similar to that of the unharvested area. It is concluded that removal of reed culms in winter has the largest effect on microclimate in spring, and that the rate of mineralization and reducing intensity in the substrate are not immediately affected. Significantly higher summer standing crop of reed after harvest may have caused lower phosphate concentration in the water column and sediment interstitial water.
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  • 23
    ISSN: 1573-5117
    Keywords: enrichment ; phosphorus ; nitrogen ; phytoplankton ; tropical reservoir
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The effects of enrichment with phosphate (0–500 µg. 1−1) and forms of nitrogen (nitrate, nitrite, ammonia an and urea) (0–3500 µgg. −1) on the phytoplankton growth of Lobo Reservoir (Brazil) were studied in July, 1979. Suspended matter, chlorophyll a, cell concentrations and the carotenoid:cchlorophyll ratio were estimated following 14 days of ‘in situ’ incubation. Phosphate alone caused no significant effects, but enrichment with nitrogen caused a substantial increase on the growth of phytoplankton. Comparison between the different forms of nitrogen showed insignificant effects after their additions with 350 µg. −1 and in combination with phosphate. However, when nitrogen was added in large quantities (3 500 µg. −1), significant differences between the nitrogeneous forms were found, with urea causing the strongest effect. In July, nitrogen is mhe main limiting nutrient to phytoplankton growth of Lobo Reservoir.
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    Numerische Mathematik 41 (1983), S. 373-398 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper introduces a new semi-implicit extrapolation method especially designed for the numerical solution of stiff systems of ordinary differential equations. The existence of a quadratic asymptotic expansion in terms of the stepsize is shown. Moreover, the new discretization is analyzed in the light of well-known stability models. The efficiency of the new integrator is clearly demonstrated by solving a series of challenging test problems including real life examples.
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    Numerische Mathematik 41 (1983), S. 345-371 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Maximum-norm stability and error estimates of best approximation and nonsmooth data types are derived for the approximate solution of a parabolic equation in one space variable, using the continuous in time Galerkin method based on piecewise polynomial approximating functions on a quasi-uniform mesh.
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  • 26
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study the difference equations obtained when a linear multistep method is applied to the scalar test equationdy/dt=λy and constant stepsizeh. LetS be the region of the absolute stability of the method, and letD be a closed subset ofS (on the Riemann sphere $$\mathbb{C}$$ ). It is shown that the solutions of these difference equations are bounded forn≧0, uniformly for λh∈D.S is itself closed in $$\mathbb{C}$$ iff ∂S is free of cusps. The question is studed by means of contractivity analysis and a matrix theorem, derived from the matrix theorem of Kreiss.
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    Numerische Mathematik 41 (1983), S. 399-422 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The paper presents a new theory for joint order and stepsize control in extrapolation methods. This theory defines a locally optimal order that can be determined along any trajectory to be computed. In addition, Shannon's information theory is applied to derive some ideal convergence model that is expected to describe the behavior of an extrapolation method over a large set of test problems. Extensive numerical comparisons document a drastic acceleration in stiff integration and a mild acceleration in non-stiff integration by the new device. Moreover, a significant increase in reliability, robustness, and portability of the extrapolation codes is achieved.
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    Numerische Mathematik 42 (1983), S. 299-310 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A new approach to the problem of numerically integrating stiff differential systems is described. In this approach a linear multistep method (the basic method) is split into a kind of predictor-corrector scheme, where the predictor is also implicit. If this splitting is done in an appropriate manner, the modified method has considerably better stability properties than the basic method. As a result, splitting methods are particularly useful for problems where conventional integration methods experience stability difficulties. In particular some highly stable split linear multistep methods based on backward differentiation formulae are derived and a highly stable variable step implementation is proposed.
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    Numerische Mathematik 42 (1983), S. 311-322 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 N 30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary This paper presents Galerkin approximations for solutions of two dimensional interface problems by solving corresponding boundary integral equations. These are obtained by simple layer potential operators only. Due to the strong ellipticity of the integral equations the Galerkin procedure converges with optimal order. Smoothness of the given data implies high convergence rates for the layers.
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    Numerische Mathematik 42 (1983), S. 349-357 
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary In this paper theD-stability properties of some classes of perturbed collocation methods are investigated. Among others we show the implicit Runge-Kutta methods described by Ehle-Chipman to beD-stable. We also give implicit Runge-Kutta methods that are bothD-stable andA-stable but notB-stable. Finally we indicate in what senseB-stability is stronger thanA-stability together withD-stability. The results of this paper are based on recent results of Nørsett and Wanner on perturbed collocation methods.
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    Numerische Mathematik 41 (1983), S. 55-62 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The finite element method with Laplace transform of time variable is proposed for the solution of hyperbolic equations. Error estimates in Hardy spaces of functions with values in Sobolev spaces are derived. Due to the isometric isomorphism of Hardy spaces with weighted Hilbert spaces these estimates are valid also for original formulations of hyperbolic equations.
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    Numerische Mathematik 41 (1983), S. 165-175 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65LO5 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The extrapolated midpoint rule is a popular way to solve the initial value problem for a system of ordinary differential equations. As originally formulated by Gragg, the results are smoothed to remove the weak instability of the midpoint rule. It is shown that this smoothing is not necessary. A cheaper smoothing scheme is proposed. A way to exploit smoothing to increase the robustness of extrapolation codes is formulated.
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    Numerische Mathematik 41 (1983), S. 255-279 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L15 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Some methods for evaluating the characteristic exponents in connection with Newton's iteration are applied for solving the eigenvalue problem related to the finite Hill's differential equation or, in particular, Mathieu's equation. By using these methods a high accuracy is achieved, furthermore a complete error analysis, which yields rather realistic error bounds, is possible.
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    Numerische Mathematik 42 (1983), S. 15-30 
    ISSN: 0945-3245
    Keywords: AMS: 65L10 ; 34C25 ; 34K10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An iterative method is presented which starting from a lower or from an upper periodic solution, provides a monotone sequence converging to a periodic solution of (1). With some restrictions on the growth off, the method extends to functional differential equations of type (1′). Two numerical examples with an “a posteriori” error analysis are given.
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    Numerische Mathematik 42 (1983), S. 51-64 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N99 ; 35L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Engquist and Majda [3] proposed a pseudodifferential operator as asymptotically valid absorbing boundary condition for hyperbolic equations. (In the case of the wave equation this boundary condition is valid at all frequencies.) Here, least-squares approximation of the symbol of the pseudodifferential operator is proposed to obtain differential operators as boundary conditions. It is shown that for the wave equation this approach leads to Kreiss well-posed initial boundary value problems and that the expectation of the reflected energy is lower than in the case of Taylor- and Padé-approximations [3, 4]. Numerical examples indicate that this method works even more effectively for hyperbolic systems. The least-squares approach may be used to generate the boundary conditions automatically.
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    Numerische Mathematik 42 (1983), S. 77-95 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N99 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Brakhage and Werner, Leis and Panich suggested to reduce the exterior Dirichlet boundary value problem for the Helmholtz equation to an integral equation of the second kind which is uniquely solvable for all frequencies by seeking the solution in the form of a combined double- and single-layer potential. We present an analysis of the appropriate choice of the parameter coupling the double- and single-layer potential in order to minimize the condition number of the integral operator.
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    Numerische Mathematik 42 (1983), S. 65-76 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 N 20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We consider here a general class of algorithms for the numerical solution of variational inequalities. A convergence proof is given and in particular a multi-grid method is described. Numerical results are presented for the finite-difference discretization of an obstacle problem for minimal surfaces
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    Numerische Mathematik 42 (1983), S. 119-123 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N10 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Many difference methods for the numerical solution of elliptic boundary value problems lead to systems of linear equations whose matrices areM-matrices and which therefore have nonnegative inverses. In this paper it is shown, that these difference methods are at most consistent of second order.
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  • 39
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    Numerische Mathematik 42 (1983), S. 173-194 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We consider the stationary Navier-Stokes equations, written in terms of the primitive variables, in the case where both the partial differential equations and boundary conditions are inhomogeneous. Under certain conditions on the data, the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed. A conforming finite element method is presented and optimal estimates for the error of the approximate solution are proved. In addition, the convergence properties of iterative methods for the solution of the discrete nonlinear algebraic systems resulting from the finite element algorithm are given. Numerical examples, using an efficient choice of finite element spaces, are also provided.
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    Numerische Mathematik 42 (1983), S. 271-290 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65J10, 65L20, 65M10 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Consider a linear autonomous system of ordinary differential equations with the property that the norm |U(t)| of each solutionU(t) satisfies |U(t)|≦|U(0)| (t≧0). We call a numerical process for solving such a system contractive if a discrete version of this property holds for the numerical approximations. A givenk-step method is said to be unconditionally contractive if for each stepsizeh〉0 the numerical process is contractive. In this paper a general theory is given which yields necessary and sufficient conditions for unconditional contractivity. It turns out that unconditionally contractive methods are subject to an order barrierp≦1. Further the concept of a contractivity threshold is studied, which makes it possible to compare the contractivity behaviour of methods with an orderp〉1 as well. Most theoretical results in this paper are formulated for differential equations in arbitrary Banach spaces. Applications are given to numerical methods for solving ordinary as well as partial differential equations.
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  • 41
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    Numerische Mathematik 42 (1983), S. 359-377 
    ISSN: 0945-3245
    Keywords: AMS 65L05 ; 65L07 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary This paper is concerned with the stability of multistep methods for ordinary initial-value problems on grids with variable mesh-sizes. A necessary and sufficient condition for stability is given from which generalizations of recent results by Gear et al. and by Zlatev can be obtained as special cases. As an application the stability of the variable BDF-formulas is treated.
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    Numerische Mathematik 42 (1983), S. 379-389 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L20 ; 15A60 ; 65M20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary If the field of values of a matrixA is contained in the left complex halfplaneH and a functionf mapsH into the unit disc then ∥f(A)∥2≦1 by a theorem of J.v. Neumann. We prove a theorem of this type, only the field of values ofA is used for functions which are absolutely bounded by one in only part ofH. An extension can be used to show norm-stability of single step methods for stiff differential equations. The results are applicable among others to several subdiagonal Padé approximations which are notA-stable.
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  • 43
    ISSN: 1573-5117
    Keywords: cypress swamp ; nitrogen ; nutrient cycling ; periphytic algae ; phosphorus ; phytoplankton
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    Topics: Biology
    Notes: Abstract Both periphytic and planktonic algae are found in areas of the seasonally flooded Great Dismal Swamp (Virginia, U.S.A.). The dynamics of these algae were studied in a cypress stand and the periphytic algae appeared to be important as nutrient conservers. Clear temporal patterns in phytoplankton dominance were also observed.
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    Hydrobiologia 101 (1983), S. 49-58 
    ISSN: 1573-5117
    Keywords: forest water ecosystems ; phosphatases ; phosphorus ; phosphatase budget ; acid lakes
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    Topics: Biology
    Notes: Abstract The activity of acid phosphatases was followed for one year in Lake Gårdsjön as well as in the inlet and the outlet of the lake. A budget of the phosphatases was calculated, including an estimation of the production of phosphatases. The phosphatase activity was also measured in two basins upstream of L. Gårdsjön: the north basin and the south basin of L. Stora Hästevatten. The acid phosphatase activity was very high compared with reported alkaline phosphatase activities in other lakes. About 95% of the phosphatases in L. Gårdsjön was produced in the lake, and the production was highest in early summer. Small Chrysophyceae (〈 10 µm) probably produced the majority of the acid phosphatases in the investigated lakes, and accordingly could be favoured in environments with low phosphorus supply due to their ability to produce large amounts of phosphatases.
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    Hydrobiologia 104 (1983), S. 231-236 
    ISSN: 1573-5117
    Keywords: rotifers ; phosphorus ; nitrogen ; excretion ; temperature ; body weight
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    Topics: Biology
    Notes: Abstract Two series of experiments were carried out to determine the relation of the rate of phosphorus and nitrogen excretion by the planktonic rotifers to ambient temperature and individual body weights of these animals. The following formulas describing this relation were obtained: EP=0.0154 W−1.27 e0.096T EN=0.0879 W−1.01 e0.088 T, where EP and EN denote the rate of P and N excretion, respectively, in µg · mg dry wt−1 · h−1, W is body weight in µg dry weight, and T is temperature in °C.
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    Hydrobiologia 100 (1983), S. 101-112 
    ISSN: 1573-5117
    Keywords: nutrient limitation ; phosphorus ; nitrogen ; phytoplankton biomass ; tropical lakes ; Kenya
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    Topics: Biology
    Notes: Abstract Two of three Kenyan lakes studied between November 1979 and October 1980 have very short 33PO4 turnover times, indicating a high phosphorus (P) demand throughout the year. The P turnover time in Lakes Oloidien and Sonachi is as rapid as in the most P deficient temperate zone lakes. The third lake, Lake Naivasha, has a lower overall P demand and a wide seasonal range, with lowest demand between November 1979 and February 1980 when a P deficiency was unlikely. On an annual basis the Lake Naivasha status is, however, not statistically different from that recorded during the summer in Lake Memphremagog, a generally P-limited temperate zone lake. Lake Naivasha and Lake Oloidien fit well to the line of best fit for the Dillon-Rigler relationship relating total phosphorus (TP) and chlorophyll a derived in temperate zone lakes. Thus, temperate zone models predicting aspects of lake behaviour on the basis of TP may also be applicable to these two tropical lakes. Saline lake Sonachi had not only a short P turnover time but also responded dramatically to the fertilization of enclosures with P. However, it does not fit the TP-chla or the total nitrogen-chla plots from the temperate zone. This suggests that, in this saline lake at least, much of the TP is unavailable to the algae, with some of it in a particulate form that is readily extracted with boiling water. The epilimnetic N:P ratios also characterize lakes Oloidien and Sonachi lakes as highly P deficient and lake Naivasha as more moderately P limited. A single set of measurements in Winam Gulf (Lake Victoria) also showed a rapid P turnover time and thus P limitation, but as in lake Sonachi much of the TP was in a non-algal particulate form. Occasional measurements in three other hypertrophic and saline lakes suggest them to be primarily light limited on the basis of their very high photosynthetic cover. These findings support the hypothesis of a primary P limitation for those lakes not light limited, and contradicts literature suggestions that nitrogen is the primary limiting element in tropical lakes.
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    Nutrient cycling in agroecosystems 4 (1983), S. 151-154 
    ISSN: 1573-0867
    Keywords: phosphorus ; proportion ; mango ; whole tree ; leaves ; bark ; wood ; roots
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Quantities of phosphorus present in different component parts of mango trees were estimated from July 1977 to June 1978 at the Horticultural Farm of the Gujarat Agricultural University, India. Because of high variation in the dry weight of the trees it was not possible to assess annual requirement of P by the trees. Hence a measure of comparability between P present in different months was sought to be established by expressing the quantity of P in a part of the tree as percentage of that in the whole tree.
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    Nutrient cycling in agroecosystems 4 (1983), S. 155-164 
    ISSN: 1573-0867
    Keywords: nitrogen ; phosphorus ; fertilization ; Norway spruce ; quartz-porphyry site ; reforestation
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Growth of young Norway spruce plantations on quartz-porphyry sites can be improved by applying phosphorus fertilizer as this acid parent rock is extremely poor in phosphorus. If fertilization is performed in connection with reforestation, the increment in height and volume of the developing crop increases for a period of about ten years. Additional liming prolongs the duration of the P-fertilization effect up to 20 years. Liming stabilizes phosphorus in an available form in the humus layer and upper soil horizon. Nitrogen deficiency occurs only 10 to 15 years after planting and N applied up to then has no positive effect on spruce growth.
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    Nutrient cycling in agroecosystems 4 (1983), S. 281-285 
    ISSN: 1573-0867
    Keywords: mango ; foliar spray ; orthophosphoric acid ; phosphorus ; urea ; utilisation
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Orthophosphoric acid (0.5%) was sprayed along with and without 2 per cent urea on the mango (Mangifera indica L) cv. Langra trees in the months of September, November or March as well as in all the three months. There was an improvement of fruit set in the sprayed treatments which was high after March sprays. Significantly higher yields were obtained in triple spray treatments along with urea. The percentage of phosphorus in the fruits was raised by the sprays. The yield of phosphorus in the fruits was highest in March spray treatment and progressively less in November and September spray treatments. It was concluded that the urea given along with phosphorus improved the utilisation of phosphorus in the fruits by providing a better balance of nutrients.
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    ISSN: 1436-5057
    Keywords: 65L05 ; CR: 5.17 ; Numer. Analysis ; verallgemeinerte Runge-Kutta-Methoden ; steife Probleme
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    Topics: Computer Science
    Description / Table of Contents: Abstract Adaptive Runge-Kutta-methods are considered. Investigations of stability for these linear implicit methods are studied. For the application a LS-stable method of order four with an adaptive stepsize control is proposed. Test results for 25 stiff initial value problems for different tolerances are discussed.
    Notes: Zusammenfassung Es werden adaptive Runge-Kutta-Verfahren betrachtet und Stabilitätsuntersuchungen für diese linear impliziten Methoden durchgeführt. Für die Anwendung wird ein LS-stabiles Verfahren vierter Ordnung mit einer angepaßten Schrittweitenkontrolle vorgeschlagen. Testergebnisse von 25 stiff Anfangswertproblemen für verschiedenen Toleranzen werden diskutiert.
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    Numerische Mathematik 40 (1982), S. 179-199 
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; Primary 65N30 ; Secondary 35R35 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Two problems are considered in the paper: the first of them is connected with elliptic variational inequalities and consists in developing a moving obstacle algorithm for approximating the unknown free boundary; the other problem is linked with numerical solution of the Stefan problem, which is formulated in the similar way as in the elliptic case. Some computational aspects are also discussed in the paper.
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    Numerische Mathematik 40 (1982), S. 207-227 
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    Keywords: AMS(MOS): 65M30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Several regularization methods for parabolic equations backwards in time together with the usual additional constraints for their solution are considered. The error of the regularization is estimated from above and below. For a “boundary value problem in time”-method, finite elements as well as a time discretization are introduced and the error with respect to the regularized solution is estimated, thus giving an overall error of the discrete regularized problem. The algorithm is tested in simple numerical examples.
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    Numerische Mathematik 39 (1982), S. 221-230 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary In this paper Adams type methods for the special case of neutral functional differential equations are examined. It is shown thatk-step methods maintain orderk+1 for sufficiently small step size in a sufficiently smooth situation. However, when these methods are applied to an equation with a “non-smooth” solution the order of convergence is only one. Some computational considerations are given and numerical experiments are presented.
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    Numerische Mathematik 39 (1982), S. 309-324 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L10 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A method for improvement of the numerical solution of differential equations by incorporation of asymptotic approximations is investigated for a class of singular perturbation problems. Uniform error estimates are derived for this method when implemented in known difference schemes and applied to linear second order O.D.E.'s. An improvement by a factor ofε n+1 can be obtained (where ɛ is the “small” parameter andn is the order of the asymptotic approximation) for a small amount of extra work. Numerical experiments are presented.
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    Numerische Mathematik 39 (1982), S. 341-350 
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    Keywords: AMS(MOS): 65L10 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We discuss the construction of three-point finite difference approximations and their convergence for the class of singular two-point boundary value problems: (x α y′)′=f(x,y), y(0)=A, y(1)=B, 0〈α〈1. We first establish a certain identity, based on general (non-uniform) mesh, from which various methods can be derived. To obtain a method having order two for all α∈(0,1), we investigate three possibilities. By employing an appropriate non-uniform mesh over [0,1], we obtain a methodM 1 based on just one evaluation off. For uniform mesh we obtain two methodsM 2 andM 3 each based on three evaluations off. For α=0,M 1 andM 2 both reduce to the classical second-order method based on one evaluation off. These three methods are investigated, theirO(h 2)-convergence established and illustrated by numerical examples.
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    Numerische Mathematik 39 (1982), S. 371-404 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65 N 30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The purpose of this paper is to study the approximation of the Von Karman equations by the mixed finite element scheme of Miyoshi and to follow the solutions arcs at a neighbourhood of the first eigenvalue of the linearized problem. This last problem is solved by a continuation method.
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    Numerische Mathematik 39 (1982), S. 449-463 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L65 ; CR: 5.17 ; AMS (MOS): 65L65 ; CR: 5.17
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    Topics: Mathematics
    Description / Table of Contents: Summary In [10] a general procedureV is presented to obtain spline approximations by collocation for the solutions of initial value problems for first order ordinary differential equations. In this paper the attainable order of convergence with respect to the maximum norm is characterized in dependence of the parameters involved inV; in particular the appropriate choice of the collocation points is considered.
    Notes: Zusammenfassung In [10] ist ein allgemeines VerfahrenV beschrieben, das die Lösungen von Anfangswertproblemen bei gewöhnlichen Differentialgleichungen erster Ordnung durch Splines approximiert. Die Konstruktion der Splines erfolgt hierbei mittels Kollokation. In dieser Arbeit wird die maximal erreichbare Konvergenzordnung vonV bezüglich der Maximumnorm in Abhängigkeit aller Parameter vonV charakterisiert, insbesondere wird auf die geeignete Wahl der Kollokationsknoten eingegangen.
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    Numerische Mathematik 40 (1982), S. 169-177 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The stability and accuracy of some explicit nonlinear methods for the numerical integration of stiff systems of ordinary differential equations are investigated. It is shown, that in the general case they can produce the essential error. The special class of stiff systems is singled out, for which these methods are highly efficient. Some numerical results are also presented.
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    Numerische Mathematik 40 (1982), S. 319-328 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65J05, 65L15 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Although multiparameter eigenvalue problems, as for example Mathieu's differential equation, have been known for a long time, so far no work has been done on the numerical treatment of these problems. So in this paper we extend the spectral theory for one parameter (cf. [7, II, VII]) to multiparameter eigenvalue problmes, formulate in the framework of discrete approximation a convergent numerical treatment, establish algebraic bifurcation equations for the intersection points of the eigenvalue curves and illustrate this with some numerical examples.
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    Numerische Mathematik 40 (1982), S. 373-406 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30, 65M20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We extend in this paper the analysis of a posteriori estimates of the space discretization error presented in a previous paper [3] for time-independent space meshes. In the context of the model problem studied there, results are given relating the effectiveness of the error estimator to properties of the solution, space meshes, and manner in which the meshes change. A procedure based upon this theory is presented for the adaptive construction of time-dependent meshes. The results of some computational experiments show that this procedure is practically very effective and suggest that it can be used to control the space discretization error in more general problems.
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    Nutrient cycling in agroecosystems 3 (1982), S. 13-16 
    ISSN: 1573-0867
    Keywords: cocoa ; nitrogen ; phosphorus ; soil analysis ; Nigeria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract No extensive investigation on the effect of fertilizers on Amazon cocoa variety (Theobroma cacao L.) has been performed in Nigeria. Therefore eight fertilizer treatments involving nitrogen and phosphorus, replicated six times at four locations across southern Nigeria, were established in 1973. The four N levels (N0, N1, N2, N3) involved were 0, 80, 160 and 240 kg ha−1 y−1, and the two P levels (P0, P1) were 0 and 67 kg ha−1 y−1. Results of the first 5 years of fertilizer application are reported. Response to P was observed at all locations, and the response was statistically significant at 2 of the locations. There was no response to the application of nitrogen. The data suggest, however, that there is only a response to phosphorus when nitrogen is applied.
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    Numerische Mathematik 38 (1982), S. 141-154 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 35 A 40 ; 35 K 05 ; 65 N 15 ; 65 K 05 ; 80 A 20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A nonlinear approximation technique for the numerical solution of certain free boundary problems is proposed. The method is shown for a degenerate one-dimensional Stefan problem. For this problem, an error estimate, which is independent of the used algorithm, is derived. Numerical examples are discussed.
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    Numerische Mathematik 40 (1982), S. 329-337 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A widely used technique for improving the accuracy of solutions of initial value problems in ordinary differential equations is local extrapolation. It is well known, however, that when using methods appropriate for solving stiff systems of ODES, the stability of the method can be seriously degraded if local extrapolation is employed. This is due to the fact that performing local extrapolation on a low order method is equivalent to using a higher order formula and this high order formula may not be suitable for solving stiff systems. In the present paper a general approach is proposed whereby the correction term added on in the process of local extrapolation is in a sense a rational, rather than a polynomial, function. This approach allows high order formulae with bounded growth functions to be developed. As an example we derive anA-stable rational correction algorithm based on the trapezoidal rule. This new algorithm is found to be efficient when low accuracy is requested (say a relative accuracy of about 1%) and its performance is compared with that of the more familiar Richardson extrapolation method on a large set of stiff test problems.
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    Numerische Mathematik 40 (1982), S. 339-371 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 65M20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary In this first of two papers, computable a posteriori estimates of the space discretization error in the finite element method of lines solution of parabolic equations are analyzed for time-independent space meshes. The effectiveness of the error estimator is related to conditions on the solution regularity, mesh family type, and asymptotic range for the mesh size. For clarity the results are limited to a model problem in which piecewise linear elements in one space dimension are used. The results extend straight-forwardly to systems of equations and higher order elements in one space dimension, while the higher dimensional case requires additional considerations. The theory presented here provides the basis for the analysis and adaptive construction of time-dependent space meshes, which is the subject of the second paper. Computational results show that the approach is practically very effective and suggest that it can be used for solving more general problems.
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    Numerische Mathematik 38 (1982), S. 39-52 
    ISSN: 0945-3245
    Keywords: AMS (MOS): Primary 65L10 ; Secondary 35R35 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary An approximate method for nonlinear problems with functional constraints is considered, in which the constraint in the whole domain is replaced by the constraint on a manifold of lower dimension. The stability criterion is introduced, and convergence theorems are proved for the onedimensional problem. Numerical results for the elastic-plastic torsion problem are given.
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    Numerische Mathematik 38 (1982), S. 365-382 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary This paper considers the problems of minimizing Gateaux-differentiable functionals over subsets of real Banach spaces defined by a non-linear equality constraint. The existence of a Lagrange multiplier is proved, together with approximation results on the constrained subset, provided a nonlinear compatibility condition, generalizing the classical inf-sup condition, is satisfied. These ideas are applied to equilibrium problems in incompressible finite elasticity and lead to convergence results for these problems.
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    Numerische Mathematik 38 (1982), S. 447-453 
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary As is known [4]. theC o Galerkin solution of a two-point boundary problem using piecewise polynomial functions, hasO(h 2k ) convergence at the knots, wherek is the degree of the finite element space. Also, it can be proved [5] that at specific interior points, the Gauss-Legendre points the gradient hasO(h k+1) convergence, instead ofO(h k ). In this note, it is proved that on any segment there arek−1 interior points where the Galerkin solution is ofO(h k+2), one order better than the global order of convergence. These points are the Lobatto points.
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    Numerische Mathematik 38 (1982), S. 467-471 
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65L20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The approximation of linear systemsy′=−A(t)y+b(t) by backward differentiation methods up to order 5 is considered. It is proved that the error does not increase if the real symmetric matrixA(t) is positive definite andA′(t) is negative semi-definite.
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    Numerische Mathematik 39 (1982), S. 15-37 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 N 30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We make several assumptions on a nonlinear evolution problem, ensuring the existence of a Hopf bifurcation. Under a fairly general approximation condition, we define a discrete problem which retains the bifurcation property and we prove an error estimate between the branches of exact and approximate periodic solutions.
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    Numerische Mathematik 39 (1982), S. 39-50 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary In this paper we derive error estimates for infinite element method used in the approximation of solutions of interface problems. Furthermore, approximations of stress intensity factors are given. The infinite element method may be considered as a certain scheme of mesh refinement, but it has the advantages that the refinement is easy to be constructed that the stiffness matrix can be calculated efficiently, and that an approximate solution which has a singularity at the singular point can be also obtained.
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  • 71
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    Numerische Mathematik 38 (1982), S. 1-30 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary In the first two papers of this series [4, 5], we have studied a general method of approximation of nonsingular solutions and simple limit points of nonlinear equations in a Banach space. We derive here general approximation results of the branches of solutions in the neighborhood of a simple bifurcation point. The abstract theory is applied to the Galerkin approximation of nonlinear variational problems and to a mixed finite element approximation of the von Kármán equations.
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    Numerische Mathematik 39 (1982), S. 97-112 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We introduce some new families of finite element approximation for the stationary Stokes and Navier Stokes equations in a bounded domain in ℝ3. These elements can used tetahedrons or cubes. The approximation satisfie exactly the incompressibility condition.
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    Hydrobiologia 87 (1982), S. 193-200 
    ISSN: 1573-5117
    Keywords: primary productivity ; phosphorus ; EDTA
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    Topics: Biology
    Notes: Abstract Lake Monroe is the largest body of water in Indiana with a daily mean productivity of 220 mg · C · m−2 · day−1 in an observed range from 26 to 714 m · C · M−2 day−1. It is a medium soft reservoir; the acid combining capacity varies from 0.28 to 0.71 meq · l−1 with a mean slightly above 0.5 meq · l−1. The results of diurnal changes in major nutrients, the C, N, and P ratios, and bioassay experiments indicated that phosphorus is the major limiting nutrient on algal photosynthesis in this lake. Surface photo-inhibition may be used to indicate the sufficiency of light for the species of algae in the water. The low productivity in December, January, February, and early March can be attributed to light limitation due to low water transparency.
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  • 74
    ISSN: 1573-5117
    Keywords: phosphorus ; nutrient cycling ; stratification ; epilimnion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Phosphorus regeneration from lake sediments, and subsequent migration to trophogenic surface water, significantly contributes to the lake nutrient budgets and algal bloom conditions in some lake types. Decomposition of organic matter in deep water and sediments results in the accumulation of regenerated nutrients, alternate electron acceptors (reduced products of anaerobic respiration = COD), carbon dioxide, and depletion of dissolved oxygen (electron acceptor in aerobic respiration). Thermal stratification creates spatial segregation of trophogenic and tropholytic environments in the lake, resulting in gradients between sediments, hypolimnion, and the epilimnion. Exchange of oxygen, nutrients, and reduced alternate electron acceptors between the hypolimnion and epilimnion affects the productivity of a lake. Secchi depth, temperature, and dissolved oxygen profiles were determined twice each week from May 1980 to October 1980 at each of five lake stations. Nutrient concentration profiles, including total soluble and total phosphorus, ammonium-N, nitrate, soluble Kjeldahl, and total Kjeldahl nitrogen were determined twice each month. Epilimnetic algal samples were collected twice each week using Kemmerer and water column ‘straw’ amplers. Cell counts of total, green, bluegreen, and diatom algae groups were made. Three methods were used to describe hypolimnetic-epilimnetic exchange, including coefficients of eddy diffusion (based on lake heat budget), a graphical method of defining thermocline location, and relative thermal resistance to mixing (RTRM, based on density differences). All three methods yeilded comparable estimates of net seasonal transport. The graphical and RTRM methods described events occurring at shorter intervals (greater resolution). We find general agreement between the three methods of describing hypolimnetic-epilimnetic transport. The frequency of sampling resulted in increased resolution of thermal profiles (in time), allowing accurate estimation of short-term nutrient flux into epilimnetic waters. An algal bloom event occurred 5 to 12 days following erosion of the top of the metalimnion to below the aerobic-anaerobic interface. The lag time to peak algal concentration, following such events, decreased through the summer (June = 12 days, September = 5 days)
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  • 75
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    Hydrobiologia 91-92 (1982), S. 537-547 
    ISSN: 1573-5117
    Keywords: lake acidification ; neutralization ; buffer capacity ; liming ; cation exchange ; humic sediment ; phosphorus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Until now, additions of lime have been used to restore the buffering capacity of acidified lakes, but an alternative method which is more effective in the treatment of lakes with organogenic sediments has recently been applied in a full-scale experiment. The method, called CONTRACID, is based on the cation exchange properties of lake sediment. A sodium carbonate (soda ash) solution is injected into the sediment (by a harrow), so that the sediment becomes sodium stocked. A reverse exchange occurs during subsequent acidification. Liming has a limited effect on humic lakes, since Ca-humates have a reduced reverse exchange ability and also the lime, which remains undissolved, is rendered inactive. Ionic exchange processes and nutrient transport were studied in water/sediment cores and in situ enclosures after additions of soda ash-, lye- and lime solutions with subsequent re-acidification. Sodium carbonate additions in laboratory systems resulted in a sorption to the sediment of 42–62% of the added sodium ions (5 eq m−2) and a release of 14–78 mg Pm−2 sediment. Similar results were obtained in the enclosures where phosphorus release stimulated algal growth. Sediment pH, elevated by the sodium base addition, was lowered by re-acidification. Limed systems released no phosphorus and only about 25% of the added lime remained active for future neutralization. With the injection of the sodium carbonate solution into the sediment, only about 12% of the added sodium was recovered in lake water by spring circulation. Lake water alkalinity was then 0.12 meq l−1 and pH 6.7. Total phosphorus had been raised by 0.007 mg P l−1 causing an increase in phytoplankton biomass. Observations indicate that manipulations of acidic lake sediment according to the CONTRACID method create a long-lasting neutralizing capacity and a biological stimulation (through phosphorus release), which makes the method an attractive alternative to frequent liming.
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    Hydrobiologia 91-92 (1982), S. 549-558 
    ISSN: 1573-5117
    Keywords: lake restoration ; sediment dredging ; nitrogen ; phosphorus ; algal assays
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract An increased load of domestic wastewater to Lake Trehörningen induced oxygen-poor water conditions and the development of a reduced sulphide-rich sediment layer. Severely polluted, the lake did not recover, even after advanced wastewater treatment and sewage diversion. Restoration measures with suction dredging and macrophyte elimination were applied in 1975 and 1976. The loose topmost sediment was pumped into an embanked and overgrown bay which was used as a settling pond. The activities also included a restoration of the shorelines. This project is the largest restoration programme carried out in Sweden on a single lake, corresponding to a cost of about US $2 000 000. The restoration of Lake Trehörningen was followed by a highly intensive research programme which included water chemistry and algal assays. The concentrations of phosphate and total phosphorus decreased by 73 and 50% respectively, as summer average values, two years after the restoration. However, the concentrations of phosphorus are still too high to permit this element to act as a prime algal growth-limiting nutrient. The algal biomass has also remained at the same magnitude as before the restoration. Nitrate-N concentrations showed a tenfold increase, based on average values for the summer period. However, based on the results of the algal assays, a rapid and marked response was obvious, with a drastic decline in the algal growth potential. In addition, the water quality of the tributaries was frequently of an objectionable character (0.1–0.2 g P m−3). The nutrient loading from these sources exceeds the critical level for the lake, and measures have now been carried out to treat all the inflowing waters for the removal of phosphorus.
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    Hydrobiologia 91-92 (1982), S. 603-610 
    ISSN: 1573-5117
    Keywords: phytoplankton ; tripton ; phosphorus ; mineralization ; regeneration and diffusion
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    Topics: Biology
    Notes: Abstract Tripton sedimentation was investigated in the eutrophic Lake Lugano (Ponte Tresa basin) from October 1979 to October 1980. The annual amount of tripton collected was 748 g · m−2 · y−1. Phosphorus, nitrogen and organic carbon fluxes into the hypolimnion were estimated to be 1.9, 16.2 and 121 g · m−2y−1 respectively. Mineralization rates into the trophogenic layer varied from 11% to 19% per day during summer stratification. The regeneration processes contribute about 60% of the calculated P deficit in the epilimnion. The tripton is decomposed mostly in the metalimnion, out of the euphotic zone; from here the phosphorus is carried back to the overlying waters by diffusion processes.
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  • 78
    ISSN: 1573-5117
    Keywords: leaf-conditioning ; microorganisms ; nitrogen ; carbon ; phosphorus ; Alnus rugosa ; Populus tremuloides ; Myrica gale
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    Topics: Biology
    Notes: Abstract Myrica gale, Alnus rugosa and Populus tremuloides leaves were incubated ‘in situ’ in the oligotrophic acid waters of the Canadian Shield (James Bay, Quebec) in order to follow microorganic decomposition, respiration and chemical transformations. Respiratory activities in decomposing speckled alder and trembling aspen leaves were more important than that in sweet gale. In spite of low nutrient concentrations in the water, nitrogen concentration increased in the three species while phosphorus levels increased only in the speckled alder during decomposition.
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    Hydrobiologia 91-92 (1982), S. 431-446 
    ISSN: 1573-5117
    Keywords: phosphorus ; regeneration ; fluxes ; estuarine
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    Topics: Biology
    Notes: Abstract The flux of dissolved reactive phosphate from Potomac riverine and estuarine sediments is controlled by processes occurring at the water-sediment interface and within surficial sediment.In situ benthic fluxes (0.1 to 2.0 mmoles m−2 day−1) are generally five to ten times higher than calculated diffusive fluxes (0.020 to 0.30 mmoles m−2 day−1). The discrepancy between the two flux estimates is greatest in the transition zone (river mile 50 to 70) and is attributd to macrofaunal irrigation. Bothin situ and diffusive fluxes of dissolved reactive phosphate from Potomac tidal river sediments are low while those from anoxic lower estuarine sediments are high. The net accumulation rate of phosphorus in benthic sediment exhibits an inverse pattern. Thus a large fraction of phosphorus is retained by Potomac tidal river sediments, which contain a surficial oxidized layer and oligochaete worms tolerant of low oxygen conditions, and a large fraction of phosphorus is released from anoxic lower estuary sediments. Tidal river sediment pore waters are in equilibrium with amorphous Fe (OH)3 while lower estuary pore waters are significantly undersaturated with respect to this phase. Benthic regeneration of dissolved reactive phosphorus is sufficient to supply all the phosphorus requirements for net primary production in the lower tidal river and transition-zone waters of the Potomac River Estuary. Benthic regeneration supplies approximately 25% as much phosphorus as inputs from sewage treatment plants and 10% of all phosphorus inputs to the tidal Potomac River. When all available point source phosphorus data are put into a steady-state conservation of mass model and reasonable coefficients for uptake of dissolved phosphorus, remineralization of particulate phosphorus, and sedimentation of particulate phosphorus are used in the model, a reasonably accurate simulation of dissolved and particulate phosphorus in the water column is obtained for the summer of 1980.
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  • 80
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    Hydrobiologia 91-92 (1982), S. 537-547 
    ISSN: 1573-5117
    Keywords: lake acidification ; neutralization ; buffer capacity ; liming ; cation exchange ; humic sediment ; phosphorus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Until now, additions of lime have been used to restore the buffering capacity of acidified lakes, but an alternative method which is more effective in the treatment of lakes with organogenic sediments has recently been applied in a full-scale experiment. The method, called CONTRACID, is based on the cation exchange properties of lake sediment. A sodium carbonate (soda ash) solution is injected into the sediment (by a harrow), so that the sediment becomes sodium stocked. A reverse exchange occurs during subsequent acidification. Liming has a limited effect on humic lakes, since Ca-humates have a reduced reverse exchange ability and also the lime, which remains undissolved, is rendered inactive. Ionic exchange processes and nutrient transport were studied in water/sediment cores andin situ enclosures after additions of soda ash-, lye- and lime solutions with subsequent re-acidification. Sodium carbonate additions in laboratory systems resulted in a sorption to the sediment of 42–62% of the added sodium ions (5 eq m−2) and a release of 14–78 mg Pm−2 sediment. Similar results were obtained in the enclosures where phosphorus release stimulated algal growth. Sediment pH, elevated by the sodium base addition, was lowered by re-acidification. Limed systems released no phosphorus and only about 25% of the added lime remained active for future neutralization. With the injection of the sodium carbonate solution into the sediment, only about 12% of the added sodium was recovered in lake water by spring circulation. Lake water alkalinity was then 0.12 meq l−1 and pH 6.7. Total phosphorus had been raised by 0.007 mg P l−1 causing an increase in phytoplankton biomass. Observations indicate that manipulations of acidic lake sediment according to the CONTRACID method create a long-lasting neutralizing capacity and a biological stimulation (through phosphorus release), which makes the method an attractive alternative to frequent liming.
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  • 81
    ISSN: 1573-5117
    Keywords: oligotrophic lakes ; Equisetum ; carbon ; phosphorus ; nitrogen
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Stores and flows of carbon, phosphorus and nitrogen in a littoral Equisetum stand were studied in 1978–1980 in the oligotrophic, mesohumic lake Pääjärvi, southern Finland. The major carbon and nutrient stores were sediment and Equisetum. The seasonal cycle of the macrophyte vegetation had a profound influence on the whole littoral ecosystem. In spring, when only dead remains of Equisetum were present above ground, there were few differences in nutrient, chlorophyll a and zooplankton concentrations between the littoral and the open lake; phytoplankton and epiphytes were the major producers. In early June, when new shoots of Equisetum reached the water surface, water exchange between the littoral and the open lake started to diminish, and the characteristic features of a closed macrophyte zone gradually developed: by August the P, Chl a and zooplankton concentrations in the littoral were 5–10 times those in the open lake. From late June until autumn Equisetum was overwhelmingly dominant both in biomass and in production. The measured total primary production and respiration values indicated a high rate of internal cycling of carbon and nutrients. The daily P requirements of plant growth exceeded the total P stored in the water by a factor of 2–4, and also exceeded the release of nutrients in excretion. High N:P ratios in the water (total 10–64, inorganic 18–171) suggested that P was probably always the limiting nutrient. The P content of the annual production of Equisetum in Pääjärvi was 2.3% of the mean annual P load, and 5.3% of the mean total P storage in the water volume of the lake.
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    Hydrobiologia 91-92 (1982), S. 489-490 
    ISSN: 1573-5117
    Keywords: laboratory experiments ; sediment types ; phosphorus ; silicon ; sediment-water exchange
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    Topics: Biology
    Notes: Extended abstract Lake Grevelingen is a brackish water lake in the SW Netherlands. The lake has an area of 108 km2, a mean depth of 5.3 m (maximum 48 m), a mean chlorinity of 13 to 16%0 Cl−, and a hydraulic residence time of about 8 years. Mass budget studies have shown a consistent seasonal pattern in the phosphorus sediment-water exchange in Lake Grevelingen (Kelderman 1980). From May to August a P mobilization from the sediment takes place, estimated atca. 12.5 mg P · m−2 · day−1. The sediment accumulatesca. 5.5 mg P · m−2 · day−1 during the rest of the year. Temperature may be an important factor in establishing this pattern. Sediment-water exchange was studied by means of laboratory experiments under specified conditions. Sediment cores (30 cm depth, 11 cm diameter) were taken at four stations in the lake, with sediment types varying from medium- to muddy sand (Fig. 1). The cores with overlying water (ca. 21) were placed in the dark at 5 °C in thermostatically controlled water baths. After a week's incubation time the temperature was slowly raised, such that after three weeks eight cores (four sediment types, duplicates) were at 5 °C, eight were at 10 °C, eight at 15 °C and eight at 20 °C. The same procedure was applied to the four control cores, containing lake water.
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  • 83
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    Hydrobiologia 91-92 (1982), S. 537-547 
    ISSN: 1573-5117
    Keywords: lake acidification ; neutralization ; buffer capacity ; liming ; cation exchange ; humic sediment ; phosphorus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Until now, additions of lime have been used to restore the buffering capacity of acidified lakes, but an alternative method which is more effective in the treatment of lakes with organogenic sediments has recently been applied in a full-scale experiment. The method, called CONTRACID, is based on the cation exchange properties of lake sediment. A sodium carbonate (soda ash) solution is injected into the sediment (by a harrow), so that the sediment becomes sodium stocked. A reverse exchange occurs during subsequent acidification. Liming has a limited effect on humic lakes, since Ca-humates have a reduced reverse exchange ability and also the lime, which remains undissolved, is rendered inactive. Ionic exchange processes and nutrient transport were studied in water/sediment cores andin situ enclosures after additions of soda ash-, lye- and lime solutions with subsequent re-acidification. Sodium carbonate additions in laboratory systems resulted in a sorption to the sediment of 42–62% of the added sodium ions (5 eq m−2) and a release of 14–78 mg Pm−2 sediment. Similar results were obtained in the enclosures where phosphorus release stimulated algal growth. Sediment pH, elevated by the sodium base addition, was lowered by re-acidification. Limed systems released no phosphorus and only about 25% of the added lime remained active for future neutralization. With the injection of the sodium carbonate solution into the sediment, only about 12% of the added sodium was recovered in lake water by spring circulation. Lake water alkalinity was then 0.12 meq l−1 and pH 6.7. Total phosphorus had been raised by 0.007 mg P l−1 causing an increase in phytoplankton biomass. Observations indicate that manipulations of acidic lake sediment according to the CONTRACID method create a long-lasting neutralizing capacity and a biological stimulation (through phosphorus release), which makes the method an attractive alternative to frequent liming.
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  • 84
    ISSN: 1573-5117
    Keywords: microbial metabolism ; phosphorus ; sediments ; oligotrophic lake
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Rapid microbial metabolism and a large phosphorus uptake potential were observed in surface sediments of Lake George, New York. This sediment (termed the flocculent layer) also exhibited a phosphorus limited condition and a large reservoir of inorganic phosphorus associated with humic substances. These observations suggest that the empirically observed phosphorus retention in oligotrophic lake sediments may be promoted by a rapid cycling of phosphorus between microflora and its associated organic matter.
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    Hydrobiologia 94 (1982), S. 173-176 
    ISSN: 1573-5117
    Keywords: phosphorus ; chlorophyll a ; microcosm
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    Topics: Biology
    Notes: Abstract The correlation between total dissolved phosphorus input concentrations and periphytic chlorophyll a concentrations was examined after a four-week colonization period on artificial substrates in large, continuous-flow microcosms. A significant correlation was established; the data produced a linear regression and substantiated a recently proposed curvilinear regression analysis. The curvilinear equation can be used in future microcosm studies as a predictive aid for regulating phosphorus input concentrations.
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    Hydrobiologia 91-92 (1982), S. 111-119 
    ISSN: 1573-5117
    Keywords: phosphorus ; bioavailability ; point source ; diffuse source ; Great Lakes ; bioassay ; eutrophication
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Control of phytoplankton production in the Great Lakes can be achieved most efficiently by limiting inputs of biologically available P. We report the results of studies performed to characterize the chemical forms and availability of particulate P in wastewater and tributaries which enter the lower Lakes, the eroding bluffs which border Lake Erie, and bottom samples from the near-shore of western Lake Erie. Rates of release of available P were estimated from a simple first-order model of the process, as observed during algal bioassays. Available P in wastewater samples, as a fraction of total particulate P, was affected minimally by wastewater treatment, including chemical precipitation and filtration; it correlated well with levels of total particulate P. Available particulate P levels in fluvial suspended sediments showed regional uniformity, but appeared to be strongly dependent on levels of both NaOH-P and CDB-P. Rates of release of available P decreased during wastewater treatment to values which were similar in magnitude to those observed for fluvial sediments. Release rates, however, were not related to any of the particulate P fractions which were measured. Analysis of the bluff and bottom samples indicated that P availability in the former was negligible, but the latter contained levels which approached those of wastewater particulates, though available P was released from the bottom sediments at relatively low rates.
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    Hydrobiologia 91-92 (1982), S. 241-252 
    ISSN: 1573-5117
    Keywords: pollution ; rivers ; transport ; calculation ; phosphorus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Human activities generate many pollutants from different land uses. These pollutants include nutrients (e.g., phosphorus and nitrogen), toxic substances (e.g., heavy metals and pesticides), and other substances (e.g., chlorides and salts). These materials often enter a river at some upstream point and are transported downstream by the flowing water. Many substances are transported both during storms and during normal river flow and often the major portion of the transport occurs during the storms. This paper considers the quantification of transport primarily during storms. First, the characteristics of storm transport are discussed. Then, a calculation method for estimating the distance of travel for sediment related materials is presented. Third, a technique to estimate the amount of a given chemical passing a point in a stream over a specified period of time is presented. The last part of this paper contains a technique for tracing the movement of substances through a river network. In particular, this procedure yields information as to the source of given pollutants over the entire Storm period.
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    Hydrobiologia 96 (1982), S. 105-111 
    ISSN: 1573-5117
    Keywords: nitrogen ; phosphorus ; exrretion ; food quality ; zooplankton
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    Topics: Biology
    Notes: Abstract Rates of nitrogen and phosphorus release from individualDaphnia magna were determined by measuring ammonia and soluble reactive phosphorus in successive 10-min incubations in small (0.05 ml) vessels after the animals were removed from their food. Release rates of both nutrients were generally highest initially and decreased with time after removal. The ratio of nitrogen to phosphorus released increased with time after animals were removed from an artificial detritus/bacterial food; ratios were lower and changed with time less for animals fed algae. These data suggest errors may be introduced by assumptions of constant stoichiometry for nutrient release in varying environments.
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    Hydrobiologia 86 (1982), S. 129-132 
    ISSN: 1573-5117
    Keywords: aquatic models ; phytoplankton primary production ; chlorophyll a ; phosphorus ; humic water
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract A method for predicting the mean seasonal chlorophyll a concentration, the mean seasonal in vitro phytoplankton primary productivity per unit volume, the maximum daily production per unit volume and the seasonal integral production in brown-water lakes is presented. The production values can be calculated when the mean annual concentration of total phosphorus and the mean annual colour of the water are known. This method has been developed especially for practical water pollution studies to permit rapid and inexpensive estimates of major biological consequences of changes in effluent loads. The method can be applied for brown-water lakes where phosphorus is the limiting nutrient for primary production.
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    Hydrobiologia 91-92 (1982), S. 489-490 
    ISSN: 1573-5117
    Keywords: laboratory experiments ; sediment types ; phosphorus ; silicon ; sediment-water exchange
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Extended abstract Lake Grevelingen is a brackish water lake in the SW Netherlands. The lake has an area of 108 km2, a mean depth of 5.3 m (maximum 48 m), a mean chlorinity of 13 to 16%0 Cl−, and a hydraulic residence time of about 8 years. Mass budget studies have shown a consistent seasonal pattern in the phosphorus sediment-water exchange in Lake Grevelingen (Kelderman 1980). From May to August a P mobilization from the sediment takes place, estimated at ca. 12.5 mg P · m−2 · day−1. The sediment accumulates ca. 5.5 mg P · m−2 · day−1 during the rest of the year. Temperature may be an important factor in establishing this pattern. Sediment-water exchange was studied by means of laboratory experiments under specified conditions. Sediment cores (30 cm depth, 11 cm diameter) were taken at four stations in the lake, with sediment types varying from medium- to muddy sand (Fig. 1). The cores with overlying water (ca. 21) were placed in the dark at 5 °C in thermostatically controlled water baths. After a week's incubation time the temperature was slowly raised, such that after three weeks eight cores (four sediment types, duplicates) were at 5 °C, eight were at 10 °C, eight at 15 °C and eight at 20 °C. The same procedure was applied to the four control cores, containing lake water.
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    Hydrobiologia 91-92 (1982), S. 603-610 
    ISSN: 1573-5117
    Keywords: phytoplankton ; tripton ; phosphorus ; mineralization ; regeneration and diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Tripton sedimentation was investigated in the eutrophic Lake Lugano (Ponte Tresa basin) from October 1979 to October 1980. The annual amount of tripton collected was 748 g · m−2 · y−1. Phosphorus, nitrogen and organic carbon fluxes into the hypolimnion were estimated to be 1.9, 16.2 and 121 g · m−2y−1 respectively. Mineralization rates into the trophogenic layer varied from 11% to 19% per day during summer stratification. The regeneration processes contribute about 60% of the calculated P deficit in the epilimnion. The tripton is decomposed mostly in the metalimnion, out of the euphotic zone; from here the phosphorus is carried back to the overlying waters by diffusion processes.
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    Hydrobiologia 91-92 (1982), S. 431-446 
    ISSN: 1573-5117
    Keywords: phosphorus ; regeneration ; fluxes ; estuarine
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The flux of dissolved reactive phosphate from Potomac riverine and estuarine sediments is controlled by processes occurring at the water-sediment interface and within surficial sediment.In situ benthic fluxes (0.1 to 2.0 mmoles m−2 day−1) are generally five to ten times higher than calculated diffusive fluxes (0.020 to 0.30 mmoles m−2 day−1). The discrepancy between the two flux estimates is greatest in the transition zone (river mile 50 to 70) and is attributd to macrofaunal irrigation. Bothin situ and diffusive fluxes of dissolved reactive phosphate from Potomac tidal river sediments are low while those from anoxic lower estuarine sediments are high. The net accumulation rate of phosphorus in benthic sediment exhibits an inverse pattern. Thus a large fraction of phosphorus is retained by Potomac tidal river sediments, which contain a surficial oxidized layer and oligochaete worms tolerant of low oxygen conditions, and a large fraction of phosphorus is released from anoxic lower estuary sediments. Tidal river sediment pore waters are in equilibrium with amorphous Fe (OH)3 while lower estuary pore waters are significantly undersaturated with respect to this phase. Benthic regeneration of dissolved reactive phosphorus is sufficient to supply all the phosphorus requirements for net primary production in the lower tidal river and transition-zone waters of the Potomac River Estuary. Benthic regeneration supplies approximately 25% as much phosphorus as inputs from sewage treatment plants and 10% of all phosphorus inputs to the tidal Potomac River. When all available point source phosphorus data are put into a steady-state conservation of mass model and reasonable coefficients for uptake of dissolved phosphorus, remineralization of particulate phosphorus, and sedimentation of particulate phosphorus are used in the model, a reasonably accurate simulation of dissolved and particulate phosphorus in the water column is obtained for the summer of 1980.
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  • 93
    ISSN: 1573-5117
    Keywords: bioturbation ; modelling ; sediment ; phosphorus ; Chironomus anthracinus ; Potamothrix hammoniensis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract A multilayer sediment-water exchange model was used to evaluate the importance of bioturbation in the profundal sediments of L. Esrom. The temporal variation of the vertical distribution of sedimentary phosphorus fractions was modelled with an objective function of 1.50. Deviations between measured and simulated values occurred in the spring, where the measured pool of sedimentary phosphorus sharply declined in the surface sediments. The application of a model for the activity ofChironomus anthracinus based on biomass, oxygen consumption and temperature improved the model in the spring period. The downwards transport of easy-degradable surface sediments reduced the average release of sedimentary phosphorus from 12 mg P · m−2 · day−1 to 11 mg P · M−2 · day−1. The introduction of a similar model for the other important burrowing species in L. Esrom,Potamothrix hammoniensis, lowered the objective function to 1.37 and increased the average release to 12.5 mg P · m−2 · day−1. The minor role of bioturbation in sediment processes is discussed.
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  • 94
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    Hydrobiologia 91-92 (1982), S. 241-252 
    ISSN: 1573-5117
    Keywords: pollution ; rivers ; transport ; calculation ; phosphorus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Human activities generate many pollutants from different land uses. These pollutants include nutrients (e.g., phosphorus and nitrogen), toxic substances (e.g., heavy metals and pesticides), and other substances (e.g., chlorides and salts). These materials often enter a river at some upstream point and are transported downstream by the flowing water. Many substances are transported both during storms and during normal river flow and often the major portion of the transport occurs during the storms. This paper considers the quantification of transport primarily during storms. First, the characteristics of storm transport are discussed. Then, a calculation method for estimating the distance of travel for sediment related materials is presented. Third, a technique to estimate the amount of a given chemical passing a point in a stream over a specified period of time is presented. The last part of this paper contains a technique for tracing the movement of substances through a river network. In particular, this procedure yields information as to the source of given pollutants over the entire Storm period.
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  • 95
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    Hydrobiologia 91-92 (1982), S. 549-558 
    ISSN: 1573-5117
    Keywords: lake restoration ; sediment dredging ; nitrogen ; phosphorus ; algal assays
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract An increased load of domestic wastewater to Lake Trehörningen induced oxygen-poor water conditions and the development of a reduced sulphide-rich sediment layer. Severely polluted, the lake did not recover, even after advanced wastewater treatment and sewage diversion. Restoration measures with suction dredging and macrophyte elimination were applied in 1975 and 1976. The loose topmost sediment was pumped into an embanked and overgrown bay which was used as a settling pond. The activities also included a restoration of the shorelines. This project is the largest restoration programme carried out in Sweden on a single lake, corresponding to a cost of about US $2 000 000. The restoration of Lake Trehörningen was followed by a highly intensive research programme which included water chemistry and algal assays. The concentrations of phosphate and total phosphorus decreased by 73 and 50% respectively, as summer average values, two years after the restoration. However, the concentrations of phosphorus are still too high to permit this element to act as a prime algal growth-limiting nutrient. The algal biomass has also remained at the same magnitude as before the restoration. Nitrate-N concentrations showed a tenfold increase, based on average values for the summer period. However, based on the results of the algal assays, a rapid and marked response was obvious, with a drastic decline in the algal growth potential. In addition, the water quality of the tributaries was frequently of an objectionable character (0.1–0.2 g P m−3). The nutrient loading from these sources exceeds the critical level for the lake, and measures have now been carried out to treat all the inflowing waters for the removal of phosphorus.
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  • 96
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    Hydrobiologia 91-92 (1982), S. 697-700 
    ISSN: 1573-5117
    Keywords: sediments ; Mössbauer spectroscopy ; iron ; phosphorus ; geochemistry ; analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Iron compounds of phosphorus form a large part of the phosphorus bound in sediments. Mössbauer spectroscopy is a technique that enables us to study, directly, chemical forms of iron in solid samples. Mössbauer spectroscopy allowed us to check, directly, the selectivity of the extraction scheme for soil phosphorus proposed by Chang & Jackson (1957), but only as far as the iron compounds are concerned. It appears that selectivity of the extraction method leaves much to be desired.
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  • 97
    ISSN: 1573-5117
    Keywords: microbial metabolism ; phosphorus ; sediments ; oligotrophic lake
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Rapid microbial metabolism and a large phosphorus uptake potential were observed in surface sediments of Lake George, New York. This sediment (termed the flocculent layer) also exhibited a phosphorus limited condition and a large reservoir of inorganic phosphorus associated with humic substances. These observations suggest that the empirically observed phosphorus retention in oligotrophic lake sediments may be promoted by a rapid cycling of phosphorus between microflora and its associated organic matter.
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  • 98
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    Hydrobiologia 91-92 (1982), S. 489-490 
    ISSN: 1573-5117
    Keywords: laboratory experiments ; sediment types ; phosphorus ; silicon ; sediment-water exchange
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Extended abstract Lake Grevelingen is a brackish water lake in the SW Netherlands. The lake has an area of 108 km2, a mean depth of 5.3 m (maximum 48 m), a mean chlorinity of 13 to 16%0 Cl−, and a hydraulic residence time of about 8 years. Mass budget studies have shown a consistent seasonal pattern in the phosphorus sediment-water exchange in Lake Grevelingen (Kelderman 1980). From May to August a P mobilization from the sediment takes place, estimated atca. 12.5 mg P · m−2 · day−1. The sediment accumulatesca. 5.5 mg P · m−2 · day−1 during the rest of the year. Temperature may be an important factor in establishing this pattern. Sediment-water exchange was studied by means of laboratory experiments under specified conditions. Sediment cores (30 cm depth, 11 cm diameter) were taken at four stations in the lake, with sediment types varying from medium- to muddy sand (Fig. 1). The cores with overlying water (ca. 21) were placed in the dark at 5 °C in thermostatically controlled water baths. After a week's incubation time the temperature was slowly raised, such that after three weeks eight cores (four sediment types, duplicates) were at 5 °C, eight were at 10 °C, eight at 15 °C and eight at 20 °C. The same procedure was applied to the four control cores, containing lake water.
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  • 99
    ISSN: 1573-5117
    Keywords: phosphorus ; nutrient cycling ; stratification ; epilimnion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Phosphorus regeneration from lake sediments, and subsequent migration to trophogenic surface water, significantly contributes to the lake nutrient budgets and algal bloom conditions in some lake types. Decomposition of organic matter in deep water and sediments results in the accumulation of regenerated nutrients, alternate electron acceptors (reduced products of anaerobic respiration = COD), carbon dioxide, and depletion of dissolved oxygen (electron acceptor in aerobic respiration). Thermal stratification creates spatial segregation of trophogenic and tropholytic environments in the lake, resulting in gradients between sediments, hypolimnion, and the epilimnion. Exchange of oxygen, nutrients, and reduced alternate electron acceptors between the hypolimnion and epilimnion affects the productivity of a lake. Secchi depth, temperature, and dissolved oxygen profiles were determined twice each week from May 1980 to October 1980 at each of five lake stations. Nutrient concentration profiles, including total soluble and total phosphorus, ammonium-N, nitrate, soluble Kjeldahl, and total Kjeldahl nitrogen were determined twice each month. Epilimnetic algal samples were collected twice each week using Kemmerer and water column ‘straw’ amplers. Cell counts of total, green, bluegreen, and diatom algae groups were made. Three methods were used to describe hypolimnetic-epilimnetic exchange, including coefficients of eddy diffusion (based on lake heat budget), a graphical method of defining thermocline location, and relative thermal resistance to mixing (RTRM, based on density differences). All three methods yeilded comparable estimates of net seasonal transport. The graphical and RTRM methods described events occurring at shorter intervals (greater resolution). We find general agreement between the three methods of describing hypolimnetic-epilimnetic transport. The frequency of sampling resulted in increased resolution of thermal profiles (in time), allowing accurate estimation of short-term nutrient flux into epilimnetic waters. An algal bloom event occurred 5 to 12 days following erosion of the top of the metalimnion to below the aerobic-anaerobic interface. The lag time to peak algal concentration, following such events, decreased through the summer (June = 12 days, September = 5 days)
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  • 100
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    Hydrobiologia 91-92 (1982), S. 697-700 
    ISSN: 1573-5117
    Keywords: sediments ; Mössbauer spectroscopy ; iron ; phosphorus ; geochemistry ; analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Iron compounds of phosphorus form a large part of the phosphorus bound in sediments. Mössbauer spectroscopy is a technique that enables us to study, directly, chemical forms of iron in solid samples. Mössbauer spectroscopy allowed us to check, directly, the selectivity of the extraction scheme for soil phosphorus proposed by Chang & Jackson (1957), but only as far as the iron compounds are concerned. It appears that selectivity of the extraction method leaves much to be desired.
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