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  • 1
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    Mathematical programming 58 (1993), S. 243-255 
    ISSN: 1436-4646
    Keywords: Linear programming ; interior point algorithm ; primal—dual potential function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper is concerned with selection of theρ-parameter in the primal—dual potential reduction algorithm for linear programming. Chosen from [n + $$\sqrt n $$ , ∞), the level ofρ determines the relative importance placed on the centering vs. the Newton directions. Intuitively, it would seem that as the iterate drifts away from the central path towards the boundary of the positive orthant,ρ must be set close ton + $$\sqrt n $$ . This increases the relative importance of the centering direction and thus helps to ensure polynomial convergence. In this paper, we show that this is unnecessary. We find for any iterate thatρ can be sometimes chosen in a wide range [n + $$\sqrt n $$ , ∞) while still guaranteeing the currently best convergence rate of O( $$\sqrt n $$ L) iterations. This finding is encouraging since in practice large values ofρ have resulted in fast convergence rates. Our finding partially complements the recent result of Zhang, Tapia and Dennis (1990) concerning the local convergence rate of the algorithm.
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  • 2
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    Mathematical programming 59 (1993), S. 133-150 
    ISSN: 1436-4646
    Keywords: Linear programming ; interior-point methods ; combined phase I—phase II
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper describes an affine potential reduction algorithm for linear programming that simultaneously seeks feasibility and optimality. The algorithm is closely related to a similar method of Anstreicher. The new features are that we use a two-dimensional programming problem to derive better lower bounds than Anstreicher, that our direction-finding subproblem treats phase I and phase II more symmetrically, and that we do not need an initial lower bound. Our method also allows for the generation of a feasible solution (so that phase I is terminated) during the course of the iterations, and we describe two ways to encourage this behavior.
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  • 3
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    Mathematical programming 59 (1993), S. 151-162 
    ISSN: 1436-4646
    Keywords: Linear programming ; primal and dual ; superlinear and quadratic convergence ; polynomiality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Recently, Ye, Tapia and Zhang (1991) demonstrated that Mizuno—Todd—Ye's predictor—corrector interior-point algorithm for linear programming maintains the O( $$\sqrt n $$ L)-iteration complexity while exhibiting superlinear convergence of the duality gap to zero under the assumption that the iteration sequence converges, and quadratic convergence of the duality gap to zero under the assumption of nondegeneracy. In this paper we establish the quadratic convergence result without any assumption concerning the convergence of the iteration sequence or nondegeneracy. This surprising result, to our knowledge, is the first instance of a demonstration of polynomiality and superlinear (or quadratic) convergence for an interior-point algorithm which does not assume the convergence of the iteration sequence or nondegeneracy.
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  • 4
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    Mathematical programming 59 (1993), S. 413-420 
    ISSN: 1436-4646
    Keywords: Linear programming ; prize collecting ; rounding fractional solutions ; traveling salesman problem ; worst-case analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We study the version of the prize collecting traveling salesman problem, where the objective is to find a tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. We present an approximation algorithm with constant bound. The algorithm is based on Christofides' algorithm for the traveling salesman problem as well as a method to round fractional solutions of a linear programming relaxation to integers, feasible for the original problem.
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  • 5
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    Mathematical programming 62 (1993), S. 517-535 
    ISSN: 1436-4646
    Keywords: Linear programming ; Karmarkar's algorithm ; Projective algorithm ; Standard form
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In a recent paper, Shaw and Goldfarb show that a version of the standard form projective algorithm can achieve $$O\left( {\sqrt {nL} } \right)$$ step complexity, as opposed to the O(nL) step complexity originally demonstrated for the algorithm. The analysis of Shaw and Goldfarb shows that the algorithm, using a constant, fixed steplength, approximately follows the central trajectory. In this paper we show that simple modifications of the projective algorithm obtain the same complexity improvement, while permitting a linesearch of the potential function on each step. An essential component is the addition of a single constraint, motivated by Shaw and Goldfarb's analysis, which makes the standard form algorithm strictly monotone in the true objective.
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  • 6
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    European journal of nutrition 32 (1993), S. 79-92 
    ISSN: 1436-6215
    Keywords: Lineare Programmierung ; Ernährungsoptimierung ; Privathaushalt ; Optimierungsmodelle ; Linear programming ; nutrition optimization ; private households ; optimization models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary Members of private households have different nutrient requirements. In general, they eat the same dishes in different quantities. The menu plan is admissible if it corresponds to the recommended dietary allowances. It is acceptable if it meets the eating habits. It is optimal if it meets the constraints mentioned and best reaches an objective. It is the aim of this paper to describe models for the determination of optimal nutrition and to evaluate them with respect to their suitability for solving decision problems in private, multi-person-households. The fewer the model-intern restrictions in the variability of quantities of food stuffs, kind and/or quantities of dishes, the better are the “optimal” solutions that are found with the model. A simultaneous determination of kind and quantity of dishes reaches the model purpose better than a stepwise determination. This is shown in an example problem.
    Notes: Zusammenfassung In privaten Haushalten haben die Mitglieder unterschiedliche Nährstoffbedarfe. Sie verzehren im allgemeinen gleiche Speisen in unterschiedlichen Mengen. Der Speisenplan ist bedarfsgerecht, wenn er den Empfehlungen für die Nährstoffzufuhr der einzelnen Personen entspricht. Er ist akzeptabel, wenn er den Verzehrgewohnheiten der Personen entspricht. Er ist optimal, wenn er die genannten Bedingungen einhält und zusätzlich ein gegebenes Ziel bestmöglich erreicht. Die Bestimmung eines optimalen Speisenplans erfolgt anhand von Modellen. Es ist das Ziel des Beitrags, verschiedene Modelle zur Bestimmung einer optimalen Ernährung darzustellen und im Hinblick auf ihre Eignung zur Anwendung auf Entscheidungsprobleme im privaten Mehrpersonenhaushalt zu beurteilen. Je geringer die modellinterne Einschränkung in der Variabilität von Lebensmittelmengen, Speisenarten und/oder Speisenmengen, desto bessere ‚optimale‘ Lösungen können mit dem Modell gefunden werden. Eine simultane Bestimmung von Speisenart und -menge erfüllt den Modellzweck besser als eine sukzessive Bestimmung. Dies konnte anhand eines Beispielproblems gezeigt werden.
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  • 7
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    Mathematical programming 59 (1993), S. 23-31 
    ISSN: 1436-4646
    Keywords: Linear programming ; duality theorem ; unimodular ; totally unimodular ; interior point methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we consider a linear programming problem with the underlying matrix unimodular, and the other data integer. Given arbitrary near optimum feasible solutions to the primal and the dual problems, we obtain conditions under which statements can be made about the value of certain variables in optimal vertices. Such results have applications to the problem of determining the stopping criterion in interior point methods like the primal—dual affine scaling method and the path following methods for linear programming.
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  • 8
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    Annals of operations research 46-47 (1993), S. 409-430 
    ISSN: 1572-9338
    Keywords: Linear programming ; Phase I ; nonlinear programming ; least squares ; quadratic programming ; strict improvement ; degeneracy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Instead of trying to recognize and avoid degenerate steps in the simplex method (as some variants do), we have developed a new Phase I algorithm that is impervious to degeneracy. The new algorithm solves a non-negative least-squares problem in order to find a Phase I solution. In each iteration, a simple two-variable least-squares subproblem is used to select an incoming column to augment a set of independent columns (called “basic”) to get a strictly better fit to the right-hand side. Although this is analogous in many ways to the simplex method, it can be proved that strict improvement is attained at each iteration, even in the presence of degeneracy. Thus cycling cannot occur, and convergence is guaranteed. This algorithm is closely related to a number of existing algorithms proposed for non-negative least-squares and quadratic programs. When used on the 30 smallest NETLIB linear programming test problems, the computational results for the new Phase I algorithm were almost 3.5 times faster than a particular implementation of the simplex method; on some problems, it was over 10 times faster. Best results were generally seen on the more degenerate problems.
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  • 9
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    Annals of operations research 46-47 (1993), S. 107-138 
    ISSN: 1572-9338
    Keywords: Linear programming ; interior point methods ; degeneracy ; polynomial algorithms ; global and local convergence ; basis recovery ; numerical performance ; sensitivity analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The publication of Karmarkar's paper has resulted in intense research activity into Interior Point Methods (IPMs) for linear programming. Degeneracy is present in most real-life problems and has always been an important issue in linear programming, especially in the Simplex method. Degeneracy is also an important issue in IPMs. However, the difficulties are different in the two methods. In this paper, we survey the various theoretical and practical issues related to degeneracy in IPMs for linear programming. We survey results, which, for the most part, have already appeared in the literature. Roughly speaking, we shall deal with the effect of degeneracy on the following: the convergence of IPMs, the trajectories followed by the algorithms, numerical performance, and finding basic solutions.
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  • 10
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    Annals of operations research 46-47 (1993), S. 235-248 
    ISSN: 1572-9338
    Keywords: Linear programming ; generalized networks ; simplex method ; degeneracy ; lexicography ; cycling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper introduces an analytical approach for studying lexicography in generalized network problems. The equations obtained can help us to understand and to extend the existing theory. First, it is verified that all nonzero elements have the same sign in each row vector of a basis inverse for a generalized network (GN) problem with positive multipliers. However, this property does not necessarily hold when there exist negative multipliers. Second, we developed a strategy to select the dropping arc in the GN simplex algorithm when addressing GN problems with positive andnegative multipliers. This strategy is also based on lexicography and requires performing some comparisons. However, the values to be compared are already known since they can be obtained as a by-product of the calculations necessary to compute the basis representation of the entering arc. Consequently, the computational effort per pivot step isO(n) in the worst case. This worst case effort is the same as that required by the strongly convergent rules for selecting the dropping arc in the method of strong convergence.
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    Annals of operations research 46-47 (1993), S. 203-233 
    ISSN: 1572-9338
    Keywords: Linear programming ; simplex method ; pivot rules ; cycling ; recursion ; minimal index rule ; parametric programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The purpose of this paper is to discuss the various pivot rules of the simplex method and its variants that have been developed in the last two decades, starting from the appearance of the minimal index rule of Bland. We are mainly concerned with finiteness properties of simplex type pivot rules. Well known classical results concerning the simplex method are not considered in this survey, but the connection between the new pivot methods and the classical ones, if there is any, is discussed. In this paper we discuss three classes of recently developed pivot rules for linear programming. The first and largest class is the class of essentially combinatorial pivot rules including minimal index type rules and recursive rules. These rules only use labeling and signs of the variables. The second class contains those pivot rules which can actually be considered as variants or generalizations or specializations of Lemke's method, and so they are closely related to parametric programming. The last class has the common feature that the rules all have close connections to certain interior point methods. Finally, we mention some open problems for future research.
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  • 12
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    Annals of operations research 46-47 (1993), S. 431-442 
    ISSN: 1572-9338
    Keywords: Linear programming ; degeneracy ; network simplex algorithm ; pivoting ; minimal cost network flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A characteristic feature of the primal network simplex algorithm (NSA) is that it usually makes a large number of degenerate iterations. Though cycling and even stalling can be avoided by recently introduced pivot rules for NSA, the practical efficiency of these rules is not known yet. For the case when the simplex algorithm is used to solve the continuous linear programming (LP) problem there exists a practical anti-cycling procedure that proved to be efficient. It is based on an expanding relaxation of the individual bound on the variables. In this paper we discuss the adaptation of this method to NSA, taking advantage of the special integer nature of network problems. We also give an account of our experience with these ideas as they are experimentally implemented in the MINET network LP solver. Reductions of CPU time have been achieved on a smaller set of specially structured real-life problems.
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  • 13
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    BIT 33 (1993), S. 512-528 
    ISSN: 1572-9125
    Keywords: 65D10 ; 65D07 ; 41A15 ; 41A29 ; Data fitting ; smoothing ; shape preservation ; constrained least squares approximation ; polynomial splines ; B-splines
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An efficient algorithm for computing a smoothing polynomial splines under inequality constraints on derivatives is introduced where both order and breakpoints ofs can be prescribed arbitrarily. By using the B-spline representation ofs, the original semi-infinite constraints are replaced by stronger finite ones, leading to a least squares problem with linear inequality constraints. Then these constraints are transformed into simple box constraints by an appropriate substitution of variables so that efficient standard techniques for solving such problems can be applied. Moreover, the smoothing term commonly used is replaced by a cheaply computable approximation. All matrix transformations are realized by numerically stable Givens rotations, and the band structure of the problem is exploited as far as possible.
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  • 14
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    Advances in computational mathematics 1 (1993), S. 1-37 
    ISSN: 1572-9044
    Keywords: Refinement equations ; up-function ; entire functions of exponential type ; subdivision algorithms ; cube spline ; (AMS) 34K99 ; 41A15 ; 41A25 ; 41A63
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the study of a general class of functional equations covering as special cases the relation which defines theup-function as well as equations which arise in multiresolution analysis for wavelet construction. We discuss various basic properties of solutions to these functional equations such as regularity, polynomial containment within the space spanned by their integer shifts and their computability by subdivision algorithms.
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  • 15
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    Numerische Mathematik 66 (1993), S. 123-137 
    ISSN: 0945-3245
    Keywords: 41A55 ; 41A15 ; 41A05 ; 65D32 ; 65D30 ; 65D07 ; 65D05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The Gregory rule is a well-known example in numerical quadrature of a trapezoidal rule with endpoint corrections of a given order. In the literature, the methods of constructing the Gregory rule have, in contrast to Newton-Cotes quadrature,not been based on the integration of an interpolant. In this paper, after first characterizing an even-order Gregory interpolant by means of a generalized Lagrange interpolation operator, we proceed to explicitly construct such an interpolant by employing results from nodal spline interpolation, as established in recent work by the author and C.H. Rohwer. Nonoptimal order error estimates for the Gregory rule of even order are then easily obtained.
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  • 16
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    Trees 8 (1993), S. 99-103 
    ISSN: 1432-2285
    Keywords: Robinia pseudoacacia L. ; Hydrogen uptake ; Hydrogenase ; Nitrogen fixation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Hydrogen uptake is thought to increase the efficiency of nitrogen fixation by recycling H2 produced by nitrogenase that would otherwise be lost by diffusion. Here we demonstrate the capacity of eight Rhizobium strains to take up molecular hydrogen. Uptake by nodule homogenates from Robinia pseudoacacia was measured amperometrically under nitrogenase repression. Markedly lower activities were found than in soybean nodules. In addition hydrogenase activity was detected by the ability of bacteroids to reduce methylene blue in the presence of hydrogen. It was demonstrated that hydrogenase structural genes are present in the black locust symbiont, Rhizobium sp. strain R1, using hybridization with a plasmid, which contained hydrogenase genes from R. leguminosarum bv. viceae.
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    Mathematical programming 59 (1993), S. 345-360 
    ISSN: 1436-4646
    Keywords: Linear programming ; interior point method ; active set strategy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We will present a potential reduction method for linear programming where only the constraints with relatively small dual slacks—termed “active constraints”—will be taken into account to form the ellipsoid constraint at each iteration of the process. The algorithm converges to the optimal feasible solution in O( $$\sqrt n $$ L) iterations with the same polynomial bound as in the full constraints case, wheren is the number of variables andL is the data length. If a small portion of the constraints is active near the optimal solution, the computational cost to find the next direction of movement in one iteration may be considerably reduced by the proposed strategy.
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  • 18
    ISSN: 1436-4646
    Keywords: Linear programming ; quadratic programming ; convex programming ; randomized algorithms ; fixed dimension optimization problems ; complexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We extend Clarkson's randomized algorithm for linear programming to a general scheme for solving convex optimization problems. The scheme can be used to speed up existing algorithms on problems which have many more constraints than variables. In particular, we give a randomized algorithm for solving convex quadratic and linear programs, which uses that scheme together with a variant of Karmarkar's interior point method. For problems withn constraints,d variables, and input lengthL, ifn = Ω(d 2), the expected total number of major Karmarkar's iterations is O(d 2(logn)L), compared to the best known deterministic bound of O( $$\sqrt n$$ L). We also present several other results which follow from the general scheme.
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  • 19
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    Mathematical programming 62 (1993), S. 41-67 
    ISSN: 1436-4646
    Keywords: Linear programming ; Dantzig—Wolfe decomposition ; large-scale systems ; parallel processing ; hypercube architecture
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Decomposition algorithms for block-angular linear programs give rise to a natural, coarse-grained parallelism that can be exploited by processing the subproblems concurrently within a distributed-memory environment. The parallel efficiency of the distributed approach, however, is critically dependent on the duration of the inherently serial master phase relative to that of the bottleneck subproblem. This paper investigates strategies for improving efficiency in distributed Dantzig—Wolfe decomposition by better balancing the load between the master and subproblem processors. We report computational experience on an Intel iPSC/2 hypercube multiprocessor with test problems having dimensions up to about 30 000 rows, 87 000 columns, and 200 coupling constraints.
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    Mathematical programming 62 (1993), S. 15-39 
    ISSN: 1436-4646
    Keywords: Linear programming ; interior-point methods ; symmetric indefinite systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe an implementation of a primal—dual path following method for linear programming that solves symmetric indefinite “augmented” systems directly by Bunch—Parlett factorization, rather than reducing these systems to the positive definite “normal equations” that are solved by Cholesky factorization in many existing implementations. The augmented system approach is seen to avoid difficulties of numerical instability and inefficiency associated with free variables and with dense columns in the normal equations approach. Solving the indefinite systems does incur an extra overhead, whose median is about 40% in our tests; but the augmented system approach proves to be faster for a minority of cases in which the normal equations have relatively dense Cholesky factors. A detailed analysis shows that the augmented system factorization is reliable over a fairly large range of the parameter settings that control the tradeoff between sparsity and numerical stability.
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    Mathematical programming 62 (1993), S. 119-131 
    ISSN: 1436-4646
    Keywords: Linear programming ; interior point algorithm ; complexity ; potential function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We propose a potential-reduction algorithm which always uses the primal—dual affine-scaling direction as a search direction. We choose a step size at each iteration of the algorithm such that the potential function does not increase, so that we can take a longer step size than the minimizing point of the potential function. We show that the algorithm is polynomial-time bounded. We also propose a low-complexity algorithm, in which the centering direction is used whenever an iterate is far from the path of centers.
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    Mathematical programming 62 (1993), S. 497-515 
    ISSN: 1436-4646
    Keywords: Linear programming ; primal—dual methods ; optimal face ; strict complementarity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We study the problem of finding a point in the relative interior of the optimal face of a linear program. We prove that in the worst case such a point can be obtained in O(n 3 L) arithmetic operations. This complexity is the same as the complexity for solving a linear program. We also show how to find such a point in practice. We report and discuss computational results obtained for the linear programming problems in the NETLIB test set.
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    Algorithmica 9 (1993), S. 64-83 
    ISSN: 1432-0541
    Keywords: Linear programming ; Interior-point methods ; Projective methods ; Combined phase 1-phase 2
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We compare the projective methods for linear programming due to de Ghellinck and Vial, Anstreicher, Todd, and Fraley. These algorithms have the feature that they approach feasibility and optimality simultaneously, rather than requiring an initial feasible point. We compare the directions used in these methods and the lower-bound updates employed. In many cases the directions coincide and two of the lower-bound updates give the same result. It appears that Todd's direction and Fraley's lower-bound update have slight advantages, and this is borne out in limited computational testing.
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  • 24
    ISSN: 1432-0541
    Keywords: Linear programming ; Karmarkar's algorithm ; Potential function ; Primal-dual, Modified method ; Rank-one updates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider partial updating in Kojima, Mizuno, and Yoshise's primal-dual potential reduction algorithm for linear programming. We use a simple safeguard condition to control the number of updates incurred on combined primal-dual steps. Our analysis allows for unequal steplengths in the primal and dual variables, which appears to be a computationally significant factor for primal-dual methods. The safeguard we use is a primal-dual Goldstein-Armijo condition, modified to deal with the unequal primal and dual steplengths.
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    Numerische Mathematik 65 (1993), S. 63-75 
    ISSN: 0945-3245
    Keywords: 41A15 ; 65DO5 ; 65D15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We give a complete characterization of the Hermite interpolation problem by periodic splines with Birkhoff knots. As a dual result we derive the characterization of the Birkhoff interpolation by periodic splines with multiple knots.
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    Numerische Mathematik 66 (1993), S. 281-294 
    ISSN: 0945-3245
    Keywords: 41A15 ; 60F15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The purpose of this paper is to study the convergence of smoothingD m -splines relative to sets of data perturbed by a random noise. Conditions of almost sure convergence and error estimates are given.
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    Constructive approximation 9 (1993), S. 123-166 
    ISSN: 1432-0940
    Keywords: Primary 41A63 ; 46C99 ; Secondary 41A30 ; 41A15 ; 42B99 ; 46E20 ; Wavelets ; Multiresolution ; Shift-invariant spaces ; Box splines
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new approach for the construction of wavelets and prewavelets onR d from multiresolution is presented. The method uses only properties of shift-invariant spaces and orthogonal projectors fromL 2(R d ) onto these spaces, and requires neither decay nor stability of the scaling function. Furthermore, this approach allows a simple derivation of previous, as well as new, constructions of wavelets, and leads to a complete resolution of questions concerning the nature of the intersection and the union of a scale of spaces to be used in a multiresolution.
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    Constructive approximation 9 (1993), S. 191-208 
    ISSN: 1432-0940
    Keywords: Primary 28C20 ; 41A15 ; 46E30 ; 60J65 ; Secondary 60E15 ; 62J10 ; Wiener measure ; Brownian motion ; Spline approximation ; Orthonormal spline system ; Franklin system ; Orlicz spaces ; Hölder classes ; Covariance ; Correlation ; Gaussian vectors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract There are three results proved in this paper. The first one characterizes the Hölder classes in Orlicz spaces by the coefficients of the orthogonal spline expansions of the Franklin type. The second one gives a sharp estimate for the correlation of two random variables obtained as a composition of two Borel functions with the components of a given two-dimensional Gaussian vector. The third one is obtained with the help of the first two and it states that the Wiener measure is concentrated on the Banach space of Hölder functions with exponent 1/2 but in the norm of the Orlicz spaceL M * withM(t)=expt(t 2)−1.
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    Constructive approximation 9 (1993), S. 209-236 
    ISSN: 1432-0940
    Keywords: Primary 41A63 ; 46C99 ; Secondary 41A30 ; 41A15 ; 42B99 ; 46E20 ; Courant interpolating function ; Linear splines ; Hexagonal filter banks ; Biorthogonal wavelets ; multiresolution analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study a class of subband coding schemes allowing perfect reconstruction for a bidimensional signal sampled on the hexagonal grid. From these schemes we construct biorthogonal wavelet bases ofL 2(R 2) which are compactly supported and such that the sets of generating functionsψ 1,ψ 2,ψ 3 for the synthesis and $$\tilde \psi _1 , \tilde \psi _2 , \tilde \psi _3 ,$$ for the analysis, as well as the scaling functions φ and $$\tilde \varphi $$ , are globally invariant by a rotation of 2π/3. We focus on the particular case of linear splines and we discuss how to obtain a higher regularity. We finally present the possibilities of sharp angular frequency resolution provided by these new bases.
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    Constructive approximation 9 (1993), S. 263-281 
    ISSN: 1432-0940
    Keywords: 15A23 ; 15A24 ; 39B42 ; 41A15 ; 42C15 ; 47A62 ; Splines ; Wavelets ; Matrix equations ; Hurwitz matrices ; Toeplitz matrices ; Two-slanted matrices ; Matrix factorization ; Total positivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Given two function spacesV 0,V 1 with compactly supported basis functionsC i, Fi, i∈Z, respectively, such thatC i can be written as a finite linear combination of theF i's, we study the problem of decomposingV 1 into a direct sum ofV 0 and some subspaceW ofV 1 in such a way thatW is spanned by compactly supported functions and that eachF i can be written as a finite linear combination of the basis functions inV 0 andW. The problem of finding such locally finite decompositions is shown to be equivalent to solving certain matrix equations involving two-slanted matrices. These relations may be reinterpreted in terms of banded matrices possessing banded inverses. Our approach to solving the matrix equations is based on factorization techniques which work under certain conditions on minors. In particular, we apply these results to univariate splines with arbitrary knot sequences.
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    Constructive approximation 9 (1993), S. 373-389 
    ISSN: 1432-0940
    Keywords: 41A05 ; 41A15 ; 41A20 ; 65D05 ; 65D07 ; 65D17 ; 68U07 ; Geometric rational curve interpolation ; Shape preservation ; Convexity ; Parametric splines ; Conics ; Approximation order
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Five points in general position inR 2 always lie on a unique conic, and three points plus two tangents also have a unique interpolating conic, the type of which depends on the data. These well-known facts from projective geometry are generalized: an odd number 2n+1≥5 of points inR 2, if they can be interpolated at all by a smooth curve with nonvanishing curvature, will have a uniqueGC 2 interpolant consisting of pieces of conics of varying type. This interpolation process reproduces conics of arbitrary type and preserves strict convexity. Under weak additional assumptions its approximation order is ϑ(h 5), whereh is the maximal distance of adjacent data pointsf(t i ) sampled from a smooth and regular planar curvef with nonvanishing curvature. Two algorithms for the construction of the interpolant are suggested, and some examples are presented.
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    Constructive approximation 9 (1993), S. 407-433 
    ISSN: 1432-0940
    Keywords: 41A15 ; 41A25 ; 41A30 ; Quasi-interpolation ; Thin-plate spline ; Radial basis functions ; Order of convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Quasi-interpolation is one method of generating approximations from a space of translates of dilates of a single function ψ. This method has been applied widely to approximation by radial basis functions. However, such analysis has most often been performed in the setting of an infinite uniform grid of centers. In this paper we develop general error bounds for approximation by quasiinterpolation on ann-cube. The quasi-interpolant analyzed involves a finite number, growing ash −n , of translates of dilates of the function ψ, and a bounded number of edge functions. The centers of the translates of dilates of ψ form a uniformly spaced grid within the cube. These error bounds are then applied to approximation by thin-plate splines on a square. The result is an O(ω(f, [-1,1]2,h)) error bound for approximation by thin-plate splines supplemented with eight arctan functions.
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    Biology and fertility of soils 15 (1993), S. 35-38 
    ISSN: 1432-0789
    Keywords: Nitrogen fixation ; Eucalyptus saligna ; Albizia falcataria ; Pontoscolex corethrurus ; Litterfall
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Tree species differ in the quantity and quality of litter produced, and these differences may significantly affect ecosystem structure and function. I examined the importance of tree species in determining earthworm densities in replicated stands of Eucalyptus saligna Sm. and Albizia falcataria (L.) Fosberg, and in mixed stands (25% albizia and 75% eucalyptus). Mean earthworm densities ranged from 92 m-2 in the pure eucalyptus, to 281 m-2 in the mixture, and a maximum of 469 m-2 in the pure albizia stands. Only two earthworm species were present, Pontoscolex corethrurus and Amynthas gracilis. Leaf biomass on the forest floor was highest in the pure eucalyptus and lowest in the pure albizia stands, whereas the annual fine litterfall production was lowest in the pure eucalyptus and highest in the albizia stands. The N content of fine litterfall was correlated positively with earthworm density, and the fine litterfall biomass: N ratio was correlated negatively with earthworm density. Greater leaf biomass on the forest floor under eucalyptus stands despite lower rates of litterfall suggests that litter quality, rather than litter quantity, was primarily responsible for the greater earthworm density in the albizia stands. Some biogeochemical effects of tree species in the tropics may be mediated through effects on earthworm populations.
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    Biology and fertility of soils 15 (1993), S. 73-78 
    ISSN: 1432-0789
    Keywords: Firewood crops ; Green-leaf manure ; Macronutrients ; Nodulation ; Nitrogen fixation ; Sesbania spp. ; Acetylen reduction assay ; ARA
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary In three field trials conducted during the summer season of 1986, 1987 and 1989 in an alkaline soil, 17 accessions of annual Sesbania spp. were evaluated for nodulation, N2 fixation (acetylene reduction assay), dry weight of roots and shoots, woody biomass production, and nutrient uptake. At 50 days after sowing all the accessions were effectively nodulated (average 36.4 root nodules plant-1) with a high nodule score (3.4). There was a lot of variation in nodule volume and mass and in acetylene reduction activity but not in N content (5.2%). N uptake in shoots, roots and nodules averaged 639, 31, and 13 mg plant-1, respectively, and much of the fixed N remained in shoots. Accessions of ‘S. cannabina’ complex performed better than others. S. rostrata had poor root nodulation but exhibited excellent stem nodulation (300 nodules plant-1) even though not inoculated with Azorhizobium sp. Average concentrations of N, P, K, S, Ca, and Mg in the shoots were high, at 3.2, 0.28, 1.5, 0.28, 1.5, and 0.4% respectively, and Na was low (0.15%), reflecting the usefulness of Sesbania spp. as an integrated biofertilizer source. Green matter production was 26.0 Mg ha-1 (5.9 Mg dry matter) and N uptake was 158 kg ha-1, 54 days after sowing. Average woody biomass of six accessions at maturity, 200 days after sowing, was high (19.9 Mg ha-1), showing its potential for shortterm firewood production. Total nutrient uptake for production of woody biomass (200 days of growth) was no more demanding than growing the plant to the green-manuring stage of 50–60 days' growth.
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    ISSN: 1432-0789
    Keywords: δ 15N ; Elevation ; Nitrogen fixation ; Non-nodulating ; Glycine max ; Soybeans ; Isolines
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Dissimilarities in soil N uptake between N2-fixing and reference non-N2-fixing plants can lead to inaccurate N2 fixation estimates by N difference and 15N enrichment methods. The natural 15N abundance (δ 15N) method relies on a stabilized soil 15N pool and may provide reliable estimates of N2 fixation. Estimates based on the δ 15N and differences in N yield of nodulating and non-nodulating isolines of soybean were compared in this study. Five soybeans from maturity groups 00, IV, VI, and VIII and their respective non-nodulating isolines were grown at three elevations differing in ambient temperature and soil N availability. Despite large differences in phenological development and N yield between the non-nodulating isolines, the δ 15N values measured on seeds were relatively constant within a site. The δ 15N method consistently produced lower N2 fixation estimates than the N difference method, but only in three of the 15 observations did they differ significantly. The average crop N derived from N2 fixation across sites and maturity groups was 81% by N difference compared to 71% by δ 15N. The magnitude of difference between the two methods increased with increasing proportions of N derived from N2 fixation. These differences between the two methods were not related to differences in total N across sites or genotypes. The low N2 fixation estimates based on δ 15N might indicate that the nodulating isolines had assimilated more soil N than the non-nodulating ones. A lower variance indicated that the estimates by N difference using non-nodulating isolines were more precise than those by δ 15N. Since the differences between the estimates were large only at high N2 fixation levels (low soil N availability), either method may be used in most situations when a non-nodulating isoline is used as the reference plant. The δ 15N method may have a comparative advantage over N difference and 15N enrichment methods in the absence of a suitable non-N2-fixing reference plant such as a non-nodulating isoline.
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    Biology and fertility of soils 15 (1993), S. 275-278 
    ISSN: 1432-0789
    Keywords: Peanuts ; Arachis hypogaea ; Continuous cropping ; Nitrogen fixation ; Bradyrhizobium spp. ; Effectiveness of rhizobia
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The objective of this study was to assess the number and effectiveness of peanut rhizobia in soils of the major peanut-growing areas of Thailand. Three cropping areas, (1) continuously cropped with peanuts, (2) continuously cropped with non-legumes, and (3) non-cultivated fields, were chosen in each region. Peanut rhizobia were found in the soil at 38 to 55 sites sampled. Cultivated fields with a peanut cultivation history contained (as estimated by most probable numbers) an average of 1.6×103 cells g-1 of soil. The numbers of peanut rhizobia in most of the fallow fields and some of the noncultivated shrub or forest locations were much the same as at the sites where Arachis hypogaea was cultivated. In contrast, there were no or few (28–46 cells g-1 soil) peanut rhizobia in the majority of fields continuously cultivated with sugarcane, cassava, corn, and pineapple. It appears that in these areas the indigenous peanut rhizobial populations are not adequate in number for a maximal nodulation of peanuts. A total of 343 Bradyrhizobium isolates were tested for effectiveness and were found to vary widely in their ability to fix N2. In some areas the majority of rhizobia were quite effective while in others they were less effective than the inoculum strain THA 205 recommended in Thailand.
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    Biology and fertility of soils 16 (1993), S. 299-301 
    ISSN: 1432-0789
    Keywords: A N value ; 15N ; Nitrogen fixation ; Glycine max ; Hordeum vulgare
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Pot experiments were conducted with two soils, from Rottenhaus and Seibersdorf in Austria, to ascertain whether the rate of fertilizer N application and the test crop would influence the amount of N available in the soil as assessed by the A-value method. 15N-labelled fertilizer was applied at rates of 10, 25, 40, 60, and 100 mg N kg-1 soil, corresponding approximately to 20, 50, 80, 120 and 200 kg N ha-1 respectively, and two crop species, barley (Hordeum vulgareL.) and non-nodulating soybean (Glycine max L.) were used to determine the soil A N value under the various fertilizer regimes. The results showed that the Rottenhaus soil had a higher A N value than the Seibersdorf soil, suggesting that the former was more fertile than the latter. The A N values of both soils were significantly affected by the level of N application. When grown in the same soil, the two test crops showed significantly different fertilizer use efficiency and per cent N derived from fertilizer when the rate of N application exceeded 20 kg ha-1. Thus, the A N value as determined by the two test crops differed significantly for the same soil when the rate of N application was greater than 20 kg/ha. The difference was greater when the soil fertility level was high. The dependence of the A N value on the level of N application and the species of crop seriously compromises the suitability of this method for determining plant-associated N2 fixation. Hence, considerable caution is required when using this method to estimate plant-associated N2 fixation.
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  • 38
    ISSN: 1432-0789
    Keywords: Nitrogen fixation ; Photosynthetic bacteria ; Stem nodules ; Aeschynomene scabra ; Sesbania rostrata ; Azorhizobium caulinodans ; Erythrobacter sp. ; Roseobacter denitrificans
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Bradyrhizobial strain BTAi 1 nodulates both stems and roots of Aeschynomene spp. Previous work has shown that it contains bacteriochlorophyll a and forms photosynthetic reaction centers, and has provided indirect evidence of photosynthesis by bacteroids within stem nodules. Here we report physiological and biochemical characteristics of BTAi 1 ex planta, which also suggest the presence of photosynthetic activity. Light-stimulated uptake of 14CO2 by BTAi 1 was detected at all stages of growth. Inhibitors of photosynthesis, 1,10-orthophenanthroline and 3-(3,4-dichlorophenyl)-1,1-dimethylurea (DCMU), and the uncoupler NH4Cl, immediately suppressed light-driven 14CO2 uptake and increased O2 uptake. BTAi 1 is strictly aerobic and was unable to grow without organic C even in the light; also, it was unable to grow chemoautotrophically in an atmosphere enriched with H2 and CO2. In micro-aerobic conditions, strain BTAi 1 expressed acetylene reducing activity ex planta in an N-free medium. The highest rates of light-stimulated 14CO2 uptake and acetylene-reducing activity occurred during the exponential and early stationary phases of growth. Acetylene-reducing rates at a low glucose concentration were increased following a light-dark cycle in comparison with continuous dark conditions.
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    Numerical algorithms 5 (1993), S. 71-81 
    ISSN: 1572-9265
    Keywords: Approximation order ; multivariate splines ; polynomial splines ; 41A15 ; 65D07
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We give an algorithm which computes the approximation order of spaces of periodic piece-wise polynomial functions, given the degree, the smoothness and tesselation. The algorithm consists of two steps. The first gives an upper bound and the second a lower bound on the approximation order. In all known cases the two bounds coincide.
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    Numerical algorithms 5 (1993), S. 591-601 
    ISSN: 1572-9265
    Keywords: Quadratic box splines in three variables ; isosurface sampling ; Boltzmann transport equation ; 41A15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Numerical approximation has played a valuable supporting role in VLSI device simulation. Examples include (1) tensor product variation diminishing splines for models of transistor charges and currents and (2) continuation to find a safe operating region avoiding avalanche breakdown. More recently, quadratic box splines in three variables have been studied for use in Monte Carlo solution of the Boltzmann transport equation. The bivariate Zwart-Powell element does not directly generalize, but another particular box spline is constructed.
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    Numerical algorithms 4 (1993), S. 323-337 
    ISSN: 1572-9265
    Keywords: Multivariate polynomials ; B-patch ; B-spline ; product ; tensor product ; conversion ; pyramidal algorithm ; de Casteljau algorithm ; blossom ; polar form ; 41A15 ; 65D07
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Products and tensor products of multivariate polynomials in B-patch form are viewed as linear combinations of higher degree B-patches. Univariate B-spline segments and certain regions of simplex splines are examples of B-patches. A recursive scheme for transforming tensor product B-patch representations into B-patch representations of more variables is presented. The scheme can also be applied for transforming ann-fold product of B-patch expansions into a B-patch expansion of higher degree. Degree raising formulas are obtained as special cases. The scheme calculates the blossom of the (tensor) product surface and generalizes the pyramidal recursive scheme for B-patches.
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    Numerical algorithms 5 (1993), S. 121-129 
    ISSN: 1572-9265
    Keywords: Surface splines ; scattered data interpolation ; incompressible fluid flow ; 41A05 ; 41A15 ; 41A29 ; 41A63 ; 65D05 ; 65D07 ; 65D25 ; 76B99 ; 76D99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We show how one may interpolate a vector-valued function in two or three dimensions, whose value is (wholly or partly) known at a sufficient (but not large) number of points disposed in almost any configuration, under the condition that the interpolating function has zero divergence. The technique is based on the theory of thin-plate splines. One may use a similar scheme in the case where the data consist of flux integrals (or other linear functionals) of the unknown function.
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    Numerical algorithms 5 (1993), S. 229-245 
    ISSN: 1572-9265
    Keywords: Stable decompositions ; periodic multiresolution analysis ; pseudodifferential equations ; preconditioning ; decompositions of refinable spaces ; matrix equations ; 41A65 ; 41A15 ; 15A12 ; 15A24 ; 65N40 ; 47G05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents a brief survey of several recent applications of multilevel techniques, in particular, in connection with the solution of periodic pseudodifferential equations. It is pointed out that these applications naturally lead to certain decompositions of refinable spaces which are induced by a class of linear projectors. Then recent results on the construction of such nonorthogonal wavelets are reviewed and extended to the particular needs of the present context.
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    Advances in computational mathematics 1 (1993), S. 109-126 
    ISSN: 1572-9044
    Keywords: Hilbert space ; commuting unitary operators ; Riesz basis ; wandering subspaces ; multiresolution approximation ; duality principle ; box splines ; 41A15 ; 42C15 ; 47B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let (U=U 1, ...,U d ) be an orderedd-tuple of distinct, pairwise commuting, unitary operators on a complex Hilbert space ℋ, and letX:={x 1, ...,x r } ⊂ ℋ such that $$U^{\mathbb{Z}^d } X: = \{ U_1^{n_1 } \ldots U_d^{n_d } x_j :(n_1 , \ldots ,n_d ) \in \mathbb{Z}^d ,j = 1, \ldots ,r\} $$ is a Riesz basis of the closed linear spanV 0 of $$U^{\mathbb{Z}^d } X$$ . Suppose there is unitary operatorD on ℋ such thatV 0 ⊂D V 0 =:V 1 andU n D=DU An for alln ∈ ℤ d , whereA is ad ×d matrix with integer entries and Δ := det(A) ≠ 0. Then there is a subset Λ inV 1, withr(Δ − 1) vectors, such that $$U^{\mathbb{Z}^d } (\Gamma )$$ is a Riesz basis ofW 0, the orthogonal complement ofV 0 inV 1. The resulting multiscale and decomposition relations can be expressed in a Fourier representation by one single equation, in terms of which the duality principle follows easily. These results are a consequence of an extension, to a set of commuting unitary operators, of Robertson's Theorems on wandering subspace for a single unitary operator [24]. Conditions are given in order that $$U^{\mathbb{Z}^d } (\Gamma )$$ is a Riesz basis ofW 0. They are used in the construction of a class of linear spline wavelets on a four-direction mesh.
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    Numerische Mathematik 47 (1985), S. 191-215 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 30B70 ; 40A15 ; 41A15 ; CR: G1.2
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For continued fractionsK(a n /1) the concept of limit region is discussed, and its use for obtaining modified truncation error estimates is illustrated on examples. A certain strategy for numerical computation of limit regions is presented and illustrated on examples.
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    Constructive approximation 1 (1985), S. 137-154 
    ISSN: 1432-0940
    Keywords: 41A15 ; 41A5 ; 41A65 ; Perfect splines ; Monosplines ; Extended totally positive kernels ; Monotone norms ; Optimal quadrature formulas ; Optimal interpolation ; N-widths ; Optimal spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Generalized monosplines of least norm are shown to exist and to determine optimal approximation processes such as numerical integration, interpolation and best approximating spaces. This extends various classical results related to monosplines and perfect splines, which are particular cases of generalized monosplines. The analysis here also provides for a unified treatment of the two classical classes of monosplines and perfect splines of least norm, and of their extremal properties.
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    Constructive approximation 1 (1985), S. 305-322 
    ISSN: 1432-0940
    Keywords: 41A15 ; Box spline ; Convergence rate ; Subdivision algorithms ; Control net
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Dahmen and Micchelli [8] have shown that in general the coefficients of the refined control nets of a box spline surface converge to the surface at (at least) the rate of the refinement. The purpose of this article is to show that under mild additional assumptions the convergence rate is even quadratic. Although this rate is in general best possible, we point out under what circumstances even higher rates are obtained (locally).
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    Constructive approximation 1 (1985), S. 15-62 
    ISSN: 1432-0940
    Keywords: 41A46 ; 41A15 ; n-Widths ; Total positivity ; Eigenvalues ; Eigenfunctions ; Implicit function theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetW p (r) ={f:f∈C r−1[0, 1],f (r−1) abs.cont., ∥f (r)∥ p 〈∞}, and setB p (r) ={f:f∈W p (r) ,∥f (r)∥ p ≤1}. We find the exact Kolmogorov, Gel'fand, linear, and Bernsteinn-widths ofB p (r) inL p for allp∈(1, ∞). For the Kolmogorovn-width we show that forn≥r there exists an optimal subspace of splines of degreer−1 withn−r fixed simple knots depending onp.
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    Constructive approximation 1 (1985), S. 155-173 
    ISSN: 1432-0940
    Keywords: 41A15 ; 65D07 ; Chebyshevian B-splines ; generalized divided differences
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The fundamental recurrence relation for polynomialB-splines is generalized to ChebyshevianB-splines.
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    Constructive approximation 1 (1985), S. 183-193 
    ISSN: 1432-0940
    Keywords: 41A05 ; 41A15 ; 41A63 ; Bivariate ; Box-splines ; Interpolation ; Convergence ; Exponential type ; Whittaker operator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give necessary and sufficient conditions for the convergence of cardinal interpolation with bivariate box splines as the degree tends to infinity.
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    Plant and soil 86 (1985), S. 57-67 
    ISSN: 1573-5036
    Keywords: Azolla ; N2-fixing efficiency ; Nitrogen fixation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The productivity of three species of Azolla (A. pinnata, A. filiculoides andA. caroliniana) in outdoor culture has been evaluated at different planting densities. The highest yields were obtained with biomass concentration ranging from 40 to 70g d.w. m−2. The mean productivity over a 90 days period (from May 10th to August 10th) ranged from 10g d.w. m−2 day−1 forA. filiculoides up to 11.5 g d.w. m−2 day−1 forA. caroliniana. The nitrogen content of the dried biomasses was 48.3 mg (g d.w.)−1 forA. pinnata, 51.5mg (g d.w.)−1 forA. filiculoides and 52.3 mg (g d.w.)−1 forA. caroliniana. Very little variations of the nitrogen content of the ferns during the experimental period were observed. The nitrogen-fixing efficiency of the Azolla-Anabaena azollae symbiosis grown in outdoor conditions was evaluated both by direct measurement of the amount of N2 fixed by the culture and by the C2H2-reduction and H2-evolution tests in an air atmosphere. These tests were performed outdoor under the same environmental conditions as the growing cultures. For all the species the ratios of C2H2-reduced to N2-fixed were unexpectedly low, ranging from 2.04 (A. pinnata) to 1.50 (A. caroliniana). The results suggest that the reliability of the C2H2-reduction assay, particularly when applied to complex biological N2-fixing systems, must be re-examined.
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    Plant and soil 87 (1985), S. 49-60 
    ISSN: 1573-5036
    Keywords: Actinorhizae ; Alnus ; Frankia ; Nitrogen fixation ; Plasmids ; Restriction analysis ; Symbiosis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary After the initial screening of more than 200Frankia strains, the plasmid DNA observed in eight Frankiae was analyzed.In situ lysis was performed to obtain an estimate of their copy number and molecular weight. Four plasmid classes were distinguished, 7–9, 18–20, 30–35 and 50–55 kb. Twelve plasmids were thus analysed with restriction enzymes to determine their plasmid restriction patterns. While someFrankia plasmids with comparable molecular weights were found to be heterologous in their restriction enzyme pattern, an 8 kb plasmid found in bothFrankia sp. ArI3, isolated fromAlnus rubra andFrankia sp. CpI1 isolated fromComptonia peregrina showed undistinguishable ‘fingerprints’. Furthermore, an 18 kb plasmid found in the same two strains, also showed homologous restriction enzyme patterns. However, the copy numbers of the two ArI3 plasmids were higher than those of the CpI1 plasmids. Similarly, strains ACN1AG, $$TX41_{b^--- }^{AC} and TX38_{b^--- }^{AC} $$ , isolated fromAlnus crispa all contained a 50 kb plasmid, and the three plasmids were found upon restriction analysis to be undistinguishable. In one strain, ARgX17c isolated fromAlnus rugosa, it was found through restriction enzyme analysis that two plasmids of a similar molecular weight were in fact heterologous. The possible origin of the homologous plasmids and their potential as specificFrankia markers to be used in ecological studies are discussed.
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  • 53
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    Plant and soil 87 (1985), S. 143-152 
    ISSN: 1573-5036
    Keywords: Actinorhizae ; Elaeagnus angustifolia ; Frankia ; In vitro propagation ; Nitrogen fixation ; Nodulation ; Russian Olive ; Tissue culture
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Following the evaluation of the nutritional requirements for thein vitro propagation ofElaeagnus angustifolia, this actinorhizal species was routinely multiplied on MS, supplemented with 100 mM sucrose and 5 μM kinetin. On this medium, at a 3 week-interval, a multiplication rate of 5–10 was observed. A morphological variant occurred in culture (wet type) but it was converted into the normal type (pubescent type) by a passage on 1/2 macro MS and 1.5% agar. One hundred percent rooting was achieved in liquid medium containing 1/2 MS without growth regulators. The plantlets were transferred aseptically to a nitrogen-free artificial soil substrate and inoculated with pure cultures of differentFrankia strains which had been isolated from Elaeagnus, Shepherdia and Hippophae host plants. We thus ascertained that afterin vitro propagation, the plants retained their capacity to nodulate and sustain nitrogen fixation.
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  • 54
    ISSN: 1573-5036
    Keywords: Azospirillum ; Mustard ; Nitrogen fixation ; Rhizosphere soil ; Root association ; Seed inoculation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary A microplot field experiment was conducted in the presence or absence of P and N application to evaluate the influence of the seed inoculation of mustard (cv. Baruna T59) withAzospirillum lipoferum on N2-fixation in rhizosphere, association of the bacteria with the roots and grain yield and N uptake. Inoculation significantly increased the N content in rhizosphere soil particularly at early stage (40 days) of plant growth, which was accompanied by the increased association of the bacteria (A. lipoferum) in rhizosphere soil, root surface washing and surface-sterilized macerated root. A significant increase in grain yield and N uptake was also observed due to inoculation. Application of P particularly at the 20 kg. ha−1 level further enhanced the beneficial effect ofAzospirillum lipoferum inoculation, while N addition markedly reduced such an effect.
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  • 55
    ISSN: 1573-5036
    Keywords: Nitrate nitrogen ; Nitrate tolerance ; Nitrogen fixation ; Nodulation ; Trifolium repens ; Symbiotic variation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The variability in nodulation and nitrogen fixation traits ofTrifolium repens (cv. S. 100) supplied with abundant nitrate nitrogen was examined using an aseptic tube culture technique. Nodule numbers varied from 0 to 20 per plant and acetylene reduction activity from 0 to 49 nmol C2H4/plant per h. Plants were selected from this variable population for high, low and zero nodule numbers. Plants within groups were intercrossed and progeny used to establish high, low and zero nodule families. These were subsequently tested for nodulation and acetylene reduction activity in the presence and absence of combined nitrogen. When grown with nitrate the control populations (unselected S. 100 and Pronitro) averaged 3.05 nodules per plant, the high family averaged 4 per plant while the low line averaged 1 nodule per plant (P〈0.05). Nodule numbers were strongly correlated with acetylene reduction activity (r= +0.92) but C2H4 production was generally low, averaging respectively 4.9 and 3.1 nmol/plant per h in the high and low lines. In the absence of nitrate nodule numbers increased to an average of 50 per plant and acetylene reduction activity rose to 175.5 nmol/plant per h. There was no correlation between ability of selection lines to nodulate in the presence and absence of nitrate. The results demonstrate the existence of heritable genetic factors controlling nodulation and nitrogenase activity in the presence of nitrate, but the phenotypic expression of these characters is so strongly inhibited by nitrate that increases in nitrogen fixation in the presence of combined nitrogen which are likely to be of agricultural significance would require much greater genetic improvements than those demonstrated here. The possibilities for such improvements are discussed.
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  • 56
    ISSN: 1573-5036
    Keywords: Acetylene reduction ; Bean cultivars ; Harvest index ; 15N dilution ; Nitrogen fixation ; Nodulation ; Phaseolus vulgaris ; Rhizobium inoculation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary A field experiment was performed to assess the effects of Rhizobium inoculation and nitrogen fertilizer (100 kg N ha−1) on four cultivars of Phaseolus beans; Carioca, Negro Argel, Venezuela 350 and Rio Tibagi. In the inoculated treatment 2.5 kg N ha−1 of15N labelled fertilizer was added in order to apply the isotope dilution technique to quantify the contribution of N2 fixation to the nutrition of these cultivars. Nodulation of all cultivars in the uninoculated treatments was poor, but the cultivars Carioca and Negro Argel were well nodulated when inoculated. Even when inoculated, nodulation of the cultivars Venezuela 350 and Rio Tibagi was poor and these cultivars showed little response to inoculation in terms of nitrogen accumulation or grain yield. The estimates of the contribution of N2 fixation estimated using the isotope dilution technique, for the Carioca and Negro Argel cultivars, amounted to 31.7 and 18.4 kg N ha−1 respectively. These two cultivars produced 991 and 883 kg ha−1 of grain, respectively, when inoculated and 663 and 620 kg ha−1 with the addition of 100 kg N ha−1 of N fertilizer. The response to nitrogen was particularly poor due to high leaching losses in the very sandy soil at the experimental site. The Venezuela 350 and Rio Tibagi cultivars only responded to N fertilizer and not to inoculation with Rhizobium which stresses the great importance of selecting plant cultivars for nitrogen fixation in the field.
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  • 57
    ISSN: 1573-5036
    Keywords: Acetylene reduction ; Minesoil ; Nitrogen fixation ; Nitrogen source ; Reclamation ; Sericea lespedeza ; Surface mining
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Two growth chamber experiments were conducted to determine the response ofLespedeza cuneata (Dumont) G. Don. (sericea lespedeza) to delayed inoculation and low levels of nitrogen fertilization. Nitrogen was supplied either as NH 4 + or as NO 3 − in solution. At 0.5 and 5.0 ppm nitrogen early growth and N2(C2H2) fixation was inhibited by NH 4 + and promoted by NO 3 − . Inoculation at seeding did not negatively affect growth prior to the onset of N2(C2H2) fixation. Delayed inoculation until the trifoliate stage thus did not increase growth or N2 fixation during the first 40 days of growth. After 40 days, specific nitrogenase activity was highest for plants inoculated at the first trifoliate stage of growth. In contrast, growth and total shoot nitrogen accumulation were higher in plants inoculated at planting. The experimental results suggest that delaying inoculation is not a useful technique for improving early growth ofL. cuneata for surface mine reclamation.
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  • 58
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    Plant and soil 87 (1985), S. 1-16 
    ISSN: 1573-5036
    Keywords: Allocasuarina ; Casuarina ; Frankia ; Nitrogen fixation ; Nodulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Seedlings ofCasuarina spp. andAllocasuarina spp. were grown from seed in the greenhouse and inoculated with a nodule suspension fromC. equisetifolia. Plants ofCasuarina spp. nodulated regularly and were effective in nitrogen-fixation. Only one species ofAllocasuariona, A. lehmanniana formed root nodules. Using these plants as source of inoculum, the isolation of a newFrankia sp. HFPA11I1 (HFP022 801) was made and the strain was grown in pure culture.Frankia sp. HFPA11I1 grows well in a defined medium and shows typical morphological characteristics. In media lacking combined nitrogen, the filamentours bacterium forms terminal vesicles in abundance and differentiaties large intrahyphal or terminal sporangia containing numerous spores. This strain, used as inoculum, nodulates effectively seedlings ofC. equisietifolia andC. cunninghamiana, forming nodules with verically-growing nodule roots. Although effective in acetylene reduction, the endophyte within the nodules is filamentous and lacks veiscles. When used to inoculated seedlings ofA llocasuarina lehmanniana, Frankia sp. HFPA11I1 induces root nodules which are coralloid and lacking nodule roots. The nodules are effective in acetylene reduction and the filamentous hyphae ofFrankia within the nodule lobes lack vesicles. Effective nodulation inA. Lehmanniana depends upon environmental conditions of the seedlings and proceeds much more slowly than in Casuariana.
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  • 59
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    Plant and soil 87 (1985), S. 223-231 
    ISSN: 1573-5036
    Keywords: Nitrogen fixation ; Rhizobia ; Vigna unguiculata
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Biological nitrogen fixation is considered an important trait of cowpeas (Vigna unguiculata (L.) Walp. var. ‘California Blackeye’ No. 5) for economical production yet the process does not alone provide the quantity of nitrogen required by the plant for maximum productivity. Two experiments were undertaken to determine the potential of an increase in nodule mass and number of bacteroids resulting in increased nitrogen fixation. Cowpeas were grown in a glasshouse for 7 weeks under conditions forcing near total dependence on biological nitrogen fixation for growth. Nodule mass on the roots was varied by inoculating seeds with various ratios of effective and ineffective rhizobia that could be identified serologically and by the color of nodule formed. The results of both experiments demonstrated a linear relationship between total nodule mass formed by the effective rhizobia and quantity of nitrogen fixed. The regression coefficients were high in both experiments (r=0.99** and 0.91**). The relationship between total nitrogen fixed and total number of bacteroids of the effective strain was not consistent. In one experiment the regression coefficient was 0.93** but in the other experiment it was 0.65**. From these results it appears that there is good potential for increasing nitrogen fixation in cowpeas by increasing nodule mass. An increase in nodule mass would also result in an increase in the number of bacteroids.
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  • 60
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    Plant and soil 87 (1985), S. 445-447 
    ISSN: 1573-5036
    Keywords: Glomus fasciculatum ; Lentil ; Nitrogen fixation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Responses of lentil in unsterile soils at low, medium and high levels of plant available soil P toGlomus fasciculatum inoculation were evaluated. It was observed that growth, dry matter accumulation, nodulation, and nitrogen fixation were considerably improved in VAM inoculated plants over uninoculated control at low and medium levels of plant available soil P.
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  • 61
    ISSN: 1573-5036
    Keywords: Adaptation ; Carbon balance ; Carbon dioxide ; Environmental stress ; Heat stress ; Maintenance respiration ; Nitrogen fixation ; Salinity stress
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The fitter of two species that use different strategies to overcome the same stress may be the one that expends the least resources to cope with this stress. However, this concept has proven difficult to quantify. It is proposed here that the increase in maintenance respiration in response to stress factors such as high temperature, salinity or a high-oxygen atmosphere (one indirect effect of which is nitrogen deficiency) may provide a measure of the cost of adaptation, in terms of expenditure of assimilated carbon. A corrolary to this is that, where it can be shown that an adaptive strategy results in the expenditure of assimilates, adaptation may be enhanced by increasing carbon assimilation. Results are presented supporting the hypothesis and its corrolary.
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  • 62
    ISSN: 1573-5036
    Keywords: Mutualism ; Nitrogen fixation ; Sorghum bicolor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Sorghum plants were inoculated withAzospirillum brasilense or received an N-amended nutrient solution. Azospirillum inoculation increased plant dry weight and nitrogen assimilation by 25%. Most plant growth responses to Azospirillum were comparable to application of 2.0 mM N. Increased scavenging of nutrients, altered root permeability or nitrogen fixation are possible explanations for these effects.
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  • 63
    ISSN: 1573-5036
    Keywords: Glycine max ; Isotope dilution ; 15N techniques ; Nitrogen availability ; Nitrogen fixation ; Plant breeding ; Varietal comparison
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Soybeans (Glycine max (L.) Merr.) have a high N requirement which is fulfilled by soil N uptake and N2-fixation. This study was concerned with the effects of past yield selection on N2-fixation in soybeans. The soybean cultivars, ‘Lincoln’, ‘Shelby’, and ‘Williams’, which represent successive improvements in the ‘Lincoln’ germplasm, and a non-nodulating control were planted in a soil containing15N labelled organic matter. Two replications occurred on soil previously cropped to alfalfa and two on soil previously cropped to soybeans. Plants were harvested at five growth stages and leaf area, plant weight, total N, and atom percent15N were determined. Mature grain was harvested and yield components were also determined, as well as the total N and15N content. Cultivar differences in total dry matter were only evident at physiological maturity, when Williams contained the greatest dry matter. Williams exhibited the longest period of seed formation and seed fill and also had the highest grain yield which resulted from a larger weight per seed. The N content of the cultivars did not vary until physiological maturity when Williams contained the highest percent N. The quantity of N fixed at physiological maturity was highest for Williams and lowest for Lincoln. Fixed N contained in the harvested grain was greater for Williams than for the other two cultivars. The fraction of the total plant N derived from fixation was not greatly affected by cultivar and all cultivars acquired an average of 50% of their total N through N2-fixation. Previous cropping history greatly affected the quantity of N fixed and the fraction of the total plant N derived from fixation. Soybeans following soybeans were more dependent upon N2-fixation than soybeans following alfalfa with the former deriving 65% of the total plant N from fixation and the latter only 32%. These soybean cultivars apparently utilized soil N first and then used N2-fixation to satisfy their N requirement. The past selection for higher yield has resulted in soybean cultivars with improved capacities to fix atmospheric N2 and an improved ability to take up available soil N.
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  • 64
    ISSN: 1573-5036
    Keywords: Breeding ; Nitrate nitrogen ; Nitrogen fixation ; Nodulation ; Trifolium repens ; White clover
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Sodium nitrate applications ranging from 0.36 to 22.84 mM N were shown to depress rates of nodule formation and reduce total nitrogen fixation (acetylene reduction) in white clover plants grown in aseptic test tube culture. Low nitrate levels gave an initial depression in symbiotic activity but the reduction was of short duration and these treatments were subsequently associated with enhanced rates of nodule formation and nitrogen fixation. As a result, phenotypic variation appeared to be strongly differentially affected by the amount of nitrate present. A subsequent experiment suggested that much of the variation was a consequence of early enhancement of plant growth rates by low levels of nitrate followed by rapid depletion thus giving a transitory inhibitory effect. This was confirmed in a third experiment in which the range of nitrate concentration was held constant. Differential effects on variability in nodule formation and nitrogen fixation were then greatly reduced but there was still a residual level of plant-to-plant variation. The results have clear implications for selecting genetic variants capable of fixing di-nitrogen in the presence of combined N. The provision of a single limiting dose of combined nitrogen to a population containing individuals with inherently different growth rates can bring about variations in the phenotypic expression of symbiotic characters. These variations are unlikely to be based on genetic factors which have a direct and stable effect on nodule development and nitrogenase activity. The implications of the results for plant breeding are discussed.
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  • 65
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    Journal of optimization theory and applications 45 (1985), S. 33-39 
    ISSN: 1573-2878
    Keywords: Linear programming ; simplex method ; unrestricted variables ; simplex multipliers ; LU-factorization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Suppose that the simplex method is applied to a linear programming problem havingm equality constraints andr unrestricted variables. We give a method of performing the steps of the simplex method which reduces the arithmetic operation count byrm at each iteration. This savings in operations is achieved, since the method does not update the rows of the basis inverse associated with the unrestricted variables. Similar computational savings are achieved when the method is applied to the updating of anLU-factorization of the basis matrix.
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