Solution of the neutron transport equation by means of hermite-S ∞-theory

Summary A stable numerical approximation (H -S ) is obtained through the use of Hermite's method of order (H ) in the spatial integration of the 1D neutron transport equation. The theory for =1 is applied to a one-group shielding problem.Numerical calculations show the new method to converge much faster than earlier versions ofS -theory. Comparison ofH ₁-S with the well-knownS _N -code ANISN indicates a large gain in computing time for the former.

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Zusammenfassung Durch Anwendung der Hermiteschen Integrationsmethode der Ordnung (H ) auf die Ortsintegration der 1D Neutronentransportgleichung entsteht eine numerisch stabile Approximation (H -S ). Diese Methode wurde für =1 auf ein 1 Gruppen-Abschirmungsproblem angewandt.Numerische Rechnungen zeigen die wesentlich raschere Konvergenz der Methode verglichen mit den ursprünglichen Versionen derS -Theorie. Durch Vergleich mit dem bekanntenS _N -Code ANISN wurde gezeigt, dass mit derH ₁-S -Methode ein grosser Rechenzeitgewinn erzielt wird.

     

Estimate of the approximation of periodic functions by negative Cesàro means

The problem of approximation of continuous functions by Cesàro (C,α)-means, −1 < α < 0, in terms of L _p and C-modulus of continuity is studied.     

A look at the past and present of optimization – An editorial

This special issue of the European Journal of Operational Research is devoted to the EURO XXIV Conference, that was held at the facilities of the University of Lisbon (Portugal) from July 11 to July 14, 2010. With over 700 sessions for a total of approximately 2350 presentations, and with 2700 participants (delegates and accompanying persons) coming from 69 countries, this was the largest EURO conference ever.     

Invariance of the Bajraktarević means with respect to the Beckenbach-Gini means

Assuming that the involved functions are three times differentiable, we determine all Bajraktarevi? means which are invariant respect to the mean-type mapping of the Beckenbach-Gini mean type. Some applications in iteration theory and functional equation are presented.     

Shape optimization of an airfoil in the presence of compressible and viscous flows

The objective of this article is to present a step-by-step problem-solving procedure of shape optimization. The procedure is carried out to design an airfoil in the presence of compressible and viscous flows using a control theory approach based on measure theory. An optimal shape design (OSD) problem governed by full Navier-Stokes equations is given. Then, a weak variational form is derived from the linearized governing equations. During the procedure, because the measure theory (MT) approach is implemented using fixed geometry versus moving geometry, a proper bijective transformation is introduced. Finally, an approximating linear programming (LP) problem of the original shape optimization problem is obtained by means of MT approach that is not iterative and does not need any initial guess to proceed. Illustrative examples are provided to demonstrate efficiency of the proposed procedure.     

Fuzzy probability spaces defined by means of the fuzzy relation ‘less than’

In this paper a fuzzy relation ‘less than’ and fuzzy probability spaces on the real line are defined. Fuzzy σ-algebras of events are introduced in an analogous way to the classical theory of probability by means of the above relation. Furthermore, specific properties of the fuzzy probability measures presented here are given.     

On the approximation of conjugate functions from Holder classes by Fejér means

Получены асимптотич еские равенства для в еличин гдеr≧0 — целое, ω(t) — выпу клый модуль непрерыв ности и $$\bar \sigma _n (f;x) = - \frac{1}{\pi } \mathop \smallint \limits_{ - \pi }^\pi f(x + t)\left( {\frac{1}{2}ctg\frac{t}{2} - \frac{1}{{4(n + 1)}}\frac{{\sin (n + 1)t}}{{\sin ^2 \tfrac{1}{2}t}}} \right)dt$$ сумма Фейера функцииf(х), сопряженной сf(x).     

Extensions of solution concepts by means of multiplicative ɛ-tax games

Multiplicative ɛ-tax games are introduced that are obtained from a game by imposing a tax on any proper coalition. The imposed tax is proportional to the relative reward to the coalition for its formation from the individuals. Of particular interest is the balanced (quasi-balanced, respectively) ɛ-tax game for which the imposed tax is minimal. This least balanced (quasi-balanced) ɛ-tax game is used to extend the concept of the core (τ-value). In a similar way the stable core of a game is introduced by considering the least convex ɛ-tax game.     

Approximation of functions of Dirichlet class by Fejér means

For the Dirichlet classes D _p of holomorphic functions in the disk, we obtain the exact orders of best polynomial approximations and of upper bounds for deviations of Fejér means of Taylor series in the Hardy spaces H _p.     

On the evaluation of Hilbert transforms by means of a particular class of Turán quadrature rules

A method for evaluating Hilbert transforms, by means of Turán quadrature rules with generalized Gegenbauer weights, is presented. The main feature of these integration formulas is the independence of the nodes of their multiplicity and thus of the precision degree. The error is analyzed both from a real and a complex perspective; in this context a new representation of the remainder term of the quadrature rules with multiple nodes for the evaluation of Hilbert transforms, valid not only for the particular class of weight functions here considered, is presented. A few numerical examples are provided.Work sponsored by Ministero della Ricerca Scientifica e Tecnologia, Italy.     

Did Egyptian scribes have an algorithmic means for determining the circumference of a circle?

It has been at various times proposed in regard to Problem 10 of the Moscow Mathematical Papyrus that Egyptian scribes had developed a computational algorithm by which they could calculate the circumference of a circle of known diameter length. It has also been proposed at various times that the 7:22 ratio between a circle’s diameter and its circumference was known by the Egyptian scribes at a surprisingly early period.The present paper explores currently available evidence that lends support to each of these propositions.     

On the order of approximation by Riesz means in multiplicative systems in the classes E X [ɛ]

We establish the order of approximation by Riesz means of the Fourier series in a multiplicative system of a class of functions with given majorant of the sequence of best approximations. In some cases, approximations by Riesz means and best approximations are considered in a specific space, but, in other cases, approximations by Riesz means are considered in spaces with a stronger norm.     

Approximations of functions defined on the real axis by means of de la Vallée-Poussin operators

Asymptotic equations for upper bounds of deviations of the de la Vallée-Poussin operators on C classes in the uniform metric are obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 5, pp. 682–691, May, 1992.     

Asymptotics of series arising from the approximation of periodic functions by Riesz and Cesàro means

Asymptotic expansions in powers of δ as δ → +∞ of the series $\sum\limits_{k = 0}^\infty {( - 1)^{(\beta + 1)k} \frac{{Q((\delta ^\alpha - (ak + b)^\alpha ) + )}} {{(ak + b)^{r + 1} }}} , $ where β ∈ ?, α, a, b > 0, and r ∈ ?, while Q is an algebraic polynomial satisfying the condition Q(0) = 0, are obtained. In special cases, these series arise from the approximation of periodic differentiable functions by the Riesz and Cesàro means.     

Existence and Stability of Positive Solutions for an Elliptic Cooperative System

By discussing the properties of a linear cooperative system, the necessary and sufficient conditions for the existence of positive solutions of an elliptic cooperative system in terms of the principal eigenvalue of the associated linear system are established, and some local stability results for the positive solutions are also obtained.     

Decrease rate of the probabilities ofε-deviations for the means of stationary processes

The asymptotic behavior asn → ∞ of the normed sumsσn =n ^?1 Σ _k ^=0n?1 Xk for a stationary processX = (X _n ,n ∈ ?) is studied. For a fixedε > 0, upper estimates for P(sup _k≥n ¦σ _k ¦ ≥ε) asn → ∞ are obtained.