On the optimality of the logistic growth

The rate at which a population should grow is determined by finding the best trade-off between the loss due to the deviation from a target population size and the loss associated to the growing effort. It is also shown that, in the case of infinite-time horizon and quadratic loss functions, the optimal growth is logistic. This research was supported by the Centro Teoria dei Sistemi, CNR, and by the Italian Ministry of Public Education.     

On the Multiplicity of the Sample Maximum and the Longest Head Run

Periodica Mathematica Hungarica - Tossing a (not necessarily unbiased) coin n times let us denote the length of the longest head run by Z n and the number of head runs of such length by M n . Once...     

On the Natanzon-Turaev compactification of the Hurwitz space

Natanzon and Turaev have constructed by topological methods a compactification of the Hurwitz space, that is, the space of simple branched covers of the two-sphere. Here we show that this compactification is homeomorphic to a compactification mentioned by Diaz and Edidin (in 1996) that was constructed by algebraic methods. Using this we are able to show by example that the Natanzon-Turaev compactification can be singular, that is, not a manifold.

     

On the intersection of the maximal ideals

Some additional properties of the intersection of the maximal ideals of a compact semigroup are developed here based on results in [1] and [3]. Throughout S denotes a compact usually connected semigroup with at least one maximal proper ideal. The set of all such maximal ideals is denoted by ℳ, the intersection of the members of ℳ by R, the idempotents by E and the minimal ideal by K. Some proofs are more algebraic and in a few cases we do not need S connected. Key facts are that members of ℳ are open and dense, complements of distinct maximal ideals are disjoint and the union of any two such is S. After some generalization of results in [1] and [3], we investigate R relative to the topology of S. Necessary and sufficient conditions are found for R to be compact hence closed and for R to be open. Unlike the situation with the minimal ideal, R can be closed or open largely depending on the position of E relative to R. The following theorem summarizes necessary preliminaries from [1] and [3]. Adapted from material in Chapter 3 of the author's dissertation, written under the co-direction of Dr. John Mack and Dr. John Selden at the University of Kentucky and supported by the National Science Foundation. Support to organize and prepare this paper was provided by Mount Vernon Nazarene College.     

On the maximum deviation between the histogram and the underlying density

Summary The limiting joint distribution of the location and size of the maximum deviation between the historgram and the underlying density is derived. For smooth densities, the location and size of the maximum are asymptotically independent. The size has a limiting double-exponential distribution and the location has a limiting normal distribution.Research partially supported by NSF grant MCS-80-02535Research partially supported by NSF grant MCS-77-16974     

On the effectivization of the universality theorem for the Lerch zeta-function

In the paper one way of the effectivization of the universality theorem for the Lerch zeta-function is discussed. It is based on the estimate of the rate of convergence in a limit theorem in the space of analytic functions. Partially supported by the Lithuanian State Science and Studies Foundation. Translated from Lietuvos Matematikos Rinkinys, Vol. 40, No. 2, pp. 172–178, April–June, 2000. Translated by A. Laurinčikas     

On a convergence of the rational-trigonometric-polynomial approximations realized by the roots of the Laguerre polynomials

The paper considers a problem of approximation of functions by means of their finite number of Fourier coefficients. Convergence acceleration of approximations by the truncated Fourier series is achieved by application of polynomial and rational correction functions. Rational corrections include unknown parameters whose determination is a crucial problem. We consider an approach connected with the roots of the Laguerre polynomials and study the rates of convergence of such approximations.     

On the asymptotic behavior of the energy for the wave equations with time depending coefficients

We consider the asymptotic behavior of the total energy of solutions to the Cauchy problem for wave equations with time dependent propagation speed. The main purpose of this paper is that the asymptotic behavior of the total energy is dominated by the following properties of the coefficient: order of the differentiability, behavior of the derivatives as t → ∞ and stabilization of the amplitude described by an integral. Moreover, the optimality of these properties are ensured by actual examples. Supported by Grants-in-Aid for Young Scientists (B) (No.16740098), The Ministry of Education, Culture, Sports, Science and Technology.     

Variational characterization of the uniqueness of the optimal state for the minimal-time problem

In this paper, we give a variational characterization of the uniqueness of the optimal state in a proper linear control process for the time-optimal problem; we extend to control processes with time-variable coefficients a characterization of normality given by Hajek in Ref. 1.This work was supported by CNR-GNAFA, Rome, Italy.     

On the covering relation in the interpretability lattice of equational theories

We prove that the chapter in the interpretability lattice represented by the equational theory of Boolean algebras has a unique cover in the lattice. We conjecture that, among chapters represented by equational theories of two-element algebras, this is the only one to have a cover. Also, we prove that the chapter represented by the equational theory of Abelian groups has no cover.Presented by W. Taylor.Research supported by a Ulam Research Professorship at the University of Colorado and by NSF Grant DMS 89 04014.     

On the exact constant in the quantitative Steinitz theorem in the plane

We determine the maximal value ofr with the following property. If the convex hull of a set inR ² contains a unit circleB, then a subset of at most four points can be selected so that the convex hull of this subset contains the circle of radiusr concentric withB. That the result is sharp is shown by the example when the original set is the set of vertices of a regular pentagon circumscribed aroundB. Imre Bárány was partially supported by Hungarian National Science Foundation Grant Nos. 1907 and 1909. Aladár Heppes was partially supported by Hungarian National Science Foundation Grant No. 2583.     

On the Lower Bound of the Hausdorff Measure of the Koch Curve

This paper gives a lower bound of the Hausdorff measure of the Koch curve by means of the mass distribution principle.     

On the axiomatization of the τ-value

Summary The τ-value is a solution concept for a subclass of games with transferable utility introduced and axiomatized by Tijs (1981, 1987). In this note an alternative characterization of the τ-value by means of five axioms is offered. Two of them are well-known: efficiency and translation equivalence; the other three relate the solution of a game with the minimal and maximal aspiration vectors involved in the definition of the τ-value. This work was partially supported by Universidad del País Vasco (projects UPV 036.321-H061/91 and UPV 036.321-HA186/92).     

On the inversion of the n-dimensional Laplace transform

In this paper we study the inversion of the multidimensionalLaplace transform by a combination of a general partial-fractionexpansion formula and the theory of residues. The ideas maybe applied to nonlinear systems defined by Volterra series.     

疾病在食饵中流行的捕食与被捕食模型的分析

分析并建立了疾病在食饵中传播的生态-传染病模型,同时考虑到两种群都受密度制约因素的影响,讨论了模型解的有界性和各平衡点的存在性,利用Routh-Hurwitz判据证明了各平衡点的局部渐进稳定性,通过构造Lyapunov函数分析了各平衡点的全局渐进稳定性,得到了疾病存在与否的充分性条件.     

带生长函数的非定常森林发展系统

讨论非定常森林发展系统的动力学模型,证明了方程解的存在唯一性,并用Lyapunov稳定性理论讨论了系统的稳定性.     

On the computation of the polar FFT

We show that the polar as well as the pseudo-polar FFT can be computed very accurately and efficiently by the well-known nonequispaced FFT. Furthermore, we discuss the reconstruction of a 2d signal from its Fourier transform samples on a (pseudo)polar grid by means of the inverse nonequispaced FFT.     

Some Remarks on the Stability of the Log-Sobolev Inequality for the Gaussian Measure

This note consists of two parts. Firstly, we bound the deficit in the logarithmic Sobolev Inequality and in the Talagrand transport-entropy Inequality for the Gaussian measure, in any dimension, by means of a distance introduced by Bucur and Fragalà. Thereafter, we investigate the stability issue with tools from Fourier analysis.     

On the derivation of the velocity and fundamental traffic flow diagram from the modelling of the vehicle–driver behaviors

This paper deals with derivation of the fundamental diagram by modelling the individual driver behavior that adjusts the velocity to the density of vehicles in order to respect the braking distance. A parameter is properly introduced to model the quality of the driver–vehicle subsystem referred to the environmental conditions. Subsequently, it is shown how to use this result in order to model traffic flows by the macroscopic representation and by the kinetic theory.     

On the Liapunov-Movchan and the energy theories of stability

The asymptotic stability result obtained by Pritchard for the Benard and Taylor problems employing the Liapunov-Movchan theory is optimized by using inequalities and variational techniques. The equivalence between this result and the one obtained by the energy theory is demonstrated. Future applications as related to the symmetry of the operators are discussed.