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The paper proves a theorem about the structure of the distribution function on which the extremum of the fractionally linear functional is reached in the presence of an uncountable number of linear constraints. The problem of finding an extremal distribution function arises when determining the optimal control strategy in a class of Markov homogeneous randomized control strategies. The structure of extremal functions is described by a finite number of parameters; hence, the problem is greatly simplified since it is reduced to the search for an extremum of some function. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the extremal problem of the L1-norm of the weights for non-left-definite eigenvalue problems of vibrating string equations with separated boundary conditions. Applying the critical equations of the weights, the infimum is obtained in terms of the given eigenvalue and the parameter in boundary conditions. [ABSTRACT FROM AUTHOR]

Aimed at the puzzle that it is hardly possible to solve maximum likelihood estimate (MLE) of two-dimensional lognormal distribution function directly, the paper presents a novel solution based on extremum equivalent conversion. The puzzle could be transformed to solve the extremum of an equivalent function about independent variable, and then mathematical expression of the extremum was obtained by conventional differential method. Take the study on location in wireless sensor network as an example. The research shows that the method can obviously reduce difficulty of the puzzle and the algorithm complexity, so the presented method provides an effective solution for similar problems. [ABSTRACT FROM AUTHOR]

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The paper presents the results of a study of the in vitro growth of Escherichia coli M17 involving the processing of observational data obtained by V.M. Vorobeichikov onboard the RV Akademik Fedorov while it sailed from St. Petersburg to Antarctica and back for the period from November 13, 2002, to May 26, 2003 (48th Russian Antarctic Expedition). Conclusions are drawn on the dependence of the in vitro growth rate of Escherichia coli on the geographical location change on a planetary scale. It does not exclude the dependence of other types of microorganisms on the spatial position in the gravitational field of the Earth. It is found that the Escherichia coli lag phase duration in the equatorial zone is close to its duration in the high-latitude Antarctic zone. Simultaneously, lag phase durations at the equator and in Antarctica correspond to the lag phase duration at the central phase of a lunar eclipse. It is concluded that in vitro Escherichia coli is highly sensitive to the gravitational field strength of the Earth and to the syzygy events. [ABSTRACT FROM AUTHOR]

Following the discovery of general $L_{p}$-projection bodies by Ludwig, Haberl and Schuster determined the extremum of the volume of the polars of this family of $L_{p}$-projection bodies. In this paper, the result of Haberl and Schuster is extended to all dual quermassintegrals, and a dual counterpart for the quermassintegrals of general $L_{p}$-projection bodies is also obtained. Moreover, the extremum of the $L_{q}$-dual affine surface areas of polars of general $L_{p}$-projection bodies are determined. [ABSTRACT FROM AUTHOR]

Thermoelectric materials have attained importance because of the gargantuan energy crisis the world faces today. A thermoelectric material can be used efficiently and frequently, provided, its figure of merit ZT is increased. Also, easy availability, manufacturing, and low cost are the other factors to be considered for a novel thermoelectric material. A theoretical model is proposed in this paper for the enhancement of the figure of merit of thermoelectric materials. [ABSTRACT FROM AUTHOR]

General problems on maximizing the products of several positive real, rational and integer numbers whose sum is given are investigated. [ABSTRACT FROM AUTHOR]

Lutwak introduced the Lp-difference body of a convex body as the Firey Lp-combination of the body and its reflection at the origin. In this paper, we define the notion of asymmetric Lp-difference bodies and study some of their properties. In particular, we determine the extremal values of the volumes of asymmetric Lp-difference bodies and their polars, respectively. [ABSTRACT FROM AUTHOR]

In this paper, the extremum of second-order directional derivatives, i.e. the gradient of first-order derivatives is discussed. Given second-order directional derivatives in three nonparallel directions, or given second-order directional derivatives and mixed directional derivatives in two nonparallel directions, the formulae for the extremum of second-order directional derivatives are derived, and the directions corresponding to maximum and minimum are perpendicular to each other. [ABSTRACT FROM AUTHOR]

We have shown the possibility of mathematical analysis of complex biochemical reactions without simplifying assumptions regarding their parameters by investigating the mechanism of adenosine triphosphate (ATP) hydrolysis by the "basal" Mg2+-ATPase in which ATP (substrate), Mg2+ (essential activator) and MgATP (true substrate) compete for binding with the enzyme catalytic site. For this mechanism, we proved, using the quasi-steady state principle by Bodenstein, the existence and uniqueness of a quasi-steady state at any fixed parameters (initial reactant concentrations, positive reaction rate constants). On this basis, the definition of the initial reaction rate v as a function of the initial concentrations of ATP (x1), Mg2+ (x2), ATPase (x3) is given and the dependencies v vs. xi are investigated. We proved that at fixed initial concentrations of any two reactants, the kinetic curve v vs. xi has a unique maximum point. In different regions of the kinetic curve located before and after the maximum point, the initial rate may vary in different ways: in one region it can change more slowly than the reactant concentration, as in the case of hyperbolic dependencies, and in the other it can change much faster than the reactant concentration, as in the case of sigmoid dependencies, which is typical for regulatory enzymes. This initial rate behaviour causes the existence of four different types of bell-shaped kinetic curves. To quantify the degree of sigmoidity of kinetics, we used derivatives ∂ ln v ∂ ln x i which allowed us to estimate the maximal velocity of the initial rate change. [ABSTRACT FROM AUTHOR]

We study extrema of the Mityuk radius depending on the choice of the canonical domain. Turning to the doubly connected case allows us to use the explicit form of mapping functions onto canonical domains. We obtain the results on the localization of critical points of the Mityuk radius for two types of such domains. [ABSTRACT FROM AUTHOR]

The paper proves a theorem about the structure of the distribution function on which the extremum of the fractionally linear functional is reached in the presence of an uncountable number of linear constraints. The problem of finding an extremal distribution function arises when determining the optimal control strategy in a class of Markov homogeneous randomized control strategies. The structure of extremal functions is described by a finite number of parameters; hence, the problem is greatly simplified since it is reduced to the search for an extremum of some function.

The method for determining the capacity of shunting diesel locomotives in view of their operation features, based on using the regression analysis is given in the paper. Herewith, the main objective of the research was to identify new relationships between the factors, which practically are not considered today by current standard indicators. Using modern technical solutions allowed to create a special electronic system (mode-meter), which allowed to quantify the useful operation time of shunting locomotive per a working shift, its loading level by various shunting operations, as well as compare them with the locomotive fuel economy. Based on the regression analysis, simulation of these parameters, which allowed to determine the necessary capacity level of its propulsion system during operation at a specific worksite was conducted. The significance and importance of coefficients of the obtained regression equation was defined on PC using special software. At that, the obtained function was tested for extremum, and the optimal values of its components were found. Based on the simulation results, universal nomograms for practical definition of the required power of shunting diesel locomotives to perform simple station and hump-export works depending on the volume, capacity utilization factor, time of locomotive useful operation per shift (for station shunting) or shunting stock mass (for hump-export works), as well as fuel consumption per shift were developed. [ABSTRACT FROM AUTHOR]

Abstract: The P1 discretization of the Laplace operator on a triangulated polyhedral surface is related to geometric properties of the surface. This paper studies extremum problems for eigenvalues of the P1 discretization of the Laplace operator. Among all triangles, an equilateral triangle has the maximal first positive eigenvalue. Among all cyclic quadrilaterals, a square has the maximal first positive eigenvalue. Among all cyclic n-gons, a regular one has the minimal value of the sum of all positive eigenvalues and the minimal value of the product of all positive eigenvalues. [Copyright &y& Elsevier]

Abstract: In this paper we consider a nonlinear equation having finitely many roots in a bounded interval. Based on the so-called numerical integration method [B.I. Yun, A non-iterative method for solving non-linear equations, Appl. Math. Comput. 198 (2008) 691–699] without any initial guess, we propose iterative methods to obtain all the roots of the nonlinear equation. In the result, an algorithm to find all of the simple roots and multiple ones as well as the extrema of is developed. Moreover, criteria for distinguishing zeros and extrema are included in the algorithm. Availability of the proposed method is demonstrated by some numerical examples. [Copyright &y& Elsevier]

We investigated the kinetic model of the enzyme catalyzed reaction of the hydrolysis of adenosine triphosphate (ATP) in which ATP (substrate) and MgATP (true substrate) compete for binding with the catalytic site of the enzyme (ATPase). The goal was to accurately establish all kinds of kinetic dependences of the initial rate on the initial concentrations of the enzyme, substrate, and activator inherent in this model. The analysis was carried out under the natural condition of the experiment – the concentration of the reaction product and the rate of elementary reactions in which it participates can be neglected. No additional simplifying assumptions were used. This is necessary in order to reliably identify the reaction proceeding according to the investigated mechanism among others, which can occur in a system containing three substances, (enzyme, substrate and activator), capable of interacting with each other. For this reaction we have proved the existence of a quasi-steady state at any initial reagent concentrations. This made it possible to analyze the dependences of the initial rate on the initial concentrations of the enzyme, substrate, and activator in the general case. It has been proven that (i) the dependence of the initial rate on the initial substrate concentration (ATP) always has a unique maximum point; (ii) the dependence of the initial rate on the initial enzyme concentration always has unique maximum point; (iii) the initial rate monotonically increases with increasing activator concentration (Mg2+) until it reaches the maximum limiting level. [ABSTRACT FROM AUTHOR]

Separation properties of the local extrema of best piecewise monotonic approximations to measurements of a real univariate function are of fundamental importance to the development of efficient algorithms that calculate these approximations. Piecewise monotonic approximation to n data is expressed as the minimization of some strictly convex function of the data errors subject to the restriction that the piecewise linear interpolant to the approximated values consists of at most k monotonic sections, where k is a prescribed positive integer. The major task is to determine automatically the positions of the joins of these sections, which is a combinatorial problem that can require about O (n k − 1) combinations in order to find an optimal one. We state theorems which prove the remarkable property that the local maxima of optimal approximations with k−1 monotonic sections are separated by the local maxima of optimal approximations with k monotonic sections, and local minima are separated similarly. We describe briefly a suitable technique that makes use of this property and gives the global solution in O (n 2 + k n log 2 ⁡ n) computer operations. Some numerical results show large gains in efficiency over existing methods. Further, as an illustration, we apply the technique to 39,082 observations of daily sunspots. [ABSTRACT FROM AUTHOR]

Abstract Following the discovery of general L p $L_{p}$ -projection bodies by Ludwig, Haberl and Schuster determined the extremum of the volume of the polars of this family of L p $L_{p}$ -projection bodies. In this paper, the result of Haberl and Schuster is extended to all dual quermassintegrals, and a dual counterpart for the quermassintegrals of general L p $L_{p}$ -projection bodies is also obtained. Moreover, the extremum of the L q $L_{q}$ -dual affine surface areas of polars of general L p $L_{p}$ -projection bodies are determined.

We derive a necessary condition for an extremum for functions on stratified sets in terms of integrals of the normal derivative over spheres and use this condition to prove the strong maximum principle for the divergence operator on a stratified set. [ABSTRACT FROM AUTHOR]

Consider the operator [image omitted] acting in the Hilbert space L 2[-π, π], p(x)=-1, and q(x)=v2 x2, where v is a constant, with the periodic boundary values conditions [image omitted] Let Wk=2v(k+1/2), k≥slant0, be the eigenvalues of [image omitted] , with [image omitted] related to the maximum and minimum x=tk, j of the even Hermite Orthogonal polynomial(s) (OP). The problem is of interest in the field of optics when spiral geometries are involved. Specifically, the solutions represent the azimuthal component of the propagating modes into spiral optical fibres, previously studied. We establish two-sided asymptotic bounds for the relative extrema of the even Hermite OP and relate them to the values of v=vk, j. The ratio between the upper and the lower bounds does not exceed √3 near to the least and the largest maxima, and is very close to one in the bulk of [-√2k, √2k]. We also apply the same method to prove the inequality [image omitted] for the Bessel function, and show that it is sharp outside monotonicity region. [ABSTRACT FROM AUTHOR]

A direct numerical method is considered, which is a generalization of the Euler method for nonlocal functionals depending on functions with differently signed deviations, and also for nonlocal functionals depending on functions of two independent variables. [ABSTRACT FROM AUTHOR]

The article focuses on the study conducted in Moscow, Russia regarding the probability of simultaneous extremes of Gaussian nonstationary processes. The author discusses the probability of simultaneous extremes of two Gaussian nonstationary processes. Moreover, he talks about the asymptotic properties of large deviations of Gaussian fields.