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This paper reports on students' conceptions of minima points. Written assignments and individual interviews uncovered salient, concept images, as well as erroneous mis-out examples that mistakenly regard examples as non-examples and mis-in examples that mistakenly grant non-examples the status of examples. We used Tall and Vinner's theoretical framework to analyze the students' errors that were rooted in mathematical and in real-life contexts. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

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]