On the extremal function of the modulus of a foliation

We investigate the properties of the modulus of a foliation on a Riemannian manifold. We give necessary and sufficient conditions for the existence of the extremal function and state some of its properties. We obtain an integral formula which, in a sense, combines the integral over the manifold with the integral over the leaves. We state a relation between the extremal function and the geometry of the distribution orthogonal to a foliation.     

Application of graph-theoretic approaches to the random landscapes of the three-dimensional assignment problem

We study local optima of combinatorial optimization problems. We show that a local search algorithm can be represented as a digraph and apply recent results for spanning forests of a diagraph. We establish a correspondence between the number of local optima and the algebraic multiplicities of eigenvalues of digraph laplacians. We apply our finding to the three-dimensional assignment problem.     

Investigation of solutions to one family of mathematical models of living systems

We consider a family of integral equations used as models of some living systems. We prove that an integral equation is reducible to the equivalent Cauchy problem for a non-autonomous differential equation with point or distributed delay dependently on the choice of the survival function of system elements. We also study the issues of the existence, uniqueness, nonnegativity, and continuability of solutions. We describe all stationary solutions and obtain sufficient conditions for their asymptotic stability. We have found sufficient conditions for the existence of a limit of solutions on infinity and present an example of equations where the rate of generation of elements of living systems is described by a unimodal function (namely, the Hill function).     

Invariants of Characteristics of Some Systems of Partial Differential Equations

We introduce the notion of an invariant of characteristics for a system of first-order partial differential equations. We prove that the existence of invariants is connected with passiveness of some systems. We describe a few methods for construction of new invariants from those already known. We give a scheme for application of the invariants to reduction and integration of systems of partial differential equations. As an application we consider the equation of gas dynamics.     

Numerical analysis of a model for phase separation of a multicomponent alloy

We consider a fully discrete implicit finite-element approximationof a model for the phase separation of a multi-component alloy.We prove existence, uniqueness and stability of the numericalsolution for a sufficiently small time step. We prove convergenceto the solution of the associated continuous problem. We performa linear stability analysis of the equation and describe somenumerical experiments.     

Comatrix Coring Generalized and Equivalences of Categories of Comodules

We extend the comatrix coring to the case of a quasi-finite bicomodule. We also generalize some of its interesting properties. We study equivalences between categories of comodules over rather general corings. We particularize to the case of the adjoint pair of functors associated to a morphism of corings over different base rings. We apply our results to corings coming from entwining structures and graded structures, and we obtain new results in the setting of entwining structures and in the graded ring theory.     

Computable Linearizations of Well-partial-orderings

We analyze results on well-partial-orderings from the viewpoint of computability theory, and we answer a question posed by Diana Schmidt. We obtain the following results. De Jongh and Parikh showed that every well-partial-order has a linearization of maximal order type. We show that such a linearization can be found computably. We also show that the process of finding such a linearization is not computably uniform, not even hyperarithmetically.     

Spectra of weighted algebras of holomorphic functions

We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the spectra of weighted algebras and endow them with an analytic structure. We also deal with composition operators and algebra homomorphisms, in particular to investigate how their induced mappings act on the analytic structure of the spectrum. Moreover, a Banach–Stone type question is addressed.     

Some problems of the theory of quantum statistical systems with an energy spectrum of the fractional-power type

We consider the problem of the effective interaction potential in a quantum many-particle system leading to the fractional-power dispersion law. We show that passing to fractional-order derivatives is equivalent to introducing a pair interparticle potential. We consider the case of a degenerate electron gas. Using the van der Waals equation, we study the equation of state for systems with a fractional-power spectrum. We obtain a relation between the van der Waals constant and the phenomenological parameter ??, the fractional-derivative order. We obtain a relation between energy, pressure, and volume for such systems: the coefficient of the thermal energy is a simple function of ??. We consider Bose??Einstein condensation in a system with a fractional-power spectrum. The critical condensation temperature for 1 < ?? < 2 is greater in the case under consideration than in the case of an ideal system, where ?? = 2.     

Coupling of Systems of Hyperbolic Equations

We consider the Aw-Rascle system of hyperbolic equations which describes traffic flow phenomena on a single road. The model consists of two coupled nonlinear conservation laws in a single space dimension. We study an extension of the Aw/Rascle system to a network of roads. We derive necessary coupling conditions and introduce an obvious definition of a solution. We prove the existence of a solution to the road network problem. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the specificity of a possibility distribution

The specificity of a possibility distribution measures the degree to which the distribution allows one and only one element as its manifestation. As such it is a measure of amount of uncertainty or information. We investigate a number of issues related to specificity measures. We discuss the connection between the specificity of a possibility distribution and the entropy of a probability distribution. We describe unifying view for constructing specificity measures. We look at the relationship of the specificity of a distribution and its negation. We consider the case where the base set is continuous.     

Kernel ideals and cokernel filters of a p-algebra

We discuss congruences of p-algebras. We characterize kernel ideals of a p-algebra. Indeed, we show that an ideal of a p-algebra is a p-ideal if and only if it is a kernel ideal. We study cokernel filters of a p-algebra. We construct a class of p-algebras in which every cokernel filter is a p-filter. We also give some characterizations of Boolean congruences of a p-algebra.     

Nonlinear mathematical model of pulsed-therapy of heterogeneous tumors

In this paper, we deal with a nonlinear impulsive differential equations modelling the chemotherapy of a heterogeneous tumor. We consider the case of several drugs with instantaneous effects. We take into account the interactions between sensitive cells and drug resistant cells. We are interested in the stability of the disease. We also study the loss of stability and the bifurcation of nontrivial solutions.     

Deformation Quantization of Symplectic Fibrations

A symplectic fibration is a fibre bundle in the symplectic category (a bundle of symplectic fibres over a symplectic base with a symplectic structure group). We find the relation between the deformation quantization of the base and the fibre, and that of the total space. We consider Fedosov's construction of deformation quantization. We generalize the Fedosov construction to the quantization with values in a bundle of algebras. We find that the characteristic class of deformation of a symplectic fibration is the weak coupling form of Guillemin, Lerman, and Sternberg. We also prove that the classical moment map could be quantized if there exists an equivariant connection.     

Grassmann image of non-isotropic surface of pseudo-Euclidean space

We consider submanifolds of non-isotropic planes of the Grassman manifold of the pseudo-Euclidean space. We prove a theorem about the unboundedness of the sectional curvature of the submanifolds of the two-dimensional non-isotropic planes of the four-dimensional pseudo-Euclidean space with the help of immersion in the six-dimensional pseudo-Euclidean space of index 3. We also introduce a concept of the indicatrix of normal curvature and study the properties of this indicatrix and the Grassman image of the non-isotropic surface of the pseudo-Euclidean space. We find a connection between the curvature of the Grassman image and the intrinsic geometry of the plane. We suggest the classification of the points of the Grassman image.     

On the uniqueness of the solution of nonlinear differential-algebraic systems

We consider the Cauchy problem for a system of nonlinear ordinary differential equations unsolved for the derivative of the unknown vector function and identically degenerate in the domain. We prove a theorem on the coincidence of two smooth solutions of the considered problem. We show that, under some additional assumptions, the above-mentioned problem cannot have classical solutions with less smoothness. We obtain conditions under which the problem has a fixed finite number of solutions.     

The impact of liberalization on the productive efficiency of Indian commercial banks

We examine the productive efficiency of 70 Indian commercial banks during the early stages (1986–1991) of the ongoing period of liberalization. We use data envelopment analysis to calculate radial technical efficiency scores. We then use stochastic frontier analysis to attribute variation in the calculated efficiency scores to three sources: a temporal component, an ownership component, and a random noise component. We find publicly-owned Indian banks to have been the most efficient, followed by foreign-owned banks and privately-owned Indian banks. We also find a temporal improvement in the performance of foreign-owned banks, virtually no trend in the performance of privately-owned Indian banks, and a temporal decline in the performance of publicly-owned Indian banks. We attempt to explain these patterns in terms of the government's evolving regulatory policies.     

Global convergence and rate of convergence of a method of centers

We consider a method of centers for solving constrained optimization problems. We establish its global convergence and that it converges with a linear rate when the starting point of the algorithm is feasible as well as when the starting point is infeasible. We demonstrate the effect of the scaling on the rate of convergence. We extend afterwards, the stability result of [5] to the infeasible case anf finally, we give an application to semi-infinite optimization problems.     

Reduction and construction of exact solutions for a nonlinear system of the parabolic type

We study a system of two equations of the parabolic type with two nonlinearities depending on the sum of squares of two unknown functions. We derive conditions under which the system can be reduced to a single equation. We indicate conditions under which this equation can be reduced to a linear heat equation or to semilinear equations. We construct parametric families of exact solutions defined by elementary functions. We derive a control law providing the existence of a wide class of functions that can be realized as exact solutions.     

On maximal quantity of particles of one color in analogs of multicolor urn schemes

We deal with analogs of multicolor urn schemes such that the number of particles is not more than a given number. We introduce conditions which provide the convergence of random variables which is the maximal number of taken particles of the same color to a random variable that has values zero and one. We prove this convergence in the case when a number of taken particles is not more than a fixed number and number of colors converges to infinity. We also consider the case when the number of taken particles converges to infinity.