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We estimate the Lebesgue constants of interpolation by rational functions on one or several intervals with fixed poles having accumulation points on the interval(s). To prove it we use an analogue of the inverse polynomial image method for rational functions with fixed poles. [ABSTRACT FROM AUTHOR]

In the present paper, we establish the well-posedness of an identification problem for determining the unknown space-dependent source term in the hyperbolic-parabolic equation with nonlocal conditions. The difference scheme is constructed for the approximate solution of this source identification problem. The stability estimates for the solution of the difference scheme are presented. [ABSTRACT FROM AUTHOR]

In this paper a comparative analysis of the absolute errors of the weighted finite element method and FEM with refined meshes is performed for a model boundary value problem for the Lamé system in an L-shaped domain. For the weighted finite element method an absolute error value is by one or two orders of magnitude less than for the approximate generalized solution obtained by the FEM with graded meshes in the overwhelming majority of nodes. [ABSTRACT FROM AUTHOR]

In many engineering and science fields sensitivity analysis has become highly interesting. For the mathematical modeling of biological phenomena, researchers use sensitivity and uncertainty analysis because of its usefulness for defining important parameters for performance of the model. It can also help in the process of experimental analysis, reducing model order, estimating parameters, taking decisions or developing recommendations for decision-makers. Here, we illustrated the use of the local sensitivity analysis to explain the effect of various parameters on a threshold parameter, R0, resulting from the study of a dynamics model inside the human-host. And it is confirmed from computed elasticity indices that the most sensitive parameter to basic reproduction number is (vector contact rate) followed by rates of transmission. Moreover, a detailed parameter estimation of the model parameters and model fitting presented with the use of field data cases from Northern Nigeria using least-square fitting method. Finally, the sensitivity analysis results shows that improving the rate of environmental hygiene and facial cleanliness will attract a consequential decrease in the size of basic reproduction number, which results in the declination of the disease transmission. [ABSTRACT FROM AUTHOR]

Ternary semigroup is a universal algebra with an associative ternary operation. We give a characterization of bounded closed sets with nonempty interior of finite-dimensional Euclidean spaces by ternary semigroups of pairs of homeomorphic transformations. [ABSTRACT FROM AUTHOR]

In this extended abstract, considering the differential equations on hyperbolic plane, we investigate and establish the well-posedness of boundary value problem for hyperbolic equations in Hölder spaces. Furthermore, we establish new coercivity estimates in various Hölder norms for the solutions of such boundary value problems for hyperbolic equations. [ABSTRACT FROM AUTHOR]

A boundary value problem for the equations of heat and mass transfer in a half-space is considered, which contains in the boundary conditions derivatives of a higher order than the order of the derivative of a system of equations. The solution of the boundary problem is found in the form of a double layer potential. The lemma on finding the limit of the normal derivative of the finite order of the function in the neighborhood of the hyperplane xn = 0 is given. Using the boundary conditions, a system of integro-differential equations (SIDE) is obtained. The characteristic part of the SIDE is solved by the method of Fourier-Laplace integral transforms. The conditions for the correctness and incorrectness of the problem, expressed in terms of the given constants and boundary conditions, are found. Using the regularization method, the SIDE is reduced to a system of Volterra-Fredholm integral equations. A theorem on the solvability of the boundary value problem for a parabolic system of heat and mass transfer equations is presented. [ABSTRACT FROM AUTHOR]

In the paper, we consider stationary, linearized by Picard's iterations, Navier-Stokes equations governing the flow of a incompressible viscous fluid in the convection form in non-convex polygonal domain. An Rν -generalized solution of the problem is defined. A weighted finite element method for finding an approximate Rν-generalized solution is constructed. Numerically shown that the convergence rate does not depend on a value of the reentrant corner in the norm of the weighted Sobolev space. [ABSTRACT FROM AUTHOR]

In the present paper, hyperbolic type involutory partial differential equations with the Neumann condition are studied. The first and second order of accuracy difference schemes for the numerical solution of the initial boundary value problem for one dimensional hyperbolic type involutory partial differential equations are presented. Some numerical results are provided. [ABSTRACT FROM AUTHOR]

We consider the motion of a multidimensional viscoelastic continuum which subjects some fractional constitutive law. The weak solvability of a corresponding initial-boundary value problem is established. [ABSTRACT FROM AUTHOR]

The optimal feedback control problem for the initial–boundary value problem describing a motion of a nonlinearly viscous fluid is considered in the paper. The existence of an optimal solution that gives a minimum to a given quality functional is proved. To prove the existence of an optimal solution the topological approximation method for investigation of hydrodynamic problems is used. [ABSTRACT FROM AUTHOR]

We suggest some constructions to develop the theory of boundary value problems on manifolds with a non-smooth boundaries. We discuss basic principles for such a theory and describe main results that we have obtained to this time. Further, we show how these results are related to the theory of boundary value problems on non-smooth manifolds. [ABSTRACT FROM AUTHOR]

In this note we present that the optimal investment decision can be characterized by two boundaries that satisfy a system of coupled integral equations of Fredholm type and propose a numerical algorithm for resolution. [ABSTRACT FROM AUTHOR]

F. Bracci, M.D. Contreras, S. Díaz Madrigal [3] proved that any evaluation family of order d is described by a generalized Löwner chain. G. Ivanov and A. Vasil'ev considered randomized version of the chain and found a substitution which transforms the chain to an Itô diffusion. We generalize their result to vector randomized Löwner chain and prove there are no other possibilities to transform such Löwner chains to Itô diffusions. [ABSTRACT FROM AUTHOR]

This paper presents Multi-robot co-operative hunting behavior using Differential game approach. Two robots were used as pursuers while another robot is used as evader, the two robots (pursuers) try to search and surround the prey (evader) robot. The aim of the game is for the two robots to detect the evader at the minimum possible time while at the same time the evader dodged the pursuer to the maximum possible time. Differential game approach was used to construct the problem using system of ordinary differential equation. We give the required conditions for the two pursuers to catch the evader. It was also shown that the evader maximize the capture time, while the pursuers minimize the capture time. [ABSTRACT FROM AUTHOR]

In this paper, the Sinc-Galerkin method is applied to construct the numerical solution of telegraph equation with variable coefficients. This study shows that the Sinc-Galerkin method is a very effective and powerful tool in solving such problems numerically. [ABSTRACT FROM AUTHOR]

We study the well-posedness of the source identification problem for the two dimensional elliptic differential equation with nonlocal boundary conditions. Applying operator approaches, the exact estimates for the solution of this problem in Hölder norms are established. [ABSTRACT FROM AUTHOR]

The Riemann-Hilbert problem for the first order elliptic system is considered in the Hardy-Smirnov space. This system is reduced to an equivalent Fredholm integral system on the boundary in the space Lp. [ABSTRACT FROM AUTHOR]

In the present paper we consider the nonlocal boundary value perturbation problem { ε 2 ∂ 2 u (t , x) ∂ t 2 − (a (x) u x (t , x)) x + δ u (t , x) = f (t , x) , 0 < t < T , x ∈ (0 , l) , u (0 , x) = α u (T , x) + φ (x) , x ∈ [ 0 , l ] , u ′ (0 , x) = β u ′ (T , x) + ψ (x) , x ∈ [ 0 , l ] , u (t , 0) = u (t , l) , u x (t , 0) = u x (t , l) , 0 ≤ t ≤ T for hyperbolic equation with an arbitrary ε ∈ (0, ∞) parameter multiplying the derivative term. An asymptotic formula for the solution of this problem with a small ε parameter is presented. [ABSTRACT FROM AUTHOR]

In [1] two-sided bounds were derived for the probability of ruin of an insurance company, whose premium income is represented by an arbitrary increasing real function, the claims are dependent, integer valued r.v.s. and their inter-occurrence times are exponentially, non-identically distributed. Here we give an explicit algorithm to compute that probability. [ABSTRACT FROM AUTHOR]