Inverse problems for coefficients of nonlinear differential equations arise in investigation of various processes in heat physics, physical chemistry, hydrogeology, nuclear physics, and other sciences. Usually these problems consist in determining a coefficient of an equation, the sought coefficient depending on the solution, basing on the additional information about the solution. A large number of papers are devoted to inverse problems of such a type; see, e.g., [1,4,5,7). Of much importance for analysis of such problems and development of numerical methods for their solution is the study of the uniqueness of their solution in classes of functions of finite smoothness. Theorems of uniqueness in such classes of functions were usually proved under the assumption that the sought coefficient is known for small values of the argument [2,6,9]. A method was first proposed in [3] making it possible to prove the uniqueness of the solution to an inverse problem on the whole and without the above-mentioned assumption. This method is applied in the present paper for study of the inverse problem for a nonlinear mathematical model of sorption dynamics with mixed-diffusional kinetics.

No abstract

The estimation of the available bandwidth (AB) in an end-to-end manner can be used in several network applications to improve their performance. Several tools send pairs of packets from one end to the other and measure the packets' dispersion to infer the value of the AB. Given the fractal nature of Internet traffic, these measurements have significant errors that affect the accuracy of the estimation. This article presents the application of a clustering technique to reduce the estimation error of the available bandwidth in and end-to-end path. The clustering technique used is K-means which is applied to a tool called Traceband that is originally based on a Hidden Markov Model to perform the estimation. It is shown that using K-means in Traceband can improve its accuracy in 67.45% when the cross traffic is about 70% of the end-to-end capacity. keywords Available Bandwidth Estimation; Clustering; K-Means; Traceband.

En el trabajo se presentan tres problemas del área del Marketing que se modelan por medio de la optimización combinatoria. Los problemas de optimización combinatoria pertenecen a la clase de problemas que se consideran NP-Hard. Se presenta un enfoque de solución mediante la meta-heurística evolutiva EPSO “Optimización por enjambre de partículas evolutivas”. El TDPs consiste en determinar una división de un conjunto de unidades ubicadas en un territorio que cumple con los criterios múltiples como la compacidad, la conectividad y el equilibrio en términos de clientes y la demanda del producto; el siguiente problema es selección y diseño de un conjunto de productos para una línea de productos (PLD); el problema consiste en determinar los niveles de los atributos par producto que maximice la elección; y el último problema que se estudia es el VRPSPD resuelve el problema de distribución de la cadena de abarrotes y alimentos, determina la flota de vehículos que minimiza el tiempo de recorrido. Los problemas juegan un importante papel en la gestión del área del marketing que no debe ser ignorado en sus decisiones.

A mixed problem is considered for a system of partial differential equations modeling the process of adsorption dynamics. An existence and uniqueness theorem is proved for this problem, and the solution properties are investigated. The inverse problem is posed, involving the determination of the system coefficient given additional information about the solution. A uniqueness theorem is proved for the solution of the inverse problem.We consider the inverse problem for a model of adsorption dynamics. Inverse problems of adsorption dynamics have been studied by many authors (see, e.g., [1 -4]).Consider the following mathematical model of adsorption dynamics:Hereλ are positive constants, λ > β. The functions µ(t) and F (x) satisfy the following conditions: µ ∈ C[0, T ], µ(0) = 0,