ABSTRACT In this article, we study the existence and uniqueness of a global weak solution for the degenerate nonlinear variational inequality K x , t u " + Δ 2 u + M u 2 - Δ u + u ' ≥ f u 0 = u 0 u ' 0 = u 1 u ⌊ Σ = ∂ u ∂ η ⌊ Σ = 0 where K(x, t) is a function defined on Q = Ω × ] 0 , T [ , K ( x , t ) ≥ 0 para todo ( x , t ) ∈ Q, M a continuous real function with specific properties and f belongs to the class of functions L 2 0 , T ; H 0 1 ( Ω ). We will use the Faedo-Galerkin method, monotone operator and Compactness to prove the existence and uniqueness of weak solutions. article Kx, Kx x, K(x . FaedoGalerkin Faedo Galerkin method solutions

RESUMO Estudamos neste artigo existência e unicidade de solução fraca global para a inequação variacional não linear degenerada K x , t u " + Δ 2 u + M u 2 - Δ u + u ' ≥ f u 0 = u 0 u ' 0 = u 1 u ⌊ Σ = ∂ u ∂ η ⌊ Σ = 0 em que K(x, t) é uma função definida em Q = Ω × ] 0 , T [ , K ( x , t ) ≥ 0 para todo ( x , t ) ∈ Q, M uma função real contínua com propriedades específicas e f pertence a classe de funções L 2 0 , T ; H 0 1 ( Ω ). Usaremos o Método de Faedo-Galerkin, operador monótono e Compacidade para provar a existência e a unicidade de soluções fracas. Kx, Kx x, K(x . FaedoGalerkin, FaedoGalerkin Faedo Galerkin, Galerkin Faedo-Galerkin fracas

Abstract We introduce a new three-parameter lifetime model called the Lindley Weibull distribution, which accommodates unimodal and bathtub, and a broad variety of monotone failure rates. We provide a comprehensive account of some of its mathematical properties including ordinary and incomplete moments, quantile and generating functions and order statistics. The new density function can be expressed as a linear combination of exponentiated Weibull densities. The maximum likelihood method is used to estimate the model parameters. We present simulation results to assess the performance of the maximum likelihood estimation. We prove empirically the importance and flexibility of the new distribution in modeling two data sets.

Este artículo se dedica a la identificación numérica confiable y eficiente de los parámetros que definen la función de flujo y el coeficiente de difusión en una ecuación diferencial parcial de tipo parabólico fuertemente degenerada que es la base de un modelo matemático para procesos de sedimentación-consolidación. Para esta ecuación, el problema de valor inicial con valores en la frontera (IBVP) en el que el flujo es nulo, describe el asentamiento de una suspensión en una columna. Los parámetros para un material dado se estiman con base en repetidas soluciones numéricas del problema directo (IBVP) con una variación sistemática de los parámetros del modelo, con el objeto de minimizar sucesivamente un funcional de costo que mide la distancia entre una observación dependiente de tiempo y la correspondiente solución numérica. En este artículo se destacan dos aspectos. El primer aspecto es que en el método propuesto para la solución numérica eficiente y acertada del problema directo, se implementa un esquema explícito monótono bien conocido basado en diferencias finitas que usan tres puntos mejorado por molificación discreta. El esquema molificado utiliza una malla de más puntos pero converge con una condición CFL menos restrictiva, lo cual permite usar pasos temporales más grandes. El segundo aspecto es el exhaustivo análisis de sensibilidad y estabilidad de las funciones definidas por parámetros en el modelo y que juegan los papeles de aproximación inicial y dato observado, respectivamente.

This paper deals with the reliable and efficient numerical identification of parameters defining the flux function and the diffusion coefficient of a strongly degenerate parabolic partial differential equation (PDE), which is the basis of a mathematical model for sedimentation-consolidation processes. A zero-flux initial-boundary value problem (IBVP) posed for this PDE describes the settling of a suspension in a column. The parameters for a given material are estimated by the repeated numerical solutions of the IBVP (direct problem) under systematic variation of the model parameters, with the aim of successively minimizing a cost functional that measures the distance between a space-dependent observation and the corresponding numerical solution. Two important features of this paper are the following. In the first place, the method proposed for the efficient and accurate numerical solution of the direct problem. We implement a well-known explicit, monotone three-point finite difference scheme enhanced by discrete mollification. The mollified scheme occupies a larger stencil but converges under a less restrictive CFL condition, which allows the use of a larger time step. The second feature is the thorough sensitivity and stability analysis of the parametric model functions that play the roles of initial guess and observation data, respectively.

The paper presents the results of FPGA implementation of fuzzy Mamdani system with parametric conjunctions generated by monotone sum of basic t-norms. The system is implemented on the DE2 Altera development board using VHDL language. The system contains reconfigurable fuzzy Mamdani model with parametric membership functions and parametric operations that gives possibility to adjust the system to specific application.

Invariant theory as a study of properties of polynomials under translational transformations is developed. Class of polynomials with congruent set of eigenvalues is introduced. Evolution equations for eigenvalues and coefficients remaining the polynomial within proper class of polynomials are formulated. The connection with equations for hyper-elliptic Weierstrass and hyper-elliptic Jacobian functions is found. Algorithm of calculation of eigenvalues of the polynomials based on the evolution process is elaborated. Elements of the generalized dynamics with n-order characteristic polynomials are built.

La teoría de invariantes es un estudio de las propiedades de los polinomios que se desarrolla en las transformaciones de traslación. Se introduce una clase de polinomios congruentes con un conjunto de valores propios. Se formulan ecuaciones de evolución de los valores propios y los coeficientes del polinomio restante dentro de la clase adecuada de los polinomios. Se encuentra la conexión con las ecuaciones de Weierstrass hiperelípticas y funciones jacobiano hiper-elíptica. Son elaborados algoritmos de cálculo de valores propios de los polinomios basado en el proceso de evolución.