Functions of three variables which satisfy both the heat equation and Laplace's equation in two variables

Summability of Solutions of the Heat Equation with Inhomogeneous Thermal Conductivity in Two Variables

We investigate Gevrey order and 1-summability properties of the formal solution of a general heat equation in two variables. In particular, we give necessary and sufficient conditions for the 1-summability of the solution in a given direction. When restricted to the case of constants coefficients, these conditions coincide with those given by D. A. Lutz, M. Miyake, R. Schäfke in a 1999 article ...

Structural Equation Modeling: Categorical Variables

In the behavioral sciences, response variables are often noncontinuous, common types being dichotomous, ordinal or nominal variables, counts and durations. Conventional structural equation models (SEMs) have thus been generalized to accommodate different kinds of responses.

Errors in Variables in Simultaneous Equation Models

Eliminating Variables in Boolean Equation Systems

Systems of Boolean equations of low degree arise in a natural way when analyzing block ciphers. The cipher’s round functions relate the secret key to auxiliary variables that are introduced by each successive round. In algebraic cryptanalysis, the attacker attempts to solve the resulting equation system in order to extract the secret key. In this paper we study algorithms for eliminating the au...

Growth analysis of entire functions of two complex variables

In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.