Currently, Modelica only supports models containing constants, time-dependent variables, and time-derivatives of variables, i.e. ordinary differential and algebraic equations. In this article, we present how the Modelica language can be extended to support object-oriented modeling with partial differential equations (PDEs), in order to solve initial and boundary value problems. The techniques w...

the principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (iae) by using the bernoulli polynomials and the residual correction method. after implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown bernoulli coefficients. thismethod gives an analytic solution when t...

Let G be a semisimple algebraic group over a local field K of characteristic p. If the universal covering map Gsc → G is inseparable then no open subgroup of G(K) is finitely generated. Otherwise, for any compact open subgroup G with probability 1 two randomly chosen elements generate an open subgroup of G(K). Our main tool is a recent theorem by R. Pink characterizing compact groups linear ove...

We present a method that generates automatically algebraic invariant properties of a loop. The implementation and verification process is done in a prototype verification condition generator for imperative programs. This verification tool is integrated into the overall framework of the Theorema system, which is based on a version of higher order predicate logic and includes verification procedu...

the concept of algebraic hyperstructures introduced by marty as a generalization of ordinary algebraic structures. in an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. the concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper rings and a generalizat...

Physical Unclonable Functions (PUFs) provide cryptographic keys for embedded systems without secure non-volatile key storage. Several error correction schemes for key generation with PUFs were introduced, analyzed and implemented over the last years. This work abstracts from the typical algorithmic level and provides an algebraic view to reveal fundamental similarities and differences in the se...