Absolute Galois Group defined as Galois group of algebraic numbers regarded as extension of rationals is very difficult concept to define. The goal of classical Langlands program is to understand the Galois group of algebraic numbers as algebraic extension of rationals Absolute Galois Group (AGG) through its representations. Invertible adeles -ideles define Gl1 which can be shown to be isomorph...

Abstract This paper studies a continuous‐time stochastic linear‐quadratic (SLQ) optimal control problem on infinite‐horizon. Combining the Kronecker product theory with an existing policy iteration algorithm, data‐driven algorithm is proposed to solve problem. In contrast most methods that need all information of system coefficients, eliminates requirement three matrices by utilizing data syste...

Considering a certain construction of algebraic varieties X endowed with an action the group Aut(Fn), n < ∞, we obtain criterion for faithfulness this action. It gives infinite family

The radiation of sound waves from partially lined duct is treated by using the mode-matching method in conjunction with Wiener-Hopf technique. solution obtained modification technique and involves an infinite series unknowns which are determined system linear algebraic equations. Numerical this for various values problem parameters, whereby effects these parameters on diffraction studied. A per...

The aim of this paper is to introduce, in detail, a novel approach for tuning of anisochronic singleinput single-output controllers for infinite-dimensional feedback control systems. A class of Linear TimeInvariant Time Delay Systems (LTI TDSs) is taken as a typical representative of infinite-dimensional systems. Control design to obtain the eventual controller structure is made in the special ...

1. The existence of finite resolving systems. In an earlier paper we have announced the result that the existence of a resolving system of the Riemann manifold of an abstract field of algebraic functions (in any number of variables) or—what is the same—the local uniformization theorem implies the existence of finite resolving systems of the Riemann manifold. We have proved this result for algeb...

Digital numbers D are the world’s most popular data representation: nearly all texts, sounds and images are coded somewhere in time and space by binary sequences. The mathematical construction of the fixed-point D ' Z2 and floating-point D′ ' Q2 digital numbers is a dual to the classical constructions of the real numbers R. The domain D′ contains the binary integers N and Z, as well as Q. The a...

It is shown that, under appropriate assumptions, the continuous algebraic Riccati equation with Toeplitz matrices as coefficients has Toeplitz-like solutions. Both infinite and sequences of finite Toeplitz matrices are considered, and also studied is the finite section method, which consists in approximating infinite systems by large finite truncations. The results are proved by translating the...

It is shown that, under appropriate assumptions, the continuous algebraic Riccati equation with Toeplitz matrices as coefficients has Toeplitz-like solutions. Both infinite and sequences of finite Toeplitz matrices are considered, and also studied is the finite section method, which consists in approximating infinite systems by large finite truncations. The results are proved by translating the...