This paper investigates the optimal control problem for networked systems over multiple Markovian packet loss channels under hold-input compensation strategy. In this situation, actuator receives signals from controller via individual channels. The system is transformed into a jump linear by introducing new variable. By giving maximum principle such system, coupled difference Riccati-type equat...

We show that F has an infinite family of quasi-isometrically embedded subgroups of the form F m × Zn, for integral m, n ≥ 0. These subgroups have simple geometric but more complicated algebraic descriptions We present them to illustrate the intricate geometry of Thompson’s group F as well as the interplay between its standard finite and infinite presentations.

Controlled K-theory is used to show that algebraic K-theory of virtually abelian groups is described by an assembly map defined using possibly-infinite hyperelementary subgroups. The Farrell-Jones summand (coming from infinite subgroups) is parameterized by the rational projective space of the group.

Let A be a polynomial ring in n+ 1 variables over an arbitrary infinite field k. It is proved that for all sufficiently large n and d there is a homogeneous prime ideal p ⊂ A satisfying the following conditions. The ideal p corresponds to a component, defined over k and irreducible over s k, of a projective algebraic variety given by a system of homogeneous polynomial equations with polynomials...

This expository paper gives an elementary proof, using the Weil Conjectures for curves, that an infinite algebraic extension of a finite field is PAC and large.

This paper presents a complete (infinite) axiomatization for an algebraic construction of graphs, in which a finite fragment denotes the class of graphs with bounded tree width.

For an infinite family of monogenic trinomials \(P(X)=X^3\pm 3rbX-b\in {\mathbb {Z}}[X]\), arithmetical invariants the cubic number field \(L={\mathbb {Q}}(\theta )\), generated by a zero \(\theta\) \(P(X)\), and its Galois closure \(N=L(\sqrt{d_L})\) are determined. The conductor \(f\) cyclic relative extension \(N/K\), where \(K={\mathbb {Q}}(\sqrt{d_L})\) denotes unique quadratic subfield \(...

The paper considers the fundamental notions of manyvalued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite v...

Quadrature rules on semi-infinite and infinite intervals are considered involving weight functions of the Laguerre and Hermite type. It is shown that such quadrature rules cannot have equal coefficients and real nodes unless the algebraic degree of accuracy is severely limited.

In this paper we introduce and study some new sequence spaces of fuzzy numbers defined by I-convergence using the sequences of Orlicz functions, infinite matrix. We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces. Key WordsIdeal, I -convergent, infinite matrix, Orlicz function, fuzzy number.