This paper considers systems whose transfer functions take the form of a strictly proper rational function times a delay. A closed form expression is presented for the controller which is optimally robust with respect to perturbations measured in the gap metric. The formula allows the H 1 loop-shaping procedure of Glover-McFarlane to be carried out explicitly for this class of systems without t...

The paper is devoted to investigation of some properties of [L]-homotopy groups. It is proved, in particular, that for any finite CW -complex L, satisfying double inequality [S] < [L] ≤ [S], π [L] n (S) = Z. Here [L] denotes extension type of complex L and π [L] n (X) denotes n-th [L]-homotopy group of X .

In this paper, the matrix equation AX + XB = C is considered, where the matrices A and B have sizes m × n and n × m, respectively, the size of the unknown X is n × m, and the operator (·) denotes either the transpose or the conjugate transpose of a matrix. In the first part of the paper, necessary and sufficient conditions for the existence and uniqueness of solutions are reviewed. These condit...

This article is a continuation of [1]. It is divided into five sections. The first one contains a few useful lemmas. In the second part there is a definition of conjugate sequences and proofs of some basic properties of such sequences. The third segment treats of bounded complex sequences,next one contains description of convergent complex sequences. The last and the biggest part of the article...

Some Notation. In these notes, k denotes a number field, i.e., a finite extension of the field Q of rationals, and Ok is its ring of integers. If I is an ideal in Ok, we denote its number of residue classes |Ok/I| by NI. This number is also the positive generator of the ideal NK/QI ⊂ Z, and is a multiplicative function of ideals. By a place v of k we mean an equivalence class of non-trivial abs...

We consider the matrix equation AX + X⋆B = C , where the matrices A and B have sizes m × n and n × m, respectively, the size of the unknown X is n × m, and the operator (·)⋆ denotes either the transpose or the conjugate transpose of a matrix. In the first part of the paper, we review necessary and sufficient conditions for the existence and uniqueness of solutions. These conditions were obtaine...

The efficiency and robustness of reliability methods are two important factors in the first-order reliability method (FORM). The conjugate choice control (CCC) and directional chaos control method (DCC) are developed to improve the robustness and efficiency of the FORM formula using the stability transformation method. In this paper, the CCC and DCC methods are applied for the reliability analy...

Different topics on the differential geometry of the complex Grassmann manifold are surveyed in relation to the coherent states. A calculation of the tangent conjugate locus and conjugate locus in the complex Grassmann manifold is presented. The proofs use the Jordan’s stationary angles. Also various formulas for the distance on the complex Grassmann manifold are furnished.

conclusions vaccine based on the conjugation of p. aeruginosa pao-1 lps with dt increased anti-lps antibodies and had a significant potential to protect against pseudomonas infections. background treatment of pseudomonas aeruginosa pao-1 infections through immunological means has been proved to be efficient and protective. objectives the purpose of this study was to produce a conjugate vaccine ...

Let $$p\in (1,\infty )$$ , $$q\in [1,\infty $$s\in {\mathbb Z}_{+}$$ $$\alpha \in [0,\infty and $$\mathcal {X}$$ be $$\mathbb R^n$$ or a cube $$Q_0\subsetneqq \mathbb . In this article, the authors first introduce local John–Nirenberg–Campanato space $$jn_{(p,q,s)_{\alpha }}(\mathcal {X})$$ show that localized Campanato is limit case of as $$p\rightarrow \infty $$ By means atoms weak- $$*$$ top...