A generalized structure of complementary matrices involved in the input-state-output Inclusion Principle for linear time-invariant systems (LTI) including contractibility conditions for static state feedback controllers is well known. In this paper, it is shown how to further extend this structure in a systematic way when considering contractibility of dynamic controllers. Necessary and suffici...

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

A standard method for finding a rational number from its values modulo a collection of primes is to determine its value modulo the product of the primes via Chinese remaindering, and then use Farey sequences for rational reconstruction. Successively enlarging the set of primes if needed, this method is guaranteed to work if we restrict ourselves to “good” primes. Depending on the particular app...

We consider the multiplicative complexity of the inversion and division of bivariate power series modulo the \triangular" ideal generated by all monomials of total degree n + 1. For inversion, we obtain a lower bound of 7 8 n 2 ? O(n) opposed to an upper bound of 7 3 n 2 + O(n). The former bound holds for all elds with characteristic distinct from two while the latter is valid over elds of char...

It is well-known that two modular forms on the same congruence subgroup and of the same weight, with coefficients in the integer ring of a number field, are congruent modulo a prime ideal in this integer ring, if the first B coefficients of the forms are congruent modulo this prime ideal, where B is an effective bound depending only on the congruence subgroup and the weight of the forms. In thi...

In this paper, we nd the relationships between module contractibility of aBanach algebra and its ideals. We also prove that module contractibility ofa Banach algebra is equivalent to module contractibility of its module uniti-zation. Finally, we show that when a maximal group homomorphic image ofan inverse semigroup S with the set of idempotents E is nite, the moduleprojective tensor product l1...

H [n] = {(t1, . . . , tn) ∈ R n \ {0} | ∀j, [tj 6= 0 and t1 = t2 = · · · = tj−1 = 0] ⇒ tj > 0} ∪ {0}. LetM(H) denote the Banach algebra of all complex Borel measures with support contained in H, with the usual addition and scalar multiplication, and with convolution ∗, and the norm being the total variation of μ. It is shown that the maximal ideal space X(M(H)) of M(H), equipped with the Gelfan...

Information technology enabled exchanges in electronic markets have significant implications for buyer–supplier relaVivek Choudhury was the accepting senior editor for this paper. tionships. Building on studies that emphasize the role of intangible assets in interorganizational relationships, this study argues that buyers are less likely to use reverse auctions for supplier relationships involv...

The related inequality (1.1) was obtained by Maher [3, Theorem 3.2] who showed that, if A is normal and AT = TA, where T ∈ Cp , then ‖T − (AX −XA)‖p ≥ ‖T‖p for all X ∈ ( ), where Cp is the von Neumann-Schatten class, 1≤ p <∞, and ‖·‖p its norm. Here we show that Maher’s result is also true in the case where Cp is replaced by ( ), the ideal of all compact operators with ‖·‖∞ its norm.Which allow...

In this note, we show that cite[Corollary 3.2]{sad} is not always true. In fact, we characterize essential left $phi$-contractibility of the group algebras in terms of compactness of its related locally compact group. Also, we show that for any compact commutative group $G$, $L^{2}(G)$ is always essentially left $phi$-contractible. We discuss the essential left $phi$-contractibility of some Fou...