Displaying similar documents to “Analysis of Biochemical Mechanisms using Mathematica with Applications”

Module Connes amenability of hypergroup measure algebras

Massoud Amini (2015)

Open Mathematics

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We define the concept of module Connes amenability for dual Banach algebras which are also Banach modules with a compatible action. We distinguish a closed subhypergroup K0 of a locally compact measured hypergroup K, and show that, under different actions, amenability of K, M.K0/-module Connes amenability of M.K/, and existence of a normal M.K0/-module virtual diagonal are related.

Matrix of ℤ-module1

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2015)

Formalized Mathematics

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In this article, we formalize a matrix of ℤ-module and its properties. Specially, we formalize a matrix of a linear transformation of ℤ-module, a bilinear form and a matrix of the bilinear form (Gramian matrix). We formally prove that for a finite-rank free ℤ-module V, determinant of its Gramian matrix is constant regardless of selection of its basis. ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with...

Generalized lifting modules.

Wang, Yongduo, Ding, Nanqing (2006)

International Journal of Mathematics and Mathematical Sciences

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Milord II. Language description.

Josep Puyol-Gruart, Carles Sierra (1997)

Mathware and Soft Computing

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In this paper we describe the language . The description is made in terms of computer language concepts and not in terms of the logical semantics underlying it. In this sense the paper complements others in which the focus of the description has been either the object level multi-valued language description, or the reflective component of the architecture, or even the several applications built using it. All the necessary elements to understand how a system programmed in executes have...

Rank of Submodule, Linear Transformations and Linearly Independent Subsets of Z-module

Kazuhisa Nakasho, Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2014)

Formalized Mathematics

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In this article, we formalize some basic facts of Z-module. In the first section, we discuss the rank of submodule of Z-module and its properties. Especially, we formally prove that the rank of any Z-module is equal to or more than that of its submodules, and vice versa, and that there exists a submodule with any given rank that satisfies the above condition. In the next section, we mention basic facts of linear transformations between two Z-modules. In this section, we define homomorphism...