Similarity and consimilarity of elements in the real Cayley-Dickson algebras

The similarity and consimilarity of elements in the real quaternion, octonion and sedenion algebras, as well as in the general real Cayley-Dickson algebras are considered by solving the two fundamental equationsax=xb andax = [`(x)]bax = \bar xb in these algebras. Some consequences are also presented.     

Separations by Random Oracles and “Almost” Classes for Generalized Reducibilities

Let ≤_r and ≤_sbe two binary relations on 2^ℕ which are meant as reducibilities. Let both relations be closed under finite variation (of their set arguments) and consider the uniform distribution on 2^ℕ, which is obtained by choosing elements of 2^ℕ by independent tosses of a fair coin.Then we might ask for the probability that the lower ≤_r‐cone of a randomly chosen set X, that is, the class of all sets A with A ≤_r X, differs from the lower ≤_s‐cone of X. By c osure under finite variation, the Kolmogorov 0‐1 aw yields immediately that this probability is either 0 or 1; in case it is 1, the relations are said to be separable by random oracles.Again by closure under finite variation, for every given set A, the probability that a randomly chosen set X is in the upper ≤_r‐cone of A is either 0 or 1; let Almost_r be the class of sets for which the upper ≤_r‐cone has measure 1. In the following, results about separations by random oracles and about Almost classes are obtained in the context of generalized reducibilities, that is, for binary relations on 2^ℕ which can be defined by a countable set of total continuous functionals on 2^ℕ in the same way as the usual resource‐bounded reducibilities are defined by an enumeration of appropriate oracle Turing machines. The concept of generalized reducibility comprises a natura resource‐bounded reducibilities, but is more general; in particular, it does not involve any kind of specific machine model or even effectivity. The results on generalized reducibilities yield corollaries about specific resource‐bounded reducibilities, including several results which have been shown previously in the setting of time or space bounded Turing machine computations.     

企业财务信息系统解决方案研究

讲座了企业财务信息系统的主要特点和功能组成,提出了在企业建立财务信息系统的一般技术和基本方法,并提供了在不同类型的企业建立财务信息系统的方案。     

The solvability of two linear matrix equations

The solvability conditions of the following two linear matrix equations (i)A₁X₁B₁+A₂X₂B₂+A₃X₃B₃=C,(ii) A₁XB₁=C₁A₂XB₂=C₂ are established using ranks and generalized inverses of matrices. In addition, the duality of the three types of matrix equations

(iii) A₁X₁B₁+A₂X₂B₂+A₃X₃B₃+A₄X₄B₄=C, (iv) A₁XB₁=C₁A₂XB₂=C₂A₃XB₃=C₃A₄XB₄=C₄, (v) AXB+CXD=E are also considered.     

On some matrix equalities for generalized inverses with applications

Necessary and sufficient conditions are derived for the matrix equality A^-=PN^-Q to hold, where A^- and N^- are generalized inverses of matrices. Some consequences and applications are also given. In particular, necessary and sufficient conditions are derived for the additive decompositions C^-=A^-+B^- and to hold.     

Invariance properties of a triple matrix product involving generalized inverses

Given complex-valued matrices A, B and C of appropriate dimensions, this paper investigates certain invariance properties of the product AXC with respect to the choice of X, where X is a generalized inverse of B. Different types of generalized inverses are taken into account. The purpose of the paper is three-fold: First, to review known results scattered in the literature, second, to demonstrate the connection between invariance properties and the concept of extremal ranks of matrices, and third, to add new results related to the topic.     

Bifunctional inhibitors of mevalonate kinase and mevalonate 5-diphosphate decarboxylase

[structure: see text] A bifunctional inhibitor of mevalonate kinase and mevalonate 5-diphosphate decarboxylase was synthesized. Both enzymes are in the cholesterol biosynthetic pathway and play an important role in regulating cholesterol biosynthesis. The molecule may become a useful lead compound for further development for treating cardiovascular disease and cancer. This study provides a novel example of a single inhibitor blocking two sequential steps simultaneously in the cholesterol biosynthetic pathway.