Heuvers, K.J. and D.S. Moak, The solution of the Binet-Cauchy functional equation for square matrices, Discrete Mathematics 88 (1991) 21-32. It is shown that if f : M,(K)+ K is a nonconstant solution of the Binet-Cauchy functional equation for A, B E M,,(K) and if f(E) = 0 where E is the n x n matrix with all entries l/n then f is given by f(A) = m(det A) where m is a multiplicative function on...

‘Loop-fusion cohomology’ is defined on the continuous loop space of a manifold in terms of Čech cochains satisfying two multiplicative conditions with respect to the fusion and figure-of-eight products on loops. The main result is that these cohomology groups, with coefficients in an abelian group, are isomorphic to those of the manifold and the transgression homomorphism factors through the is...

— In this paper we consider smooth extensions of cohomology theories. In particular we construct an analytic multiplicative model of smooth K-theory. We further introduce the notion of a smooth K-orientation of a proper submersion p : W → B and define the associated push-forward p̂! : K̂(W ) → K̂(B). We show that the push-forward has the expected properties as functoriality, compatibility with pul...

Background: an important field of research in mathematics education is the initial training teachers where deficiencies disciplinary and didactic knowledge required for their profession can be evidenced. Objective: To study transformation specialized future about division fractions. Design: qualitative descriptive paradigm a case approached. Context participants: group three students who design...

Let E be an elliptic curve which is defined over Q and has stable reduction modulo a given prime p. Assuming that E is modular, one can associate to E a p-adic L-function Lp(E, s). (See [-Mz-SwD, A-V, Vi, Mz-T-T] for its construction in various cases.) This function is defined by a certain interpolation property and is analytic for seZp. In this paper, we will assume that E has split multiplica...

There is a one-to-one correspondence between classical one-dimensional infinitely divisible distributions and free infinitely divisible distributions. In this work we study the free infinitely divisible distributions corresponding to the one-dimensional type  distributions. A new characterization of classical type  distributions is given first and the class of type  classical infinitely divi...

We introduce Probabilistic Dependent Type Systems (PDTS) via a functional language based on a subsystem of intuitionistic type theory including dependent sums, which is expanded to include stochastic functions. We provide a sampling-based semantics for the language based on non-deterministic beta reduction. Further, we derive a probabilistic logic from the PDTS introduced as a direct result of ...

‎The first multiplicative Zagreb index $Pi_1(G)$ is equal to the‎ ‎product of squares of the degree of the vertices and the second‎ ‎multiplicative Zagreb index $Pi_2(G)$ is equal to the product of‎ ‎the products of the degree of pairs of adjacent vertices of the‎ ‎underlying molecular graphs $G$‎. ‎Also‎, ‎the multiplicative sum Zagreb index $Pi_3(G)$ is equal to the product of‎ ‎the sum...

background: for psychiatric disorders, comorbidity is a rule rather than exception. thus it is particularly important to study additive and multiplicative effects of multiple mental disorders on suicidal behaviors. objectives: the aim of this study was to investigate the ethnic differences in multiplicative effects of mental disorders on suicidal ideation among black adults in the united states...