‎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...

The study of Ramanujan-type congruences for functions specific to additive number theory has a long and rich history. Motivated by recent connections between divisor sums overpartitions via in arithmetic progressions, we investigate the existence classification multiplicative theory.

Constructing discrete models of stochastic partial differential equations is very delicate. Here we use modern dynamical systems theory to derive spatial discretisations of the nonlinear advection-diffusion dynamics of the stochastically forced Burgers’ partial differential equation. In a region of the domain far from any spatial boundaries, stochastic centre manifold theory supports a discrete...

Perturbation theory and renormalization group methods are used to derive a finite-size scaling theory for the partition function zeroes and thermodynamic functions in the O(n) φ 4 model in four dimensions. The leading power–law scaling behaviour is the same as that of the mean field theory. There exist, however, multiplicative logarithmic corrections which are linked to the triviality of the th...

for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

We consider multiplicative monoids of the positive integers defined by a single congruence. If a and b are positive integers such that a≤ b and a2≡ a mod b, then such a monoid (known as an arithmetic congruence monoid or an ACM) can be described as Ma,b = (a+ bN0)∪{1}. In lectures on elementary number theory, Hilbert demonstrated to students the utility of the proof of the Fundamental Theorem o...

We prove that a class of stochastic differential equations with multiplicative noise has a unique solution in a noncommutative L2 space associated with a von Neumann algebra. As examples we consider usual L2 on a measure space, Hilbert-Schmidt operators and a hyperfinite II1-factor. A problem of finding an inverse of the solution is then discussed. Finally, we explain how a stochastic different...

In this paper we introduce the notion of additive and multiplicative generators on the lattice L , which is the underlying lattice of interval-valued fuzzy set theory (which is equivalent to intuitionistic fuzzy set theory in the sense of Atanassov). We study the properties of these operators, some of which are similar to well-known results on ([0, 1],≤).

5 Equidistribution Theory 26 5.1 A Generic Equidistribution Theorem . . . . . . . . . . . . . . . . . . . . . . 27 5.2 Equidistribution at Infinite Places . . . . . . . . . . . . . . . . . . . . . . . . 30 5.3 Equidistribution at Finite Places . . . . . . . . . . . . . . . . . . . . . . . . 32 5.4 Equidistribution of Small Subvarieties . . . . . . . . . . . . . . . . . . . . . . 35 5.5 Equidist...