We determine the asymptotic behavior of Green function for zero-drift random walks confined to multidimensional convex cones. As a consequence, we prove that there is unique positive discrete harmonic these processes (up multiplicative constant); in other words, Martin boundary reduces singleton.

We consider the Cauchy problem for a degenerate fractional conservation laws driven by noise. In particular, making use of an adapted kinetic formulation, result existence and uniqueness solution is established. Moreover, unified framework also established to develop continuous dependence theory. More precisely, we demonstrate $$L^1$$ -continuous estimates on initial data, order Laplacian, diff...

We use multiple zeta functions to prove, under suitable assumptions, precise asymptotic formulas for the averages of multivariable multiplicative functions. As applications, we prove some conjectures on average number cyclic subgroups group Zm1×…×Zmn and associated with LCM function.

The equation of motion the Green's function a many-electron system is shown to be governed by multiplicative exchange-correlation potential, in contrast self-energy. Crucially, this potential simply Coulomb an hole and fulfills sum rule. formulation offers simple physical interpretation for propagation added electron or may provide route density-functional-like approximations calculating functi...

for a graph $g$ with edge set $e(g)$, the multiplicative sum zagreb index of $g$ is defined as$pi^*(g)=pi_{uvin e(g)}[d_g(u)+d_g(v)]$, where $d_g(v)$ is the degree of vertex $v$ in $g$.in this paper, we first introduce some graph transformations that decreasethis index. in application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum zagreb ...

‎for a graph $g$ with edge set $e(g)$‎, ‎the multiplicative second zagreb index of $g$ is defined as‎ ‎$pi_2(g)=pi_{uvin e(g)}[d_g(u)d_g(v)]$‎, ‎where $d_g(v)$ is the degree of vertex $v$ in $g$‎. ‎in this paper‎, ‎we identify the eighth class of trees‎, ‎with the first through eighth smallest multiplicative second zagreb indeces among all trees of order $ngeq 14$‎.

In this paper we study matrices A = (aij) whose (i, j) -entry is a function of i/j; that is, aij = f(i/j) for some f : Q → C. We obtain a formula for the truncated determinants in the case where f is multiplicative, linking them to determinants of truncated Toeplitz matrices. We apply our formula to obtain several determinants of number-theoretic matrices. Mathematics Subject Classification 200...