We prove the validity of an averaging principle for a class of systems of slow-fast reaction-diffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type. The models we have in mind are the stochastic Fitzhugh– Nagumo equation arising in neurophysiology and the Ginzburg–Landau equation arising in statistical mechanics.

Stochastic differential equations with multiplicative noise need a mathematical prescription due to different interpretations of the stochastic integral. This fact implies specific algorithms to perform numerical integrations or simulations of the stochastic trajectories. Moreover, if the multiplicative noise function is not continuous then the standard algorithms cannot be used. We present an ...

A Fibonacci integer is an integer in the multiplicative group generated by the Fibonacci numbers. For example, 77 = 21 · 55/(3 · 5) is a Fibonacci integer. Using some results about the structure of this multiplicative group, we determine a near-asymptotic formula for the counting function of the Fibonacci integers, showing that up to x the number of them is between exp(c(log x) − (log x)) and e...

We give Lambek-Carlitz type characterization for completely multiplicative reduced incidence functions in Möbius categories of full bi-nomial type. The q-analog of the Lambek-Carlitz type characterization of exponential series is also established. 1. An arithmetical function f is called multiplicative if (1.1) f (mn) = f (m)f (n) whenever (m, n) = 1 and it is called completely multiplicative if...

Today we see how to use the multiplicative weight update method to solve other problems. In many settings there is a natural way to make local improvements that “make sense.”The multiplicative weight updates analysis from last time (via a simple potential function) allows us to understand and analyse the net effect of such sensible improvements. (Formally, what we are doing in many settings is ...

Today we see how to use the multiplicative weight update method to solve other problems. In many settings there is a natural way to make local improvements that ”make sense.” The multiplicative weight updates analysis from last time (via a simple potential function) allows us to understand and analyse the net effect of such sensible improvements. (Formally, what we are doing in many settings is...

Abstract. The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the multiplicative boolean convolution of probability measures on the positive half-line is proposed. Unlike Bercovici’s multiplicative boolean convolution it ...

In this article we study the problem of finding such finite groups that the modular forms associated with all elements of these groups by means of a certain faithful representation belong to a special class of modular forms (so-called multiplicative η−products). This problem is open. We find metacyclic groups with such property and describe the Sylow p-subgroups, p 6= 2, for such groups. We als...

We consider the problem of computing the Hamming weight of an n-bit vector using a circuit with gates for addition and multiplication modulo 2 (alternatively, XOR and conjunction gates) only. The number of multiplications necessary and sufficient to build such a circuit is called the “multiplicative complexity” of the Hamming weight function, and is denoted by c∧(H). We prove c∧(H) = n−HN(n) wh...