A famous conjecture of Littlewood (c. 1930) concerns approximating two real numbers by rationals the same denominator, multiplying errors. In a lesser-known paper, Wang and Yu (Chin Ann Math 2:1–12, 1981) established an asymptotic formula for number such approximations, valid almost always. Using quantitative Koukoulopoulos–Maynard theorem Aistleitner–Borda–Hauke, together with bounds arising f...

We develop the theory of multiplicative Ehresmann connections for Lie groupoid submersions covering identity, as well their infinitesimal counterparts. construct obstructions to existence such connections, and we prove several interesting classes groupoids algebroids, including all proper groupoids. show that many notions from principal bundle have analogues in this general setup, 1-forms, curv...

We consider the stochastic non-autonomous Kuramoto-Sivashinsky equation with multiplicative white noise and colored coefficients. Due to anti-dissipative term in equation, we restrict state space on Lebesgue of odd functions then obtain a pullback random attractor $ \mathcal{A} space, where special bridge function plays an crucial role priori estimate. Moreover, prove continuity expectation for...

A multiplicative function f is said to be specially multiplicative if there is a completelymultiplicative function fA such that f(m)f(n)= ∑ d|(m,n) f (mn/d)fA(d) for allm andn. For example, the divisor functions and Ramanujan’s τ-function are specially multiplicative functions. Some characterizations of specially multiplicative functions are given in the literature. In this paper, we provide so...

In this work, mate choice is modeled by means of the abstract concept of mutual mating propensity. This only assumes that different types of couples can have different mating success. The model is adequate for any population where mating occurs among distinct types. There is no extra assumption about particular mating scheme or preference model. The concept of mutual mating propensity permits t...

Inspired by the idea of multiplicative intuitionistic preference relation (Xia MM et al. Preference relations based on intuitionistic multiplicative information, IEEE Transactions on Fuzzy Systems, 2013, 21(1): 113-133), in this paper, a new preference relation called the interval-valued multiplicative intuitionistic preference relation is developed. It is analyzed the basic operations for inte...

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit is understood in the point-wise sen...

We have discussed dynamical properties of the Tsallis entropy and the generalized Fisher information in nonextensive systems described by the Langevin model subjected to additive and multiplicative noise. Analytical expressions for the timedependent Tsallis entropy and generalized Fisher information have been obtained with the use of the q-moment approach to the Fokker-Planck equation developed...

We consider distributed estimation of a Gaussian source in a heterogenous bandwidth constrained sensor network, where the source is corrupted by independent multiplicative and additive observation noises, with incomplete statistical knowledge of the multiplicative noise. For multi-bit quantizers, we derive the closed-form mean-square-error (MSE) expression for the linear minimum MSE (LMMSE) est...

We study in this article the stochastic Zakharov-Kuznetsov equation driven by a multiplicative noise. We establish, in space dimensions two and three the global existence of martingale solutions, and in space dimension two the global pathwise uniqueness and the existence of pathwise solutions. New methods are employed to deal with a special type of boundary conditions and to verify the pathwise...