Related papers: Existence of limit of multivariable function
We prove that Menger's theorem is valid for infinite graphs, in the following strong form: let $A$ and $B$ be two sets of vertices in a possibly infinite digraph. Then there exist a set $\cp$ of disjoint $A$-$B$ paths, and a set $S$ of…
It is shown that under certain boundary conditions the virial theorem has to be modified. We analyze the origin of the extra term and compute it in particular examples. The Coulomb and harmonic oscillator with point interaction have been…
Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex…
We prove the existence of the M-function, by which we can state the limit theorem for the value-distribution of the main term in the asymptotic formula for the summatory function of the Goldbach generating function.
The work concerns invariant measures for multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the exponential ergodicity of these equations. Then for a sequence of these equations, when their coefficients…
In this paper we study the existence and continuation of solution to general fractional differential equation with Hilfer fractional derivative. First we establish new local existence theorems. Then we derive the continuation theorems. With…
This work advances knowledge of the threshold of prox-boundedness of a function; an important concern in the use of proximal point optimization algorithms and in determining the existence of the Moreau envelope of the function. In finite…
Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.
We generalize Lindeberg's proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables. The result is applied to get a similar theorem for smooth functions…
In this paper, we give one possible definition for functions of several variables applied to endomorphisms of finite dimensional C-vector spaces. This definition is consistent with the usual notion of a function of a square matrix. Some…
It has often been observed that the Multifractal Formalism and the Large Deviation Principles are intimately related. In fact, Multifractal Formalism was heuristically derived using the Large Deviations ideas. In numerous examples in which…
Random walks in random scenery are processes defined by $Z_n:=\sum_{k=1}^n\xi_{X_1+...+X_k}$, where $(X_k,k\ge 1)$ and $(\xi_y,y\in{\mathbb Z}^d)$ are two independent sequences of i.i.d. random variables with values in ${\mathbb Z}^d$ and…
Recent results by Abert, Bergeron, Biringer et al., Finis, Lapid and Mueller, and Shin and Templier have extended the limit multiplicity property to quite general classes of groups and sequences of level subgroups. Automorphic…
A formal description of a functional analysis approach to the Riemann zeta-functional equation that provides in principle an infinity of different proofs based on work by the author on the existence of dilation-invariant unitary operators…
We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontal and vertical fluctuations leading to…
We obtain the analogue of the classical result by Erd\"os and Kac on the limiting distribution of the maximum of partial sums for exchangeable random variables with zero mean and variance one. We show that, if the conditions of the central…
We consider a Neumann problem for strictly convex variational functionals of linear growth. We establish the existence of minimisers among $\operatorname{W}^{1,1}$-functions provided that the domain under consideration is simply connected.…
The work concerns about multiscale McKean-Vlasov stochastic systems. First of all, we prove an average principle for these systems in the $L^2$ sense. Moreover, a convergence rate is presented. Then we define the nonlinear filtering of…
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
The long history of the research concerning the possible existence of bound or resonant states in light multineutron systems, essentially $^3$n and $^4$n, is reviewed. Both the experimental and the theoretical points of view have been…