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We show a new functional limit theorem for weakly dependent regularly varying sequences of random vectors. As it turns out, the convergence takes place in the space of R^d valued c\`{a}dl\`{a}g functions endowed with the so-called weak M1…
We introduce the homogeneous and piecewise multilinear extensions and the eigenvalue problem for locally Lipschitz function pairs, in order to develop a systematic framework for relating discrete and continuous min-max problems. This also…
In this paper, we define finitely additive, probability and modular functions over semiring-like structures. We investigate finitely additive functions with the help of complemented elements of a semiring. We also generalize some classical…
We prove some "universality" results for topological dynamical systems. In particular, we show that for any continuous self-map $T$ of a perfect Polish space, one can find a dense, $T$-invariant set homeomorphic to the Baire space ${\mathbb…
In [14,26], new approximation classes of self-referential functions are introduced as fractal versions of the classes of polynomials and rational functions. As a sequel, in the present article, we define a new approximation class consisting…
We introduce a continuous domain for function spaces over topological spaces which are not core-compact. Notable examples of such topological spaces include the real line with the upper limit topology, which is used in solution of initial…
We consider the two-matrix model with potentials whose derivative are arbitrary rational function of fixed pole structure and the support of the spectra of the matrices are union of intervals (hard-edges). We derive an explicit formula for…
The recently modified Faddeev-Jackiw formalism for systems having one chain of four levels of only second-class constraints is applied to the non-trivial a=1 bosonized chiral Schwinger model in (1+1) dimensions as well as to one mechanical…
This paper compares different representations (in the sense of computable analysis) of a number of function spaces that are of interest in analysis. In particular subspace representations inherited from a larger function space are compared…
When $G$ is a Polish group, metrizability of the universal minimal flow has been shown to be a robust dividing line in the complexity of the topological dynamics of $G$. We introduce a class of groups, the CAP groups, which provides a neat…
We study the topological invariant $\phi$ of Kwieci\'nski and Tworzewski, particularly beyond the case of mappings with smooth targets. We derive a lower bound for $\phi$ of a general mapping, which is similarly effective as the upper bound…
Recently, the first author of this paper, used the structure of finite dimensional translation invariant subspaces of C(R,C) to give a new proof of classical Montel's theorem, about continuous solutions of Fr\'{e}chet's functional equation…
A one-to-one continuous function from a triangle to itself is defined that has both interesting number theoretic and analytic properties. This function is shown to be a natural generalization of the classical Minkowski ?(x) function. It is…
The definition of a non-trivial space of generalized functions of a complex variable allowing to consider derivatives of continuous functions is a non-obvious task, e.g. because of Morera theorem, because distributional Cauchy-Riemann…
New relations of correlation functions are found in topological string theory; one for each second cohomology class of the target space. They are close cousins of the Deligne-Dijkgraaf-Witten's puncture and dilaton equations. When combined…
The recent theorem by D. Luecking that finite rank Toeplitz-Bergman operators must be generated by a measure consisting of finitely many point masses is carried over to the many-dimensional case.
Let $M$ be a $C$-minimal structure and $T$ its canonical tree (which corresponds in an ultrametric space to the set of closed balls with radius different than $\infty$ ordered by inclusion). We present a description of definable locally…
We consider definable topological spaces of dimension one in o-minimal structures, and state several equivalent conditions for when such a topological space $\left(X,\tau\right)$ is definably homeomorphic to an affine definable space…
A function $f:X\to \mathbb R$ defined on a topological space $X$ is called returning if for any point $x\in X$ there exists a positive real number $M_x$ such that for every path-connected subset $C_x\subset X$ containing the point $x$ and…
We construct the general solution of a class of Fuchsian systems of rank $N$ as well as the associated isomonodromic tau functions in terms of semi-degenerate conformal blocks of $W_N$-algebra with central charge $c=N-1$. The simplest…