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In this paper, we introduce the concept of a pseudo weakly compact operator of order $ p $ between Banach spaces. Also we study the notion of $ p $-Dunford-Pettis relatively compact property which is in "general" weaker than the…
This paper is originally designed as a part of revision of the author's preprint math.AG/9908174 "P-adic Schwarzian triangle groups of Mumford type". Recently, Yves Andr'e pointed out a flaw in that preprint; more precisely, Proposition II…
Some basic facts about the prepotential in the SW/Whitham theory are presented. Consideration begins from the abstract theory of quasiclassical $\tau$-functions , which uses as input a family of complex spectral curves with a meromorphic…
A Boolean function $f$ on $n$ variables is said to be a bent function if the absolute value of all its Walsh coefficients is $2^{n/2}$. Our main result is a new asymptotic lower bound on the number of Boolean bent functions. It is based on…
We construct explicitly Pad\'e approximations of the second kind for a special class of G-functions. These are then applied to prove a Baker-type lower bound for linear forms in the p-adic values of these functions. Moreover, we consider…
We construct $p$-adic multiple $L$-functions in several variables, which are generalizations of the classical Kubota-Leopoldt $p$-adic $L$-functions, by using a specific $p$-adic measure. Our construction is from the $p$-adic analytic side…
In the present paper, we study a new subclass $\mathcal{M}_p(\alpha,\beta)$ of $p$--valent functions and obtain some inequalities concerning the coefficients for the desired class. Also, by use of the Hadamard product, we define a general…
This paper is devoted to the function introduced by M. P. Appell in connection with decomposition of elliptic functions of the third kind into simple elements. We show that this function (which appeared as a Fukaya triple product in…
In the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the…
We develop a notion of cell decomposition suitable for studying weak p- adic structures (reducts of p-adic fields where addition and multiplication are not (everywhere) definable). As an example, we apply this to a language with restricted…
Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of $p$-ary linear codes with two or three weights are constructed…
We obtain some regularity results for solutions to vectorial $p$-Laplace equations $$ -{\boldsymbol \Delta}_p{\boldsymbol u}=-\operatorname{\bf div}(|D{\boldsymbol u}|^{p-2}D{\boldsymbol u}) = {\boldsymbol f}(x,{\boldsymbol u})\,\, \mbox{…
We outline an algorithm for construction of functional bases of absolute invariants under the rotation group for sets of rank 2 tensors and vectors in the Euclidean space of arbitrary dimension. We will use our earlier results for symmetric…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
In the framework of the generalized measure theory the decomposable probabilistic-valued set functions are introduced with triangle functions $\tau$ in an appropriate probabilistic metric space as natural candidates for the "addition",…
This paper completes the construction of $p$-adic $L$-functions for unitary groups. More precisely, in 2006, the last three named authors proposed an approach to constructing such $p$-adic $L$-functions (Part I). Building on more recent…
We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary $p$-groups $(\mathbb{Z}_p)^d$, we introduce an averaging procedure that leads to a natural object of study: a 4-tuple of…
We construct examples of twice differentiable functions in $\mathbb{R}^n$ with continuous Laplacian and bounded Hessian. The same construction is also applicable to higher order differentiability, the Monge-Amp\`ere equation, and mean…
We construct a weak 2-functor from the bicategory of oriented tangles to a bicategory of Lagrangian cospans. This functor simultaneously extends the Burau representation of the braid groups, its generalization to tangles due to Turaev and…
In this paper we define a class of Boolean and generalized Boolean functions defined on $\mathbb{F}_2^n$ with values in $\mathbb{Z}_q$ (mostly, we consider $q=2^k$), which we call landscape functions (whose class containing generalized…