Related papers: On $\alpha$-embedded sets and extension of mapping…

For an endomorphism s of R with s^{t}=1 we prove that the truncated polynomial ring (algebra) R[w,s]/(w^{t}) embeds into M_{t}(R[z]/(z^{t})). For an involution we exhibit an embedding of R into M_{2,1}^{s}(R), where M_{2,1}^{s}(R) is the…

We explore in depth how categorical data can be processed with embeddings in the context of claim severity modeling. We develop several models that range in complexity from simple neural networks to state-of-the-art attention based…

We prove a Krieger like embedding theorem for asymptotically expansive systems with the small boundary property. We show that such a system $(X; T)$ embeds in the $K$-full shift with $h_{top}(T) < \log K $ and $\sharp Per_n(X; T) \leq…

We define $(\alpha_n)$ -regular sets in uniformly perfect metric spaces. This definition is quasisymmetrically invariant and the construction resembles generalized dyadic cubes in metric spaces. For these sets we then determine the…

We show the ergodicity of Tanaka-Ito type $\alpha$-continued fraction maps and construct their natural extensions. We also discuss the relation between entropy and the size of the natural extension domain.

We review some applications of Gr\"obner-Shirshov bases, including PBW theorems, linear bases of free universal algebras, normal forms for groups and semigroups, extensions of groups and algebras, embedding of algebras.

We compare two known methods of extending a complex, unital, commutative normed algebra so as to include solutions to sets of monic polynomials over the original algebra. (One of these is a generalisation of a construction from the thesis…

We present a unitary approach to the construction of representations and intertwining operators. We apply it to the $C^*$-algebras, groups, Gabor type unitary systems and wavelets. We give an application of our method to the theory of…

In this paper, we prove a generalization of Geraghty's fixed point theorem for multi--valued mappings.

Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and…

We study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity and error estimation.

We develop a theory of universal central extensions of Hom-Lie algebras. Classical results of universal central extensions of Lie algebras cannot be completely extended to Hom-Lie algebras setting, because of the composition of two central…

This paper is the last paper in a series of five papers. Building on earlier papers in this series, we prove an analogue of Kuratowski's characterisation of graph planarity for three dimensions. More precisely, a simply connected…

We continue the study of the Hrushovski-Kazhdan integration theory and consider exponential integrals. The Grothendieck ring is enlarged via a tautological additive character and hence can receive such integrals. We then define the Fourier…

Our main theorem is an extension of the well-known Mizoguchi-Takahaashi's fixed point theorem [N. Mizogochi and W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric space, {\it J. Math. Anal. Appl.} 141 (1989)…

We prove a generalization of a result of Peres and Schlag on the dimensions of certain exceptional sets of projections and then apply it to a geometric problem.

We present some results related to theorems of Pasynkov and Torunczyk on the geometry of maps of finite dimensional compacta.

In this paper, we first obtain an estimate of the coefficients for $\alpha$-harmonic mappings. By applying these coefficient estimates, we prove the Landau type theorem for $\alpha$-harmonic mappings defined on the unit disc $\ID$.

In this paper we provide a (negative) solution to a problem posed by Stanis{\l}aw Krajewski. Consider a recursively enumerable theory U and a finite expansion of the signature of U that contains at least one predicate symbol of arity $\ge$…

In this article we introduce a generalization of the Newton transformation to the case of a system of endomorphisms. We show that it can be used in the context of extrinsic geometry of foliations and distributions yielding new integral…