Related papers: Extensions of Scott's Graph Model and Kleene's Sec…
(1) Let 1\leq k\leq \omega. Call an atom structure \alpha weakly k neat representable, the term algebra is in \RCA_n\cap \Nr_n\CA_{n+k}, but the complex algebra is not representable. Call an atom structure neat if there is an atomic algebra…
We continue our study of operator algebras with contractive approximate identities (cais) by presenting a couple of interesting examples of operator algebras with cais, which in particular answer questions raised in previous papers in this…
This paper is intended to investigate Grassmann and Clifford algebras over Peano spaces, introducing their respective associated extended algebras, and to explore these concepts also from the counterspace viewpoint. The exterior…
Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum. Constructions of cospectral graphs help us…
Using the Evans spectral sequence and its counter-part for real $K$-theory, we compute both the real and complex $K$-theory of several infinite families of $C^*$-algebras based on higher-rank graphs of rank $3$ and $4$. The higher-rank…
The theory of algebraic extensions of Banach algebras is well established, and there are many constructions which yield interesting extensions. In particular, Cole's method for extending uniform algebras by adding square roots of functions…
Any non-degenerate quadratic form over a Hilbertian field (e.g., a number field) is isomorphic to a scaled trace form. In this work we extend this result to more general fields. In particular, prosolvable and prime-to-p extensions of a…
We propose a hypergraph expansion which facilitates the direct treatment of quantum spin models with many-site interactions via perturbative linked cluster expansions. The main idea is to generate all relevant subclusters and sort them into…
Plethysm coefficients $\mathsf{a}_{\mu[\nu]}^\lambda$ are the structure coefficients of the plethysm of Schur functions $s_\mu[s_\nu] = \sum_{\lambda} \mathsf{a}_{\mu[\nu]}^\lambda s_\lambda$. We study a bivariate generating function of…
In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…
Kleene's computability theory based on the S1-S9 computation schemes constitutes a model for computing with objects of any finite type and extends Turing's 'machine model' which formalises computing with real numbers. A fundamental…
We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…
In these lectures we study some possible higher order (of degree greater than two) extensions of the Poincar\'e algebra. We first give some general properties of Lie superalgebras with some emphasis on the supersymmetric extension of the…
We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by…
In this paper, we consider partially commutative metabelian Lie algebras whose defining graphs are cycles. We show that such algebras are universally equivalent iff the corresponding cycles have the same length. Moreover, we give an example…
We investigate (2,1):1 structures, which consist of a countable set $A$ together with a function $f: A \to A$ such that for every element $x$ in $A$, $f$ maps either exactly one element or exactly two elements of $A$ to $x$. These…
On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the…
For any complex $\alpha$ with non-zero imaginary part we show that Bernstein-Walsh type inequality holds on the piece of the curve $\{(e^z,e^{\alpha z}) : z \in \mathbb C\}$. Our result extends a theorem of Coman-Poletsky \cite{CP10} where…
We study a new flexible method to extend linearly the graph of a non-linear, and usually not bijective, function so that the resulting extension is a bijection. Our motivation comes from cryptography. Examples from symmetric cryptography…
We extend the classical Copson's inequalities so that the values of parameters involved go beyond what is currently known.