Related papers: Construction of APN permutations via Walsh zero sp…

The $SL(2,R)/U(1)$ gauged WZWN model is modified by a topological term and the accompanying change in the geometry of the two dimensional target space is determined. The possibility of this additional term arises from a symmetry in the…

For a certain class of algebras $\cal A$ we give a method for constructing Banach spaces $X$ such that every operator on $X$ is close to an operator in $\cal A$. This is used to produce spaces with a small amount of structure. We present…

We construct a simple N=(0,2) deformation of the two-dimensional Wess-Zumino model. In addition to superpotential, it includes a "twisted" superpotential. Supersymmetry may or may not be spontaneously broken at the classical level. In the…

APN permutations in even dimension are vectorial Boolean functions that play a special role in the design of block ciphers. We study their properties, providing some general results and some applications to the low-dimension cases. In…

Permutations of the form $F=L_1(x^{-1})+L_2(x)$ with linear functions $L_1,L_2$ are closely related to several interesting questions regarding CCZ-equivalence and EA-equivalence of the inverse function. In this paper, we show that $F$…

We construct a fundamental region for the action on the $2d+1$-dimensional affine space of some free, discrete, properly discontinuous groups of affine transformations preserving a quadratic form of signature $(d+1, d)$, where $d$ is any…

The primary motivation behind this paper is an attempt to provide a thorough explanation of how the Mellin transform arises naturally in a process akin to the construction of the celebrated Gelfand transform. We commence with a study of a…

We introduce and study holomorphically finitely generated (HFG) Fr\'echet algebras, which are analytic counterparts of affine (i.e., finitely generated) $\mathbb C$-algebras. Using a theorem of O. Forster, we prove that the category of…

We present an explicit construction for feedforward neural network (FNN), which provides a piecewise constant approximation for multivariate functions. The proposed FNN has two hidden layers, where the weights and thresholds are explicitly…

We derive an explicit expression for an associative star product on non-commutative versions of complex Grassmannian spaces, in particular for the case of complex 2-planes. Our expression is in terms of a finite sum of derivatives. This…

Subspace designs are a (large) collection of high-dimensional subspaces $\{H_i\}$ of $\F_q^m$ such that for any low-dimensional subspace $W$, only a small number of subspaces from the collection have non-trivial intersection with $W$; more…

The notion of (Z/2Z) x (Z/2Z)-symmetric spaces is a generalization of classical symmetric spaces, where the group Z/2Z is replaced by (Z/2Z) x (Z/2Z). In this article, a classification is given of the (Z/2Z) x (Z/2Z)-symmetric spaces G/K…

This paper deals with the problem of when, given a collection $\mathcal C$ of weakly compact operators between separable Banach spaces, there exists a separable reflexive Banach space $Z$ with a Schauder basis so that every element in…

We construct geometrically the generating fields of a W algebra which acts irreducibly on the direct sum of the cohomology rings of the Hilbert schemes of n points on a projective surface for all n. We compute explicitly the commutators…

We deduce factorization properties for a quasi-Banach module over a quasi-Banach algebra. Especially we extend a result by Hewitt and prove that if any such algebra which possess a bounded left approximate identity, then any element in the…

We show the existence of Lipschitz-free spaces verifying the Point of Continuity Property with arbitrarily high weak-fragmentability index. For this purpose, we use a generalized construction of the countably branching diamond graphs. As a…

Evaluation of low degree hypergeometric polynomials to zero defines an algebraic hypersurface in the affine space of the free parameters and the argument. This article investigates the algebraic surfaces 2F1(-N,b;c;z)=0 for N=3 and N=4. As…

Let $1$ be the all-one vector and $\odot$ denote the component-wise multiplication of two vectors in $\mathbb F_2^n$. We study the vector space $\Gamma_n$ over $\mathbb F_2$ generated by the functions $\gamma_{2k}:\mathbb F_2^n \to \mathbb…

We extend some results of Kwok-Pun Ho. In particular, it will be shown that every rearrangement-invariant quasi-Banach function space E on a totally sigma-finite measure space with a non-atomic measure can be expressed is the form…

We report the calculated fundamental band gaps of \emph{wurtzite} ternary alloys Zn$_{1-x}$M$_x$O (M=Mg, Cd) and the band offsets of the ZnO/Zn$_{1-x}$M$_x$O heterojunctions, these II-VI materials are important for electronics and…