A $$2~{\times }~2$$ 2 × 2 random switching model and its dual risk model

Queueing Systems - In this article, a special case of two coupled M/G/1-queues is considered, where two servers are exposed to two types of jobs that are distributed among the servers via a random...     

Units of ℤ(Cp × C2) and ℤ(Cp × C2 × C2)

The goal of this article is to describe a multiplicatively independent set, which generates the group of units of the integral group ring ?G, where G is either the cyclic group of order 2p or C₂ × C₂ × C_p, for a prime number p that satisfies some suitable conditions that will be specified later.     

Surfaces with $${K^2=2\mathcal{X}-2}$$ and pg ≥ 5

This note describes minimal surfaces S of general type satisfying p _g  ≥ 5 and K ² = 2p _g . For p _g  ≥ 8 the canonical map of such surfaces is generically finite of degree 2 and the bulk of the paper is a complete characterization of such surfaces with non birational canonical map. It turns out that if p _g  ≥ 13, S has always an (unique) genus 2 fibration, whose non 2-connected fibres can be characterized, whilst for p _g  ≤ 12 there are two other classes of such surfaces with non birational canonical map.     

On hybrid moments of $$\Delta _2(x)$$ Δ 2 ( x ) and $$\Delta _3(x)$$ Δ 3 ( x )

The Ramanujan Journal - Let $$k\geqslant 2$$ be a fixed natural number and $$d_k(n)$$ denote the number of ways n can be written as a product of k positive integers. We use $$\Delta _k(x)$$ to...     

Series representations for the Apery constant $$\zeta (3)$$ ζ ( 3 ) involving the values $$\zeta (2n)$$ ζ ( 2 n )

The Ramanujan Journal - In this note, using the well-known series representation for the Clausen function, we also provide some new representations of Apery’s constant $$\zeta (3)$$ . In...     

2 × 2 Permanental Ideals of Hypermatrices

We analyze the structure of ideals generated by some classes of 2 × 2 permanents of hypermatrices, generalizing [9 Laubenbacher , R. C. , Swanson , I. ( 2000 ). Permanental ideals . J. Symbolic Comput. 30 : 195 – 205 .[Crossref], [Web of Science ®] , [Google Scholar]] on 2 × 2 permanental ideals of generic matrices. We compare the obtained structure to that of the corresponding determinantal ideals in [11 Swanson , I. , Taylor , A. ( 2013 ). Minimal primes of ideals arising from conditional independence statements . J. Algebra 392 : 299 – 314 .[Crossref], [Web of Science ®] , [Google Scholar]]: as expected, the permanental ideals have many more (minimal) components. In the last two sections, we examine a few related classes of permanental ideals.     

Dedekind $$\sigma $$ σ -complete $$\ell $$ ℓ -groups and Riesz spaces as varieties

Positivity - We prove that the category of Dedekind $$\sigma $$ -complete Riesz spaces is an infinitary variety, and we provide an explicit equational axiomatization. In fact, we show that finitely...     

Frobenius–Schur Factorization for Multivalued $${\varvec{2\times 2}}$$ Matrices Linear Operator

In this paper, a new concept for a \(2\times 2\) block relation matrix is studied in a Banach space. We define a matrix linear relation and present some of its properties. It is shown that, under certain condition, we can investigate the Frobenius–Schur of relation matrices.     

On $$\gamma $$ γ - and local $$\gamma $$ γ -vectors of the interval subdivision

Journal of Algebraic Combinatorics - We show that the $$\gamma $$ -vector of the interval subdivision of a simplicial complex with a nonnegative and symmetric h-vector is nonnegative. In...     

$$I_0$$ and combinatorics at $$\lambda ^+$$λ+

We investigate the compatibility of \(I_0\) with various combinatorial principles at \(\lambda ^+\), which include the existence of \(\lambda ^+\)-Aronszajn trees, square principles at \(\lambda \), the existence of good scales at \(\lambda \), stationary reflections for subsets of \(\lambda ^{+}\), diamond principles at \(\lambda \) and the singular cardinal hypothesis at \(\lambda \). We also discuss whether these principles can hold in \(L(V_{\lambda +1})\).     

Bauer–Furuta invariants under $${\mathbb{Z}_2}$$ -actions

S. Bauer and M. Furuta defined a stable cohomotopy refinement of the Seiberg–Witten invariants. In this paper, we prove a vanishing theorem of Bauer–Furuta invariants for 4-manifolds with smooth -actions. As an application, we give a constraint on smooth -actions on homotopy K3#K3, and construct a nonsmoothable locally linear -action on K3#K3. We also construct a nonsmoothable locally linear -action on K3.      

The Iwasawa invariant $$\mu$$ μ vanishes for $$\mathbb{Z}_{2}$$ Z 2 -extensions of certain real biquadratic fields

Acta Mathematica Hungarica - For a real biquadratic field, we denote by $$\lambda$$ , $$\mu$$ and $$\nu$$ the Iwasawa invariants of cyclotomic $$\mathbb{Z}_{2}$$ -extension of $$k$$ . We give...     

Optimal portfolio selections via $$\ell _{1, 2}$$ ℓ 1 , 2 -norm regularization

Computational Optimization and Applications - There has been much research about regularizing optimal portfolio selections through $$\ell _1$$ norm and/or $$\ell _2$$ -norm squared. The common...     

A simpler proof of a Katsurada’s theorem and rapidly converging series for $$\zeta {(2n+1)}$$ ζ ( 2 n + 1 ) and $$\beta {(2n)}$$ β ( 2 n )

Annali di Matematica Pura ed Applicata (1923 -) - In a recent work on Euler-type formulae for even Dirichlet beta values, i.e., $$\beta {(2n)}$$ , I have derived an exact closed-form expression for...     

On Partition of Unities Generated by Entire Functions and Gabor Frames in $$ L^2({\mathbb R}^d) $$ and $$\ell ^2({\mathbb Z}^d)$$ℓ2(Zd)

We characterize the entire functions P of d variables, \(d\ge 2,\) for which the \({\mathbb Z}^d\)-translates of \(P\chi _{[0,N]^d}\) satisfy the partition of unity for some \(N\in \mathbb N.\) In contrast to the one-dimensional case, these entire functions are not necessarily periodic. In the case where P is a trigonometric polynomial, we characterize the maximal smoothness of \(P\chi _{[0,N]^d},\) as well as the function that achieves it. A number of especially attractive constructions are achieved, e.g., of trigonometric polynomials leading to any desired (finite) regularity for a fixed support size. As an application we obtain easy constructions of matrix-generated Gabor frames in \( L^2({\mathbb R}^d) ,\) with small support and high smoothness. By sampling this yields dual pairs of finite Gabor frames in \(\ell ^2({\mathbb Z}^d).\)     

Beurling’s theorem for SL(2,$${\mathbb{R}}$$)

We prove Beurling’s theorem for the full group SL(2,). This is the master theorem in the quantitative uncertainty principle as all the other theorems of this genre follow from it.     

Constructing 2 × 2 Bricks from Unitary Numerical Semigroups

This paper investigates numerical semigroups that yield 2 × 2 bricks. We demonstrate the existence of an infinite family of 2 × 2 bricks that includes all of the perfect 2 × 2 bricks. We provide a formula for the Frobenius numbers of these semigroups as well as a necessary and sufficient condition for the semigroups to be symmetric.