Volume 32, Issue 2

In this work, the generalized family of Hermite–Sheffer polynomials is introduced by using Euler’s integral and operational rules. Furthermore, some properties are established. In particular, generating function and determinant definition for the generalized Hermite–Sheffer polynomials are obtained. Some examples are also considered and their corresponding results are established.

By analyzing known presentations of the pure mapping groups of orientable surfaces of genus g with b boundary components and n punctures in the cases when g=0{g=0} with b and n arbitrary, and when g=1{g=1} and b+n{b+n} is at most 3, we show that these groups are isomorphic to some groups related to the braid groups and the Artin group of type D4{D_{4}}. As a corollary, we conclude that the pure mapping class groups are linear in these cases.

In this paper, we give a complete description of strongly projective semimodules over a semiring which is a finite direct product of matrix semirings over commutative chain semirings. We then classify ultramatricial algebras over commutative chain semirings by their ordered SK0{\mathrm{SK}_{0}}-groups. Consequently, we get that there is a one-one correspondence between isomorphism classes of ultramatricial algebras A whose SK0⁢(A){\mathrm{SK}_{0}(A)} is lattice-ordered over a given commutative chain semiring and isomorphism classes of countable MV-algebras.

Heyde proved that a Gaussian distribution on a real line is characterized by the symmetry of the conditional distribution of one linear form given another. The present article is devoted to an analogue of the Heyde theorem in the case when random variables take values in a locally compact Abelian group and the coefficients of the linear forms are integers.

Iwasawa algebras of compact p -adic Lie groups are completed group algebras with applications in number theory in studying class numbers of towers of number fields and representation theory of p -adic Lie groups. We previously determined an explicit presentation of the Iwasawa algebra for the first principal congruence kernel of Chevalley groups over ℤp{\mathbb{Z}_{p}} which were uniform pro- p groups in the sense of Dixon, du Sautoy, Mann and Segal. In this paper, for prime p>n+1{p>n+1}, we determine the explicit presentation, in the form of generators and relations, of the Iwasawa algebra of the pro- p Iwahori subgroup of GLn⁢(ℤp){\mathrm{GL}_{n}(\mathbb{Z}_{p})} which is not, in general, a uniform pro- p group.

This paper proves the boundedness of the generalized Riesz potentials Iρ,μ,τ⁢f{I_{\rho,\mu,\tau}f} of functions in the Morrey space L(1,φ;κ)⁢(G){L^{(1,\varphi;\kappa)}(G)} over a general measure space X , with G a bounded open set in X (or G is X){X)}, as an extension of earlier results. The modification parameter τ is introduced for the purpose of including the case where the underlying measure does not satisfy the doubling condition. What is new in the present paper is that ρ depends on x∈X{x\in X}. An example in the end of this article convincingly explains why the modification parameter τ must be introduced.

Under some pretty much weaker size conditions assumed on the integral kernels both on the unit sphere and in the radial directions, the Lp{L^{p}} boundedness was given for the rough singular integrals defined by translates of a real-analytic submanifold in ℝn{\mathbb{R}^{n}}. Certain Lp{L^{p}} estimates for the corresponding maximal rough singular integrals were also established.

In this paper, we study dimension-free Lp{L^{p}} estimates for UMD lattice-valued q -variations of Hardy–Littlewood averaging operators associated with the Euclidean balls.

Let (R,𝔪){(R,\mathfrak{m})} be a local ring of prime characteristic p and of dimension d with the embedding dimension v . Suppose the Frobenius test exponent for parameter ideals Fte⁡(R){\operatorname{Fte}(R)} of R is finite, and let Q=pFte⁡(R){Q=p^{\operatorname{Fte}(R)}}. It is shown that e⁢(R)≤Qv-d⁢(vd).e(R)\leq Q^{v-d}\binom{v}{d}. We also improve the bound for F -nilpotent rings. Our result extends the main results of Huneke and Watanabe (2015) [6] and of Katzman and Zhang (2019).[9].

We study the behaviour at infinity, in suitable weighted Lp{L^{p}}-norms, of solutions of parabolic problems associated to the second order elliptic operator L=Δ+(a-1)⁢∑i,j=1Nxi⁢xj|x|2⁢Di⁢j+c⁢x|x|2⋅∇-b⁢|x|-2,L=\Delta+(a-1)\sum_{i,j=1}^{N}\frac{x_{i}x_{j}}{|x|^{2}}D_{ij}+c\frac{x}{|x|^{% 2}}\cdot\nabla-b|x|^{-2}, where a>0{a>0} and b,c∈ℝ{b,c\in\mathbb{R}}.

We completely characterize perfect, permutative, irreducible representations of an ultragraph Leavitt path algebra. For this, we extend to ultragraph Leavitt path algebras Chen’s construction of irreducible representations of Leavitt path algebras. We show that these representations can be built from branching system and characterize irreducible representations associated to perfect branching systems. Along the way, we improve the characterization of faithfulness of Chen’s irreducible representations.

We study twisted tensor products of ϕ-coordinated modules of nonlocal vertex algebras. Furthermore, we introduce the notion of ϕ-coordinated module twistor for a ϕ-coordinated module of a nonlocal vertex algebra.

We provide an explicit canonical description of the perverse cohomology sheaves and of the primitive perverse cohomology complexes for the non-small resolution π:𝒮~→𝒮{\pi:\tilde{\mathcal{S}}\to\mathcal{S}} of a special Schubert variety 𝒮{\mathcal{S}}. For such a resolution, we also discuss a way to obtain an explicit splitting of R⁢π⁢ℚ𝒮~*{R\pi{{}_{*}}\mathbb{Q}_{\widetilde{{\mathcal{S}}}}}, in the derived category, by means of Gysin morphisms and cohomology extensions.

This article continues a line of research aimed at solving an important problem of T. Kobayashi of the existence of compact Clifford–Klein forms of reductive homogeneous spaces. We contribute to this topic by showing that almost all symmetric spaces and 3-symmetric spaces do not admit solvable compact Clifford–Klein forms (with several possible exceptions). Our basic tool is a combination of the Hirzebruch–Kobayashi–Ono proportionality principle with the theory of syndetic hulls. Using this, we prove a general theorem which yields a sufficient condition for the non-existence of compact solvable Clifford–Klein forms.

In this note we construct an infinite-dimensional Lie group structure on the group of vertical bisections of a regular Lie groupoid. We then identify the Lie algebra of this group and discuss regularity properties (in the sense of Milnor) for these Lie groups. If the groupoid is locally trivial, i.e., a gauge groupoid, the vertical bisections coincide with the gauge group of the underlying bundle. Hence, the construction recovers the well-known Lie group structure of the gauge groups. To establish the Lie theoretic properties of the vertical bisections of a Lie groupoid over a non-compact base, we need to generalise the Lie theoretic treatment of Lie groups of bisections for Lie groupoids over non-compact bases.

In this article, we study chain conditions for graph C*-algebras. We show that there are infinitely many mutually non isomorphic Noetherian (and Artinian) purely infinite graph C*-algebras with infinitely many ideals. We prove that if E is a graph, then C*⁢(E){C^{*}(E)} is a Noetherian (resp. Artinian) C*-algebra if and only if E satisfies condition (K) and each ascending (resp. descending) sequence of admissible pairs of E stabilizes.

In this paper, we first prove an isomorphism between certain spaces of Jacobi forms. Using this isomorphism, we study the mod p theory of Hermitian Jacobi forms over ℚ⁢(i){\mathbb{Q}(i)}. We then apply the mod p theory of Hermitian Jacobi forms to characterize U⁢(p){U(p)} congruences and to study Ramanujan-type congruences for Hermitian Jacobi forms and Hermitian modular forms of degree 2 over ℚ⁢(i){\mathbb{Q}(i)}.

Pólya proved in 1927 that the Riemann hypothesis is equivalent to the hyperbolicity of all of the Jensen polynomials of degree d and shift n for the Riemann Xi-function. Recently, Griffin, Ono, Rolen, and Zagier [M. Griffin, K. Ono, L. Rolen and D. Zagier, Jensen polynomials for the Riemann zeta function and other sequences, Proc. Natl. Acad. Sci. USA 116 2019, 23, 11103–11110] proved that for each degree d≥1{d\geq 1} all of the Jensen polynomials for the Riemann Xi-function are hyperbolic except for possibly finitely many n . Here we extend their work by showing that the same statement is true for suitable L -functions. This offers evidence for the generalized Riemann hypothesis.