On p-adic valuations of certain m colored p-ary partition functions

The Ramanujan Journal - Let $$k\in \mathbb {N}_{\ge 2}$$ and for given $$m\in \mathbb {Z}{\setminus }\{0\}$$ consider the sequence $$(S_{k,m}(n))_{n\in \mathbb {N}}$$ defined by the power series...     

Periodic behavior in families of numerical and affine semigroups via parametric Presburger arithmetic

Semigroup Forum - Let $$f_1(n), \ldots , f_k(n)$$ be polynomial functions of n. For fixed $$n\in \mathbb {N}$$ , let $$S_n\subseteq \mathbb {N}$$ be the numerical semigroup generated by...     

On the structure of partition which the difference of their representation function is a constant

Periodica Mathematica Hungarica - Let $$\mathbb {N}$$ be the set of nonnegative integers. For any set $$A \subset \mathbb {N}$$ , let $$R_1(A, n)$$ , $$R_2(A, n)$$ and $$R_3(A, n)$$ be the number...     

The classification of maximal inverse monoids of matrices

Semigroup Forum - Let $${\mathbb {F}}$$ be a field. The set $$M_{n}({\mathbb {F}})$$ of all $$n \times n$$ matrices over $${\mathbb {F}}$$ forms a monoid under usual matrix multiplication. We...     

Inequalities and Local Uncertainty Principles for Nilpotent Lie Groups

Mathematical Notes - Let $$\mathbb{F}_{q}$$ be a finite field, let $$\mathbb{X}$$ be a subset of the projective space ?s?1 over $$\mathbb{F}_{q}$$ parametrized by rational functions,...     

Orders generated by character values

Let $$K:=\mathbb {Q}(G)$$ be the number field generated by the complex character values of a finite group G. Let $$\mathbb {Z}_K$$ be the ring of integers of K. In this paper we investigate the suborder $$\mathbb {Z}[G]$$ of $$\mathbb {Z}_K$$ generated by the character values of G. We prove that every prime divisor of the order of the finite abelian group $$\mathbb {Z}_K/\mathbb {Z}[G]$$ divides |G|. Moreover, if G is nilpotent, we show that the exponent of $$\mathbb {Z}_K/\mathbb {Z}[G]$$ is a proper divisor of |G| unless $$G=1$$. We conjecture that this holds for arbitrary finite groups G.     

Distribution of Zeros of Exponential-Type Entire Functions with Constraints on Growth along a Line

Mathematical Notes - Let $$g\ne 0$$ be an entire function of exponential type in the complex plane $$\mathbb C$$ , and let $${\mathsf Z}=\{{\mathsf z}_k\}_{k=1,2,\dots}$$ be a sequence of points in...     

On a generalization of Schur theorem concerning resultants

Periodica Mathematica Hungarica - Let K be a field and put $${\mathcal {A}}:=\{(i,j,k,m)\in \mathbb {N}^{4}:\;i\le j\;\text{ and }\;m\le k\}$$ . For any given $$A\in {\mathcal {A}}$$ we consider...     

On the average number of subgroups of the group $${\mathbb {Z}}_m \times {\mathbb {Z}}_n$$ Z m × Z n with k-th power sequence

The Ramanujan Journal - Let $$\mathbb {Z}_{n}$$ be the additive group of residue classes modulo n. Let s(m, n) denote the total number of subgroups of the group $$\mathbb {Z}_{m} \times...     

Sufficient conditions for local equivalence of mappings

Let $$f,g:({\mathbb {R}}^n,0)\rightarrow ({\mathbb {R}}^m,0)$$ be $$C^{r+1}$$ mappings and let $$Z=\{x\in \mathbf {\mathbb {R}}^n:\nu (df (x))=0\}$$ , $$0\in Z$$ , $$m\le n$$ . We will show that if there exist a neighbourhood U of $$0\in {\mathbb {R}}^n$$ and constants $$C,C'>0$$ and $$k>1$$ such that for $$x\in U$$ $$\begin{aligned}&\nu (df(x))\ge C{\text {dist}}(x,Z)^{k-1}, \\&\left| \partial ^{s} (f_i-g_i)(x) \right| \le C'\nu (df(x))^{r+k-|s|}, \end{aligned}$$ for any $$i\in \{1,\dots , m\}$$ and for any $$s \in \mathbf {\mathbb {N}}^n_0$$ such that $$|s|\le r$$ , then there exists a $$C^r$$ diffeomorphism $$\varphi :({\mathbb {R}}^n,0)\rightarrow ({\mathbb {R}}^n,0)$$ such that $$f=g\circ \varphi $$ in a neighbourhood of $$0\in {\mathbb {R}}^n$$ . By $$\nu (df)$$ we denote the Rabier function.     

A note on commutator in the multilinear setting

Archiv der Mathematik - Let $$m\in \mathbb {N}$$ and $$\vec {b}=(b_{1}, \ldots ,b_{m})$$ be a collection of locally integrable functions. It is proved that $$b_{1},b_{2}, \ldots , b_{m}\in BMO$$ if...     

Automorphisms of threefolds of general type acting trivially in cohomology

Geometriae Dedicata - Let X be a minimal projective threefold of general type over $$\mathbb {C}$$ with only Gorenstein quotient singularities, and let $$\mathrm {Aut}_{\mathbb {Q}}(X)$$ be the...     

A Hardy–Trudinger–Moser Inequality Involving LpNorm in the Hyperbolic Space

Let B be the unit disc in R~2, H be the completion of C_0∞(B) under the norm■ .By the method of blow-up analysis and an argument of rearrangement with respect to the standard hyperbolic metric ■, we prove that, for any fixed■ ,the supremum■ .This is an analog of early results of Lu–Yang(Discrete Contin. Dyn. Syst., 2009) and Yang(Trans.Amer. Math. Soc., 2007), and extends those of Wang–Ye(Adv. Math., 2012) and Yang–Zhu(Ann.Global Anal. Geom., 2016).     

The decomposition of permutation module for infinite Chevalley groups

Let G be a connected reductive group defined over F_q, the finite field with q elements. Let B be a Borel subgroup defined over F_q. In this paper, we completely determine the composition factors of the induced module M(tr) = kG ■tr(where tr is the trivial B-module) for any field k.     

On dualization of a result of Bryce and Cossey theory

Acta Mathematica Hungarica - Let $$\sigma$$ be a partition of the set of all primes $$\mathbb{P}$$ . Let G be a finite group and $$\mathfrak{F}$$ be a Fitting class of finite groups. In the theory...     

On certain degenerate Whittaker Models for cuspidal representations of $${\mathrm{GL}_{k \cdot n}(\mathbb {F}_q)}$$ GL k · n ( F q )

Mathematische Zeitschrift - Let $$\pi $$ be an irreducible cuspidal representation of $$\mathrm {GL}_{kn}(\mathbb {F}_q)$$ . Assume that $$\pi = \pi _{\theta }$$ , corresponds to a regular...     

Winter定理和Dietz定理的推广

设G是由中心扩张1→Z_p^m→G→Z_p×…Z_p所决定的有限p-群,且|G’|≤p.确定了G的自同构群结构,推广了Winter和Dietz的工作     

A characterization of additive iterative roots of identity with respect to invariant subspaces

Aequationes mathematicae - Let $$\mathbb {K}$$ be an extension of the field  $$\mathbb {Q}$$ of rational numbers. We prove an algebraic characterization of the additive iterative roots of...     

Isomorphisms of subspaces of vector-valued continuous functions

Acta Mathematica Hungarica - We deal with isomorphic Banach–Stone type theorems for closed subspaces of vectorvalued continuous functions. Let $$\mathbb{F}=\mathbb{R}$$ or $$\mathbb{C}$$ ....     

The Spectrality of a Class of Fractal Measures on $$\mathbb{R}^{n}$$

Acta Mathematica Sinica, English Series - Let $$M=\rho^{-1}I\in M_{n}(\mathbb{R})$$ be an expanding matrix with 0 < ∣ ρ ∣ < 1 and $$D\subset\mathbb{Z}^{n}$$ be a...