Some Ricci-flat ($$\alpha ,\beta $$)-metrics

In this paper, we study a special class of Finsler metrics, \((\alpha ,\beta )\)-metrics, defined by \(F=\alpha \phi (\beta /\alpha )\), where \(\alpha \) is a Riemannian metric and \(\beta \) is a 1-form. We find an equation that characterizes Ricci-flat \((\alpha ,\beta )\)-metrics under the condition that the length of \(\beta \) with respect to \(\alpha \) is constant.     

On Ikehara type Tauberian theorems with $$O(x^\gamma )$$ remainders

Motivated by analytic number theory, we explore remainder versions of Ikehara’s Tauberian theorem yielding power law remainder terms. More precisely, for \(f:[1,\infty )\rightarrow {\mathbb R}\) non-negative and non-decreasing we prove \(f(x)-x=O(x^\gamma )\) with \(\gamma <1\) under certain assumptions on f. We state a conjecture concerning the weakest natural assumptions and show that we cannot hope for more.     

Mathematical Analysis of a Cauchy Problem for the Time-Fractional Diffusion-Wave Equation with $$ \alpha \in \left( 0,2\right) $$

This paper deals with a theoretical mathematical analysis of a Cauchy problem for the time-fractional diffusion-wave equation in the upper half-plane, \(x\in \mathbb {R}\), \(t\in \mathbb {R}^+\), where the Caputo fractional derivative of order \(\alpha \in \left( 0,2\right) \) is considered. An explicit solution to this Cauchy problem is obtained via separation of variables. A first proof of the validity of the obtained results is provided for a certain kind of initial conditions. Throughout this work a new expression of the solution to this problem and its utility for carrying out rigurous proofs are presented. Finally, several new properties of the solution are obtained.     

Inequalities for functions of the classes $$_\rho (R^n )$$

Journal of Mathematical Sciences -     

The Laplacian on $$ C(\overline \Omega) $$ with generalized Wentzell boundary conditions

In this note we prove that the Laplacian with generalized Wentzell boundary conditions on an open bounded regular domain in defined by generates an analytic semigroup of angle on for every > 0 and (for the definition of cf. (1.3)).Received: 13 July 2002     

Generators of the ring of weakly holomorphic modular functions for $$\Gamma _1(N)$$

For a positive integer N divisible by 4, 5, 6, 7 or 9, let \(\mathcal {O}_{1,N}(\mathbb {Q})\) be the ring of weakly holomorphic modular functions for the congruence subgroup \(\Gamma _1(N)\) with rational Fourier coefficients. We present explicit generators of the ring \(\mathcal {O}_{1,N}(\mathbb {Q})\) over \(\mathbb {Q}\) by making use of modular units which have infinite product expansions.     

Sharp estimates for functions of class $$ \mathop {W_2^r }\limits^ \circ ( - 1,1) $$

Doklady Mathematics -     

An $$\mathcal{O}(m\log n)$$ algorithm for the weighted stable set problem in claw-free graphs with $$\alpha ({G}) \le 3$$

Mathematical Programming - In this paper we show how to solve the Maximum Weight Stable Set Problem in a claw-free graph G(V,&nbsp;E) with $$\alpha (G) \le 3$$ in time $$\mathcal{O}(|E|\log...     

Essential stability of $$\alpha $$-core

Using the existence results in Kajii (J Econ Theory 56:194–205, 1992), we identify a class of n-person noncooperative games containing a dense residual subset of games whose cooperative equilibria are all essential. Moreover, we show that every game in this collection possesses an essential component of the \(\alpha \)-core by proving the connectivity of minimal essential subsets of the \(\alpha \)-core.     

An additive ($${\alpha, \beta}$$)-functional equation and linear mappings in Banach spaces

In this paper, we investigate the additive (\({\alpha, \beta}\))-functional equation \({f(x+y) + \bar{\alpha}f({\alpha}z) = \beta^{-1}f(\beta(x+y+z))}\) for all complex numbers \({\alpha}\) with \({|\alpha| = 1}\) and for a fixed nonzero complex number \({\beta}\). Using the fixed point method and the direct method, we prove the Hyers–Ulam stability of this additive (\({\alpha, \beta}\))-functional equation in complex Banach spaces.     

Discrete decomposability of restrictions of $$({\mathfrak {g}},K)$$ ( g,K ) -modules for $$(G,G^\sigma )$$ ( G,G σ ) with an automorphism $$\sigma $$ σ of even order

Geometriae Dedicata - In this article we show that the only 2-step nilpotent Lie groups which carry a non-degenerate left invariant Killing–Yano 2-form are the complex Lie groups. In the case...     

The $$\alpha $$-modulation transform: admissibility,coorbit theory and frames of compactly supported functions

The \(\alpha \)-modulation transform is a time-frequency transform generated by square-integrable representations of the affine Weyl–Heisenberg group modulo suitable subgroups. In this paper we prove new conditions that guarantee the admissibility of a given window function. We also show that the generalized coorbit theory can be applied to this setting, assuming specific regularity of the windows. This then yields canonical constructions of Banach frames and atomic decompositions in \(\alpha \)-modulation spaces. In particular, we prove the existence of compactly supported (in time domain) vectors that are admissible and satisfy all conditions within the coorbit machinery, which considerably go beyond known results.     

$$\bar\partial$$ -dressing method for a few $$(2+1)$$ -dimensional integrable coupling systems

Theoretical and Mathematical Physics - Several $$(2+1)$$ -dimensional integrable coupling systems are derived from two sets of auxiliary linear problems, including the integrable coupling system of...     

The Stereotype Approximation Property for the Algebras $$\mathcal C(M)$$ of Continuous Functions on Metric Spaces

Mathematical Notes -     

Application of the $$\bar\partial$$ -dressing method to a $$(2+1)$$ -dimensional equation

Theoretical and Mathematical Physics - A remarkable method for investigating solutions of nonlinear soliton equation is the $$\bar\partial$$ -dressing method. Although there are other methods that...     

On bornologicalC $$\overline V $$ (X) spaces

Archiv der Mathematik -     

Lower Bounds for the Maximum Modulus of $$\zeta \left( s \right)$$ in Small Domains of the Critical Strip

Mathematical Notes -     

$$\varvec{}$$-Classes in finite groups of conjugate type $$\varvec{(n,1)}$$(n,1)

Two elements in a group G are said to be z-equivalent or to be in the same z-class if their centralizers are conjugate in G. In a recent work, Kulkarni et al. (J. Algebra Appl., 15 (2016) 1650131) proved that a non-abelian p-group G can have at most \(\frac{p^k-1}{p-1} +1\) number of z-classes, where \(|G/Z(G)|=p^k\). Here, we characterize the p-groups of conjugate type (n, 1) attaining this maximal number. As a corollary, we characterize p-groups having prime order commutator subgroup and maximal number of z-classes.     

Beckman-Quarles type theorems for mappings from $$ \mathbb{R}^n $$ to $$ \mathbb{C}^n $$

Summary. Let We say that preserves the distance d 0 if for each implies Let A _n denote the set of all positive numbers d such that any map that preserves unit distance preserves also distance d. Let D _n denote the set of all positive numbers d with the property: if and then there exists a finite set S _xy with such that any map that preserves unit distance preserves also the distance between x and y. Obviously, We prove: (1) (2) for n 2 D _n is a dense subset of (2) implies that each mapping f from to (n 2) preserving unit distance preserves all distances, if f is continuous with respect to the product topologies on and