Duality for constrained robust sum optimization problems

Mathematical Programming - Given an infinite family of extended real-valued functions $$f_{i}$$ , $$i\in I,$$ and a family $${\mathcal {H}}$$ of nonempty finite subsets of I,  the...     

Intertwining Operators Associated to a Family of Differential-Reflection Operators

Mediterranean Journal of Mathematics - We introduce a family of differential-reflection operators $${\Lambda_{A, \varepsilon}}$$ acting on smooth functions defined on $${{\mathbb R}}$$ . Here, A is...     

A Characterization on the Spectra of Self-Affine Measures

Journal of Fourier Analysis and Applications - A discrete set $$\Lambda \subseteq {\mathbb {R}}^d$$ is called a spectrum for the probability measure $$\mu $$ if the family of functions $$\{e^{2 \pi...     

Wellposedness of NLS in Modulation Spaces

Journal of Fourier Analysis and Applications - Let $${\mathcal {R}}$$ denote the generalized Radon transform, which integrates over a family of N-dimensional smooth submanifolds $${\mathcal...     

Schlichting’s theorem for approximate subgroups

We prove Schlichting’s theorem for approximate subgroups: if $${\mathcal {X}}$$ is a uniform family of commensurable approximate subgroups in some ambient group, then there exists an invariant approximate subgroup commensurable with $${\mathcal {X}}$$.     

The $${\mathcal {F}}$$ F -transitivity and recurrence of translation semigroups on complex sectors

Semigroup Forum - In this paper, we study the $${\mathcal {F}}$$ -transitive behaviour of the translation semigroups on complex sectors, where $${\mathcal {F}}$$ is a Furstenberg family of the...     

A Tree-valued Markov Process Associated with an Admissible Family of Branching Mechanisms

Let E?R be an interval. By studying an admissible family of branching mechanisms{ψt,t ∈E} introduced in Li [Ann. Probab., 42, 41-79(2014)], we construct a decreasing Levy-CRT-valued process {Tt, t ∈ E} by pruning Lévy trees accordingly such that for each t ∈E, Tt is a ψt-Lévy tree. We also obtain an analogous process {Tt*,t ∈E} by pruning a critical Levy tree conditioned to be infinite. Under a regular condition on the admissible family of branching mechanisms, we show that the law of {Tt,t ∈E} at the ascension time A := inf{t ∈E;Tt is finite} can be represented by{Tt*,t∈E}.The results generalize those studied in Abraham and Delmas [Ann. Probab., 40, 1167-1211(2012)].     

A uniform version of a theorem by Dvir and Moran

Acta Mathematica Hungarica - Let $$0\leq d\leq n$$ be integers and $$\mathcal{F}$$ a family with $${\rm VCdim} ( \mathcal{F} \Delta \mathcal{F} )\leq d$$ . Analogously to the celebrated...     

On some families of subsemigroups of a numerical semigroup

Semigroup Forum - To a given numerical semigroup S we associate a family of subsemigroups $$\{\partial ^nS\}$$ , $$n\in {\mathbb {N}}$$ , that permits us to understand some of the structure of S....     

Positive Ground States for the Fractional Klein–Gordon–Maxwell System with Critical Exponents

Mediterranean Journal of Mathematics - Let G be a locally compact Abelian (LCA) group which possesses a covering family. We define an atomic Hardy space $$H^1(G)$$ and $$\textrm{BMO}(G)$$ of...     

A Note on 3-Divisibility of Class Number of Quadratic Field

In this paper, the authors show that there exists infinitely many family of pairs of quadratic fields Q(D^1/2) and Q((D+n)(1/2)) with D, n∈Z whose class numbers are both divisible by 3.     

On Hamiltonian Minimality of Isotropic Nonhomogeneous Tori in $$\mathbb{H}^n$$ and $$\mathbb{C} \mathrm{P}^{2n+1}$$

Mathematical Notes - We construct a family of flat isotropic nonhomogeneous tori in $$\mathbb{H}^n$$ and $$\mathbb{C}\mathrm{P}^{2n+1}$$ and find necessary and sufficient conditions for their...     

Box-total dual integrality and edge-connectivity

Mathematical Programming - Given a graph $$G=(V,E)$$ and an integer $$k\ge 1$$ , the graph $$H=(V,F)$$ , where F is a family of elements (with repetitions allowed) of E, is a k-edge-connected...     

A family of pairs of imaginary cyclic fields of degree $$(p-1)/2$$(p-1)/2 with both class numbers divisible by p

The Ramanujan Journal - Let p be a prime number with $$p\equiv 5\ (\mathrm{mod}\ {8})$$. We construct a new infinite family of pairs of imaginary cyclic fields of degree $$(p-1)/2$$ with both class...     

The Liouville-type theorem for problems with nonstandard growth derived by Caccioppoli-type estimate

Let u be a nonnegative solution to the PDI $$-\,\mathrm{div} \mathcal {A}(x, u, \nabla u)\geqslant \mathcal {B}(x,u, \nabla u)$$ in $$\Omega $$, where $$\mathcal {A}$$ and $$\mathcal {B}$$ are differential operators with p(x)-type growth. As a consequence of the Caccioppoli-type inequality for the solution u, we obtain the Liouville-type theorem under some integral condition. We simplify the assumptions on functions $$ \mathcal {A}$$ and $$ \mathcal {B}$$, and we do not restrict the range of p(x) by the dimension n, therefore we can cover quite general family of problems.     

On the Hahn-Banach theorem for groups

Let be the family of all groups such that under each subadditive functional there exists an additive functional. We show that the class is between the class of all amenable groups and the family of all groups for which the Hyers stability theorem for homomorphisms holds true. Next, we generalize the classical Hahn-Banach theorem to the class . Received: 6 May 2005     

Adjacency and transition matrices related to random walks on graphs

Journal of Algebraic Combinatorics - A pointed graph $$(\Gamma ,v_0)$$ induces a family of transition matrices in Wildberger’s construction of a hermitian hypergroup using a random walk on...     

On a Family of Complex-Valued Stochastic Processes

Doklady Mathematics - We introduce a family $${{r}_{\lambda }},\lambda \in \mathbb{C}$$ of complex-valued stochastic processes making it possible to construct a probabilistic representation for the...     

On the Ricci flow of homogeneous metrics on spheres

Annals of Global Analysis and Geometry - We study the Ricci flow of the four-parameter family of Sp $$(n+1)$$ -invariant metrics on spheres. We determine their forward behaviour and also classify...     

Quasi-arithmetic-type invariant means on probability space

Aequationes mathematicae - For a family $$(\mathscr {A}_x)_{x \in (0,1)}$$ of integral quasi-arithmetic means satisfying certain measurability-type assumptions we search for an integral mean K such...