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Rigid commutators and a normalizer chain Monatshefte Math. (IF 0.933) Pub Date : 2021-01-15 Riccardo Aragona, Roberto Civino, Norberto Gavioli, Carlo Maria Scoppola
The notion of rigid commutators is introduced to determine the sequence of the logarithms of the indices of a certain normalizer chain in the Sylow 2-subgroup of the symmetric group on \(2^n\) letters. The terms of this sequence are proved to be those of the partial sums of the partitions of an integer into at least two distinct parts, that relates to a famous Euler’s partition theorem.
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Universal power series of Seleznev with parameters in several variables Monatshefte Math. (IF 0.933) Pub Date : 2021-01-11 K. Maronikolakis, G. Stamatiou
We generalize the universal power series of Seleznev to several variables and we allow the coefficients to depend on parameters. Then, the approximable functions may depend on the same parameters. The universal approximation holds on products \(K = \displaystyle \prod \nolimits _{i = 1}^d K_i\), where \(K_i \subseteq \mathbb {C}\) are compact sets and \(\mathbb {C} {\setminus } K_i\) are connected
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Wasserstein distance, Fourier series and applications Monatshefte Math. (IF 0.933) Pub Date : 2021-01-07 Stefan Steinerberger
We study the Wasserstein metric \(W_p\), a notion of distance between two probability distributions, from the perspective of Fourier Analysis and discuss applications. In particular, we bound the Earth Mover Distance \(W_1\) between the distribution of quadratic residues in a finite field \({\mathbb {F}}_p\) and uniform distribution by \(\lesssim p^{-1/2}\) (the Polya–Vinogradov inequality implies
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Comments on “Flag-transitive block designs and unitary groups” Monatshefte Math. (IF 0.933) Pub Date : 2021-01-06 Xiaoqin Zhan, Suyun Ding
In this note we point out an error in a recent paper on flag-transitive block designs with gcd\((r,\lambda )=1\), and we prove a result correcting the error.
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Class groups of real cyclotomic fields Monatshefte Math. (IF 0.933) Pub Date : 2021-01-06 Mohit Mishra, Rene Schoof, Lawrence C. Washington
We prove that every finite abelian group G occurs as a subgroup of the class group of infinitely many real cyclotomic fields.
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Automorphisms of odd Coxeter groups Monatshefte Math. (IF 0.933) Pub Date : 2021-01-05 Tushar Kanta Naik, Mahender Singh
An odd Coxeter group W is one which admits a Coxeter system (W, S) for which all the exponents \(m_{ij}\) are either odd or infinity. The paper investigates the family of odd Coxeter groups whose associated labeled graphs \({\mathcal {V}}_{(W,S)}\) are trees. It is known that two Coxeter groups in this family are isomorphic if and only if they admit Coxeter systems having the same rank and the same
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Moore-type nonoscillation criteria for half-linear difference equations Monatshefte Math. (IF 0.933) Pub Date : 2021-01-05 Fentao Wu, Lin She, Kazuki Ishibashi
This paper deals with the half-liner difference equation $$\begin{aligned} \varDelta (r_n\phi _p(\varDelta x_n))+c_n\phi _p(x_{n+1})=0, \end{aligned}$$ where \(r_n\), \(c_n\) are real-valued sequences, \(r_n>0\) for \(n \in \mathbb {N} \cup \{0\}\), and \(\phi _p(z)=|z|^{p-2}z\) with \(p>1\) and \(\mathbb {N}\) is the set of natural numbers. The purpose of this paper is to use the function transformation
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BMO multilinear multiplier theorem of Mikhlin–Hörmander type Monatshefte Math. (IF 0.933) Pub Date : 2021-01-05 Bae Jun Park
In this paper we provide an improved BMO version of the Mikhlin–Hörmander multiplier theorem for multilinear operators.
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Subgroups of pro- p $$PD ^3$$ P D 3 -groups Monatshefte Math. (IF 0.933) Pub Date : 2021-01-04 I. Castellano, P. Zalesskii
We study 3-dimensional Poincaré duality pro-p groups in the spirit of the work by Robert Bieri and Jonathan Hillmann, and show that if such a pro-p group G has a nontrivial finitely presented subnormal subgroup of infinite index, then either the subgroup is cyclic and normal or the subgroup is cyclic and the group is polycyclic or the subgroup is Demushkin and normal in an open subgroup of G. Also
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Totient quotient and small gaps between primes Monatshefte Math. (IF 0.933) Pub Date : 2021-01-04 Lixia Dai, Hao Pan
For each \(m\ge 1\), there exists \(H=H(m)>0\) such that the set $$\begin{aligned} \bigg \{\frac{\phi (p+1)}{\phi (p-1)}:\,p\text { is prime and }[p+1,p+H]\text { contains at least }m\text { primes}\bigg \} \end{aligned}$$ is dense in \([0,+\infty )\), where \(\phi \) denotes the Euler totient function. This gives a unconditional weak form of a recent result of Garcia, Luca, Shi and Udell, which was
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A slow triangle map with a segment of indifferent fixed points and a complete tree of rational pairs Monatshefte Math. (IF 0.933) Pub Date : 2021-01-04 Claudio Bonanno, Alessio Del Vigna, Sara Munday
We study the two-dimensional continued fraction algorithm introduced in Garrity (J Number Theory 88(1):86–103, 2001) and the associated triangle map T, defined on a triangle \(\triangle \subseteq \mathbb {R}^2\). We introduce a slow version of the triangle map, the map S, which is ergodic with respect to the Lebesgue measure and preserves an infinite Lebesgue-absolutely continuous invariant measure
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Khintchine-type theorems for values of subhomogeneous functions at integer points Monatshefte Math. (IF 0.933) Pub Date : 2021-01-03 Dmitry Kleinbock, Mishel Skenderi
This work has been motivated by recent papers that quantify the density of values of generic quadratic forms and other polynomials at integer points, in particular ones that use Rogers’ second moment estimates. In this paper, we establish such results in a very general framework. Given any subhomogeneous function (a notion to be defined) \(f: \mathbb {R}^n \rightarrow \mathbb {R}\), we derive a necessary
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Existence and uniqueness results for modeling jet flow of the antarctic circumpolar current Monatshefte Math. (IF 0.933) Pub Date : 2021-01-02 JinRong Wang, Michal Fečkan, Qian Wen, Donal O’Regan
In this paper we are concerned with the analysis of a mathematical model, a two point boundary value problem for a second-order differential equation, that is used to deal with the jet flow of the antarctic circumpolar current. We present some new existence and uniqueness results when the vorticity function satisfies either a Lipschitz condition or is continuous.
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Finite groups whose maximal subgroups of order divisible by all the primes are supersolvable Monatshefte Math. (IF 0.933) Pub Date : 2021-01-02 Alexander Moretó
We study finite groups G with the property that for any subgroup M maximal in G whose order is divisible by all the prime divisors of |G|, M is supersolvable. We show that any nonabelian simple group can occur as a composition factor of such a group and that, if G is solvable, then the nilpotency length and the rank are arbitrarily large. On the other hand, for every prime p, the p-length of such a
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The asymptotic number of zeros of exponential sums in critical strips Monatshefte Math. (IF 0.933) Pub Date : 2021-01-02 Janne Heittokangas, Zhi-Tao Wen
Normalized exponential sums are entire functions of the form $$\begin{aligned} f(z)=1+H_1e^{w_1z}+\cdots +H_ne^{w_nz}, \end{aligned}$$ where \(H_1,\ldots , H_n\in {{\mathbb {C}}}\) and \(0
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A Poincare’s inequality with non-uniformly degenerating gradient Monatshefte Math. (IF 0.933) Pub Date : 2021-01-01 Farman Mamedov
In homogeneous space (\(\mathbb {R}^N, d, \mu \)) we explore Poincare’s type inequality $$\begin{aligned} \Vert f-\overline{f}_{\Omega , v}\Vert _{q, v}\le C \Vert \nabla _\lambda f \Vert _{p}, \,\,\,\, q \ge p\ge 1 \end{aligned}$$ on estimation of weighted Lebesgue norm of a Lipschitz continuous function \(f: \Omega \rightarrow \mathbb {R}\) over the bounded convex domain \(\Omega \subset \mathbb
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Correction to: Construction of some Chowla sequences Monatshefte Math. (IF 0.933) Pub Date : 2020-12-26 Ruxi Shi
The article Construction of some Chowla sequences, written by Ruxi Shi was originally published electronically on the publisher’s internet portal on October 10, 2020 without open access. With the author(s)’ decision to opt for Open Choice the copyright of the article changed on November 25, 2020 to © [The author(s)] [2020] and the article is forthwith distributed under a Creative Commons Attribution
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On systems of parabolic variational inequalities with multivalued terms Monatshefte Math. (IF 0.933) Pub Date : 2020-12-26 Siegfried Carl, Vy. K. Le
In this paper we present an analytical framework for the following system of multivalued parabolic variational inequalities in a cylindrical domain \(Q=\varOmega \times (0,\tau )\): For \(k=1,\dots , m\), find \(u_k\in K_k\) and \(\eta _k\in L^{p'_k}(Q)\) such that $$\begin{aligned}&u_k(\cdot ,0)=0\ \text{ in } \varOmega ,\ \ \eta _k(x,t)\in f_k(x,t,u_1(x,t), \dots , u_m(x,t)), \\&\langle u_{kt}+A_k
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Solution concepts, well-posedness, and wave breaking for the Fornberg–Whitham equation Monatshefte Math. (IF 0.933) Pub Date : 2020-12-21 Günther Hörmann
We discuss concepts and review results about the Cauchy problem for the Fornberg–Whitham equation, which has also been called Burgers–Poisson equation in the literature. Our focus is on a comparison of various strong and weak solution concepts as well as on blow-up of strong solutions in the form of wave breaking. Along the way we add aspects regarding semiboundedness at blow-up, from semigroups of
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Infinite products related to generalized Thue–Morse sequences Monatshefte Math. (IF 0.933) Pub Date : 2020-11-27 Yao-Qiang Li
Given an integer \(q\ge 2\) and \(\theta _1,\ldots ,\theta _{q-1}\in \{0,1\}\), let \((\theta _n)_{n\ge 0}\) be the generalized Thue–Morse sequence, defined to be the unique fixed point of the morphism $$\begin{aligned} 0\mapsto & {} 0\theta _1\cdots \theta _{q-1}\\ 1\mapsto & {} 1\overline{\theta }_1\cdots \overline{\theta }_{q-1} \end{aligned}$$ beginning with \(\theta _0:=0\), where \(\overline{0}:=1\)
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2-Adic properties for the numbers of representations in the alternating groups Monatshefte Math. (IF 0.933) Pub Date : 2020-11-20 Yugen Takegahara
Let A be the direct product of a cyclic group of order \(2^u\) with \(u\ge 1\) and a cyclic group of order \(2^v\) with \(u\ge v\ge 0\). There are some 2-adic properties of the number \(h(A,A_n)\) of homomorphisms from A to the alternating group \(A_n\) on n-letters, which are similar to those of the number of homomorphisms from A to the symmetric group on n-letters. The exponent of 2 in the decomposition
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Well-posedness and regularity for fractional damped wave equations Monatshefte Math. (IF 0.933) Pub Date : 2020-11-20 Yong Zhou, Jia Wei He
In this paper, we study the well-posedness and regularity of mild solutions for a class of time fractional damped wave equations, which the fractional derivatives in time are taken in the sense of Caputo type. A concept of mild solutions is introduced to prove the existence for the linear problem, as well as the regularity of the solution. We also establish a well-posed result for nonlinear problem
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Invariant densities for composed piecewise fractional linear maps Monatshefte Math. (IF 0.933) Pub Date : 2020-11-16 Fritz Schweiger
The starting point for this paper was the following problem: If we know the invariant densities for two maps S and T can we say something about the invariant density of the map \(U = T \circ S\)? This problem seems not to be touched on within ergodic theory. In this note we look at the inverse problem. Let the invariant density for \(U = T \circ S\) be known. What can we say about invariant densities
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A note on pronormal p -subgroups of finite groups Monatshefte Math. (IF 0.933) Pub Date : 2020-11-16 Suli Liu, Haoran Yu
In this note, we investigate the influence of pronormal p-subgroups on the structure of finite groups. We not only simplify, but also generalize some main results of Liu et al. (J Algebra Appl 19:2050110, 2020), Shen et al. (Monatshefte Math 175:629–638, 2014) and Yu and Lai (Monatshefte Math 181:745–747, 2016). We also prove that for p-subgroups of finite groups, the concept of pronormal subgroups
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On the nilpotent probability and supersolvability of finite groups Monatshefte Math. (IF 0.933) Pub Date : 2020-11-16 Huaquan Wei, Huilong Gu, Jiao Li, Liying Yang
Let G be a finite group. We denote by \(Nil_G(x)\) the set of elements \(y\in G\) such that \(\langle x,y\rangle \) is a nilpotent subgroup and by \(\nu _1(G)\) and \(\nu (G)\) the probability that two randomly chosen elements of G respectively generate an abelian subgroup and a nilpotent subgroup. A group G is called an \({\mathcal {N}}\)-group if \(Nil_G(x)\) is a group for all \(x\in G\). It is
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Groups with a solvable subgroup of prime-power index Monatshefte Math. (IF 0.933) Pub Date : 2020-11-16 Raimundo Bastos, Csaba Schneider
In this paper we describe some properties of groups G that contain a solvable subgroup of finite prime-power index (Theorem 1 and Corollaries 2–3). We prove that if G is a non-solvable group that contains a solvable subgroup of index \(p^{\alpha }\) (for some prime p), then the quotient \(G/\mathsf{Rad}{(}G)\) of G over the solvable radical is asymptotically small in comparison to \(p^{\alpha }!\)
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Hypocoercivity and sub-exponential local equilibria Monatshefte Math. (IF 0.933) Pub Date : 2020-11-13 E. Bouin, J. Dolbeault, L. Lafleche, C. Schmeiser
Hypocoercivity methods are applied to linear kinetic equations without any space confinement, when local equilibria have a sub-exponential decay. By Nash type estimates, global rates of decay are obtained, which reflect the behavior of the heat equation obtained in the diffusion limit. The method applies to Fokker-Planck and scattering collision operators. The main tools are a weighted Poincaré inequality
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Factoring Solovay-random extensions, with application to the reduction property Monatshefte Math. (IF 0.933) Pub Date : 2020-11-12 Vladimir Kanovei, Vassily Lyubetsky
If a real a is random over a model M and \(x\in M[a]\) is another real then either (1) \(x\in M\), or (2) \(M[x]=M[a]\), or (3) M[x] is a random extension of M and M[a] is a random extension of M[x]. This result may belong to the old set theoretic folklore. It appeared as Exapmle 1.17 in Jech’s book “Multiple forcing” without the claim that M[x] is a random extension of M in (3), but, likely, it has
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On the rank of a finite group of odd order with an involutory automorphism Monatshefte Math. (IF 0.933) Pub Date : 2020-11-12 Cristina Acciarri, Pavel Shumyatsky
Let G be a finite group of odd order admitting an involutory automorphism \(\phi \), and let \(G_{-\phi }\) be the set of elements of G transformed by \(\phi \) into their inverses. Note that \([G,\phi ]\) is precisely the subgroup generated by \(G_{-\phi }\). Suppose that each subgroup generated by a subset of \(G_{-\phi }\) can be generated by at most r elements. We show that the rank of \([G,\phi
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Existence and multiplicity of periodic solutions for a class of second-order ordinary differential equations Monatshefte Math. (IF 0.933) Pub Date : 2020-09-22 Xiaoling Han, Hujun Yang
In this paper, we study the existence of positive periodic solutions for a class of non-autonomous second-order ordinary differential equations $$\begin{aligned} x''+\alpha x' +a(t)x^{n}-b(t)x^{n+1}+c(t)x^{n+2}=0, \end{aligned}$$ where \(\alpha \in {\mathbb {R}} \) is a constant, n is a finite positive integer, and a(t), b(t), c(t) are continuous periodic functions. By using Mawhin’s continuation theorem
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Positive solutions to integral boundary value problems from geophysical fluid flows Monatshefte Math. (IF 0.933) Pub Date : 2020-09-22 Wenlin Zhang, Michal Fečkan, JinRong Wang
The mathematical model of the Antarctic Circumpolar Current with integral boundary conditions is established and the explicit expression of green’s function is obtained. The existence and uniqueness of solutions are proved by using the mixed monotone operator theory. The sufficient conditions for the existence of positive solutions of the model are given and the existence of positive solutions with
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Geometry of compact lifting spaces Monatshefte Math. (IF 0.933) Pub Date : 2020-08-31 Gregory R. Conner, Wolfgang Herfort, Petar Pavešić
We study a natural generalization of inverse systems of finite regular covering spaces. A limit of such a system is a fibration whose fibres are profinite topological groups. However, as shown in Conner et al. (Topol Appl 239:234–243, 2018), there are many fibrations whose fibres are profinite groups, which are far from being inverse limits of coverings. We characterize profinite fibrations among a
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Properties of normal harmonic mappings Monatshefte Math. (IF 0.933) Pub Date : 2020-08-30 Hua Deng, Saminathan Ponnusamy, Jinjing Qiao
In this paper, we present several necessary and sufficient conditions for a harmonic mapping to be normal. Also, we discuss maximum principle and five-point theorem for normal harmonic mappings. Furthermore, we investigate the convergence of sequences for sense-preserving normal harmonic mappings and show that the asymptotic values and angular limits are identical for normal harmonic mappings.
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On eigenvalue problems related to the laplacian in a class of doubly connected domains Monatshefte Math. (IF 0.933) Pub Date : 2020-09-22 Sheela Verma, G. Santhanam
We study eigenvalue problems in some specific class of doubly connected domains. In particular, we prove the following. 1. Let \(B_1\) be an open ball in \({\mathbb {R}}^n\), \(n>2\) and \(B_0\) be an open ball contained in \(B_1\). Then the first eigenvalue of the problem $$\begin{aligned} \begin{array}{rcll} \varDelta u &{}=&{} 0 \, &{} \text{ in } \, B_1 \setminus {\overline{B}}_0 , \\ u &{}=&{}
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Local well-posedness and time regularity for a fifth-order shallow water equations in analytic Gevrey–Bourgain spaces Monatshefte Math. (IF 0.933) Pub Date : 2020-09-22 Aissa Boukarou, Kaddour Guerbati, Khaled Zennir
This paper studies a Cauchy problems for fifth-order shallow water equations with nonlinear terms in (1). With data in analytic Gevrey spaces on the line, we prove that the problem is well defined. We also treat the regularity in time which belongs to \(G^{5\sigma }\) near zero for every x on the line. The proof is based mainly on bilinear and trilinear estimates in the analytic Gevrey–Bourgain spaces
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On members of Lucas sequences which are products of factorials Monatshefte Math. (IF 0.933) Pub Date : 2020-07-31 Shanta Laishram, Florian Luca, Mark Sias
We show that if \(\{U_n\}_{n\ge 0}\) is a Lucas sequence, then the largest n such that \(|U_n|=m_1!m_2!\cdots m_k!\) with \(1\le m_1\le m_2\le \cdots \le m_k\) satisfies \(n<\) 62,000. When the roots of the Lucas sequence are real, we have \(n\in \{1, 2, 3, 4, 6, 12\}\). As a consequence, we show that if \(\{X_n\}_{n\ge 1}\) is the sequence of X-coordinates of a Pell equation \(X^2-dY^2=\pm 1\) with
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Periodic points in random substitution subshifts Monatshefte Math. (IF 0.933) Pub Date : 2020-08-26 Dan Rust
We study various aspects of periodic points for random substitution subshifts. In order to do so, we introduce a new property for random substitutions called the disjoint images condition. We provide a procedure for determining the property for compatible random substitutions—random substitutions for which a well-defined abelianisation exists. We find some simple necessary criteria for primitive, compatible
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Radix expansions and connectedness of planar self-affine fractals Monatshefte Math. (IF 0.933) Pub Date : 2020-08-25 Lian Wang, King-Shun Leung
Let A be an expanding matrix with characteristic polynomial \(f(x)=x^2+px+3\) and \(\mathcal {D}=\{0,v,\ell v+kAv\}\) be a digit set where \(\ell ,k\in {\mathbb {Z}},\ v\in {\mathbb {R}}^2\) so that \(\{v,Av\}\) is linearly independent. It is well known that there exists a unique self-affine fractal T satisfying \(AT=T+\mathcal {D}\). In this paper, we give a complete characterization for the connectedness
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On the reducibility systems of two linear first-order ordinary differential equations Monatshefte Math. (IF 0.933) Pub Date : 2020-08-25 G. A. Grigorian
Some global solvability criteria for the scalar Riccati equations are used to establish new reducibility criteria for systems of two linear first-order ordinary differential equations. Some examples are presented.
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Average frequencies of digits in infinite IFS’s and applications to continued fractions and Lüroth expansions Monatshefte Math. (IF 0.933) Pub Date : 2020-08-12 L. Olsen, M. West
The detailed investigation of the distribution of frequencies of digits of points belonging to attractors K of Infinite iterated functions systems (IIFS’s) is a fundamental and important problem in the study of attractors of IIFS’s. This paper studies the Baire category of different families of sets of points belonging to attractors of IIFS’s characterised by the behaviour of the frequencies of their
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Global dynamics for a charged and colliding plasma in presence of a massive scalar field on the Robertson–Walker spacetime Monatshefte Math. (IF 0.933) Pub Date : 2020-08-08 Marcelin Kenmogne Noumo, Norbert Noutchegueme, Roger Tagne Wafo
We consider the coupled Einstein–Maxwell–Boltzmann system with cosmological constant in presence of a massive scalar field. The background metric is that of Friedman–Lemaître–Robertson–Walker space time in the spatially homogeneous case where the unknown functions only depend on time and not on the space variables \((x^i)\), \(i=1,2,3\). By combining the energy estimates method with that of characteristics
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Quadratic cyclic sequences Monatshefte Math. (IF 0.933) Pub Date : 2020-08-06 Paul Baird, Ali Fardoun, Zeina Ghazo Hanna
We explore relations between cyclic sequences determined by a quadratic difference relation, cyclotomic polynomials, Eulerian digraphs and walks in the plane. These walks correspond to closed paths for which at each step one must turn either left or right through a fixed angle. In the case when this angle is \(2 \pi /n\), then non-symmetric phenomena occurs for \(n\ge 12\). Examples arise from algebraic
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A geometrical demonstration for continuation of solutions of the generalised BBM equation Monatshefte Math. (IF 0.933) Pub Date : 2020-08-05 Priscila Leal da Silva, Igor Leite Freire
A simple proof that if the generalised BBM equation has a solution vanishing on an open set of its domain then the solution is necessarily zero is given. In particular, the only compactly supported solution of the equation under consideration is the identically vanishing one.
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A note on blow-up criteria for a class of nonlinear dispersive wave equations with dissipation Monatshefte Math. (IF 0.933) Pub Date : 2020-08-03 Xijun Deng
In this note, we study the Cauchy problem for a class of nonlinear dispersive wave equation with dissipative term on the real line. We establish a new local-in-space blow-up criterion. Our results improve the corresponding ones in the previous paper.
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On the decrease of velocity with depth in irrotational periodic water waves Monatshefte Math. (IF 0.933) Pub Date : 2020-08-01 Luigi Roberti
We give an alternative proof for a classical result (due to Longuet-Higgins) that provides an estimate for the decay rate with depth of the velocity beneath two-dimensional, spatially periodic, irrotational water waves over a flat bed. Furthermore, an improvement to the same estimate is presented.
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On products of groups and indices not divisible by a given prime Monatshefte Math. (IF 0.933) Pub Date : 2020-07-22 María José Felipe, Lev S. Kazarin, Ana Martínez-Pastor, Víctor Sotomayor
Let the group \(G = AB\) be the product of subgroups A and B, and let p be a prime. We prove that p does not divide the conjugacy class size (index) of each p-regular element of prime power order \(x\in A\cup B\) if and only if G is p-decomposable, i.e. \(G=O_p(G) \times O_{p'}(G)\).
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The independence graph of a finite group Monatshefte Math. (IF 0.933) Pub Date : 2020-07-22 Andrea Lucchini
Given a finite group G, we denote by \(\Delta (G)\) the graph whose vertices are the elements G and where two vertices x and y are adjacent if there exists a minimal generating set of G containing x and y. We prove that \(\Delta (G)\) is connected and classify the groups G for which \(\Delta (G)\) is a planar graph.
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Separation bodies: a conceptual dual to floating bodies Monatshefte Math. (IF 0.933) Pub Date : 2020-07-05 Rolf Schneider
Let K be a convex body in Euclidean space \({\mathbb R}^d\), and let a translation invariant, locally finite Borel measure on the space of hyperplanes in \({{\mathbb {R}}}^d\) be given. For \(\delta \ge 0\), we consider the set of all points x for which the set of hyperplanes separating K and x has measure at most \(\delta \). This defines the separation body of K, with respect to the given measure
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Landau-type theorems and bi-Lipschitz theorems for bounded biharmonic mappings Monatshefte Math. (IF 0.933) Pub Date : 2020-07-01 Shi-Fei Chen, Ming-Sheng Liu
In this paper, we first establish five versions of Landau-type theorems for five classes of bounded biharmonic mappings \(F(z)=|z|^2G(z)+H(z)\) on the unit disk \({\mathbb {D}}\) with \(G(0)=H(0)=J_F(0)-1=0\), which improve the related results of earlier authors. In particular, two versions of those Landau-type theorems are sharp. Then we derive five bi-Lipschitz theorems for these classes of bounded
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A convolution property of univalent harmonic right half-plane mappings Monatshefte Math. (IF 0.933) Pub Date : 2020-06-29 Md Firoz Ali, Vasudevarao Allu, Nirupam Ghosh
We consider the convolution of right half-plane harmonic mappings in the unit disk \(\mathbb {D}:=\{z\in \mathbb {C}:\, |z|<1\}\) with respective dilatations \( e^{i \alpha }(z + a)/(1 + a z)\) and \(-z\), where \(-1< a < 1\) and \(\alpha \in \mathbb {R}\). We prove that such convolutions are locally univalent and convex in the horizontal direction under certain condition.
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Möbius orthogonality for q -semimultiplicative sequences Monatshefte Math. (IF 0.933) Pub Date : 2020-06-28 Jakub Konieczny
We show that all q-semimultiplicative sequences are asymptotically orthogonal to the Möbius function, thus proving the Sarnak conjecture for this class of sequences. This generalises analogous results for the sum-of-digits function and other digital sequences which follow from previous work of Mauduit and Rivat.
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Partially smooth universal Taylor series on products of simply connected domains Monatshefte Math. (IF 0.933) Pub Date : 2020-06-28 Giorgos Kotsovolis
Using a recent Mergelyan type theorem, we show the existence of universal Taylor series on products of planar simply connected domains \(\Omega _i\) that extend continuously on \(\prod \nolimits _{i=1}^{d}(\Omega _i \cup S_i)\), where \(S_i\) are subsets of \(\partial \,\Omega _i\), open in the relative topology. The universal approximation occurs on every product of compact sets \(K_i\) such that
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Characterization of eigenfunctions of the Laplace–Beltrami operator through heat propagation in small time Monatshefte Math. (IF 0.933) Pub Date : 2020-06-27 Muna Naik, Rudra P. Sarkar
On rank one Riemannian symmetric spaces of noncompact type, which accommodates all hyperbolic spaces, we show that characterization of the eigenfunctions/eigendistributions of the Laplace–Beltrami operator, through the action of the heat operator is possible only when we confine in a small time. The results are different from their counter parts in the Euclidean spaces. All results and their proofs
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Orientation at singularities of harmonic functions Monatshefte Math. (IF 0.933) Pub Date : 2020-06-24 Juan Arango, Hugo Arbeláez, Jheison Rivera
We find a simple expression in complex terms for homogeneous harmonic polynomials, which we use to express the Laurent series of a harmonic function around an isolated singularity. Also, we show a residue theorem and study the orientation at isolated singularities through the use of complex dilatation, focusing on those points where orientation is not preserved nor reversed, making essential the concept
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Barbashin-type conditions for exponential stability of linear cocycles Monatshefte Math. (IF 0.933) Pub Date : 2020-06-24 Davor Dragičević
We formulate new conditions of Barbashin type for exponential stability of linear cocycles on arbitrary Banach spaces. We consider both cocycles over maps and flows. Our arguments rely on ergodic theory.
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Hyperuniform point sets on the sphere: probabilistic aspects Monatshefte Math. (IF 0.933) Pub Date : 2020-06-24 Johann S. Brauchart, Peter J. Grabner, Wöden Kusner, Jonas Ziefle
The concept of hyperuniformity has been introduced by Torquato and Stillinger in 2003 as a notion to detect structural behaviour intermediate between crystalline order and amorphous disorder. The present paper studies a generalisation of this concept to the unit sphere. It is shown that several well studied determinantal point processes are hyperuniform.
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The Wielandt–Hartley theorem for submaximal $$\mathfrak {X}$$X -subgroups Monatshefte Math. (IF 0.933) Pub Date : 2020-06-05 Danila Revin, Saveliy Skresanov, Andrey Vasil’ev
A nonempty class \(\mathfrak {X}\) of finite groups is called complete if it is closed under taking subgroups, homomorphic images and extensions. We consider two definitions of submaximal \(\mathfrak {X}\)-subgroups suggested by H. Wielandt and discuss which one better suits the task of determining maximal \(\mathfrak {X}\)-subgroups. We prove that these definitions are not equivalent yet the Wielandt–Hartley
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The $$C^*$$C∗ -algebra of the semi-direct product $$K < imes A$$K⋉A Monatshefte Math. (IF 0.933) Pub Date : 2020-06-03 Hedi Regeiba, Jean Ludwig
Let \(G=K < imes A\) be the semi-direct product group of a compact group K acting on an abelian locally compact group A. We describe the \(C^*\)-algebra \(C^*(G)\) of G in terms of an algebra of operator fields defined over the spectrum of G, generalizing previous results obtained for some special classes of such groups.
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On the Cauchy problem for a modified Camassa–Holm equation Monatshefte Math. (IF 0.933) Pub Date : 2020-06-02 Zhaonan Luo, Zhijun Qiao, Zhaoyang Yin
In this paper, we first study the local well-posedness for the Cauchy problem of a modified Camassa–Holm equation in nonhomogeneous Besov spaces. Then we obtain a blow-up criteria and present a blow-up result for the equation. Finally, with proving the norm inflation we show the ill-posedness occurs to the equation in critical Besov spaces.
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Inclusion modulo nonstationary Monatshefte Math. (IF 0.933) Pub Date : 2020-05-31 Gabriel Fernandes, Miguel Moreno, Assaf Rinot
A classical theorem of Hechler asserts that the structure \(\left( \omega ^\omega ,\le ^*\right) \) is universal in the sense that for any \(\sigma \)-directed poset \({\mathbb {P}}\) with no maximal element, there is a ccc forcing extension in which \(\left( \omega ^\omega ,\le ^*\right) \) contains a cofinal order-isomorphic copy of \({\mathbb {P}}\). In this paper, we prove the following consistency
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