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Rendiconti del Seminario Matematico
della Università di Padova
The Mathematical Journal of the University of Padua

ISSN 0041-8994
e-ISSN: 2240-2926

Forthcoming Articles

(Last update: February 7, 2018)

The following articles will soon be published in this journal. Their publication status can be :

  • online first – final version available (without page numbers nor DOI);
  • accepted – manuscript available.

To view the abstract, or download the full paper in PDF[1], click on the article's title.

Online first

  • This section is momentarily empty

    Abstract: See the paper itself.

    received , accepted ( pages)
    download: online first pdf ()

Accepted Papers

  • Finite groups with the pp-embedding property

    Stocka, Agnieszka
    Institute of Mathematics
    University of Bialystok
    K. Ciolkowskiego 1M
    15-245 Bialystok

    Abstract: A subset $X$ of a finite group $G$ is called g-independent if there is no proper subset $Y$ of $X$ such that $\langle Y,\Phi(G) \rangle = \langle X,\Phi(G) \rangle.$ The group $G$ has the embedding property if every g-independent subset of $G$ can be embedded in a minimal generating set of $G$. If $X$ is a set of prime power order elements, then we say that $G$ has the pp-embedding property. In this note we classify all finite solvable groups with the pp-embedding property. Moreover we prove that this class is equal to the class of finite solvable groups with the embedding property.

    received 26.10.2017, accepted 19.01.2018 (11 pages)
    download: manuscript pdf (296K)
  • Regularity results for quasilinear degenerate elliptic obstacle problems in Carnot groups

    Du, Guangwei and Niu, Pengcheng and Han, Junqiang
    Department of Applied Mathematics
    Northwestern Polytechnical University

    Abstract: See the article

    received 18.03.2017, accepted 09.12.2017 (32 pages)
    download: manuscript pdf (464K)
  • On the generalized $\sigma$-Fitting subgroup of finite groups

    Hu, Bin and Huang, Jianhong and Skiba, Alexander N.
    Hu, Huang
    School of Mathematics and Statistics
    Jiangsu Normal University
    Xuzhou, 221116
    P. R. China
    Department of Mathematics
    Francisk Skorina Gomel State University
    Gomel 246019

    Abstract: see the article

    received 26.02.2017, accepted 29.11.2017 (15 pages)
    download: manuscript pdf (234K)
  • On the monotonicity of Hilbert functions

    Puthenpurakal, Tony Joseph
    Department of Mathematics
    Indian Institute of Technology Bombay
    Mumbai 400 076

    Abstract: In this paper we show that a large class of one-dimensional Cohen-Macaulay local rings $(A,\mathfrak{m})$ has the property that if $M$ is a maximal Cohen-Macaulay $A$-module then the Hilbert function of $M$ (with respect to $\mathfrak{m}$) is non-decreasing. Examples include
    (1) Complete intersections $A = Q/(f,g)$ where $(Q,\mathfrak{n})$ is regular local of dimension three and $f \in \mathfrak{n}^2 \setminus \mathfrak{n}^3$.
    (2) One dimensional Cohen-Macaulay quotients of a two dimensional Cohen-Macaulay local ring with pseudo-rational singularity.

    received 16.02.2017, accepted 09.11.2017 (7 pages)
    download: manuscript pdf (248K)
  • Zeros of irreducible characters of metabelian $p$-groups

    Wilde, Tom
    2 Amner Road
    London SW11 6AA

    Abstract: We show that if $\chi$ is an irreducible complex character of a metabelian $p$ - group $P,$ where $p$ is an odd prime, and if $x\in P$ satisfies $\chi(x)\neq 0$, then the order of $x$ divides $|P|/\chi(1)^2.$

    received 21.06.2017, accepted 09.11.2017 (9 pages)
    download: manuscript pdf (304K)
  • Cohen-Macaulayness and sequentially Cohen-Macaulayness of monomial ideals

    Noormohammadi, Hassan and Rahimi, Ahad
    Department of Mathematics
    Azarbaijan Shahid Madani University
    Department of Mathematics
    Razi University

    Abstract: In this paper, we give a characterization for Cohen--Macaulay rings $R/I$ where $I\subset R=K[y_1, \dots, y_n]$ is a monomial ideal which satisfies $\rm{bigsize}\, I=\rm{size}\, I$. Next, we let $S=K[x_1,\ldots,x_m, y_1,\ldots,y_n]$ be a polynomial ring and $I\subset S$ a monomial ideal. We study the sequentially Cohen-Macaulayness of $S/I$ with respect to $Q=(y_1,\ldots,y_n)$. Moreover, if $I\subset R$ is a monomial ideal such that the associated prime ideals of $I$ are in pairwise disjoint sets of variables, a classification of $R/I$ to be sequentially Cohen-Macaulay is given. Finally, we compute $\rm{grade}\,(Q, M)$ where $M$ is a sequentially Cohen-Macaulay $S$-module with respect to $Q$.

    received 02.04.2017, accepted 23.10.2017 (14 pages)
    download: manuscript pdf (323K)
  • On generalized $\Pi$-property of subgroups of finite groups

    Yu, Haoran
    School of Mathematics
    Jilin University
    No. 2699 Qianjin Street

    Abstract: In this note, we extend the concept of $\Pi$-property of subgroups of finite groups and generalize some recent results. In particular, we generalize the main results of Li et al. [8] and Miao et al. [9].

    received 28.08.2017, accepted 23.10.2017 (17 pages)
    download: manuscript pdf (345K)
  • On the uniqueness of the factorization of power digraphs modulo n

    Sawkmie, Amplify and Singh, Madan Mohan
    Department of Mathematics
    North-Eastern Hill University
    Department of Basic Sciences & Social Sciences
    North-Eastern Hill University

    Abstract: For each pair of integers $n=\prod_{i=1}^{r}p_i^{e_i}$ and $k \geq 2$, a digraph $G(n,k)$ is one with vertex set $\{0,1,\ldots ,n-1\}$ and for which there exists a directed edge from $x$ to $y$ if $x^k \equiv y \pmod n$. Using the Chinese Remainder Theorem, the digraph $G(n,k)$ can be written as a direct product of digraphs $G(p_i^{e_i},k)$ for all $i$ such that $1 \leq i \leq r$. A fundamental constituent $G_{P}^{*}(n,k)$, where $P \subseteq Q=\{p_1,p_2,\ldots,p_r\}$, is a subdigraph of $G(n,k)$ induced on the set of vertices which are multiples of $\prod_{{p_i} \in P}p_i$ and are relatively prime to all primes $p_j \in Q \smallsetminus P$. In this paper, we investigate the uniqueness of the factorization of trees attached to cycle vertices of the type $0$, $1$, and $(1,0)$, and in general, the uniqueness of $G(n,k)$. Moreover, we provide a necessary and sufficient condition for the isomorphism of the fundamental constituents $G_{P}^{*}(n,k_1)$ and $G_{P}^{*}(n,k_2)$ of $G(n,k_1)$ and $G(n,k_2)$ respectively for $k_1 \neq k_2$.

    received 01.06.2017, accepted 20.10.2017 (28 pages)
    download: manuscript pdf (460K)
  • Semisimple groups that are quasi-split over a tamely ramified extension

    Gille, Philippe
    Université Claude Bernard Lyon 1
    CNRS UMR 5208
    Institut Camille Jordan
    43 Blvd. du 11 novembre 1918
    F-69622 Villeurbane cedex

    Abstract: Let $K$ be a discretly henselian field whose residue field is separably closed. Answering a question raised by G. Prasad, we show that a semisimple $K$-group $G$ is quasi-split if and only if it quasi-splits after a finite tamely ramified extension of $K$.

    received 07.07.2017, accepted 16.10.2017 (9 pages)
    download: manuscript pdf (318K)
  • Complex manifolds as families of homotopy algebras

    Bellier-Millès, Joan
    Institut de Mathématiques de Toulouse
    UMR5219, Université de Toulouse
    F-31062 Toulouse Cedex 9

    Abstract: We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex structure on a smooth manifold corresponds in this way to a family of algebras indexed by the points of the manifold.

    received 24.03.2017, accepted 25.09.2017 (38 pages)
    download: manuscript pdf ()
  • A brief journey through extensions of rational groups

    Friedenberg, Stefan
    University of Stralsund
    Zur Schwedenschanze 15
    18435 Stralsund

    Abstract: Let $A$ and $B$ be rational groups, i.e. torsion-free groups of rank-1 and thus subgroups of the rational numbers. This paper gives a short overview of the structure of $\text{Ext}\,(A,B)$ especially considering some interesting classes of torsion-free pairs.

    received 06.03.2017, accepted 20.09.2017 (5 pages)
    download: manuscript pdf ()
  • Algebraic cycles on a very special EPW sextic

    Laterveer, Robert
    Institut de Recherche Mathématique Avancée
    CNRS _ Université de Strasbourg
    7 Rue René Descartes
    67084 Strasbourg CEDEX

    Abstract: Motivated by the Beauville--Voisin conjecture about Chow rings of powers of $K3$ surfaces, we consider a similar conjecture for Chow rings of powers of EPW sextics. We prove part of this conjecture for the very special EPW sextic studied by Donten--Bury et alii. We also prove some other results concerning the Chow groups of this very special EPW sextic, and of certain related hyperk\"ahler fourfolds.

    received 22.06.2016, accepted 28.08.2017 (27 pages)
    download: manuscript pdf (320K)
  • Algèbres de distributions et ${\cal D}$-modules arithmétiques

    Huyghe, Christine and Schmidt, Tobias
    Université de Strasbourg
    7, rue René Descartes
    67084 Strasbourg cedex
    Université de Rennes 1
    Campus de Beaulieu
    35042 Rennes cedex

    Abstract: Let $p$ be a prime number, $V$ a complete discrete valuation ring of unequal caracteristics $(0,p)$, $G$ a smooth affine algebraic group over $Spec \,V$. Using partial divided powers techniques of Berthelot, we construct arithmetic distribution algebras, with level $m$, generalizing the classical construction of the distribution algebra. We also construct the weak completion of the classical distribution algebra over a finite extension $K$ of ${\bf Q}_p$ . We then show that these distribution algebras can be identified with invariant arithmetic differential operators over $G$, and prove a coherence result when the ramification index of $K$ is $ received 13.10.2015, accepted 07.07.2017 (66 pages)
    download: manuscript pdf (778K)

  • Countable recognizability and residual properties of groups

    De Giovanni, Francesco and Trombetti, Marco
    Dipartimento di Matematica e Applicazioni
    Università di Napoli Federico II
    Complesso Universitario Monte S. Angelo
    Via Cintia,

    Abstract: A class of groups {\mgoth X} is said to be countably recognizable if a group belongs to~{\mgoth X} whenever all its countable subgroups lie in {\mgoth X}. It is proved here that the class of groups whose subgroups are closed in the profinite topology is countably recognizable. Moreover, countably detectable properties of the finite residual of a group are studied.

    received 17.01.2017, accepted 29.05.2017 (11 pages)
    download: manuscript pdf (306K)
  • A result on a singular Cauchy problem with a radial point revisited using microdifferential calculus

    Getmanenko, Alexander
    Department of Mathematics
    Edificio Mario Laserna Cra 1 Este No 19A
    40 Bogota
    Universidad de los Andes

    Abstract: We study the ramified Cauchy problem for a linear PDE with a radial point using the theory of microdifferential operators.

    received 23.09.2016, accepted 11.05.2017 (20 pages)
    download: manuscript pdf (447K)
  • Mostow s fibration for canonical embeddings of compact homogeneous $CR$ manifolds

    Marini, Stefano and Nacinovich, Mauro
    Dipartimento di Matematica e Fisica
    III Università di Roma
    Largo San Leonardo Murialdo, 1
    00146 Roma

    Abstract: We define a class of compact homogeneous $CR$ manifolds which are bases of Mostow fibrations having total spaces equal to their canonical complex realizations and Hermitian fibers. This is used to establish isomorphisms between their tangential Cauchy-Riemann cohomology groups and the corresponding Dolbeault cohomology groups of the embeddings.

    received 17.12.2016, accepted 09.05.2017 (30 pages)
    download: manuscript pdf (278K)
  • Marcinkiewicz-type interpolation theorem for Morrey-type spaces and its corollaries

    Burenkov, V. I. and Chigambayeva, D. K. and Nursultanov, E. D.
    RUDN University
    S. M. Nikol’skii Institute
    6 Miklukho-Maklay St
    Moscow, 117198

    Abstract: We introduce a class of Morrey-type spaces $M^\lambda_{p,q}$, which includes classical Morrey spaces and discuss their properties. We prove a Marcinkiewicz-type interpolation theorem. This theorem is then applied to obtaining the boundedness in the introduced Morrey-type spaces of the Riesz potential and singular integral operator.

    received 05.10.2016, accepted 26.04.2017 (20 pages)
    download: manuscript pdf (173K)
  • Motifs et adjoints

    Kahn, Bruno
    Institut de Mathématiques de Jussieu - PRG
    Case 247
    4 place Jussieu
    75252 Paris Cedex 05

    Abstract: We show in many cases the existence of adjoints to extension of scalars on categories of motivic nature, in the framework of field extensions. This is to be contrasted with the more classical situation where one deals with a finite type morphism of schemes. Among various applications, one is a construction of a ``Tate-\v Safarevi\v c motive" attached to an abelian variety over a function field. We also deduce a possible approach to \text{Bloch's} conjecture on surfaces, by reduction to curves.

    received 18.11.2015, accepted 22.03.2017 (44 pages)
    download: manuscript pdf (702K)
  • Definable categories and $\mathbb{T}$-motives

    Barbieri-Viale, Luca and Prest, Mike
    Dipartimento di Matematica "F. Enriques"
    Università degli Studi di Milano
    Via C. Saldini, 50
    I-20133 Milano
    School of Mathematics
    University of Manchester
    Oxford Road
    Manchester M13 9PL

    Abstract: Making use of Freyd's free abelian category on a preadditive category we show that if $T:D\rightarrow \mathcal{A}$ is a representation of a quiver $D$ in an abelian category $\mathcal{A}$ then there is an abelian category $\mathcal{A} (T)$, a faithful exact functor $F_T: \mathcal{A} (T) \to \mathcal{A}$ and an induced representation $\tilde T: D \to \mathcal{A} (T)$ such that $F_T\tilde T= T$ universally. We then can show that $\mathbb{T}$-motives as well as Nori's motives are given by a certain category of functors on definable categories.

    received 03.10.2016, accepted 15.03.2017 (18 pages)
    download: manuscript pdf (395K)
  • Nunke’s problem for abelian $p$-groups of uncountable length

    Keef, Patrick
    Department of Mathematics
    Whitman College
    Walla Walla, WA 99362

    Abstract: \textit{Nunke's Problem} asks when the torsion product of two abelian $p$-groups is a direct sum of countable reduced groups. In previous work the author gave a complete answer to this question when the groups involved have countable length. In this paper a complete answer is given in the case of groups of uncountable length, at least in any set-theoretic universe in which $2^{\aleph_1}=\aleph_2$.

    received 18.01.2017, accepted 03.03.2017 (18 pages)
    download: manuscript pdf (292K)
  • The isoperimetric problem in Grushin space$\mathbb{R}^{h+1}$ with density $|x|^p$

    He, Guoqing and Zhao, Peibiao
    School of Science
    Nanjing University of Science and Technology
    Nanjing 210094
    P. R. China

    Abstract: In this paper we study the isoperimetric problem in a class of $x$-spherically symmetric sets in the Grushin space $\mathbb{R}^{h+1}$ with density $|x|^p$, $p>-h+1$. First we prove the existence of weighted isoperimetric sets. Then we deduce that, up to a vertical translation, a dilation and a negligible set, the weighted isoperimetric set is only of the form $\big\{(x,y)\in \mathbb{R}^{h+1}:|y|<\int_{\arcsin|x|}^{\frac{\pi}{2}}\sin^{\alpha+1}(t)dt,\hspace{2mm}|x|<1\big\}$.

    received 31.01.2017, accepted 24.02.2017 (17 pages)
    download: manuscript pdf (423K)
  • Cyclic subgroup commutativity degrees of finite groups

    Tarnauceanu, Marius and Lazorec, Mihai-Silviu
    Faculty of Mathematics
    Al. I. Cuza University

    Abstract: In this paper we introduce and study the concept of cyclic subgroup commutativity degree of a finite group $G$. This quantity measures the probability of two random cyclic subgroups of $G$ commuting. Explicit formulas are obtained for some particular classes of groups. A criterion for a finite group to be an Iwasawa group is also presented.

    received 13.12.2016, accepted 21.02.2017 (15 pages)
    download: manuscript pdf (311K)
  • Weak local-global compatibility and ordinary representations

    Chojecki, Przemyslaw
    Instytut Matematyczny PAN
    Ul. Sniadeckich 8
    00-656 Warsawa

    Abstract: We introduce a general formalism with minimal requirements under which we are able to prove the pro-modular Fontaine-Mazur conjecture. We verify it in the ordinary case using the recent construction of Breuil and Herzig.

    received 04.07.2016, accepted 13.02.2017 (22 pages)
    download: manuscript pdf (436K)
  • Some sufficient conditions for p-nilpotence of a finite group

    Li, Changwen and Huang, Jianhong and Hu, Bin
    School of Mathematics and Statistics
    Jiangsu Normal University
    Xuzhou, 221116

    Abstract: In this paper, we give some new characterizations of finite $p$-nilpotent groups by using the notion of $\mathcal{H}C$-subgroups and extend several recent results.

    received 28.09.2016, accepted 17.01.2017 (8 pages)
    download: manuscript pdf (98K)
  • On an open problem about $\pi$-quasi-$\mathcal{F}$-groups

    Zhang, Chi and Zhang, Li and Huang, Jianhong
    Department of Mathematics
    University of Science and Technology of China
    Hefei, 230026
    P.R. China
    Department of Mathematics
    University of Science and Technology of China
    Hefei, 230026
    P.R. China
    School of Mathematics and Statistics
    Jiangsu Normal UniversityXuzhou, 22 1116
    P.R. China

    Abstract: Let $\mathfrak{F}$ be a class of finite groups, $p$ a prime and $\pi$ a set of some primes. A finite group $G$ is called a $p$-quasi-$\mathfrak{F}$-group (respectively, by $\pi$-quasi-$\mathfrak{F}$-group) provided that for every $\mathfrak{F}$-eccentric $G$-chief factor $H/K$ of order divisible by $p$ (respectively, by at least one prime in $\pi$), the automorphisms of $H/K$ induced by all elements of $G$ are inner. In this paper, we obtain the characterizations of $p$-quasi-$\mathfrak{F}$-groups and $\pi$-quasi-$\mathfrak{F}$-groups, which give a positive answer to an open problem in the book [3].

    received 29.07.2016, accepted 04.11.2016 (8 pages)
    download: manuscript pdf (336K)
  • On $W$-$S$-permutable subgroups of finite groups

    Gao, Jinxin and Guo, Xiuyun
    Department of Mathematics
    Shanghai University
    Shanghai 200444
    P. R. China

    Abstract: A subgroup $H$ of a finite group $G$ is said to be $W$-$S$-permutable in $G$ if there is a subgroup $K$ of $G$ such that $G=HK$ and $H\cap K$ is a nearly $S$-permutable subgroup of $G$. In this article, we analyse the structure of a finite group $G$ by using the properties of $W$-$S$-permutable subgroups and obtain some new characterizations of finite $p$-nilpotent groups and finite supersolvable groups. Some known results are generalized.

    received 20.04.2016, accepted 06.10.2016 (12 pages)
    download: manuscript pdf (355)
  • On $H_\sigma$-permutably embedded subgroups of finite groups

    Guo, Wenbin and Zhang, Chi and Skiba, Alexander N. and Sinitsa, Darya A.
    Guo Zhang
    Department of Mathematics
    University of Science and Technology of China
    Hefei 230026
    P. R. China
    Skiba Sinitsa
    Department of Mathematics
    Francisk Skorina Gomel State University
    Gomel 246019

    Abstract: Let $G$ be a finite group. Let $\sigma =\{\sigma_{i} | i\in I\}$ be a partition of the set of all primes $\Bbb{P}$ and $n$ an integer. We write $\sigma (n) =\{\sigma_{i} |\sigma_{i}\cap \pi (n)\ne \emptyset \}$, $\sigma (G) =\sigma (|G|)$. A set $ {\cal H}$ of subgroups of $G$ is said to be a complete Hall $\sigma $-set of $G$ if every member of ${\cal H}\setminus \{1\}$ is a Hall $\sigma _{i}$-subgroup of $G$ for some $\sigma _{i}$ and ${\cal H}$ contains exact one Hall $\sigma _{i}$-subgroup of $G$ for every $\sigma _{i}\in \sigma (G)$. A subgroup $A$ of $G$ is called: (i) a $\sigma$-Hall subgroup of $G$ if $\sigma (A) \cap \sigma (|G:A|)=\emptyset$; (ii) ${\sigma}$-permutable in $G$ if $G$ possesses a complete Hall $\sigma$-set ${\cal H}$ such that $AH^{x}=H^{x}A$ for all $H\in {\cal H}$ and all $x\in G$. We say that a subgroup $A$ of $G$ is $H_{\sigma}$-permutably embedded in $G$ if $A$ is a ${\sigma}$-Hall subgroup of some ${\sigma}$-permutable subgroup of $G$. We study finite groups $G$ having an $H_{\sigma}$-permutably embedded subgroup of order $|A|$ for each subgroup $A$ of $G$. Some known results are generalized.

    received 07.06.2016, accepted 18.08.2016 (13 pages)
    download: manuscript pdf (187K)
  • Test modules for flatness

    Alizade, Rafail and Durgun, Yilmaz
    Yasar University
    Department of Mathematics
    35100, Izmir
    Bitlis Eren University
    Department of Mathematics
    13000, Bitlis

    Abstract: A right $R$-module $M$ is said to be a test module for flatness (shortly: an f-test module) provided for each left $R$-module $N$, $Tor(M,N)=0$ implies $N$ is flat. $f$-test modules are flat version of the Whitehead test modules for injectivity defined by Trlifaj. In this paper the properties of f-test modules are investigated and are used to characterize various families of rings. The structure of a ring over which every (finitely generated) right $R$-module is flat or f-test is investigated. Abelian groups that are Whitehead test modules for injectivity or f-test are characterized.

    received 22.02.2015, accepted 14.06.2016 (15 pages)
    download: manuscript pdf (129K)
  • On the piecewise approximation of bi-Lipschitz curves

    Pratelli, Aldo and Radici, Emanuela
    Department of Mathematics
    University of Erlangen
    Cauerstrasse 11
    90158 Erlangen

    Abstract: In this paper we deal with the task of uniformly approximating an $L$-biLipschitz curve by means of piecewise linear ones. This is rather simple if one is satisfied to have approximating functions which are $L'$-biLipschitz, for instance this was already done with $L'=4L$ in [3, Lemma~5.5]. The main result of this paper is to do the same with $L'=L+\varepsilon$ (which is of course the best possible result); in the end, we generalize the result to the case of closed curves.

    received 12.05.2015, accepted 31.05.2016 (30 pages)
    download: manuscript pdf (408K)
  • Configurations of points on degenerate varieties and properness of moduli spaces

    Abramovich, Dan and Fantechi, Barbara
    Department of Mathematics
    Box 1917
    Brown University
    Providence, RI, 02912
    Via Bonomea 265
    34136 Trieste

    Abstract: see the paper itself

    received 19.09.2014, accepted 01.04.2016 (16 pages)
    download: manuscript pdf (341K)
  • A comparison of logarithmic overconvergent de Rham-Witt and log-crystalline cohomology for projective smooth varieties with normal crossing divisor

    Langer, Andreas and Zink, Thomas
    University of Exeter
    Exeter, EX4 4QF
    Devon UK
    Fakultät für Mathematik
    Universität Bielefeld
    Postfach 100131
    D-33501 Bielefeld

    Abstract: In this note we derive for a smooth projective variety $X$ with normal crossing divisor $Z$ an integral comparison between the log-crystalline cohomology of the associated log-scheme and the logarithmic overconvergent de Rham-Witt cohomology defined by Matsuue. This extends our previous result that in the absence of a divisor $Z$ the crystalline cohomology and overconvergent de Rham-Witt cohomology are canonically isomorphic.

    received 07.09.2015, accepted 14.03.2016 (6 pages)
    download: manuscript pdf (221K)
  • Primary group rings

    Chin, Angelina Y. M. and Qua, K. T.
    Institute of Mathematical Sciences
    Faculty of Science
    University of Malaya
    50603 Kuala Lumpur

    Abstract: Let $R$ be an associative ring with identity and let $J(R)$ denote the Jacobson radical of $R$. We say that $R$ is primary if $R/J(R)$ is simple Artinian and $J(R)$ is nilpotent. In this paper we obtain necessary and sufficient conditions for the group ring $RG$, where $G$ is a nontrivial abelian group, to be primary.

    received 25.08.2015, accepted 23.02.2016 (5 pages)
    download: manuscript pdf (89K)
  • A construction of a uniform continuous minimizing movement associated with a singular functional

    Yamaura, Yoshihiko
    Department of Mathematics
    College of Humanities and Sciences
    Nihon University
    3-25-40, Sakurajosui, Setagaya
    Tokyio 156-8550

    Abstract: A minimizing movement is constructed associated with a singular functional introduced by Alt and Caffarelli in order to study a free boundary problem. The main purpose of the present research is to construct a minimizing movement, which is uniformly continuous with respect to both time and space variables. The strategy is to regularize the singular term of time discretized functionals, and then to pass to the limit in the regularization parameter in the sense of $\mit\Gamma$-convergence keeping the time discretization parameter fixed.

    received 30.06.2015, accepted 04.02.2016 (27 pages)
    download: manuscript pdf (192K)
  • Existence of stationary solutions for some integro-differential equations with superdiffusion

    Vougalter, Vitali and Volpert, Vitaly
    Department of Mathematics
    University of Toronto
    Ontario, M5S 2E4
    Institute Camille Jordan
    UMR 5208 CNRS
    University Lyon 1
    Villeurbane, 69622

    Abstract: The work deals with the existence of solutions of an integro-differential equation arising in population dynamics in the case of anomalous diffusion. The proof of existence of solutions relies on a fixed point technique. Solvability conditions for non-Fredholm elliptic operators in unbounded domains are being used.

    received 20.07.2015, accepted 28.01.2016 (16 pages)
    download: manuscript pdf (329K)
  • A new characterization of some families of finite simple groups

    Foroudi Ghasemabadi, Mahnaz and Iranmanesh, Ali and Ahanjideh, Milad
    Department of pure Mathematics
    Faculty of Mathematical Sciences
    Tarbiat Modares University

    Abstract: Let $G$ be a finite group. A vanishing element of $G$ is an element $g\in G$ such that $\chi(g)=0$ for some irreducible complex character $\chi$ of $G$. Denote by ${\rm Vo}(G)$ the set of the orders of vanishing elements of $G$. In this paper, we prove that if $G$ is a finite group such that ${\rm Vo}(G)={\rm Vo}(M)$ and $|G|=|M|$, then $G\cong M$, where $M$ is a sporadic simple group, an alternating group, a projective special linear group $L_2(p)$, where $p$ is an odd prime or a finite simple $K_{n}$-group, where $n\in \{3,4\}$. These results confirm the conjecture posed in [17] for the simple groups under study.

    received 12.02.2015, accepted 18.01.2016 (16 pages)
    download: manuscript pdf (164K)
  • A harmonic mean inequality for the digamma function and related results

    Alzer, Horst and Jameson, Graham J. O.
    Morsbacher Str, 10
    51545 Waldbröl
    Department of Mathematics and Statistics
    Lancaster University
    Lancaster LA1 4YF 

    Abstract: We present some inequalities and a concavity property of the digamma function $\psi=\Gamma'/\Gamma$, where $\Gamma$ denotes Euler's gamma function. In particular, we offer a new characterization of Euler's constant $\gamma=0.57721...$. We prove that $-\gamma$ is the minimum of the harmonic mean of $\psi(x)$ and $\psi(1/x)$ for $x>0$.

    received 19.08.2015, accepted 11.01.2016 (6 pages)
    download: manuscript pdf (256K)
  • Wavelet transform of Beurling-Björck type ultradistributions

    Pathak, R. S. and Singh, Abhishek
    DST Centre for Interdisciplinary Mathematical Sciences
    Faculty of Science
    Banaras Hindu University
    Varanasi - 221 005

    Abstract: Wavelet transform of a distribution in $\mathscr{M}_{\omega}^{'}$ involving wavelet of infraexponential decay (subexponential decay) is studied. An inversion formula is obtained which is valid in the weak topology of $\mathcal{D}^{'}$. A discussion on extension of the results to ultradistribution space of compact support is also given.

    received 21.08.2015, accepted 11.01.2016 (11 pages)
    download: manuscript pdf (151K)
  • Strong local-global compatibility in the $p$-adic Langlands program for $U(2)$

    Chojecki, Przemyslaw and Sorensen, Claus
    Mathematical Institute, University of Oxford
    Andrew Wiles Building, Radcliffe Observatory Quarter
    Woodstock Road
    Oxford OX2 6GG
    Department of Mathematics, UCSD 
    9500 Gilman Dr. #0112 
    La Jolla, CA 92093-0112 USA

    Abstract: For certain mod $p$ Galois representations $\bar{\rho}$, arising from modular forms on definite unitary groups in two variables, we express the $\bar{\rho}$-part of completed cohomology $\hat{H}_{\bar{\rho}}^0$ (away from $\Sigma=\Sigma_p\cup \Sigma_0$) as a tensor product $\Pi_p\otimes \Pi_{\Sigma_0}$. Here $\Pi_p$ is attached to the universal deformation $\rho^{univ}$ via the $p$-adic local Langlands correspondence for $\text{GL}_2(\mathbb{Q}_p)$, and $\Pi_{\Sigma_0}$ is given by the local Langlands correspondence in families, of Emerton and Helm.

    received 09.05.2015, accepted 20.11.2015 (17 pages)
    download: manuscript pdf (448K)
  • Coverings of commutators in profinite groups

    Acciarri, Cristina and Shumyatsky, Pavel
    Department of Mathematics
    University of Brasilia
    70910-900 Brazil

    Abstract: Let $w$ be a group-word. Suppose that the set of all $w$-values in a profinite group $G$ is contained in a union of countably many subgroups. It is natural to ask in what way the structure of the verbal subgroup $w(G)$ depends on the properties of the covering subgroups. The present article is a survey of recent results related to that question. In particular we survey results on finite and countable coverings of word-values (mostly commutators) by procyclic, abelian, nilpotent, and soluble subgroups, as well as subgroups with finiteness conditions. The last section of the paper is devoted to relation of the described results with Hall's problem on conciseness of group-words.

    received 29.10.2015, accepted 19.11.2015 (19 pages)
    download: manuscript pdf (320K)
  • Weak local-global compatibility in the p-adic Langlands program for U(2)

    Chojecki, Przemyslaw and Sorensen, Claus
    Mathematical Institute, University of Oxford
    Andrew Wiles Building, Radcliffe Observatory Quarter
    Woodstock Road
    Oxford OX2 6GG
    Department of Mathematics, UCSD 
    9500 Gilman Dr. #0112 
    La Jolla, CA 92093-0112 USA 

    Abstract: We study the completed cohomology $\hat{H}^0$ of a definite unitary group $G$ in two variables associated with a CM-extension $\mathcal{K}/F$. When the prime $p$ splits, we prove that (under technical asumptions) the $p$-adic local Langlands correspondence for $\text{GL}_2(\Bbb{Q}_p)$ occurs in $\hat{H}^0$. As an application, we obtain a result towards the Fontaine-Mazur conjecture over $\mathcal{K}$: if $x$ is a point on the eigenvariety such that $\rho_x$ is geometric (and satisfying additional hypotheses which we suppress), then $x$ must be a classical point. Thus, not only is $\rho_x$ modular, but the weight of $x$ defines an accessible refinement. This follows from a recent result of Colmez (which describes the locally analytic vectors in $p$-adic unitary principal series), knowing that $\rho_x$ admits a triangulation compatible with the weight.

    received 09.05.2015, accepted 25.10.2015 (28 pages)
    download: manuscript pdf (512K)
  • Cyclic non-$S$-permutable subgroups and non-normal maximal subgroups

    Rezaeezadeh, Gholamreza R. and Aghajari, Zahra
    Faculty of Mathematical Science
    Department of Pure Mathematics
    Shahrekord University
    P. O. Box 115

    Abstract: A finite group $G$ is said to be a $T$-group (resp. $PT$-group, $PST$-group) if normality (resp. permutability, $S$-permutability) is a transitive relation. Ballester-Bolinches et al. gave some new characterizations of the soluble $T$-, $PT$- and $PST$-groups. A finite group $G$ is called a $T_c$-group (resp. ${PT}_c$-group, ${PST}_c$-group) if each cyclic subnormal subgroup is normal (resp. permutable, $S$-permutable) in $G$. The present work defines the ${NNM}_c$-, ${PNM}_c$-, and ${SNM}_c$-groups and presents new characterizations of the wider classes of soluble $T_c$-, ${PT}_c$-, and ${PST}_c$-groups.

    received 23.02.2015, accepted 23.07.2015 (7 pages)
    download: manuscript pdf (83K)
  • Example of minimizer of the average-distance problem with non closed set of corners

    Lu, Xin Yang
    Department of Mathematical Sciences
    Carnegie Mellon University
    Pittsburg, PA, 15213
    United States

    Abstract: The average-distance problem, in the penalized formulation, involves minimizing \begin{equation*} E_\mu^\lambda(\Sigma):=\int_{{\mathbb R}^d} \inf_{y\in\Sigma} |x-y|\operatorname{d}\mu(x)+\lambda{\mathcal H}^1(\Sigma), \end{equation*} among {compact, connected sets $\Sigma$, where ${\mathcal H}^1$ denotes the 1-Hausdorff measure}, $d\geq 2$, $\mu$ is a given measure and $\lambda$ a given parameter. Regularity of minimizers is a delicate problem. It is known that even if $\mu$ is absolutely continuous with respect to Lebesgue measure, $C^1$ regularity does not hold in general. An interesting question is whether the set of corners, i.e. points where $C^1$ regularity does not hold, is closed. The aim of this paper is to provide an example of minimizer whose set of corners is not closed, with reference measure $\mu$ absolutely continuous with respect to Lebesgue measure.

    received 10.02.2015, accepted 06.07.2015 (27 pages)
    download: manuscript pdf (544K)

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