ISSN 00418994
eISSN: 22402926

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.

Stocka, Agnieszka publication status: accepted

Du, Guangwei and Niu, Pengcheng and Han, Junqiang publication status: accepted

Hu, Bin and Huang, Jianhong and Skiba, Alexander N. publication status: accepted

Puthenpurakal, Tony Joseph publication status: accepted

Wilde, Tom publication status: accepted

Noormohammadi, Hassan and Rahimi, Ahad publication status: accepted

Yu, Haoran publication status: accepted

Sawkmie, Amplify and Singh, Madan Mohan publication status: accepted

Gille, Philippe publication status: accepted

BellierMillès, Joan publication status: accepted

Friedenberg, Stefan publication status: accepted

Laterveer, Robert publication status: accepted

Huyghe, Christine and Schmidt, Tobias publication status: accepted

De Giovanni, Francesco and Trombetti, Marco publication status: accepted

Getmanenko, Alexander publication status: accepted

Marini, Stefano and Nacinovich, Mauro publication status: accepted

Burenkov, V. I. and Chigambayeva, D. K. and Nursultanov, E. D. publication status: accepted

Kahn, Bruno publication status: accepted

BarbieriViale, Luca and Prest, Mike publication status: accepted

Keef, Patrick publication status: accepted

He, Guoqing and Zhao, Peibiao publication status: accepted

Tarnauceanu, Marius and Lazorec, MihaiSilviu publication status: accepted

Chojecki, Przemyslaw publication status: accepted

Li, Changwen and Huang, Jianhong and Hu, Bin publication status: accepted

Zhang, Chi and Zhang, Li and Huang, Jianhong publication status: accepted

Gao, Jinxin and Guo, Xiuyun publication status: accepted

Guo, Wenbin and Zhang, Chi and Skiba, Alexander N. and Sinitsa, Darya A. publication status: accepted

Alizade, Rafail and Durgun, Yilmaz publication status: accepted

Pratelli, Aldo and Radici, Emanuela publication status: accepted

Abramovich, Dan and Fantechi, Barbara publication status: accepted

Langer, Andreas and Zink, Thomas publication status: accepted

Chin, Angelina Y. M. and Qua, K. T. publication status: accepted

Yamaura, Yoshihiko publication status: accepted

Vougalter, Vitali and Volpert, Vitaly publication status: accepted

Foroudi Ghasemabadi, Mahnaz and Iranmanesh, Ali and Ahanjideh, Milad publication status: accepted

Alzer, Horst and Jameson, Graham J. O. publication status: accepted

Pathak, R. S. and Singh, Abhishek publication status: accepted

Chojecki, Przemyslaw and Sorensen, Claus publication status: accepted

Acciarri, Cristina and Shumyatsky, Pavel publication status: accepted

Chojecki, Przemyslaw and Sorensen, Claus publication status: accepted

Rezaeezadeh, Gholamreza R. and Aghajari, Zahra publication status: accepted

Lu, Xin Yang publication status: accepted

This section is momentarily empty publication status: online first
Online first
Accepted Papers
 Stocka, Agnieszka
Institute of Mathematics
University of Bialystok
K. Ciolkowskiego 1M
15245 Bialystok
Poland Abstract: A subset $X$ of a finite group $G$ is called gindependent 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 gindependent 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 ppembedding property.
In this note we classify all finite solvable groups with the ppembedding 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 (296K)
 Du, Guangwei and Niu, Pengcheng and Han, Junqiang
Department of Applied Mathematics
Northwestern Polytechnical University
Xian
China Abstract: See the article received 18.03.2017, accepted 09.12.2017 (32 pages)
download: manuscript (464K)
 Hu, Bin and Huang, Jianhong and Skiba, Alexander N.
Hu, Huang
School of Mathematics and Statistics
Jiangsu Normal University
Xuzhou, 221116
P. R. China
Skiba
Department of Mathematics
Francisk Skorina Gomel State University
Gomel 246019
Belarus
Abstract: see the article received 26.02.2017, accepted 29.11.2017 (15 pages)
download: manuscript (234K)
 Puthenpurakal, Tony Joseph
Department of Mathematics
Indian Institute of Technology Bombay
Powai
Mumbai 400 076
India
Abstract: In this paper we show that a large class of onedimensional CohenMacaulay local rings $(A,\mathfrak{m})$ has the property that if $M$ is a maximal CohenMacaulay $A$module then the Hilbert function of $M$ (with respect to $\mathfrak{m}$) is nondecreasing. 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 CohenMacaulay quotients of a two dimensional CohenMacaulay local ring with pseudorational singularity.
received 16.02.2017, accepted 09.11.2017 (7 pages)
download: manuscript (248K)
 Wilde, Tom
2 Amner Road
London SW11 6AA
UK 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 (304K)
 Noormohammadi, Hassan and Rahimi, Ahad
Department of Mathematics
Azarbaijan Shahid Madani University
Tabriz
Iran
Department of Mathematics
Razi University
Kermanshah
Iran
Abstract: In this paper, we give a characterization for CohenMacaulay 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 CohenMacaulayness 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 CohenMacaulay is given.
Finally, we compute $\rm{grade}\,(Q, M)$ where $M$ is a sequentially CohenMacaulay $S$module with respect to $Q$. received 02.04.2017, accepted 23.10.2017 (14 pages)
download: manuscript (323K)
 Yu, Haoran
School of Mathematics
Jilin University
No. 2699 Qianjin Street
Changchun
China 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 (345K)
 Sawkmie, Amplify and Singh, Madan Mohan
Department of Mathematics
NorthEastern Hill University
Shillong793022
India
Department of Basic Sciences & Social Sciences
NorthEastern Hill University
Shillong793022
India 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 $\{0,1,\ldots ,n1\}$ 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 (460K)
 Gille, Philippe
Université Claude Bernard Lyon 1
CNRS UMR 5208
Institut Camille Jordan
43 Blvd. du 11 novembre 1918
F69622 Villeurbane cedex
France 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 quasisplit if and only if it quasisplits after a finite tamely
ramified extension of $K$.
received 07.07.2017, accepted 16.10.2017 (9 pages)
download: manuscript (318K)
 BellierMillès, Joan
Institut de Mathématiques de Toulouse
UMR5219, Université de Toulouse
CNRS, UPS IMT
F31062 Toulouse Cedex 9
France 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 ()
 Friedenberg, Stefan
University of Stralsund
Zur Schwedenschanze 15
18435 Stralsund
Germany
Abstract: Let $A$ and $B$ be rational groups, i.e. torsionfree groups of rank1 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 torsionfree pairs. received 06.03.2017, accepted 20.09.2017 (5 pages)
download: manuscript ()
 Laterveer, Robert
Institut de Recherche Mathématique Avancée
CNRS _ Université de Strasbourg
7 Rue René Descartes
67084 Strasbourg CEDEX
France Abstract: Motivated by the BeauvilleVoisin 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 DontenBury 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 (320K)
 Huyghe, Christine and Schmidt, Tobias
IRMA
Université de Strasbourg
7, rue René Descartes
67084 Strasbourg cedex
France
IRMAR
Université de Rennes 1
Campus de Beaulieu
35042 Rennes cedex
France 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 (778K)
 De Giovanni, Francesco and Trombetti, Marco
Dipartimento di Matematica e Applicazioni
Università di Napoli Federico II
Complesso Universitario Monte S. Angelo
Via Cintia,
Napoli
Italy 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 (306K)
 Getmanenko, Alexander
Department of Mathematics
Edificio Mario Laserna Cra 1 Este No 19A
40 Bogota
Colombia
Universidad de los Andes
Colombia 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 (447K)
 Marini, Stefano and Nacinovich, Mauro
Dipartimento di Matematica e Fisica
III Università di Roma
Largo San Leonardo Murialdo, 1
00146 Roma
Italy 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 CauchyRiemann cohomology groups and the corresponding
Dolbeault cohomology groups of the embeddings. received 17.12.2016, accepted 09.05.2017 (30 pages)
download: manuscript (278K)
 Burenkov, V. I. and Chigambayeva, D. K. and Nursultanov, E. D.
RUDN University
S. M. Nikol’skii Institute
6 MiklukhoMaklay St
Moscow, 117198
Russia
Abstract: We introduce a class of Morreytype spaces $M^\lambda_{p,q}$, which includes classical Morrey spaces and discuss their properties. We prove a Marcinkiewicztype interpolation theorem. This theorem is then applied to obtaining the boundedness in the introduced Morreytype spaces of the Riesz potential and singular integral operator. received 05.10.2016, accepted 26.04.2017 (20 pages)
download: manuscript (173K)
 Kahn, Bruno
Institut de Mathématiques de Jussieu  PRG
Case 247
4 place Jussieu
75252 Paris Cedex 05
France 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 (702K)
 BarbieriViale, Luca and Prest, Mike
Dipartimento di Matematica "F. Enriques"
Università degli Studi di Milano
Via C. Saldini, 50
I20133 Milano
Italy
School of Mathematics
University of Manchester
Oxford Road
Manchester M13 9PL
UK 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 (395K)
 Keef, Patrick
Department of Mathematics
Whitman College
Walla Walla, WA 99362
USA 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 settheoretic universe in which $2^{\aleph_1}=\aleph_2$.
received 18.01.2017, accepted 03.03.2017 (18 pages)
download: manuscript (292K)
 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
$\big\{(x,y)\in
\mathbb{R}^{h+1}:y<\int_{\arcsinx}^{\frac{\pi}{2}}\sin^{\alpha+1}(t)dt,\hspace{2mm}x<1\big\}$. received 31.01.2017, accepted 24.02.2017 (17 pages)
download: manuscript (423K)
 Tarnauceanu, Marius and Lazorec, MihaiSilviu
Faculty of Mathematics
Al. I. Cuza University
Iasi
Romania 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 (311K)
 Chojecki, Przemyslaw
Instytut Matematyczny PAN
Ul. Sniadeckich 8
00656 Warsawa
Poland Abstract: We introduce a general formalism with minimal requirements under which we are able to prove the promodular FontaineMazur 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 (436K)
 Li, Changwen and Huang, Jianhong and Hu, Bin
School of Mathematics and Statistics
Jiangsu Normal University
Xuzhou, 221116
China
lcw2000@126.com 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 (98K)
 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 (336K)
 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 (355)
 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
Belarus
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 (187K)
 Alizade, Rafail and Durgun, Yilmaz
Yasar University
Department of Mathematics
35100, Izmir
Turkey
Bitlis Eren University
Department of Mathematics
13000, Bitlis
Turkey
Abstract: A right $R$module $M$ is said to be a test module for
flatness (shortly: an ftest 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 ftest 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 ftest is investigated.
Abelian groups that are Whitehead test modules for injectivity or ftest are characterized. received 22.02.2015, accepted 14.06.2016 (15 pages)
download: manuscript (129K)
 Pratelli, Aldo and Radici, Emanuela
Department of Mathematics
University of Erlangen
Cauerstrasse 11
90158 Erlangen
Germany 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 (408K)
 Abramovich, Dan and Fantechi, Barbara
Department of Mathematics
Box 1917
Brown University
Providence, RI, 02912
U.S.A
SISSA
Via Bonomea 265
34136 Trieste
Italy
Abstract: see the paper itself received 19.09.2014, accepted 01.04.2016 (16 pages)
download: manuscript (341K)
 Langer, Andreas and Zink, Thomas
University of Exeter
Mathematics
Exeter, EX4 4QF
Devon UK
Fakultät für Mathematik
Universität Bielefeld
Postfach 100131
D33501 Bielefeld
Germany Abstract: In this note we derive for a smooth projective variety $X$ with normal crossing
divisor $Z$ an integral comparison between the logcrystalline cohomology of the
associated logscheme and the logarithmic overconvergent de RhamWitt cohomology
defined by Matsuue. This extends our previous result that in the absence of a
divisor $Z$ the crystalline cohomology and overconvergent de RhamWitt cohomology are
canonically isomorphic. received 07.09.2015, accepted 14.03.2016 (6 pages)
download: manuscript (221K)
 Chin, Angelina Y. M. and Qua, K. T.
Institute of Mathematical Sciences
Faculty of Science
University of Malaya
50603 Kuala Lumpur
Malaysia 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 (89K)
 Yamaura, Yoshihiko
Department of Mathematics
College of Humanities and Sciences
Nihon University
32540, Sakurajosui, Setagaya
Tokyio 1568550
Japan 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 (192K)
 Vougalter, Vitali and Volpert, Vitaly
Department of Mathematics
University of Toronto
Ontario, M5S 2E4
Canada
Institute Camille Jordan
UMR 5208 CNRS
University Lyon 1
Villeurbane, 69622
France Abstract: The work deals with the existence of solutions of an integrodifferential
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 nonFredholm elliptic operators in
unbounded domains are being used. received 20.07.2015, accepted 28.01.2016 (16 pages)
download: manuscript (329K)
 Foroudi Ghasemabadi, Mahnaz and Iranmanesh, Ali and Ahanjideh, Milad
Department of pure Mathematics
Faculty of Mathematical Sciences
Tarbiat Modares University
Tehran
Iran 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 (164K)
 Alzer, Horst and Jameson, Graham J. O.
Morsbacher Str, 10
51545 Waldbröl
Germany
Department of Mathematics and Statistics
Lancaster University
Lancaster LA1 4YF
UK
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 (256K)
 Pathak, R. S. and Singh, Abhishek
DST Centre for Interdisciplinary Mathematical Sciences
Faculty of Science
Banaras Hindu University
Varanasi  221 005
India 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 (151K)
 Chojecki, Przemyslaw and Sorensen, Claus
Mathematical Institute, University of Oxford
Andrew Wiles Building, Radcliffe Observatory Quarter
Woodstock Road
Oxford OX2 6GG
England
Department of Mathematics, UCSD
9500 Gilman Dr. #0112
La Jolla, CA 920930112 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 (448K)
 Acciarri, Cristina and Shumyatsky, Pavel
Department of Mathematics
University of Brasilia
BrasiliaDF
70910900 Brazil Abstract: Let $w$ be a groupword. 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 wordvalues (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 groupwords. received 29.10.2015, accepted 19.11.2015 (19 pages)
download: manuscript (320K)
 Chojecki, Przemyslaw and Sorensen, Claus
Mathematical Institute, University of Oxford
Andrew Wiles Building, Radcliffe Observatory Quarter
Woodstock Road
Oxford OX2 6GG
England
chojecki@maths.ox.ac.uk
Department of Mathematics, UCSD
9500 Gilman Dr. #0112
La Jolla, CA 920930112 USA
csorensen@ucsd.edu
Abstract: We study the completed cohomology $\hat{H}^0$ of a definite unitary group $G$ in two variables associated with a CMextension $\mathcal{K}/F$. 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 FontaineMazur 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 (512K)
 Rezaeezadeh, Gholamreza R. and Aghajari, Zahra
Faculty of Mathematical Science
Department of Pure Mathematics
Shahrekord University
P. O. Box 115
Shahrekord
Iran 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. BallesterBolinches 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)
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 Lu, Xin Yang
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburg, PA, 15213
United States Abstract: The averagedistance problem, in the penalized formulation, involves
minimizing
\begin{equation*}
E_\mu^\lambda(\Sigma):=\int_{{\mathbb R}^d} \inf_{y\in\Sigma} xy\operatorname{d}\mu(x)+\lambda{\mathcal H}^1(\Sigma),
\end{equation*}
among {compact, connected sets $\Sigma$, where
${\mathcal H}^1$ denotes the 1Hausdorff 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 (544K)
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