- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 06:40:13
12
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RSMUP&vol=133&update_since=2024-03-29
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2013)
133
2015
0
Evaluations of a continued fraction of Ramanujan
Nikos
Bagis
, PELLAS, GREECE
M. Lawrence
Glasser
Clarkson University, POTSDAM, UNITED STATES
Continued fractions, Ramanujan, evaluations
We study the properties of a general continued fraction of Ramanujan. In certain cases we evaluate it completely.
Number theory
Special functions
1
10
10.4171/RSMUP/133-1
http://www.ems-ph.org/doi/10.4171/RSMUP/133-1
Mixed Hodge complexes and higher extensions of mixed Hodge modules on algebraic varieties
Florian
Ivorra
Université de Rennes 1, RENNES CEDEX, FRANCE
Mixed Hodge modules, mixed Hodge complexes
In [1, 2] A. Beilinson provides a description of the bounded derived category of polarizable mixed Hodge structures in terms of the more flexible triangulated category of polarizable mixed Hodge complexes. In this work we provide a partial generalization of this result to higher dimension.
Algebraic geometry
11
77
10.4171/RSMUP/133-2
http://www.ems-ph.org/doi/10.4171/RSMUP/133-2
Finite $p$-supersoluble groups with some $E$-$S$-supplemented subgroups
Changwen
Li
Xuzhou Normal University, XUZHOU, CHINA
Xiaolong
Yu
University of Scinece and Technology of China, HEFEI, ANHUI, CHINA
Na
Tang
Huaiyin Normal University, HUAIYIN, CHINA
$S$-permutable, $E-S$-supplemented, $p$-supersoluble
Let $H$ be a subgroup of a group $G$ and $H_{eG}$ denote the subgroup of $H$ generated by all those subgroups of $H$ which are $S$-permutably embedded in $G$. $H$ is said to be $E$-$S$-supplemented in $G$ if there exists a subnormal subgroup $T$ of $G$ such that $G=HT$ and $H\cap T\leq H_{eG}$. In this paper, we investigate the influence of some $E$-$S$-supplemented subgroups on the structure of finite group. Some new characterizations of $p$-supersoluble groups are obtained.
Group theory and generalizations
79
90
10.4171/RSMUP/133-3
http://www.ems-ph.org/doi/10.4171/RSMUP/133-3
Pure injective and $\ast$-pure injective LCA groups
Peter
Loth
Sacred Heart University, FAIRFIELD, UNITED STATES
Locally compact abelian groups, pure injectives, $ast$-pure injectives, topologically pure projectives
A proper short exact sequence $0\to A\to B\to C\to 0$ in the category $\mathcal L$ of locally compact abelian (LCA) groups is called $\ast$-pure if the induced sequence $0\to A[n]\to B[n]\to C[n]\to 0$ is proper exact for all positive integers $n$. An LCA group is called $\ast$-pure injective in $\mathcal L$ if it has the injective property relative to all $\ast$-pure sequences in $\mathcal L$. In this paper, we give a complete description of the $\ast$-pure injectives in $\mathcal L$. They coincide with the injectives in $\mathcal L$ and therefore with the pure injectives in $\mathcal L$. Dually, we determine the topologically pure projectives in $\mathcal L$.
Group theory and generalizations
Topological groups, Lie groups
91
102
10.4171/RSMUP/133-4
http://www.ems-ph.org/doi/10.4171/RSMUP/133-4
Character difference digraphs over finite fields
Risto
Atanasov
Western Carolina University, CULLOWHEE, UNITED STATES
Mark
Budden
Western Carolina University, CULLOWHEE, UNITED STATES
Joshua
Lambert
Armstrong Atlantic State University, SAVANNAH, UNITED STATES
Paley graphs, Jacobi sums
We generalize the notion of Paley digraphs by defining and studying character difference digraphs for characters defined on the multiplicative groups of finite fields.
Combinatorics
Number theory
103
115
10.4171/RSMUP/133-5
http://www.ems-ph.org/doi/10.4171/RSMUP/133-5
Groups having complete bipartite divisor graphs for their conjugacy class sizes
Roghayeh
Hafezieh
Gebze Institute of Technology, GEBZE, TURKEY
Pablo
Spiga
Università degli Studi di Milano-Bicocca, MILANO, ITALY
Bipartite divisor graph, conjugacy class size, extra-special group
Given a finite group $G$, the bipartite divisor graph for its conjugacy class sizes is the bipartite graph with bipartition consisting of the set of conjugacy class sizes of $G\setminus\mathbf Z (G)$ (where $\mathbf Z (G)$ denotes the centre of $G$) and the set of prime numbers that divide these conjugacy class sizes, and with $\{p,n\}$ being an edge if gcd$(p,n)\neq 1$. In this paper we construct infinitely many groups whose bipartite divisor graph for their conjugacy class sizes is the complete bipartite graph $K_{2,5}$, giving a solution to a question of Taeri [15].
General
117
123
10.4171/RSMUP/133-6
http://www.ems-ph.org/doi/10.4171/RSMUP/133-6
Des $\pi$-exponentielles I: vecteurs de Witt annulés par Frobenius et algorithme de (leur) rayon de convergence
Rodolphe
Richard
, PLOUISY, FRANCE
$\pi$-exponentials, $p$-adic differential equations, kernel of Frobenius endomorphism of Witt vectors over a $p$-adic ring, radius of convergence function, algorithm
Our object is the theory of "$\pi$-exponentials" Pulita developed in his thesis, generalising Dwork's and Robba's exponentials and extending Matsuda's work: We start with an abstract algebra statement about the structure of the kernel of iterations of the Frobenius endomorphism on the ring of Witt vectors with coordinates in the ring of integers of an ultrametric extension of $\mathbb Q_p$. Provided sufficiently (ramified) roots of unity are available, it is, unexpectedly simply, a principal ideal with respect to an explicit generator essentially given by Pulita's $\pi$-exponential. This result is a consequence and a reformulation of core facts of Pulita's theory. It happened to be simpler to prove directly than reformulating Pulita's results. Its translation in terms of series is very elementary, and gives a criterion for solvabilty and integrality for $p$-adic exponential series of polynomials. We explain how to deduce an explicit formula of their radius of convergence, and even the function radius of convergence. We recover this way, in elementary terms, with a new proof, and important simplifications, an algorithm of Christol based similarly on Pulita's work. One concrete advantage is: one can easily prove rigorous complexity bounds about the implied algorithm from our explicit formula. We also add there and there refinements and observation, notably hinting some of the finer informations that can also given by the algorithm. \newline One of the appendix produce a computation which gives finer estimates on the coefficients of these series. It should provide useful in proving complexity bounds for various computational use involving these series. It is not apparent yet in the present work, but should be in latter projected developments, the series under consideration are the base object for some exponential sums on finite fields via $p$-adic approach, namely via rigid cohomology with rank one coefficients. \newline Convergence radius and coefficients estimates are involved studying the efficiency of computational implementations of these objects. The understanding of convergence radius of $p$-adic differential equations is a subject undergoing active developments, and we here provide a fine theoretical and computational study of the simplest of cases. \newline This initiate a projected series of articles. We start here, with the case of the affine line as a base space, a Witt vectors paradigm. This provides an alternative purely algebraic approach of Pulita’s theory; the richness of Witt vectors theory allow suppleness and efficiency in working with~$\pi$-exponentials, which will prove efficient later in the series.
Field theory and polynomials
Commutative rings and algebras
Algebraic geometry
125
158
10.4171/RSMUP/133-7
http://www.ems-ph.org/doi/10.4171/RSMUP/133-7
$\alpha$-isoptics of a triangle and their connection to $\alpha$-isoptic of an oval
Małgorzata
Michalska
Uniwersytet Marii Curie-Skłodowskiej, LUBLIN, POLAND
Witold
Mozgawa
Uniwersytet Marii Curie-Skłodowskiej, LUBLIN, POLAND
Isoptic curve, convex curve, support function, envelope, oval
For a fixed positive angle $\alpha$, $\alpha
Differential geometry
Convex and discrete geometry
159
172
10.4171/RSMUP/133-8
http://www.ems-ph.org/doi/10.4171/RSMUP/133-8
Classification of rings with unit graphs having domination number less than four
S.
Kiani
Islamic Azad University, TEHRAN, IRAN
H.R.
Maimani
Institute for Research in Fundamental Sciences (IPM), TEHRAN, IRAN
M.R.
Pournaki
Institute for Research in Fundamental Sciences (IPM), TEHRAN, IRAN
S.
Yassemi
Institute for Research in Fundamental Sciences (IPM), TEHRAN, IRAN
Unit graph, domination number, total domination number, finite ring
Let $R$ be a finite commutative ring with nonzero identity. The unit graph of $R$ is the graph obtained by setting all the elements of $R$ to be the vertices and defining distinct vertices $x$ and $y$ to be adjacent if and only if $x+y$ is a unit element of $R$. In this paper, a classification of finite commutative rings with nonzero identity in which their unit graphs have domination number less than four is given.
Combinatorics
Commutative rings and algebras
173
195
10.4171/RSMUP/133-9
http://www.ems-ph.org/doi/10.4171/RSMUP/133-9
On a class of weighted Gauss-type isoperimetric inequalities and applications to symmetrization
Michele
Marini
Scuola Normale Superiore, PISA, ITALY
Berardo
Ruffini
Université Grenoble I, SAINT MARTIN D'HERES CEDEX, FRANCE
Weighted isoperimetric inequalities, symmetrizations, rearrangements
We solve a class of weighted isoperimetric problems of the form $$ \mathrm {min}\left\{\int_{\partial E}w e^V\,dx:\int_E e^V\,dx=\mathrm {constant}\right\}$$ where $w$ and $V$ are suitable functions on $\mathbb R^d$. As a consequence, we prove a comparison result for the solutions of degenerate elliptic equations.
Real functions
Partial differential equations
197
214
10.4171/RSMUP/133-10
http://www.ems-ph.org/doi/10.4171/RSMUP/133-10
Almost-periodic solution of linearized Hasegawa–Wakatani equations with vanishing resistivity
Shintaro
Kondo
Meiji University, TOKYO, JAPAN
Hasegawa–Wakatani equations, Hasegawa–Mima equation, drift wave turbulence, Sobolev spaces, Stepanov-almost-periodic function
In this paper we consider the zero-resistivity limit for linearized Hasegawa–Wakatani equations in a cylindrical domain when the initial data are Stepanov-almost-periodic to the axial direction. We prove two results: one is the existence and uniqueness of a strong Stepanov-almost-periodic solution to the initial boundary value problem for linearized Hasegawa–Wakatani equations with zero resistivity; another is the convergence of the solution of linearized Hasegawa–Wakatani equations established in [24] to the solution of the problem studied at the first stage as the resistivity tends to zero. In the proof we obtain two useful lemmas for Stepanov-almost-periodic functions.
Partial differential equations
Fourier analysis
Statistical mechanics, structure of matter
215
239
10.4171/RSMUP/133-11
http://www.ems-ph.org/doi/10.4171/RSMUP/133-11
Automorphism-invariant modules
Adel
Alahmadi
King Abdulaziz University, JEDDAH, SAUDI ARABIA
Alberto
Facchini
Università di Padova, PADOVA, ITALY
Nguyen
Khanh Tung
Università di Padova, PADOVA, ITALY
Automorphism-invariant modules, injective envelopes
A module $M$ is called automorphism-invariant if it is invariant under automorphisms of its injective envelope. In this paper, we study the endomorphism rings of automorphism-invariant modules and their injective envelopes. We investigate some cases where automorphism-invariant modules are quasi-injective and a connection between automorphism-invariant modules and boolean rings.
Associative rings and algebras
241
259
10.4171/RSMUP/133-12
http://www.ems-ph.org/doi/10.4171/RSMUP/133-12