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European Mathematical Society Publishing House
2024-03-28 20:42:31
13
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RSMUP&vol=132&update_since=2024-03-28
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
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European Mathematical Society Publishing House
Zuerich, Switzerland
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132
2014
0
Finer regularity of an entropy solution for 1-d scalar conservation laws with non uniform convex flux
Adimurthi
Tata Institute of Fundamental Research, BANGALORE, INDIA
Shyam Sundar
Ghoshal
Université de Franche-Comté, BESANÇON CEDEX, FRANCE
G.D. Veerappa
Gowda
Tata Institute of Fundamental Research, BANGALORE, INDIA
Hamilton–Jacobi equation, scalar conservation laws, characteristic lines, sbv functions, uniformly convex
Consider a scalar conservation law in one space dimension with initial data in $ L^\infty.$ If the flux $ \kern 1pt f$ is in $ C^2$ and locally uniformly convex, then for all $ t> 0$ , the entropy solution is locally in BV (functions of bounded variation) in space variable. In this case it was shown in [5], that for all most every $ t > 0$ , locally, the solution is in SBV (Special functions of bounded variations). Furthermore it was shown with an example that for almost everywhere in $ t> 0$ cannot be removed. This paper deals with the regularity of the entropy solutions of the strict convex $ C^1$ flux $f$ which need not be in $ C^2$ and locally uniformly convex. In this case, the entropy solution need not be locally in BV in space variable, but the composition with the derivative of the flux function is locally in BV. Here we prove that, this composition is locally is in SBV on all most every $ t> 0$. Furthermore we show that this is optimal.
Partial differential equations
Combinatorics
1
24
10.4171/RSMUP/132-1
http://www.ems-ph.org/doi/10.4171/RSMUP/132-1
Positive solutions for a semipositone problem involving nonlocal operator
Ghasem
Afrouzi
University of Mazandaran, BABOLSAR, IRAN
N.T.
Chung
Quang Binh University, QUANG BINH, VIETNAM
S.
Shakeri
University of Mazandaran, BABOLSAR, IRAN
Kirchhoff type problems, semipositone, positive solution, sub and supersolutions
In this article, we are interested in the existence of positive solutions for the following Kirchhoff type problems $$\cases{ -M\Big (\int\limits _ {{\Omega} }\vert \nabla u\vert ^p\,dx\Big){\rm div}\big (\vert \nabla u\vert ^{p-2}\nabla u\big) = {\lambda} a(x)\,f(u)-{\mu}{\ in\ } {\Omega},\cr u =0 {\ on\ } x \in \partial {\Omega},}$$ where $ {\Omega} $ is a bounded smooth domain of $ R^N, 1< p< N , M: R^+_ 0\to R^+$ is a continuous and increasing function, $ {\lambda}, {\mu} $ are two positive parameters, $ a\in C(\overline {\Omega} ) , a(x)\geq a_ 0> 0$ , and $ f$ is a $ C^1([0,\infty ))$ function such that $ f(0)=0 , f(t)> 0$ for all $ 0< t< t_ 0$ and $f(t)\leq 0$ for all $ t \geq t_ 0$ , where $ t_ 0> 0$ .
Partial differential equations
25
32
10.4171/RSMUP/132-2
http://www.ems-ph.org/doi/10.4171/RSMUP/132-2
Harmonic numbers and finite groups
Sekhar Jyoti
Baishya
The North Eastern Hill University Library, MEGHALAYA, INDIA
Ashish Kumar
Das
The North Eastern Hill University Library, MEGHALAYA, INDIA
Finite groups, harmonic numbers, harmonic groups
Given a finite group $ G , $ let $ {\tau} (G)$ be the number of normal subgroups of $ G$ and $ {\sigma} (G)$ be the sum of the orders of the normal subgroups of $ G$ . The group $ G$ is said to be harmonic if $ H(G):=\vert G\vert {\tau} (G)/{\sigma} (G)$ is an integer. In this paper, all finite groups for which $ 1 \leq H(G) \leq 2$ have been characterized. Harmonic groups of order $ pq$ and of order $pqr$ , where $ p< q< r$ are primes, are also classified. Moreover, it has been shown that if $ G$ is harmonic and $ G \not \cong C_ 6$, then $ {\tau} (G) \geq 6$.
Number theory
Group theory and generalizations
33
43
10.4171/RSMUP/132-3
http://www.ems-ph.org/doi/10.4171/RSMUP/132-3
Almost periodic functions on groupoids
Farid
Behrouzi
Institute for Research in Fundamental Sciences (IPM), TEHRAN, IRAN
Groupoids, almost period function
In this paper we generalize the notion of almost periodic functions on groups to the corresponding notion for groupoids. We prove a number of theorems about almost periodic functions in this general setting. We show that the set of almost periodic functions on a groupoid $ G , AP(G),$ is a C*-subalgebra of $ \ell ^{\infty }(G)$ . We investigate some topological properties of the maximal ideal space of $ AP(G) , {\mathfrak {b}}(G),$ and we obtain a continuous partial operation on ${\mathfrak {b}}G$ . Also, we study almost periodic functions on groupoids defined by an equivalence relation on a set $ X$ and obtain a compactification of $ X.$
Topological groups, Lie groups
45
59
10.4171/RSMUP/132-4
http://www.ems-ph.org/doi/10.4171/RSMUP/132-4
Galois points for a plane curve and its dual curve
Satoru
Fukasawa
Yamagata University, YAMAGATA, JAPAN
Kei
Miura
Ube National College of Technology, UBE, YAMAGUCHI, JAPAN
Galois point, plane curve, dual curve, self-dual curve
A point $ P$ in projective plane is said to be Galois for a plane curve of degree at least three if the function field extension induced by the projection from $ P$ is Galois. Further we say that a Galois point is extendable if any birational transformation by the Galois group can be extended to a linear transformation of the projective plane. In this article, we propose the following problem: {\it If a plane curve has a Galois point and its dual curve has one, what is the curve?} We give an answer. We show that the dual curve of a smooth plane curve does not have a Galois point. On the other hand, we settle the case where both a plane curve and its dual curve have extendable Galois points. Such a curve must be defined by $ X^d-Y^eZ^{d-e}=0$ , which is a famous self-dual curve.
Algebraic geometry
Field theory and polynomials
61
74
10.4171/RSMUP/132-5
http://www.ems-ph.org/doi/10.4171/RSMUP/132-5
Lattice graphs with non-concurrent longest cycles
Ali Dino
Jumani
Shah Abdul Latif University, SINDH, PAKISTAN
Carol
Zamfirescu
Technische Universität Dortmund, DORTMUND, GERMANY
Tudor
Zamfirescu
Technische Universität Dortmund, DORTMUND, GERMANY
Lattice graphs, longest cycles
No hypohamiltonian graphs are embeddable in the planar square lattice. This lattice contains, however, graphs in which every vertex is missed by some longest cycle. In this paper we present graphs with this property, embeddable in various lattices, and of remarkably small order.
Combinatorics
75
82
10.4171/RSMUP/132-6
http://www.ems-ph.org/doi/10.4171/RSMUP/132-6
Perverse sheaves on semiabelian varieties
Thomas
Krämer
École Polytechnique, PALAISEAU Cedex, FRANCE
Perverse sheaf, semiabelian variety, convolution product, generic vanishing theorem, Tannakian category
We give a Tannakian description for the category of perverse sheaves on semiabelian varieties. Our construction is based on a vanishing theorem for the hypercohomology of perverse sheaves and extends earlier results for tori and abelian varieties. As an application we explain how perverse sheaves on abelian varieties can be studied in terms of semiabelian degenerations via a Tannakian interpretation for the functor of nearby cycles.
Algebraic geometry
Several complex variables and analytic spaces
83
102
10.4171/RSMUP/132-7
http://www.ems-ph.org/doi/10.4171/RSMUP/132-7
Stability of Cartan–Eilenberg Gorenstein categories
Li
Liang
Lanzhou Jiatong University, LANZHOU (GANSU), CHINA
Gang
Yang
Lanzhou Jiatong University, LANZHOU (GANSU), CHINA
Gorenstein categories, Cartan–Eilenberg Gorenstein categories, projective generators, injective cogenerators
We study Cartan-Eilenberg Gorenstein categories by introducing ${\rm {CE}} $ -projective ${\rm {CE}} $ -generators and ${\rm {CE}} $ -injective ${\rm {CE}} $ -cogenerators in the paper. We give a relationship between injective cogenerators (resp., projective generators) introduced by Sather-Wagstaff, Sharif and White and ${\rm {CE}} $ -injective ${\rm {CE}} $-cogenerators (resp., ${\rm {CE}} $-projective ${\rm {CE}} $-generators). As applications, we prove some stability results of Cartan-Eilenberg Gorenstein categories.
Category theory; homological algebra
103
122
10.4171/RSMUP/132-8
http://www.ems-ph.org/doi/10.4171/RSMUP/132-8
NSE characterization of projective special linear group $L_5(2)$
Shitian
Liu
Sichuan University of Science and Engineering, SICHUAN, CHINA
Element order, projective special linear group, Thompson's problem, number of elements of the same order
Let $ G$ be a group and $ {\omega} (G)$ be the set of element orders of $ G$. Let $ k\in {\omega} (G)$ and $ s_ {k}$ be the number of elements of order $ k$ in $ G$. Let nse$ (G)=\big \{ s_{k}\,\big \vert \;k\in {\omega} (G) \big \}$. In Khatami et al. and Liu, $ L_ {3}(2)$ and $ L_ {3}(4)$ are uniquely determined by nse$ (G)$. In this paper, we prove that if $ G$ is a group such that nse$ (G)= nse( L_ {5}(2)$), then $ G\cong L_ {5}(2)$.
Group theory and generalizations
123
132
10.4171/RSMUP/132-9
http://www.ems-ph.org/doi/10.4171/RSMUP/132-9
Classicality of overconvergent Hilbert eigenforms: case of quadratic residue degrees
Yichao
Tian
Chinese Academy of Sciences, BEIJING, CHINA
Let $ F$ be a real quadratic field, $ p$ be a rational prime inert in $ F$, and $ N\geq 4$ be an integer coprime to $ p$. Consider an overconvergent $ p$-adic Hilbert eigenform $ f$ for $ F$ of weight $ (k_ 1,k_ 2)\in {\bf Z} ^{2}$ and level $ {\it \Gamma} _ {00}(N)$. We prove that if the slope of $ f$ is strictly less than $ \min \{k_ 1,k_ 2\}-2$ , then $ f$ is a classical Hilbert modular form of level $ {\it \Gamma} _ {00}(N)\cap {\it \Gamma} _ {0}(p)$ .
General
133
229
10.4171/RSMUP/132-10
http://www.ems-ph.org/doi/10.4171/RSMUP/132-10
Simple sufficient conditions for bounded turning
Nikolai
Tuneski
Sts Cyril and Methodius University, SKOPJE, MACEDONIA
Maslina
Darus
Universiti Kebangsaan Malaysia, BANGI SELANGOR, MALAYSIA
Elena
Gelova
University Goce Delcev, STIP, MACEDONIA
Analytic function, bounded turning, real part, modulus
Let $ f$ be an analytic function in the open unit disk normalized such that $ f(0)=f'(0)-1=0.$ In this paper the modulus and the real part of the linear combination of $ f'(z)$ and $ f(z)/z$ is studied and conditions when $ f$ is of bounded turning are obtained.
Functions of a complex variable
231
238
10.4171/RSMUP/132-11
http://www.ems-ph.org/doi/10.4171/RSMUP/132-11
A characterization of automorphism groups of simple $K_3$-groups
Dapeng
Yu
Southwest University, CHONGQING, CHINA
Jinbao
Li
Chongqing University of Arts and Sciences, CHONGQING, CHINA
Guiyun
Chen
Southwest University, CHONGQING, CHINA
Yanheng
Chen
Chongqing Three Gorges University, CHONGQING, CHINA
Simple $K_3$-groups, conjugacy classes sizes, characterization
In this paper, a new characterization of automorphism groups of simple $K_ 3$-groups is presented.
Group theory and generalizations
239
247
10.4171/RSMUP/132-12
http://www.ems-ph.org/doi/10.4171/RSMUP/132-12
A class of Caffarelli–Kohn–Nirenberg type inequalities on the H-type group
Shutao
Zhang
China Jiliang University, HANGZHOU, CHINA
Yazhou
Han
China Jiliang University, HANGZHOU, CHINA
Jingbo
Dou
XI'AN University of Finance and Economics, XIAN, SHAANXI, CHINA
Caffarelli–Kohn_Nirenberg type inequality, Hardy–Sobolev type inequality, H-type group
This work is devoted to establish a class of Caffarelli-Kohn-Nirenberg type inequalities on the H-type group. Inspired by the idea of Chern J.L. and Lin C.S., a function transformation is introduced. Combining some elementary inequalities and some accurate estimates, we establish a class of weighted Hardy-Sobolev type inequalities and then obtain our main result, namely Caffarelli-Kohn-Nirenberg type inequalities on the H-type group.
Partial differential equations
Topological groups, Lie groups
Real functions
249
266
10.4171/RSMUP/132-13
http://www.ems-ph.org/doi/10.4171/RSMUP/132-13