Showing papers in "Rendiconti del Seminario Matematico della Università di Padova in 2017"
TL;DR: In this paper, a concavity property of the digamma function ψ = Γ′/Γ, where Γ denotes Euler's gamma function, was shown.
Abstract: We present some inequalities and a concavity property of the digamma function ψ = Γ′/Γ, where Γ denotes Euler’s gamma function. In particular, we offer a new characterization of Euler’s constant γ = 0.57721.... We prove that −γ is the minimum of the harmonic mean of ψ(x) and ψ(1/x) for x > 0. Mathematics Subject Classification (2010). 33B15, 39B62, 41A44.
16 citations
TL;DR: In this article, the authors developed a method to deduce the number c(P0(G)) of components of a graph by considering the components of its possible quotient graphs / �.
Abstract: We develop a method to deduce the number c() of components of a graph by consideration of the components of its possible quotient graphs / �. We present an effective procedure for computing c() when / � and Aut() have suitable properties. We apply that procedure to P0(G), the proper power subgraph of a finite group G, finding a formula for c(P0(G)), which is particularly expressive when GSn, is a fusion controlled permutation group. We rely on some quotient graphs of P0(G): the proper quotient power graph e P0(G), the proper order graph O0(G) and the proper power type graph P0(T (G)). We exhibit the strong link between those graphs dealing with G = Sn, finding simultaneously c(P0(Sn)) as well as the number of components of O0(Sn) and P0(T (Sn)).
14 citations
TL;DR: In this paper, the wavelet transform has been extended to distributions, and inversion formulae have been established in the distribution setting by Pathak et al. using duality arguments.
Abstract: Wavelet analysis has been used for intrinsic characterizations of important function and distribution spaces ([10], [11]). Recently, the wavelet transform has been extended to distributions, and inversion formulae have been established in distribution setting by Pathak [13, 14], Pathak et al [16, 17, 18] and Pandey [12] using duality arguments. Wavelets of subexponential decay whose Fourier transform have compact support i.e. band limited wavelets, were investigated by Dziubański and Hernández [7]. Pathak and Singh [17] extended the work of Dziubański and Hernández and studied wavelets with more general decay (infraexponential decay) whose Fourier
14 citations
TL;DR: For certain modp Galois representations, arising from modular forms on denite unitary groups in two variables, the -part of completed cohomology can be expressed as a tensor product p 0, where p is attached to the universal deformation univ via the p-adic local Langlands correspondence for GL2(Qp) as discussed by the authors.
Abstract: For certain modp Galois representations , arising from modular forms on denite unitary groups in two variables, we express the -part of completed cohomology ^ H 0 (away from = p[ 0) as a tensor product p 0 . Here p is attached to the universal deformation univ via the p-adic local Langlands correspondence for GL2(Qp), and 0 is given by the local Langlands correspondence in families, of Emerton and Helm. 1 2
13 citations
TL;DR: The anomalous diffusion term corresponds to the change of genotype via small random mutations, and the nonlocal term describes large mutations.
Abstract: which appears in cell population dynamics. The space variable x is correspondent to the cell genotype, u(x, t) stands for the cell density as a function of their genotype and time. The right side of this equation describes the evolution of cell density due to cell proliferation, mutations and cell influx. Namely, the anomalous diffusion term corresponds to the change of genotype via small random mutations, and the nonlocal term describes large mutations. In this context g(u) is the rate of cell birth which depends on u (density dependent proliferation), and the function K(x − y) shows the proportion of newly born cells which change their genotype from y to x.
9 citations
TL;DR: In this paper, it was shown that if G is a finite group such that Vo(G) = Vo(M) and |G| = |M |, then G ∼= M, where M is a sporadic simple group, an alternating group, a projective special linear group L2(p), where p is an odd prime or a finite simple Kn-group, where n ∈ {3, 4}.
Abstract: Let G be a finite group. A vanishing element of G is an element g ∈ G such that χ(g) = 0 for some irreducible complex character χ of G. Denote by 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 Vo(G) = Vo(M) and |G| = |M |, then G ∼= M , where M is a sporadic simple group, an alternating group, a projective special linear group L2(p), where p is an odd prime or a finite simple Kn-group, where n ∈ {3, 4}. These results confirm the conjecture posed in [17] for the simple groups under study. Mathematics Subject Classification (2010). 20C15; 20D05.
8 citations
TL;DR: In this article, the notion of a Tits arrangement on a convex open cone was introduced as a special case of (infinite) simplicial arrangements, and the standard constructions of subarrangements and restrictions were known in the case of finite hyperplane arrangements, which are known in this more general setting.
Abstract: We introduce the notion of a Tits arrangement on a convex open cone as a special case of (infinite) simplicial arrangements. Such an object carries a simplicial structure similar to the geometric representation of Coxeter groups. The standard constructions of subarrangements and restrictions, which are known in the case of finite hyperplane arrangements, work as well in this more general setting.
7 citations
TL;DR: In this paper, the properties of f-test modules are investigated and are used to characterize various families of rings, and the structure of a ring over which every (finitely generated) right R-module is flat or F-test is investigated.
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. Mathematics Subject Classification (2010). 16A50; 16D40; 18G25.
6 citations
TL;DR: A survey of recent results on finite and countable coverings of word-values (mostly commutators) by procyclic, abelian, nilpotent, and soluble subgroups can be found in this article.
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.
5 citations
TL;DR: The average distance problem in the penalized formulation of the average distance minimization problem involves minimizing as mentioned in this paper, where the objective is to minimize the total distance of the shortest path to the target.
Abstract: The average-distance problem, in the penalized formulation, involves minimizing
5 citations
TL;DR: In this article, strongly invariant subgroups for several classes of Abelian groups are introduced. But these subgroups are not invariant for all classes of groups and are not strongly inert for all groups.
Abstract: Mixing in a natural way the notions of fully inert (see [6]) and strongly invariant (see [4]) subgroups of Abelian groups, we introduce the strongly inert subgroups which we determine for several classes of Abelian groups. Mathematics Subject Classification (2010). 20K27, 20K30, 20K10.
TL;DR: In this paper, some criteria for p-supersolvablity of a finite group were obtained and some known results concerning weakly S-semipermutable subgroups were extended.
Abstract: In this note, we obtain some criteria for p-supersolvablity of a finite group and extend some known results concerning weakly S-semipermutable subgroups. Mathematics Subject Classification (2010). 20D10.
TL;DR: In this article, a degeneration formula for Gromov-Witten invariants of schemes and stacks is developed, generalizing the approach of Jun Li[Li01, Li02].
Abstract: and prove their properness using a universalconstruction introduced in [ACFW11]. We then use these spaces for aconcrete application, as explained in the next paragraph.In [AF11], a degeneration formula for Gromov–Witten invariants ofschemes and stacks is developed, generalizing the approach of Jun Li[Li01, Li02]. This in particular requires proving properness of Li’s stackof pre-deformable stable maps in the case where the target (X,D) orW → B is a Deligne–Mumford stack. One could simply adapt Li’s
TL;DR: In this paper, a local theorem of existence and uniqueness of solutions of the equations of stationary axially symmetric vacuum gravitational fields in the general theory of relativity close to the flat space solution is proved using the implicit function theorem in Banach spaces.
Abstract: A local theorem of existence and uniqueness of solutions of the equations of stationary axially symmetric vacuum gravitational fields in the general theory of relativity close to the flat space solution is proved using the implicit function theorem in Banach spaces. Mathematics Subject Classification (2010). 83C10, 83C05
TL;DR: In this article, the authors study how the number of components of a graph can be expressed through the number and properties of the components of the quotient graph of the graph, and they partially rely on classic qualifications of graph homomorphisms such as locally constrained homomorphism and on the concept of equitable partition and orbit partition.
Abstract: We study how the number $c(X)$ of components of a graph $X$ can be expressed through the number and properties of the components of a quotient graph $X/\sim.$ We partially rely on classic qualifications of graph homomorphisms such as locally constrained homomorphisms and on the concept of equitable partition and orbit partition. We introduce the new definitions of pseudo-covering homomorphism and of component equitable partition, exhibiting interesting inclusions among the various classes of considered homomorphisms. As a consequence, we find a procedure for computing $c(X)$ when the projection on the quotient $X/\sim$ is pseudo-covering. That procedure becomes particularly easy to handle when the partition corresponding to $X/\sim$ is an orbit partition.
TL;DR: The structure of the centralizers of arbitrary finite subgroups in Hall's universal group is studied by B. Hartley by using the property of existential closed structure of Hall's Universal group in the class of locally finite groups as mentioned in this paper.
Abstract: The structure of the centralizers of elements and finite abelian subgroups in Hall’s universal group is studied by B. Hartley by using the property of existential closed structure of Hall’s universal group in the class of locally finite groups. The structure of the centralizers of arbitrary finite subgroups were an open question for a long time. Here by using basic group theory and the construction of P. Hall we give a complete description of the structure of centralizers of arbitrary finite subgroups in Hall’s universal group. Namely we prove the following. Let U be the Hall’s universal group and F be a finite subgroup of U . Then the centralizer CU (F ) is isomorphic to an extention of Z(F ) by U . Mathematics Subject Classification (2010). 20E32, 20F50.
TL;DR: Ballester et al. as mentioned in this paper gave new characterizations of the soluble Tc-, PT c-, and PST c-groups and defined the NNMc, PNMc-, and SNMc-groups.
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 Tc-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 NNMc-, PNMc-, and SNMc-groups and presents new characterizations of the wider classes of soluble Tc-, PT c-, and PST c-groups. Mathematics Subject Classification (2010). 20F16; 20E28; 20E15.
TL;DR: Aminimizing movement associated with a singular functional introduced by Alt and Caffarelli in order to study a free boundary problem is constructed in this paper, which is uniformly continuous with respect to both time and space variables.
Abstract: Aminimizing 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 Γ -convergence keeping the time discretization parameter fixed. Mathematics Subject Classification (2010). 35J20
[...]
TL;DR: In this article, the necessary and sufficient conditions for the group ring RG, where G is a nontrivial abelian group, to be primary were obtained, assuming that the Jacobson radical of R is simple Artinian and J(R) is nilpotent.
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. Mathematics Subject Classification (2010). 16S34; 16U99.
TL;DR: In this article, it was shown that the Lusin type approximation property of Lipschitz functions with C 1 functions does not hold with respect to a general Radon measure.
Abstract: We add to the literature the following observation. If µ is a singular measure on the real line which assigns measure zero to every porous set and f : R ! R is a Lipschitz function which is non-differentiable µ-a.e. then for every C 1 function g : R ! R there holds µ{x 2 R : f(x) = g(x)} = 0. In other words the Lusin type approximation property of Lipschitz functions with C 1 functions does not hold with respect to a general Radon measure. Moreover we discuss, only in the one-dimensional setting, how the result contained in (Alberti, A Lusin type theorem for gradients, J. Funct. Anal., 100 (1991)) could be extended and improved when the Lebesgue measure is replaced by an arbitrary Radon measure.
TL;DR: In this article, it was shown that HnilQ(aut1(X)) 6 cocatQ(Baut 1(X)), when X is a simply connected CW-complex of finite type and that the equality holds when Baut 1 (X) is coformal.
Abstract: Our main purpose in this paper is to resolve, in a rational homotopy theory context, the following open question asked by S. Theriault : Given a topological space X, what one may say about the nilpotency of aut1(X) when the cocategory of its classifying space Baut1(X) is finite? Here aut1(X) denotes the path component of the identity map in the set of self homotopy equivalences of X. More precisely, we prove that HnilQ(aut1(X)) 6 cocatQ(Baut1(X)), when X is a simply connected CW-complex of finite type and that the equality holds when Baut1(X) is coformal. Many intersections with other popular open questions will be discussed. Mathematics Subject Classification (2010). 55P62; 55P10.
TL;DR: In this article, the authors investigate ring-theoretic properties of weakly Laskerian R-modules and show that they behave as Noetherian ones in many respects.
Abstract: Let R be a commutative ring with identity. We investigate some ring-theoretic properties of weakly Laskerian R-modules. Our results indicate that weakly Laskerian rings behave as Noetherian ones in many respects. However, we provide some examples to illustrate the strange behavior of these rings in some other respects.
TL;DR: In this paper, the problem of uniformly approximating an Lipschitz curve with piecewise linear approximations was dealt with, and the main result of this paper is to do the same with $L'=L+ \varepsilon (which is of course the best possible result).
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 [Daneri-Pratelli, 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.
TL;DR: Local loop near-rings as mentioned in this paper are a generalization of near-rings, where the additive structure is not necessarily associative, and prove a useful detection principle for localness.
Abstract: We study loop near-rings, a generalization of near-rings, where the additive structure is not necessarily associative. We introduce local loop near-rings and prove a useful detection principle for localness. Mathematics Subject Classification (2010). 16Y30, 20N05.
TL;DR: In this paper, the author accepted manuscript is available from Universita di Padova via the DOI in this record and the final version of the accepted manuscript can be found in the public domain.
Abstract: This is the author accepted manuscript. The final version is available from Universita di Padova via the DOI in this record.