Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.56 (2024)

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https://www.openstarts.units.it/handle/10077/36459

Contents

Eglantina Kalluçi, Bujar Xh. Fejzullahu
New inequalities for the confluent hypergeometric function

Gianni Bosi, Roberto Daris, Gabriele Sbaiz
New characterizations of completely useful topologies in mathematical utility theory

Horst Alzer, Mehdi Hassani
Inequalities for the arithmetic mean of the first n prime numbers

Prasenjit Bal, Susmita Sarkar
Characterizations of strongly star-Rothberger spaces by means of sequential singletonic intersection property and selection principles

Ina Hajdini, Orlin Stoytchev
The fundamental group of SO(n) via quotients of braid groups

Benedetto Silvestri
Construction of strong derivable maps via functional calculus of unbounded spectral operators in Banach spaces

Hassina Grar, Zahira Kebaili
A new version of projection method for variational inequalities problem with nonlinear constraints

Adriano Peixoto
Existence of positive solution for a nonlinear problem with mixed conditions

Raquel Mallavibarrena, Ragni Piene
On fundamental forms and osculating bundles

Alessandro Calamai, Matteo Franca, Michal Pospíšil
On the dynamics of non-autonomous systems in a neighborhood of a homoclinic trajectory

Parthiba Das, Prasenjit Bal
Statistical Convergence Restricted by Weight Functions and its Application in the Variation of γ-covers

Ahmed Rikouane, Mohamed Laghdir
Duality for a properly efficient solution of bilevel multiobjective fractional programming problems with extremal-value function

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Browsing Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.56 (2024) by Title

Now showing 1 - 13 of 13
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    A new version of projection method for variational inequalities problem with nonlinear constraints
    (2024)
    Grar, Hassina
    ;
    Kebaili, Zahira
    We have proposed in [7], a new projection or extragradient method to solve many variational inequalities problem classes. The corresponding algorithm is established under continuity and pseudomonotonicity of the underlining mapping. The numerical implementation results express its remarkable efficiency. In this paper, we extend the application of this algorithm to the class of nonlinear constraints. The main idea is to linearize the constraints in the neighbourhood of each iterate, then we calculate the necessary projections. It is important to point out that most of the theoretical results already obtained in our previous work will be modified and justified according to the class of problems studied in this paper. The global convergence is proven under weak hypothesis. The numerical results are very encouraging and show that the method is also very efficient to solve this class of problems.
      35  31
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    Characterizations of strongly star-Rothberger spaces by means of sequential singletonic intersection property and selection principles
    (2024)
    Bal, Prasenjit
    ;
    Sarkar, Susmita
    In this paper, using families of closed sets and a few modifications to the finite intersection features, we characterize the Rothberger Space and the Star-Rothberger Space. We also provide the selection principles that, in a reversed approach, can represent the Rothberger spaces and the star-Rothberger Spaces.
      36  89
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    Construction of strong derivable maps via functional calculus of unbounded spectral operators in Banach spaces
    (2024)
    Silvestri, Benedetto
    We provide sufficient conditions for the existence of a strong derivable map and calculate its derivative by employing a result in our previous work on strong derivability of maps arising by functional calculus of an unbounded scalar type spectral operator R in a Banach space and the generalization to complete locally convex spaces of a classical result valid in the Banach space context. We apply this result to obtain a sequence of integrals converging to an integral of a complete locally convex space extension of a map arising by functional calculus of R.
      109  33
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    Duality for a properly efficient solution of bilevel multiobjective fractional programming problems with extremal-value function
    (2024)
    Rikouane, Ahmed
    ;
    Laghdir, Mohamed

    In this paper, we establish some results regarding the optimality conditions and duality properties for properly efficient solutions of a constrained bilevel multiobjective fractional programming problem (P) with an extremal-value function. These results are obtained by applying a parametric approach to reduce the problem (P) to a parametric problem (Pμ) with μ ∈ Rp, and we obtain optimality conditions for properly efficient solutions for these problems. Furthermore, we define a dual problem of (Pμ) and we establish some results on duality.

      108  50
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    Existence of positive solution for a nonlinear problem with mixed conditions
    (2024)
    Peixoto, Adriano
    In this work, we prove the existence of a positive solution to the second-order nonlinear problem u′′ + f(t, u, u′) = 0 with mixed boundary conditions, where f is an Lp-Carath´eodory function satisfying certain properties. Three boundary conditions are analysed. Furthermore, we also prove the existence of a positive solution to the problem u′′ + b(t)g(u) = 0, where b(t) is an L1 function and g(u) is a continuous function. The proofs of the results are based on the Mawhin’s coincidence degree.
      36  34
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    Inequalities for the arithmetic mean of the first n prime numbers
    (2024)
    Alzer, Horst
    ;
    Hassani, Mehdi
    Abstract. Let An be the (unweighted) arithmetic mean of the first n prime numbers. We prove that for n ≥ 2, An1+α/(n*log(n)) ≤ An+1 ≤ An1+β/(n*log(n)) with the best possible constants α ≈ 0.43525 and β ≈ 1.22596. The right-hand side improves a result given by Z.-W. Sun in 2013.
      101  102
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    New characterizations of completely useful topologies in mathematical utility theory
    (2024)
    Bosi, Gianni
    ;
    Daris, Roberto
    ;
    Sbaiz, Gabriele
    Let X be an arbitrary set. Then a topology t on X is said to be completely useful if every upper semicontinuous linear (total) preorder ≾ on X can be represented by an upper semicontinuous real-valued order preserving function. In this paper, appealing, simple and new characterizations of completely useful topologies will be proved, therefore clarifying the structure of such topologies.
      53  39
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    New inequalities for the confluent hypergeometric function
    (2024)
    Kalluçi, Eglantina
    ;
    Fejzullahu, Bujar Xh.
    In this paper, we obtain some new inequalities for the confluent hypergeometric function. These results, at least for large argument, improve the well-known inequalities of Y. L. Luke and B. C. Carlson.
      60  93
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    On fundamental forms and osculating bundles
    (2024)
    Mallavibarrena, Raquel
    ;
    Piene, Ragni
    We define higher order fundamental forms and osculating spaces of projective algebraic varieties, using sheaves of principal parts. We show that the mth fundamental form can be viewed as the differential of the (m−1)th Gauss map, and explain why the vanishing of the mth fundamental form implies that the variety is contained in a general (m − 1)th osculating space. Pointwise, the fundamental forms give linear systems on the projectivized tangent spaces. We show that, at each point, the Jacobian of the mth fundamental form is contained in the (m − 1)th fundamental form. In the case of ruled varieties, we describe these linear systems. We discuss conditions for a surface to be ruled, in terms of the second fundamental form and the Fubini cubic.
      107  65
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    On the dynamics of non-autonomous systems in a neighborhood of a homoclinic trajectory
    (2024)
    Calamai, Alessandro
    ;
    Franca, Matteo
    ;
    Pospíšil, Michal
    This article is devoted to the study of a 2-dimensional piecewise smooth (but possibly) discontinuous dynamical system, subject to a non-autonomous perturbation; we assume that the unperturbed system admits a homoclinic trajectory ⃗γ(t). Our aim is to analyze the dynamics in a neighborhood of ⃗γ(t) as the perturbation is turned on, by defining a Poincar´e map and evaluating fly time and space displacement of trajectories performing a loop close to ⃗γ(t). Besides their intrinsic mathematical interest, these results can be thought of as a first step in the analysis of several interesting problems, such as the stability of a homoclinic trajectory of a non-autonomous ODE and a possible extension of Melnikov chaos to a discontinuous setting.
      87  50
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    Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.56 (2024)
    (2024)
    The journal Rendiconti dell’Istituto di Matematica dell’Università di Trieste was founded in 1969 by Arno Predonzan, with the aim of publishing original research articles in all fields of mathematics. Rendiconti dell’Istituto di Matematica dell’Universit`a di Trieste has been the first Italian mathematical journal to be published also on-line. The access to the electronic version of the journal is free. All published articles are available on-line. In 2008 the Dipartimento di Matematica e Informatica, the owner of the journal, decided to renew it. The name of the journal however remained unchanged, but the subtitle An International Journal of Mathematics was added. The journal can be obtained by subscription, or by reciprocity with other similar journals. Currently more than 100 exchange agreements with mathematics departments and institutes around the world have been entered in. The articles published by Rendiconti dell’Istituto di Matematica dell’Universit`a di Trieste are reviewed/indexed by MathSciNet, Zentralblatt Math, Scopus, OpenStarTs.
      68  1224
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    Statistical Convergence Restricted by Weight Functions and its Application in the Variation of γ-covers
    (2024)
    Das, Parthiba
    ;
    Bal, Prasenjit

    In this paper, we utilize a weight function g to regulate the pace of the statistical convergence in a topological space. We extend the notion of statistical convergence to weighted statistical convergence by utilizing the weighted density. Using this intriguing idea of convergence, a new variation of γ-covers (referred to as sg-γ cover) is introduced. Subsequently some topological analysis are conducted on the class of sg-γ coverings. It is demonstrated that the new class of sg-γ coverings lies some where between the class of γ-covers and the class of s-γ cover classes.

      46  37
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    The fundamental group of SO(n) via quotients of braid groups
    (2024)
    Hajdini, Ina
    ;
    Stoytchev, Orlin
    Some topological properties of a Lie group can be deduced by studying a discrete group of homotopy classes of paths from the identity to elements of a finite subgroup of the given Lie group. In this way a "skeleton" of the universal cover is constructed in terms of generators and relations. We use this approach to describe an algebraic derivation of the well-known fact that the fundamental group of SO(n) is isomorphic to Z/2Z when n ≥ 3. The fundamental group of SO(n) appears in our treatment as a subgroup of the center of a finite factor of the braid group Bn, obtained by imposing one additional relation and turns out to be a nontrivial central extension by Z/2Z of the corresponding group of rotational symmetries of the hyperoctahedron in dimension n.
      20  134