Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.55 (2023)https://www.openstarts.units.it/handle/10077/347092024-11-13T09:04:16Z2024-11-13T09:04:16Z101Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.55 (2023)https://www.openstarts.units.it/handle/10077/357592024-03-13T12:34:07Z2023-01-01T00:00:00Zdc.title: Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.55 (2023)
2023-01-01T00:00:00ZThree general uniqueness theorems for BVPs of ODEs with applicationsVidossich, Giovannihttps://www.openstarts.units.it/handle/10077/355772024-10-06T16:51:50Z2023-01-01T00:00:00Zdc.title: Three general uniqueness theorems for BVPs of ODEs with applications
dc.contributor.author: Vidossich, Giovanni
dc.description.abstract: We prove three uniqueness theorems for BVPs of ODEs whose unusual assumptions allow to prove existence results for BVPs related to various types of linear and nonlinear boundary conditions.
2023-01-01T00:00:00ZOn generating functions of extended Jacobi polynomialsChongdar, Asit KumarChongdar, AmartyaMohanta, Sushanta Kumarhttps://www.openstarts.units.it/handle/10077/354902024-10-06T16:51:50Z2023-01-01T00:00:00Zdc.title: On generating functions of extended Jacobi polynomials
dc.contributor.author: Chongdar, Asit Kumar; Chongdar, Amartya; Mohanta, Sushanta Kumar
dc.description.abstract: In this paper we have obtained some novel generating functions of Fn(α, β−α; x) – a modified form of the extended Jacobi polynomial Fn(α, β; x) – by means of Weisner’s group-theoretic method with the suitable interpretation of the parameter α of the polynomial under consideration. Moreover, we have shown that the generating functions involving the extended Jacobi polynomial Fn(α, β; x) derived in [2], obtained by using the same Weisner’s group-theoretic method with the suitable interpretation of (α, β), can be easily obtained from our results. Finally, a group-theoretic method of obtaining general bilateral generating relation from general unilateral generating relation is also discussed.
2023-01-01T00:00:00ZTopology of the space of measure-preserving transformations of the circleBoukhecham, HoussamOunesli, Hamzahttps://www.openstarts.units.it/handle/10077/354882024-10-06T16:51:50Z2023-01-01T00:00:00Zdc.title: Topology of the space of measure-preserving transformations of the circle
dc.contributor.author: Boukhecham, Houssam; Ounesli, Hamza
dc.description.abstract: In this paper we prove that the space of circle expanding maps of degree 2 preserving Lebesgue measure is an arc-connected space homeomorphic to an infinite-dimensional Lie group whose fundamental group is Z. The techniques involved in the proof are rather unexpected and lead to a formulation of a conjecture generalizing this result to higher dimensional infra-nilmanifolds.
2023-01-01T00:00:00ZA natural basis for intersection numbersEynard, BertrandLewański, Danilohttps://www.openstarts.units.it/handle/10077/354872024-10-06T16:51:50Z2023-01-01T00:00:00Zdc.title: A natural basis for intersection numbers
dc.contributor.author: Eynard, Bertrand; Lewański, Danilo
dc.description.abstract: We advertise elementary symmetric polynomials ei as the natural basis for generating series Ag,n of intersection numbers of ψ-classes on the moduli space of stable curves of genus g with n marked
points. Closed formulae for Ag,n are known for genera 0 and 1 — this approach provides formulae for g = 2, 3, 4, together with an algorithm to compute the formula for any g.
The claimed naturality of the ei basis relies in the unexpected vanishing of some coefficients with a clear pattern. As an application of the conjecture, we find new integral representations of Ag,n, which recover expressions for the Weil-Petersson volumes in terms of Bessel functions.
2023-01-01T00:00:00ZComplex Weyl symbols of metaplectic operators: An elementary approachCahen, Benjaminhttps://www.openstarts.units.it/handle/10077/354862024-10-06T16:51:50Z2023-01-01T00:00:00Zdc.title: Complex Weyl symbols of metaplectic operators: An elementary approach
dc.contributor.author: Cahen, Benjamin
dc.description.abstract: We give explicit formulas for the Berezin symbols and the complex Weyl symbols of the metaplectic representation operators by using the holomorphic representations of the Jacobi group. Then we recover some known formulas for the symbols of the metaplectic operators in the classical Weyl calculus, in particular for the classical Weyl symbol of the exponential of an operator whose Weyl symbol is a quadratic form.
2023-01-01T00:00:00ZOne-ended 3-manifolds without locally finite toric decompositionsMaillot, Sylvainhttps://www.openstarts.units.it/handle/10077/354852024-10-06T16:51:50Z2023-01-01T00:00:00Zdc.title: One-ended 3-manifolds without locally finite toric decompositions
dc.contributor.author: Maillot, Sylvain
dc.description.abstract: We introduce a class of one-ended open 3-manifolds which can be ‘recursively’ defined from two compact 3-manifolds, and construct examples of manifolds in this class which fail to have a toric decomposition in the sense of Jaco-Shalen and Johannson.
2023-01-01T00:00:00ZIntegrability aspects of the dynamical forest modelSulaiman, EvanAmen, AzadAziz, Waleedhttps://www.openstarts.units.it/handle/10077/354842024-10-06T16:51:50Z2023-01-01T00:00:00Zdc.title: Integrability aspects of the dynamical forest model
dc.contributor.author: Sulaiman, Evan; Amen, Azad; Aziz, Waleed
dc.description.abstract: In this paper, we study the integrability problem of a mathematical models of forests with two age classes of the form, ẋ =ρy − (y − 1)²x − sx, ẏ = x − hy, where ρ, h, s ∈ R. We proved that the system has a unique Darboux polynomial if and only if ρ = 0. The model has only two or three exponential factors if h ≠ 0 or h = 0, respectively. It is also, showed that the system admits a Darboux first integral if and only if ρ = h = 0 and has no analytic first integral in any neighborhood of fixed point except when ρ = h = 0.
2023-01-01T00:00:00ZOn meromorphic solutions of a certain type of nonlinear differential-difference equationMajumder, SujoyPramanik, Debabratahttps://www.openstarts.units.it/handle/10077/347112024-10-06T16:51:50Z2023-01-01T00:00:00Zdc.title: On meromorphic solutions of a certain type of nonlinear differential-difference equation
dc.contributor.author: Majumder, Sujoy; Pramanik, Debabrata
dc.description.abstract: The main objective of the paper is to give the specific forms of the meromorphic solutions of the equation
$f^{n}(z)f(z+c)+P_{d}(z,f)=p_{1}(z)e^{\alpha_{1}(z)}+p_{2}(z)e^{\alpha_{2}(z)}$,
where $c\in \mathbb{C}\setminus\{0\}$, $P_d(z,f)$ is a differential-difference polynomial in $f$ of degree $d\leq n-1$ with small functions of $f$ as its coefficients, $p_1, p_2(\not\equiv 0)$ are rational functions and $\alpha_1$, $\alpha_2$ are non-constant polynomials.
2023-01-01T00:00:00ZExistence and exponential decay of solutions for magnetic effected piezoelectric beams with second sound and distributed delay termDouib, Madanihttps://www.openstarts.units.it/handle/10077/347102024-10-06T16:51:50Z2023-01-01T00:00:00Zdc.title: Existence and exponential decay of solutions for magnetic effected piezoelectric beams with second sound and distributed delay term
dc.contributor.author: Douib, Madani
dc.description.abstract: This paper is concerned with a system of magnetic effected piezoelectric beams with distributed delay term, where the heat flux is given by Cattaneo’s law (second sound). We prove the existence and the uniqueness of the solution using the semigroup theory. Then, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.
2023-01-01T00:00:00Z