{"title":"Generalized principal logarithms and Riemannian properties of a class of subgroups of (mathbf {U_n}) endowed with the Frobenius bi-invariant metric","authors":"Donato Pertici, Alberto Dolcetti","doi":"10.1007/s11565-024-00561-1","DOIUrl":"10.1007/s11565-024-00561-1","url":null,"abstract":"<div><p>We study the geometric-differential properties of a wide class of closed subgroups of <span>(U_n)</span> endowed with a natural bi-invariant metric. For each of these groups, we explicitly express the distance function, the diameter, and, above all, we parametrize the set of minimizing geodesic segments with arbitrary endpoints <span>(P_0)</span> and <span>(P_1)</span> by means of the set of generalized principal logarithms of <span>(P_0^*P_1)</span> in the Lie algebra of the group. We prove that this last set is a non-empty disjoint union of a finite number of compact submanifolds of <span>(mathfrak {u}_n)</span> diffeomorphic to suitable (and explicitly determined) homogeneous spaces.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142778373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Static perfect fluid spacetimes on f-Kenmotsu 3-manifolds","authors":"Uday Chand De, Arpan Sardar","doi":"10.1007/s11565-024-00576-8","DOIUrl":"10.1007/s11565-024-00576-8","url":null,"abstract":"<div><p>The present article deals with static perfect fluid spacetimes on <i>f</i>-Kenmotsu 3-manifolds. At first, we demonstrate if a 3-dimensional <i>f</i>-Kenmotsu manifold with constant scalar curvature as the spatial factor of a static perfect fluid spacetime, then either it is a space of constant sectional curvature or <span>(grad, psi )</span> is pointwise collinear with <span>(xi )</span> and the warping function of the static perfect fluid spacetime is given by <span>(psi = k_1 t + k_2)</span>, <span>(k_1 ne 0)</span>. As a result, we establish that if a cosymplectic manifold of dimension three with constant scalar curvature is the spatial factor of a static perfect fluid spacetime, then either it is flat or, the manifold becomes a space of constant sectional curvature. Next, we show that under certain restrictions if a 3-dimensional <i>f</i>-Kenmotsu manifold is the spatial factor of a static perfect fluid spacetime, then either the manifold is a space of constant sectional curvature or, the manifold is locally isometric to either the flat Euclidean space <span>(mathcal {R}^3)</span> or the Riemannian product <span>(mathcal {R}times M^2(c))</span>, where <span>(M^2(c))</span> represents a Kahler surface with constant curvature <span>(cne 0)</span>, provided <span>(xi psi =0)</span> and <span>(xi tilde{f} =0)</span>. Lastly, we have cited an example of an <i>f</i>-Kenmotsu manifold to validate our result.\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142778369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Building a random network with a given expected giant component","authors":"Lorenzo Federico, Ayoub Mounim","doi":"10.1007/s11565-024-00575-9","DOIUrl":"10.1007/s11565-024-00575-9","url":null,"abstract":"<div><p>In this work we show that given any integer-valued random variable <i>D</i> with finite mean such that <span>(mathbb {E}[D]>2)</span> and <span>(mathbb {P}(Dge 1)=1)</span>, it is possible to build a configuration model whose giant component has degree distribution that converges in probability to <i>D</i> and give a way to compute the starting degree distribution to achieve this property.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142778375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bivariate generalization for operators involving Appostol-Genocchi polynomial","authors":"Km. Lipi, Naokant Deo","doi":"10.1007/s11565-024-00562-0","DOIUrl":"10.1007/s11565-024-00562-0","url":null,"abstract":"<div><p>This article is primarily concerned with the bivariate generalization of operators involving a class of orthogonal polynomials called Apostol-Genocchi polynomials. The rate of convergence can be determined in terms of partial and total modulus of continuity as well as the order of approximation can be achieved by means of a Lipschitz-type function and Peetre’s K-functional. In addition, we put forth a conceptual extension known as the “generalized boolean sum (GBS)” for these bivariate operators, which aims to establish the degree of approximation for Bögel continuous functions. In this study, we utilize the Mathematica Software to present a series of graphical illustrations that effectively showcase the rate of convergence for the bivariate operators. The graphs indicate that, in the case of certain functions, the bivariate operators exhibits superior convergence when <span>(alpha )</span> is less than <span>(beta )</span>. Based on our analysis and comparison of the error of approximation between the bivariate operators and the corresponding GBS operators, it can be deduced that the GBS operators exhibit a faster convergence towards the function.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The parallel postulate","authors":"Victor Pambuccian","doi":"10.1007/s11565-024-00572-y","DOIUrl":"10.1007/s11565-024-00572-y","url":null,"abstract":"<div><p>This is a survey of what is known regarding weaker versions of the Euclidean parallel postulate, culminating with a splitting of the parallel postulate into two weaker and independent incidence-geometric axioms. Among the weaker versions are: the rectangle axiom, stating that there exists a rectangle; the <i>Lotschnittaxiom</i>, stating that the perpendiculars to the sides of a right angle intersect, and Aristotle’s axiom, stating that the distances between the sides of an angle grow indefinitely. Several statements that are equivalent, with plane absolute geometry as a background, to each of these axioms, as well as an analysis of their syntactic simplicity are presented. The parallel postulate is found to be equivalent to the conjunction of the following two axioms: “Given three parallel lines, there is a line that intersects all three of them\" and “Given a line <i>a</i> and a point <i>P</i> on <i>a</i>, as well as two intersecting lines <i>m</i> and <i>n</i>, both parallel to <i>a</i>, there exists a line <i>g</i> through <i>P</i> which intersects <i>m</i> but not <i>n</i>.\"</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An inertial method for solving bilevel variational inequality problems with fixed point constraints","authors":"Yirga Abebe Belay, Habtu Zegeye, Oganeditse A. Boikanyo, Dintle Kagiso, Hagos Hailu Gidey","doi":"10.1007/s11565-024-00571-z","DOIUrl":"10.1007/s11565-024-00571-z","url":null,"abstract":"<div><p>In this paper, we introduce and study an inertial algorithm for solving bilevel variational inequality problems with a fixed point constraint involving a uniformly continuous pseudomonotone mapping in the lower level variational inequality problem and a demimetric mapping for the fixed point constraint. We prove a strong convergence theorem under some suitable conditions on the control sequences. We also provide a numerical example to demonstrate the effectiveness of the method. \u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142754023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spectral analysis of operator matrices: limit point insights","authors":"Aymen Bahloul","doi":"10.1007/s11565-024-00573-x","DOIUrl":"10.1007/s11565-024-00573-x","url":null,"abstract":"<div><p>This paper explores the potential of local spectral theory to investigate the limit point set of the descent spectrum of upper triangular operator matrices, denoted by <span>({mathcal {T}})</span>, on Banach spaces. We rigorously prove that transitioning from the accumulation set of the diagonal descent spectrum, denoted by <span>( hbox {Acc} sigma _{textrm{d}}({mathcal {T}}_textbf{diag}))</span>, to that of the complete descent spectrum, <span>( hbox {Acc} sigma _{textrm{d}}({mathcal {T}}))</span>, involves removing specific subsets within <span>( hbox {Acc} sigma _{textrm{d}}(A_1) cap hbox {Acc} sigma _{textrm{a}}(A_2) cap hbox {Acc} sigma _{textrm{a}}(A_3))</span>. Additionally, we present sufficient conditions that ensure the limit points of the descent spectrum of the operator matrix encompass the combined limit points of its diagonal entry spectra. This significantly addresses a longstanding question posed by Campbell (Linear Multilinear Algebra 14:195–198, 1983) regarding the limit points for the descent spectrum of the last <span>(3 times 3)</span> operator matrix form. Specifically, Campbell inquired about developing new methods to analyze the spectral properties of such matrices without resorting to partitioning their entries, a challenge that has remained unresolved for decades. Our findings provide a comprehensive solution, illustrating that a deeper understanding of the spectral behavior can be achieved by considering the entire matrix structure collectively.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142753955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Location of zeros of quaternionic polynomials","authors":"Idrees Qasim","doi":"10.1007/s11565-024-00568-8","DOIUrl":"10.1007/s11565-024-00568-8","url":null,"abstract":"<div><p>In this manuscript, we investigate bounds for the zeros of quaternionic polynomials with restricted coefficients. We find an annular region that contains all the zeros of a quaternionic polynomial. Moreover, we find zero-free regions thereby obtain improvement of Eneström-Kakeya theorem for quaternionic polynomials.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142691874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Asymptotic behavior of laminated beams with Kelvin-Voigt damping","authors":"Victor R. Cabanillas, Teófanes Quispe Méndez","doi":"10.1007/s11565-024-00559-9","DOIUrl":"10.1007/s11565-024-00559-9","url":null,"abstract":"<div><p>This work considers a one-dimensional system consisting of two identical Timoshenko beams. The model considers that an adhesive layer of small thickness joins the two surfaces, thus producing an interfacial slip under homogeneous mixed Neumann-Dirichlet-Dirichlet boundary conditions. We introduce a Kelvin-Voigt type damping into the rotation equation, and we study the well-posedness of the problem and the asymptotic behavior of the solutions using techniques from the semigroup theory of linear operators and the frequency domain method. When the wave’s propagation speeds are equal in both beams, we show that the Kelvin-Voigt dissipative term acting on the rotation equation is sufficient to obtain the exponential decay of the solutions while maintaining the structural dissipation characteristic of the model. When these propagation speeds differ, we show the lack of exponential decay and prove that the solutions decay polynomially with a decay rate of <span>(t^{-frac{1}{2}})</span>. We prove, finally, that this decay rate is optimal.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Borel exceptional values of q-shift polynomials","authors":"M. Tejuswini, N. Shilpa","doi":"10.1007/s11565-024-00570-0","DOIUrl":"10.1007/s11565-024-00570-0","url":null,"abstract":"<div><p>This paper deals with the extension of Hayman Conjecture to q-shift differential polynomials generated by meromorphic functions. We prove that the differential polynomials assumes every finite value infinitely often when sharing two Borel exceptional Values with appropriate conditions. Few examples are given to prove that the conditions are inevitable.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}