{"title":"On balancing and Lucas-balancing numbers expressible as product of two k-Fibonacci numbers","authors":"Bibhu Prasad Tripathy, Bijan Kumar Patel","doi":"10.1007/s11565-026-00742-0","DOIUrl":"10.1007/s11565-026-00742-0","url":null,"abstract":"<div><p>A positive integer <i>n</i> is called a balancing number if there exists a positive integer <i>r</i> such that <span>(1 + 2 + cdots + (n-1) = (n+1) + (n+2) + cdots + (n+r))</span>. The corresponding value <i>r</i> is known as the balancer of <i>n</i>. If <i>n</i> is a balancing number, then <span>(8n^{2}+1)</span> is a perfect square, and its positive square root is called a Lucas-balancing number. For any integer <span>(k ge 2)</span>, let <span>({F_{n}^{(k)} }_{n ge -(k-2)})</span> denote the <i>k</i>-generalized Fibonacci sequence, which starts with <span>(0, dots ,1)</span>(<i>k</i> terms) where each next term is the sum of the preceding <i>k</i> terms. In this paper, we investigate all balancing and Lucas-balancing numbers that can be expressed as a product of two <i>k</i>-generalized Fibonacci numbers.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148903451","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":"Special affine graph transforms and commutator defects of position-decorated graph laplacians","authors":"Owais Ahmad","doi":"10.1007/s11565-026-00751-z","DOIUrl":"10.1007/s11565-026-00751-z","url":null,"abstract":"<div><p>A finite-dimensional theory of special-affine transforms is developed for position-decorated spectral graphs. A Hermitian graph Laplacian generates a normalized frequency observable, while a normalized diagonal decoration supplies the position observable. Their ordered exponentials define graph Weyl operators, which are coupled to Iwasawa and three-shear graph linear-canonical factors. The resulting transforms are unitary and covariant under decorated graph isomorphisms, including monomial gauge-permutation equivalence for Hermitian directed Laplacians. The commutator generator is proved to be Hilbert–Schmidt orthogonal to the Laplacian commutant, yielding an exact defect formula and a weighted-Laplacian eigenproblem for selecting the position decoration. Quantitative Baker–Campbell–Hausdorff estimates control local Weyl, Egorov, homogeneous, and full special-affine composition errors. For odd-prime cycles, quantized exponentials of centered position and momentum matrices recover the clock-shift system and its exact finite Weil covariance. Frame criteria, canonical Parseval preconditioning, and a reproducible sensor-graph experiment quantify reconstruction accuracy, noise amplification, conditioning trade-offs, and factorization dependence. The theory therefore connects finite operator obstructions with computable graph-transform design.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148903383","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":"Interpolating the power mean Inequalities for Positive Definite and Sectorial Matrices","authors":"H. Mohammadzadehkan, S. Malekinejad, M. Sababheh","doi":"10.1007/s11565-026-00679-4","DOIUrl":"10.1007/s11565-026-00679-4","url":null,"abstract":"<div><p>In this paper, we introduce new inequalities for positive definite matrices using the interpolational paths of the power means. Specifically, for positive definite matrices <span>( A, B)</span>, given <span>( q le 1 le p )</span> with <span>( q ne p )</span> and <span>( 0< nu le mu < 1 )</span>, we prove that </p><div><div><span>$$ frac{nu }{mu } le frac{A , m_{p,nu } , B - A , m_{q, nu } , B}{A , m_{p,mu } , B - A , m_{q, mu } , B} le frac{1 - nu }{1 - mu }, $$</span></div></div><p>where <span>(A , m_{p,mu } , B)</span> stands for the interpolational path of the power means. We also introduce the interpolational path for sectorial and accretive matrices, deriving inequalities similar to those in the positive definite case by applying the aforementioned inequality. Additionally, we extend these results to sectorial and accretive matrices. We demonstrate that the proposed interpolational path preserves sectorial properties. These findings contribute to the broader study of matrix means, refining inequalities and improving approximations in matrix analysis. In the final section, we derive nuanced inequalities that describe how the geometric mean distributes over the power mean, clarifying the relationships between these matrix means.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148903384","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":"Optimum solutions for delay integral equations via condensing operators and measure of noncompactness","authors":"A. Pradhan, D. K. Patel, M. Gabeleh","doi":"10.1007/s11565-026-00745-x","DOIUrl":"10.1007/s11565-026-00745-x","url":null,"abstract":"<div><p>Delay integral equations provide an effective framework for modelling dynamic systems by incorporating the influence of past states on present behaviour and future evolution. Such equations arise naturally in applications including population dynamics, control theory, and engineering systems with aftereffects. In this paper, we establish the existence of optimal solutions for a system of delay integral equations (DIEs) with a constant delay <span>(rho >0)</span>. To this end, we introduce a new best proximity point (and pair) result in a reflexive Banach space (strictly convex) via a newly proposed condensing operator using the idea of measure of noncompactness. As a consequence, coupled best proximity point results are obtained. Finally, a numerical example is presented to illustrate the applicability and effectiveness of the theoretical results.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148903450","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":"A De Giorgi conjecture on the regularity of minimizers of Cartesian area in 1D","authors":"Giovanni Bellettini, Shokhrukh Yu Kholmatov","doi":"10.1007/s11565-026-00732-2","DOIUrl":"10.1007/s11565-026-00732-2","url":null,"abstract":"<div><p>We prove a <span>(C^{1,1})</span>-regularity result for minimizers of the functional </p><div><div><span>$$ int _I sqrt{1+|Du|^2} + int _I |u-g|ds,quad uin BV(I), $$</span></div></div><p>provided <span>(Isubset mathbb {R})</span> is a bounded open interval and <span>(Vert gVert _infty )</span> is sufficiently small, thus partially establishing a De Giorgi conjecture in dimension one and codimension one. We also extend our result to a suitable anisotropic setting.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-026-00732-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148903380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Q-tensors on Riemannian manifolds with concurrent-recurrent vector fields and its applications in spacetimes","authors":"Gaurab Mitra, Avijit Sarkar, Tarak Mandal","doi":"10.1007/s11565-026-00743-z","DOIUrl":"10.1007/s11565-026-00743-z","url":null,"abstract":"<div><p>In the present article, our aim is to investigate some geometric characteristics of the <i>Q</i>-tensors on Riemannian manifolds equipped with concurrent-recurrent vector fields (<b>CRVF</b>, in short). At first, we analyze the nature of <i>Q</i>-flat Riemannian manifolds admitting concurrent-recurrent vector fields. We also discuss some differential forms of <i>Q</i> tensors on Riemannian manifolds associated with <b>CRVF</b>. Next we prove that for a <i>Q</i>-symmetric Riemannian manifold admitting <b>CRVF</b>, <span>(Omega )</span> is a constant function. Also we construct a concrete non-trivial example that proves the existence of <b>CRVF</b> and validate some of our results. Moreover, we explore certain results on <i>Q</i>-flat tensors in the framework of perfect fluid mixed quasi-Einstein spacetimes.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148903448","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}
Maykel Belluzi, Flank D. M. Bezerra, Maria J. M. Silva
{"title":"Fractional counterpart of a higher-order abstract Cauchy problem","authors":"Maykel Belluzi, Flank D. M. Bezerra, Maria J. M. Silva","doi":"10.1007/s11565-026-00744-y","DOIUrl":"10.1007/s11565-026-00744-y","url":null,"abstract":"<div><p>In this paper, we consider the fractional powers of a linear operator associated with a higher-order abstract Cauchy problem defined by a linear parabolic equation. We also characterize the domain of the fractional powers and discuss the solvability of the fractional equation.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-026-00744-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148903449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
G. M. Sachin, U. S. Mahabaleshwar, Giulio Lorenzini, David Laroze
{"title":"Heat and mass transfer impact on Casson nanofluid flow across a stretching surface along with activation energy","authors":"G. M. Sachin, U. S. Mahabaleshwar, Giulio Lorenzini, David Laroze","doi":"10.1007/s11565-026-00726-0","DOIUrl":"10.1007/s11565-026-00726-0","url":null,"abstract":"<div><p>Hybrid nanofluids, with their advanced thermophysical properties and promising role in boosting heat transfer efficiency, have become a key area of focus for many researchers in the current era of technology. Novelty of this paper is mainly involved with heat transmission in variable thickness geometry in the existence of an inclined magnetic field, activation energy, and non-linear thermal radiation. Hybrid nanofluid composites are made by dissolving <span>(Al_{2} O_{3})</span>(Aluminium oxide) and <span>(TiO_{2})</span>(Titanium oxide) In base fluid, engine oil. The modified governing equations for momentum and temperature, under relevant boundary conditions, are solved numerically using the precise and efficient bvp-4c Method. The Consequences of an inclined magnetic field, non-linear thermal radiation, power index of velocity, and activation energy are analysed thoroughly, and the outcomes are plotted graphically. Based on the results, we can observe that the fluid velocity decreases as a results considering a magnetic field that is inclined. As the power index velocity rises, the velocity profile reveals a decline.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148903565","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":"Unbounded absolutely weak weak Dunford–Pettis operators","authors":"A. El Kaddouri, Marouan Bengraine, O. Aboutafail","doi":"10.1007/s11565-026-00737-x","DOIUrl":"10.1007/s11565-026-00737-x","url":null,"abstract":"<div><p>In this work, we introduce a new class of operators called unbounded absolutely weak weak Dunford–Pettis operators. We investigate fundamental properties of this class and establish several characterizations. In particular, we examine its relationships with existing operator classes and provide conditions under which these operators arise naturally. Furthermore, connections with <span>(sigma )</span>-uaw compact sets and Dunford–Pettis sets are discussed.\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148838112","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":"Pseudodifferential operators on time-frequency shift invariant ultradistributions with periodic symbols","authors":"Gianluca Garello, Alessandro Morando","doi":"10.1007/s11565-026-00740-2","DOIUrl":"10.1007/s11565-026-00740-2","url":null,"abstract":"<div><p>In the present paper the authors study pseudodifferential operators with periodic symbols acting on time-frequency shift invariant spaces of generalized ultradistributions. Particular attention is devoted to symbols satisfying suitable Gelfand–Shilov type regularity conditions, which exhibit periodicity with respect to appropriate lattice structures. In this framework, we show how periodicity allows us to represent the corresponding operators in terms of time-frequency shifts. We then establish continuity and invertibility results on a broad class of Banach spaces of ultradistributions, extending previous results known in the tempered distribution setting. The analysis provides a natural functional framework for treating non-polynomial weights, including weights with exponential growth at infinity.\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-026-00740-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148838108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}