{"title":"Nil-primary ideals of a commutative ring","authors":"Faranak Farshadifar","doi":"10.1007/s11565-026-00668-7","DOIUrl":"10.1007/s11565-026-00668-7","url":null,"abstract":"<div><p>Let <i>R</i> be a commutative ring with identity and <i>Nil</i>(<i>R</i>) be the set of all nilpotent elements of <i>R</i>. In this paper, we introduce the notion of nil-primary ideals as a generalization of primary ideals and we investigate some nil-versions of the well-known results about primary ideals. We say that a proper ideal <i>P</i> of <i>R</i> is a <i>nil-primary ideal</i> if there exists <span>(x in Nil(R))</span> such that whenever <span>(ab in P)</span> for some <span>(a, b in R)</span>, then <span>(ain P)</span> or <span>(b^n in P)</span> or <span>(a+x in P)</span> or <span>(b^n+x in P)</span> for some <span>({n in mathbb N})</span>.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148236490","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":"Bi-amalgamations subject to the nil-clean-like conditions","authors":"Loubna Es-Salhi, Mohamed Chhiti","doi":"10.1007/s11565-026-00711-7","DOIUrl":"10.1007/s11565-026-00711-7","url":null,"abstract":"<div><p>In this paper we introduce new classes of rings namely <span>(S_{1,n})</span> nil-clean (resp., <span>(S_{n,2})</span> nil-clean and <span>(S_{sum ,2})</span> nil-clean) rings, and <span>(SI^n)</span> rings as generalizations of nil-clean and boolean rings, respectively. We provide necessary and sufficient conditions for bi-amalgamations to inherit these properties. Our results are supported by illustrative examples arising as bi-amalgamations.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148236491","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":"Lacunary statistical convergence in A-metric space via modulus function","authors":"Humma Javed Sheikh, Kuldip Raj, M. Mursaleen","doi":"10.1007/s11565-026-00702-8","DOIUrl":"10.1007/s11565-026-00702-8","url":null,"abstract":"<div><p>This paper systematically develops the theory of <i>m</i>-lacunary statistical convergence and strong <i>m</i>-lacunary summability of order <span>(alpha )</span> within the framework of <i>A</i>-metric spaces, a higher-order generalization of ordinary metric spaces wherein distances are measured among <i>n</i>-tuples of points. By combining an unbounded modulus function <i>m</i>, a lacunary sequence <span>(vartheta = (t_r))</span>, and a real order parameter <span>(alpha in (0,1])</span>, we introduce the sequence spaces <span>(AS_vartheta ^{m,alpha })</span> and <span>(Aomega _vartheta ^{m,alpha })</span>, along with the related variants <span>(Aomega ^alpha [vartheta ,m])</span>, <span>(Aomega _{vartheta ,m}^{m,alpha })</span>, and <span>(Aomega _{vartheta ,m}^alpha )</span>. Precise inclusion relations among these spaces and their connections to classical lacunary statistical, <i>m</i>-statistical, and ordinary statistical convergence are established. The results highlight the role of conditions such as the growth rate of the modulus function, boundedness of the <i>A</i>-metric space, and lacunary refinement in governing convergence behavior. The results unify and extend several strands of summability theory to the very general setting of <i>A</i>-metric spaces, highlighting the intricate interplay between the modulus growth, the lacunary block structure, the order parameter, and the boundedness of the ambient space. As an application, the developed theory is applied to fixed point iterations in A-metric spaces, showing that Picard iteration sequences generated by contraction mappings satisfy suitable <i>m</i>-lacunary statistical convergence and summability conditions. The paper thereby provides a foundational hierarchy of convergence notions with potential applications in fixed point theory, stability analysis of iterative methods, and functional analysis on generalized metric structures.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148236627","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":"Some results on J-primary ideals of commutative rings","authors":"Nabil Zeidi","doi":"10.1007/s11565-026-00701-9","DOIUrl":"10.1007/s11565-026-00701-9","url":null,"abstract":"<div><p>Let <i>R</i> be a commutative ring with identity, and let <i>J</i>(<i>I</i>) denote the Jacobson radical of an ideal <i>I</i> of <i>R</i>. In this paper, we study <i>J</i>-primary ideals, which generalize both primary ideals and <i>J</i>-ideals. A proper ideal <i>I</i> of <i>R</i> is said to be <i>J</i>-primary, if for every <span>(a, bin R)</span>, <span>(abin I)</span> implies that <span>(ain J(I))</span> or <span>(bin I)</span>. We investigate some basic properties of <i>J</i>-primary ideals in a commutative ring. We also characterize rings in which every proper ideal is <i>J</i>-primary, showing that a ring has this property if and only if it is quasi-local. Furthermore, we establish the existence of <i>J</i>-primary decompositions in Noetherian rings as an extension of the classical Lasker-Noether theorem.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172855","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":"Solutions of n-variable quadratic mappings with stability results","authors":"Abasalt Bodaghi, Hulya Inceboz, Berna Arslan","doi":"10.1007/s11565-026-00703-7","DOIUrl":"10.1007/s11565-026-00703-7","url":null,"abstract":"<div><p>In this study, an <i>n</i>-variable quadratic functional equation is introduced, and its general solutions are obtained. Several concrete examples are provided to illustrate the existence of such solutions. In addition, the stability result established by Bae and Park [12] is revisited and corrected. In continuation, by using the classical (direct) method, Găvruţa-type and Hyers–Ulam–Rassias-type stability results for the <i>n</i>-variable quadratic functional equation are established in normed spaces.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-026-00703-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173062","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}
Fatima Elgadiri, Hasnaa Lahmadi, Khadija Hraif, Abdellatif Akhlidj, Anas Rachid
{"title":"The windowed second Hankel-Clifford transform: properties and uncertainty principles","authors":"Fatima Elgadiri, Hasnaa Lahmadi, Khadija Hraif, Abdellatif Akhlidj, Anas Rachid","doi":"10.1007/s11565-026-00705-5","DOIUrl":"10.1007/s11565-026-00705-5","url":null,"abstract":"<div><p>Within this work, we introduce the windowed second Hankel–Clifford transform, a localized integral transform that extends the classical Hankel–Clifford framework by incorporating a window function, enabling simultaneous spatial and spectral analysis. We establish key properties of the transform, including a precise reconstruction formula, a Plancherel theorem, and the existence of a reproducing kernel that characterizes the associated transform space. Furthermore, we develop a comprehensive theory of uncertainty principles in this setting, proving analogues of the Donoho–Stark and Lieb inequalities, as well as deriving new entropic uncertainty bounds. These results generalize classical uncertainty principles to the windowed, weighted, and radially symmetric context of the second Hankel–Clifford transform, with potential implications for harmonic analysis, signal processing, and Clifford analysis. To illustrate the effectiveness of the proposed approach, a numerical section is included, providing a comparison between the classical and windowed second Hankel–Clifford transforms and highlighting the advantages of the windowed formulation in capturing localized features of signals.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172729","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":"Equations of motion for a dissociating diatomic gas","authors":"Fumioki Asakura","doi":"10.1007/s11565-026-00704-6","DOIUrl":"10.1007/s11565-026-00704-6","url":null,"abstract":"<div><p>The aim of this paper is to study thermodynamic properties of a diatomic gas accompanied by dissociation induced by a strong shock wave. We propose a model of dissociating diatomic gas and compute the adiabatic exponent and the Grüneisen coefficient. The equations of motion are derived from conservation of mass, momentum and energy, which are supplemented by the first and second law of thermodynamics, state equations and the local equilibrium condition for dissociation. These equations constitute a strictly hyperbolic system, which guarantees that the initial value problem is locally well-posed. However the geometric properties of the system are complicated so that there is a region where convexity (genuine nonlinearity) fails for forward and backward characteristic fields. By detailed analyses of the Rankine-Hugoniot conditions, we show that the thermodynamic state behind a single front is uniquely determined by the state ahead of it and the speed of the flow behind it. Hence the temperature of the media behind the shock front is determined by these data.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172731","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":"Non-polynomial spline method for time-fractional Volterra integro-differential equations","authors":"Aynalem Tafere Chekole, Mesfin Mekuria Woldaregay, Kewani Welay Brhane, Gemechis File Duressa","doi":"10.1007/s11565-026-00696-3","DOIUrl":"10.1007/s11565-026-00696-3","url":null,"abstract":"<div><p>In this study, we present the numerical solution of time-fractional Volterra integro-differential reaction-convection-diffusion equations. The time-fractional derivative is in the Caputo sense of order <span>(gamma in (0< gamma < 1))</span>. To approximate the time-fractional derivative, the finite difference techniques of the L1-2 and L1-2-3 methods are applied on uniform mesh. The integral part is treated using the Simpson’s 1/3 rule. The semi-discretization process yields a set of two point boundary value problems. To solve the resulting boundary value problems, a non-polynomial cubic spline method is applied. The optimal error estimation and convergence analysis are established under suitable regularity assumptions on the initial data and the true solution of the considered model problem. We investigated theoretically and verified numerically the behavior of the proposed higher-order numerical method. The order of convergence for the discrete scheme on the L1-2 method is <span>(O(tau ^{3-gamma } + h^4))</span>, while for the L1-2-3 method is <span>(O(tau ^{4-gamma } + h^4))</span> where <span>(tau )</span> and <i>h</i> are mesh parameters in time and space discretization, respectively. To validate the accuracy and effectiveness of the proposed method, it is tested with some examples supported by graphs and tables. The obtained results are compared with those from existing literature. The comparison demonstrates that the proposed schemes yields superior accuracy.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172732","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":"On Kirchhoff–Choquard equations with double phase structure","authors":"Ayoub Lamane, Ahmed Aberqi, Mhamed Elmassoudi","doi":"10.1007/s11565-026-00698-1","DOIUrl":"10.1007/s11565-026-00698-1","url":null,"abstract":"<div><p>We study a double-phase Choquard–Kirchhoff problem and prove the existence of a non-trivial weak solution. This problem extends the standard Kirchhoff equation through a double-phase operator describing anisotropic, heterogeneous diffusion and simultaneously incorporating Kirchhoff and non–homogeneous Choquard nonlinearities. Our analysis relies on variational methods and the Hardy-Littlewood-Sobolev inequality. These findings generaliz/e various existing results.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172471","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}
S. C. Shiralashetti, Priyanka I. Kulkarni, Savita I. Hanaji
{"title":"Gegenbauer wavelet operational matrix of derivative method for the analysis of Erying-Powell dusty fluid flow with quadratic convection, quadratic radiation and entropy generation","authors":"S. C. Shiralashetti, Priyanka I. Kulkarni, Savita I. Hanaji","doi":"10.1007/s11565-026-00684-7","DOIUrl":"10.1007/s11565-026-00684-7","url":null,"abstract":"<div><p>The Gegenbauer wavelet operational matrix of derivative method has been presented to solve the non-linear system of ordinary differential equation that arise in the investigation of an unsteady Eyring-Powell dusty fluid flow with quadratic convection, Ohmic heating, quadratic radiation, viscous dissipation, Cattaneo-Christov heat flux, convective boundary and entropy generation. Validation of the proposed approach is done by contrasting the outcomes of the test problems with the Runge–Kutta Fehlberg 4th–5th order method and exact solutions and by comparing the outcomes of dusty fluid problem for a few fixed parameters with the solutions obtained in literature. The effect of diverse quantities is studied. It is inferred that the Erying-Powell fluid parameters <span>(varepsilon)</span> and <span>(alpha)</span> have entirely different effects on flow behaviour and heat transmission. Quadratic convection and thermal relaxation parameters decrease the temperature. Higher magnetic parameter and Brinkman number improves entropy generation and declines Bejan number. The proposed method is easy and efficient tool to solve the differential equations arising in dusty fluid flow problems.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172468","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}
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