International Journal of Theoretical Physics最新文献

{"title":"Exact Solutions and Wave Dynamics of the (2+1)-Dimensional Kadomtsev-Petviashvili-Boussinesq Equation via Bilinear Neural Network Method","authors":"Haoyu Bai,&nbsp;Xiaochun Sun,&nbsp;Jihong Zhang","doi":"10.1007/s10773-026-06346-w","DOIUrl":"10.1007/s10773-026-06346-w","url":null,"abstract":"<div><p>This paper investigates exact analytical solutions of the (2+1)-dimensional Kadomtsev-Petviashvili-Boussinesq (KPB) equation using the Bilinear Neural Network Method (BNNM). By combining the Hirota bilinear method with neural network architectures, we construct diverse solution structures including periodic lump solutions, double-lump solutions, superposition of soliton and lump solutions, and breather solutions. The method employs both single-hidden-layer and double-hidden-layer neural network architectures with various activation function combinations to generate rich solution families. Through systematic parameter selection and symbolic computation via Maple, we obtain multiple exact analytical solutions and visualize their dynamical behaviors using three-dimensional plots, density plots, and line plots. Compared to traditional methods, BNNM reduces the number of algebraic equations by approximately 27%-36% when constructing complex interaction solutions, thereby significantly reducing symbolic computation cost. The obtained solutions exhibit significant physical relevance: periodic lump solutions characterize localized propagation in shallow water waves, breather solutions correspond to oscillatory ion-acoustic waves in plasmas, and soliton-lump superposition solutions reflect wave interaction mechanisms in nonlinear optical systems. This research extends the application scope of neural network methods in solving nonlinear partial differential equations and provides valuable insights for understanding wave phenomena in plasma physics, fluid dynamics, and nonlinear optics.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Normalized Solutions and Numerical Approximation for a Critical p-Laplacian Schrödinger–Bopp–Podolsky System with Variable Mass and Logarithmic Nonlinearity","authors":"Salah Boulaaras,&nbsp;Yassine Chargui,&nbsp;Rafik Guefaifia","doi":"10.1007/s10773-026-06345-x","DOIUrl":"10.1007/s10773-026-06345-x","url":null,"abstract":"&lt;div&gt;&lt;p&gt;This paper is devoted to the study of the existence, qualitative properties, and numerical approximation of normalized solutions for a class of critical Schrödinger–Bopp–Podolsky systems in &lt;span&gt;(mathbb {R}^3)&lt;/span&gt;, involving the &lt;i&gt;p&lt;/i&gt;-Laplacian operator, logarithmic nonlinearities, critical Sobolev growth, and nonlocal electromagnetic interactions. More precisely, we consider the system &lt;/p&gt;&lt;div&gt;&lt;div&gt;&lt;span&gt;$$ {left{ begin{array}{ll} -varDelta _p u + V(varepsilon x)|u|^{p-2}u + M(x)|u|^{p-2}u + kappa phi u qquad = lambda |u|^{p-2}u + vartheta |u|^{p-2}u log |u|^p + mu |u|^{q-2}u + |u|^{p^*-2}u, -varDelta phi + a^2 varDelta ^2 phi = 4pi u^2, end{array}right. } qquad xin mathbb {R}^3, $$&lt;/span&gt;&lt;/div&gt;&lt;/div&gt;&lt;p&gt;subject to the mass constraint &lt;/p&gt;&lt;div&gt;&lt;div&gt;&lt;span&gt;$$ int _{mathbb {R}^3} |u|^p,dx = rho ^p, $$&lt;/span&gt;&lt;/div&gt;&lt;/div&gt;&lt;p&gt;where &lt;span&gt;(varDelta _p u = textrm{div}(|nabla u|^{p-2}nabla u))&lt;/span&gt; denotes the &lt;i&gt;p&lt;/i&gt;-Laplace operator, &lt;span&gt;(pin (1,3))&lt;/span&gt;, &lt;span&gt;(p^*=frac{3p}{3-p})&lt;/span&gt; is the critical Sobolev exponent, &lt;span&gt;(varepsilon &gt;0)&lt;/span&gt; is a small semiclassical parameter, and &lt;span&gt;(lambda in mathbb {R})&lt;/span&gt; is a Lagrange multiplier associated with the normalization. The parameters &lt;span&gt;(rho , a, kappa , vartheta , mu &gt; 0)&lt;/span&gt; are given constants, &lt;span&gt;(V:mathbb {R}^3rightarrow mathbb {R})&lt;/span&gt; is an external potential, and &lt;span&gt;(M:mathbb {R}^3rightarrow mathbb {R})&lt;/span&gt; is a variable mass coefficient. The exponent &lt;i&gt;q&lt;/i&gt; satisfies &lt;span&gt;(p&lt;q&lt;p+frac{p^2}{3})&lt;/span&gt;. The main novelty of this work lies in the introduction and analysis of a Schrödinger–Bopp–Podolsky system combining &lt;i&gt;variable mass effects&lt;/i&gt; and &lt;i&gt;mixed nonlinearities&lt;/i&gt;, including logarithmic, subcritical, and critical growth terms, within a normalized framework. This setting significantly extends existing results by incorporating spatial inhomogeneities and competing nonlinear interactions, which fundamentally modify the variational structure of the problem. In particular, the presence of the variable mass term &lt;i&gt;M&lt;/i&gt;(&lt;i&gt;x&lt;/i&gt;) destroys translation invariance and affects the concentration behavior of solutions, while the logarithmic nonlinearity introduces non-polynomial growth that requires refined functional tools. To overcome these difficulties, we develop a variational approach on a normalized constraint manifold, employ Orlicz space techniques to handle the logarithmic term, use a reduction method for the nonlocal Bopp–Podolsky field, and apply concentration–compactness principles adapted to critical growth. The simultaneous presence of the &lt;i&gt;p&lt;/i&gt;-Laplacian, logarithmic nonlinearity, critical exponent, and nonlocal coupling necessitates a nonstandard combination of analytical techniques beyond classical frameworks. We prove the existence and multiplicity of normalized solutions for sufficiently small &lt;span&gt;(varepsilon &gt;0)&lt;/span&gt; and show that these solutions concentrate near the global minima of the external","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147830161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On (mathscr {T})-Based Orthomodular Dynamic Algebras","authors":"Jan Paseka,&nbsp;Juanda Kelana Putra,&nbsp;Richard Smolka","doi":"10.1007/s10773-026-06334-0","DOIUrl":"10.1007/s10773-026-06334-0","url":null,"abstract":"<div><p>This paper establishes a categorical equivalence between the category <span>(mathbb {COL})</span> of complete orthomodular lattices and the category <span>(mathscr {T}mathbb {ODA})</span> of <span>(mathscr {T})</span>-based orthomodular dynamic algebras. Complete orthomodular lattices serve as the static algebraic foundation for quantum logic, modeling the testable properties of quantum systems. In contrast, <span>(mathscr {T})</span>-based orthomodular dynamic algebras, which are specialized unital involutive quantales, formalize the composition and quantum-logical properties of quantum actions. This result refines prior connections between orthomodular lattices and dynamic algebras, provides a constructive bridge between static and dynamic quantum logic perspectives, and extends naturally to Hilbert lattices and broader quantum-theoretic structures.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum Teleportation of an Arbitrary Unknown F-Dimensional Entangled State via D-Dimensional Entangled States","authors":"Huang-rui Lei,&nbsp;Jian-gang Tang,&nbsp;Jia-yin Peng","doi":"10.1007/s10773-026-06347-9","DOIUrl":"10.1007/s10773-026-06347-9","url":null,"abstract":"<div><p>This paper establishes a protocol for the teleportation of an arbitrary unknown <i>f</i>-dimensional multi-particle entangled state using high-dimensional two-particle entangled channels. We first construct a set of completely orthogonal non-symmetric bases to enable a deterministic teleportation scheme for an <i>f</i>-dimensional two-particle state via two <i>d</i>-dimensional maximally entangled two-qudit states (<span>(d&gt;f)</span>). Within this framework, the sender executes non-symmetric basis measurements on their particles, and the receiver applies specific unitary operations, contingent upon the measurement outcomes, to faithfully reconstruct the original state. We then extend this protocol to accommodate non-maximally entangled channels, demonstrating that the arbitrary two-particle state can be probabilistically recovered through the introduction of auxiliary qubits and suitable local operations, with the corresponding success probability provided. Analysis confirms that the non-maximally entangled scheme generalizes its deterministic counterpart. Finally, both schemes are directly scalable to teleport an arbitrary unknown <i>f</i>-dimensional <i>k</i>-particle entangled state utilizing <i>k</i> <i>d</i>-dimensional two-qudit channels.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermodynamic Investigation of the QCD Phase Transition through the PNJL and Color-Singlet Bag Models in the Light of Lattice QCD Results","authors":"M. A. Lakehal,&nbsp;A. Ait El Djoudi,&nbsp;B. Moussaoui","doi":"10.1007/s10773-026-06308-2","DOIUrl":"10.1007/s10773-026-06308-2","url":null,"abstract":"<div><p>We study the thermodynamic properties of the deconfinement phase transition in quantum chromodynamics (QCD) for two light quark flavors, by using two effective models: the Polyakov–Nambu–Jona-Lasinio (PNJL) model and the MIT Bag Model with a color-singletness condition (Bag-CS) for the quark-gluon plasma (QGP). In the former, we analyze the impact of the Vandermonde (VdM) parameter <span>(K)</span> on the Polyakov loop potential and in the latter, we use a switching function for the equations of state of the hadronic and QGP phases to allow for a smooth crossover between the two phases and we examine the role of the bag constant <span>(B)</span> in controlling the stability of the strongly interacting matter. Several physical quantities are calculated in both models, at vanishing chemical potential and finite temperatures. Our findings suggest that small values of the VdM parameter <span>(K)</span> in the PNJL model and large values of the bag constant <span>(B)</span> in the Bag-CS model lead to a better consistent description of the QCD phase transition. There is a good agreement with lattice QCD results for a broad temperature range, and both models have an evident convergence in the crossover region.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cosmological Dynamics of Rényi Holographic Dark Energy in (f(R,T)) Gravity with Kantowski–Sachs Geometry","authors":"Shakeel Khan,&nbsp;Rishikumar Agrawal,&nbsp;Ather Husain,&nbsp;N. Myrzakulov,&nbsp;S. H. Shekh","doi":"10.1007/s10773-026-06343-z","DOIUrl":"10.1007/s10773-026-06343-z","url":null,"abstract":"<div><p>In the present study, we explore the cosmological implications of Rényi holographic dark energy within the framework of <span>(f(R,T))</span> gravity by considering an anisotropic Kantowski–Sachs space time. To obtain exact solutions, we employ Berman’s law corresponding to a constant deceleration parameter and assume a proportional relationship between the shear scalar and the expansion scalar. The derived model exhibits a gradual decrease in the RHDE density as the Universe evolves, eventually tending toward a finite positive value at late times. At the same time, the pressure remains negative throughout the evolution and approaches a nearly constant value in the asymptotic regime. The behaviour of the equation of state parameter indicates a transition from values near zero to more negative values, supporting the onset of accelerated expansion. Our analysis shows that the Null Energy Condition (NEC) and the Dominant Energy Condition (DEC) remain satisfied; however, the Strong Energy Condition (SEC) is violated, consistent with late-time acceleration. Statefinder diagnostics reveal that the model evolves toward the ΛCDM fixed point. Although the squared sound speed is negative, reflecting non-canonical perturbative behaviour common in modified gravity, the background evolution remains well behaved. Overall, RHDE in <span>(f(R,T))</span> gravity provides a viable description of late-time cosmic acceleration.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Semiclassical Einstein Equations in Cosmological Spacetimes","authors":"Paolo Meda","doi":"10.1007/s10773-026-06339-9","DOIUrl":"10.1007/s10773-026-06339-9","url":null,"abstract":"<div><p>The semiclassical Einstein equation describes the backreaction of quantum matter fields on classical background spacetimes. This conference proceeding reviews some recent results obtained by N. Pinamonti, D. Siemssen and the author [Ann. Henri Poincaré <b>22</b>, 3965–4015, 2021] on the initial-value problem of the semiclassical Einstein equation coupled to a quantum, massive, scalar field with arbitrary coupling to the scalar curvature in cosmological spacetimes. The central issue of the problem arises from the fact that the linearized expectation value of the renormalized stress-energy tensor of the quantum matter field hides a nonlocal contribution depending on the highest derivative. This is encoded in an unbounded, tame operator which lose derivatives, and thus it prevents a direct analysis of the dynamical equation. The system can nevertheless be reformulated as an inverse problem, allowing one to isolate and invert the highest-derivative contribution. In this form, existence and uniqueness of solutions can be established using Banach fixed-point methods. This proceeding is based on the talk given by the author at the <i>IQSA2025 Intermediate conference</i> (Tropea, Italy).</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10773-026-06339-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Schrödinger–Poisson Systems with Double Logarithmic and Nonlocal Sources","authors":"Salah Boulaaras,&nbsp;Mohammad Alnegga","doi":"10.1007/s10773-026-06338-w","DOIUrl":"10.1007/s10773-026-06338-w","url":null,"abstract":"<div><p>In this paper, we introduce a new class of Schrödinger–Poisson type systems characterized by multi-scale logarithmic nonlinearities and nonlocal interactions. The model is governed by the coupled system </p><div><div><span>$$ left{ begin{array}{ll} -Delta u + V(x)u + phi u = lambda u + g(x,u,phi ), &amp; x in mathbb {R}^3, -Delta phi = u^2, &amp; x in mathbb {R}^3, end{array}right. $$</span></div></div><p>where <span>(u:mathbb {R}^3 rightarrow mathbb {R})</span> represents the wave function, <span>(phi :mathbb {R}^3 rightarrow mathbb {R})</span> denotes the electrostatic potential generated by the particle density, <span>(V:mathbb {R}^3 rightarrow mathbb {R})</span> is a continuous external potential satisfying <span>(V(x)ge V_0&gt;0)</span>, and <span>(lambda in mathbb {R})</span> is a real parameter. The nonlinear term <span>(g:mathbb {R}^3 times mathbb {R}times mathbb {R}rightarrow mathbb {R})</span> is defined by </p><div><div><span>$$ g(x,u,phi ) = u log (1+|u|^alpha ) + beta (x),u log log (e+|u|^gamma ) + eta ,phi u log (1+|u|^2), $$</span></div></div><p>where <span>(alpha ,gamma &gt;0)</span>, <span>(beta :mathbb {R}^3 rightarrow mathbb {R})</span> is a bounded function, and <span>(eta &gt;0)</span> is a parameter describing the strength of the nonlocal coupling. This formulation introduces a new interaction mechanism between the wave function and the self-consistent electrostatic field, significantly extending classical Schrödinger–Poisson and Schrödinger–Bopp–Podolsky models studied in the literature. In contrast to recent works that mainly consider power-type or single logarithmic nonlinearities, the present framework incorporates double-logarithmic growth together with nonlocal logarithmic coupling, leading to a richer and more intricate variational structure. From a mathematical perspective, the presence of iterated logarithmic terms requires the development of refined analytical tools beyond standard Sobolev settings. By combining variational methods, generalized growth inequalities, and concentration–compactness techniques, we establish the existence of nontrivial weak solutions and prove the existence of infinitely many geometrically distinct solutions via genus theory. Moreover, we analyze the concentration behavior of solutions, showing that they localize near the global minima of the potential <i>V</i>(<i>x</i>). The results obtained in this work significantly extend existing theories for Schrödinger–Poisson type systems by capturing multi-scale nonlinear effects and strong nonlocal interactions. Finally, numerical simulations presented in tabular form confirm the theoretical findings, illustrating convergence properties, multiplicity of energy levels, and the influence of the parameters <span>(eta )</span> and <span>(gamma )</span> on the qualitative behavior of solutions.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hamiltonian Thermodynamics on Symplectic Manifolds","authors":"Aritra Ghosh,&nbsp;E. Harikumar","doi":"10.1007/s10773-026-06301-9","DOIUrl":"10.1007/s10773-026-06301-9","url":null,"abstract":"<div><p>We describe a symplectic approach towards thermodynamics in which thermodynamic transformations are described by (symplectic) Hamiltonian dynamics. Upon identifying the spaces of equilibrium states with Lagrangian submanifolds of a symplectic manifold, we present a Hamiltonian description of thermodynamic processes where the space of equilibrium states of a system in a certain ensemble is contained in the level set on which the Hamiltonian assumes a constant value. In particular, we work out two explicit examples involving the ideal gas and then describe a Hamiltonian approach towards constructing maps between related thermodynamic systems, e.g., the ideal (non-interacting) gas and interacting gases. Finally, we extend the theory of symplectic Hamiltonian dynamics to describe (a) the free expansion of the ideal gas which involves irreversible generation of entropy, and (b) a symplectic port-Hamiltonian framework for the ideal gas which is exemplified through two problems, namely, the problem of isothermal expansion against a piston and that of heat transfer between a heat bath and the gas via a thermal conductor.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147797015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Equal Majorana Phases from a Minimal and Predictive Neutrino Texture","authors":"Sagar Tirtha Goswami,&nbsp;Pralay Chakraborty,&nbsp;Subhankar Roy","doi":"10.1007/s10773-026-06341-1","DOIUrl":"10.1007/s10773-026-06341-1","url":null,"abstract":"<div><p>We propose a new, minimal Majorana neutrino mass matrix texture and study its predictions within a partial tri-bimaximal (TBM) mixing scheme, where <span>(sin theta _{12} = 1/sqrt{3})</span> and <span>(sin theta _{23} = 1/sqrt{2})</span>, with <span>(theta _{13})</span> and <span>(delta )</span> treated as free parameters. The texture forbids <span>(theta _{13} = 0)</span> and does not correspond to a <span>(mu )</span>–<span>(tau )</span> symmetric structure. As a notable feature, the texture predicts the equality of the Majorana phases. In addition, we find that the predictions show distinct behavior depending on the sign of a single real texture parameter. The texture is realized through a hybrid framework of one Type-I seesaw and two Type-II seesaw mechanisms under an extended symmetry group, <span>(SU(2)_L otimes U(1)_Y otimes A_4 otimes Z_{10} otimes Z_{7})</span> with properly chosen model parameters. The texture is seen to favor the normal hierarchy for neutrino masses.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147797004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}