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INVERSE SOURCE PROBLEM FOR SUBDIFFUSION EQUATION WITH A GENERALIZED IMPEDANCE BOUNDARY CONDITION 具有广义阻抗边界条件的亚扩散方程的反源问题
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00025-9
Mansur I. Ismailov, Muhammed Çiçek
{"title":"INVERSE SOURCE PROBLEM FOR SUBDIFFUSION EQUATION WITH A GENERALIZED IMPEDANCE BOUNDARY CONDITION","authors":"Mansur I. Ismailov,&nbsp;Muhammed Çiçek","doi":"10.1016/S0034-4877(24)00025-9","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00025-9","url":null,"abstract":"<div><p>The paper considers an inverse problem for a one-dimensional time-fractional subdiffusion equation with a generalized impedance boundary condition. This boundary condition is given by a second-order spatial differential operator imposed on the boundary. The inverse problem is the problem of determining the time dependent source parameter from the energy measurement. The well-posedness of the inverse problem is established by applying the Fourier expansion in terms of eigenfunctions of a spectral problem which has the spectral parameter also in the boundary condition, Volterra type integral equation with the kernel may have a diagonal singularity and fractional type Gronwall inequality.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 179-194"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880226","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}
引用次数: 0
NEW QUANTUM CODES DERIVED FROM THE DIRECT PRODUCT OF RINGS, USING CYCLIC CODES OVER THE RING 利用环上的循环码，从环的直接乘积推导出新的量子密码
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00027-2
Pooja Soni, Manju Pruthi, Arun Kumar Yadav
{"title":"NEW QUANTUM CODES DERIVED FROM THE DIRECT PRODUCT OF RINGS, USING CYCLIC CODES OVER THE RING","authors":"Pooja Soni,&nbsp;Manju Pruthi,&nbsp;Arun Kumar Yadav","doi":"10.1016/S0034-4877(24)00027-2","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00027-2","url":null,"abstract":"<div><p>This research paper discusses the construction of novel and better quantum codes from the direct product of <em>t</em>-copies of ring <em>R</em> (discussed in Section 2), using cyclic codes over <em>R</em> by employing the CSS construction technique. Here, we present an overview of the structure and essential properties of a ring <em>R</em>. Furthermore, we analyze the distance-preserving nature of the Gray map in Subsection 2.1. Here, we also investigate maximum distance separable (MDS) codes by using the concept of quantum singleton defect (QSD), which indicates the overall quality of codes. To demonstrate the practicality of our findings, we provide illustrative examples implemented using the Magma software.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 213-229"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880209","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}
引用次数: 0
RICCI SOLITONS AND RICCI BI-CONFORMAL VECTOR FIELDS ON THE LIE GROUP ℍ2 × ℝ 里奇孤子和里奇双共形矢量场上的谎群ℍ2 × ℝ
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00028-4
Shahroud Azami, Mehdi Jafari
{"title":"RICCI SOLITONS AND RICCI BI-CONFORMAL VECTOR FIELDS ON THE LIE GROUP ℍ2 × ℝ","authors":"Shahroud Azami,&nbsp;Mehdi Jafari","doi":"10.1016/S0034-4877(24)00028-4","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00028-4","url":null,"abstract":"<div><p>In the present paper, we investigate the 3-dimensional Lie group (ℍ<sup>2</sup> × ℝ, <em>g</em>) where <em>g</em> is a left-invariant Riemannian metric and we determine the Ricci solitons and Ricci bi-conformal vector fields on it.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 231-239"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880210","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}
引用次数: 0
New regularity criteria for an MHD Darcy-Forchheimer fluid 多流体力学达西-福克海默流体的新规则性标准
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00008-9
Saeed ur Rahman, José Luis Díaz Palencia
{"title":"New regularity criteria for an MHD Darcy-Forchheimer fluid","authors":"Saeed ur Rahman,&nbsp;José Luis Díaz Palencia","doi":"10.1016/S0034-4877(24)00008-9","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00008-9","url":null,"abstract":"<div><p>The purpose of the presented article is to develop some new global regularity criteria for a magnetohydrodynamic (MHD) fluid flowing in a saturated porous medium. The effect of the porous medium, over the fluid flow, is characterized by a Darcy–Forchheimer law. The fluid, under study, is considered as one-dimensional and flowing in the <em>x–</em>direction with velocity component <em>u.</em> In addition, such a component is assumed to vary with the <em>y–</em>direction, i.e. <em>u</em>(<em>y</em>). Then, given the vorticity function\u0000<span><math><mrow><mi>w</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mo>∂</mo><mi>u</mi></mrow><mrow><mo>∂</mo><mi>y</mi></mrow></mfrac></mrow></math></span>, such that\u0000<span><math><mrow><msubsup><mrow><mrow><mo>‖</mo><mi>w</mi><mo>‖</mo></mrow></mrow><mrow><mtext>BMO</mtext></mrow><mn>2</mn></msubsup></mrow></math></span> is sufficiently small, we develop the regularity criteria under the scope of the <em>L</em><sup>2</sup> space. We extend our results to the spaces <em>L<sup>s</sup></em>, where <em>s</em> &gt; 2. Afterward, we prove the Liouville-type theorem for the MHD Darcy–Forchheimer flow equation. Eventually, we obtain some characterization about the asymptotic behaviour of solutions, particularly, the nonuniform convergence in <em>L</em><sup>2</sup> for\u0000<span><math><mrow><mi>t</mi><mo>→</mo><mo>∞</mo></mrow></math></span>.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 1","pages":"Pages 21-36"},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000089/pdfft?md5=0d1891c76d0aee709cdeee928726e3d4&pid=1-s2.0-S0034487724000089-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139975999","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}
引用次数: 0
Galilean and Carrollian Hodge star operators 伽利略和卡罗尔霍奇星算子
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00007-7
Marián Fecko
{"title":"Galilean and Carrollian Hodge star operators","authors":"Marián Fecko","doi":"10.1016/S0034-4877(24)00007-7","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00007-7","url":null,"abstract":"<div><p>The standard Hodge star operator is naturally associated with metric tensor (and orientation). It is routinely used to concisely write down physics equations on, say, Lorentzian spacetimes. On Galilean (Carrollian) spacetimes, there is no canonical (nonsingular) metric tensor available. So, the usual construction of the Hodge star does not work. Here we propose analogs of the Hodge star operator on Galilean (Carrollian) spacetimes. They may be used to write down important physics equations, e.g. equations of Galilean (Carrollian) electrodynamics.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 1","pages":"Pages 1-19"},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000077/pdfft?md5=95dc18d8cfd864d5e9758bc25b1ea4dd&pid=1-s2.0-S0034487724000077-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139975998","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}
引用次数: 0
Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems 交折射、余折射、接触和共接触哈密顿系统的四元数的列积分性
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00009-0
R. Azuaje
{"title":"Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems","authors":"R. Azuaje","doi":"10.1016/S0034-4877(24)00009-0","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00009-0","url":null,"abstract":"<div><p>In this paper we present the theorem on Lie integrability by quadratures for time-independent Hamiltonian systems on symplectic and contact manifolds, and for time-dependent Hamiltonian systems on cosymplectic and cocontact manifolds. We show that having a solvable Lie algebra of constants of motion for a Hamiltonian system is equivalent to having a solvable Lie algebra of symmetries of the vector field defining the dynamics of the system, which allows us to find solutions of the equations of motion by quadratures.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 1","pages":"Pages 37-56"},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000090/pdfft?md5=c065113fa688f685b26c838f8320fc3d&pid=1-s2.0-S0034487724000090-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139976000","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}
引用次数: 0
Zero-error correctibility and phase retrievability for twirling channels 旋转信道的零误差可纠正性和相位可检索性
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00012-0
Deguang Han, Kai Liu
{"title":"Zero-error correctibility and phase retrievability for twirling channels","authors":"Deguang Han,&nbsp;Kai Liu","doi":"10.1016/S0034-4877(24)00012-0","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00012-0","url":null,"abstract":"<div><p>A twirling channel is a quantum channel induced by a continuous unitary representation\u0000<span><math><mrow><mi>π</mi><mo>=</mo><msubsup><mo>∑</mo><mi>i</mi><mo>⊕</mo></msubsup><mrow><msub><mi>m</mi><mi>i</mi></msub><msub><mi>π</mi><mi>i</mi></msub></mrow></mrow></math></span> on a compact group <em>G</em>, where π<sub><em>i</em></sub> are inequivalent irreducible representations. Motivated by a recent work [<span>8</span>] on minimal mixed unitary rank of Φ<em><sub>π</sub></em>, we explore the connections of the independence number, zero-error capacity, quantum codes, orthogonality index and phase retrievability of the quantum channel Φ<em><sub>π</sub></em> with the irreducible representation multiplicities <em>m<sub>i</sub></em> and the irreducible representation dimensions dim\u0000<span><math><mrow><msub><mi>H</mi><mrow><msub><mi>π</mi><mi>i</mi></msub></mrow></msub></mrow></math></span>. In particular, we show that the independence number of Φ<em><sub>π</sub></em> is the sum of the multiplicities, the orthogonal index of Φ<em><sub>π</sub></em> is exactly the sum of those representation dimensions, and the zero-error capacity is equal to log\u0000<span><math><mrow><mrow><mo>(</mo><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>d</mi></msubsup><mrow><msub><mi>m</mi><mi>i</mi></msub></mrow></mrow><mo>)</mo></mrow></mrow></math></span>. We also present a lower bound for the phase retrievability in terms of the minimal length of phase retrievable frames for ℂ<sup><em>n</em></sup></p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 1","pages":"Pages 87-102"},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000120/pdfft?md5=c13c155f18d2d613dd2d69aa31d00367&pid=1-s2.0-S0034487724000120-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139976004","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}
引用次数: 0
Higher order polynomial complex invariants for one-dimensional anharmonic potentials 一维非谐波势的高阶多项式复不变式
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00011-9
S.B. Bhardwaj, Ram Mehar Singh, Vipin Kumar, Narender Kumar, Fakir Chand, Shalini Gupta
{"title":"Higher order polynomial complex invariants for one-dimensional anharmonic potentials","authors":"S.B. Bhardwaj,&nbsp;Ram Mehar Singh,&nbsp;Vipin Kumar,&nbsp;Narender Kumar,&nbsp;Fakir Chand,&nbsp;Shalini Gupta","doi":"10.1016/S0034-4877(24)00011-9","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00011-9","url":null,"abstract":"<div><p>Exact quadratic in momenta complex invariants are investigated for both time independent and time dependent one-dimensional Hamiltonian systems possessing higher order nonlinearities within the framework of the rationalization method. The extended complex phase space approach is utilized to map a real system into complex space. Such invariants are expected to play a role in the analysis of complex trajectories and help to understand some new phenomena associated with complex potentials.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 1","pages":"Pages 71-86"},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000119/pdfft?md5=7de74f018141c5f672b53eea0e7fe658&pid=1-s2.0-S0034487724000119-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139976002","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}
引用次数: 0
A note on the magnetic multipole polynomials 关于磁多极多项式的说明
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00014-4
Giuseppe Dattoli, Mariano Carpanese, Emanuele Di Palma, Alberto Petralia
{"title":"A note on the magnetic multipole polynomials","authors":"Giuseppe Dattoli,&nbsp;Mariano Carpanese,&nbsp;Emanuele Di Palma,&nbsp;Alberto Petralia","doi":"10.1016/S0034-4877(24)00014-4","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00014-4","url":null,"abstract":"<div><p>A family of two variable polynomials naturally emerges from the expansion in multipoles of a magnetic field. The order of the expansion fixes the polynomial degree and the multipolar content: dipole, quadrupole, sextupole and so on. The associated polynomials share analogies with Hermite-type families. The relevant properties are studied, within an umbral framework, which simplifies the derivation of the associated mathematical technicalities. We take advantage from this analogy to present a fairly general discussion about the properties of the “magnetic” polynomials. We touch on the possibility of embedding the results of the present study in a dedicated algorithm for the analysis of the transport of a charged beam in a magnetic structure.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 1","pages":"Pages 121-127"},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000144/pdfft?md5=e7262f46398b4f88b7e6034a078ff7ac&pid=1-s2.0-S0034487724000144-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139976003","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}
引用次数: 0
A unified approach to the generalized uncertainty principle 广义不确定性原理的统一方法
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-02-01 DOI: 10.1016/S0034-4877(24)00010-7
Afzal Raghavi, Ramazan Ali Mohammadian, Saeed Mohammadi
{"title":"A unified approach to the generalized uncertainty principle","authors":"Afzal Raghavi,&nbsp;Ramazan Ali Mohammadian,&nbsp;Saeed Mohammadi","doi":"10.1016/S0034-4877(24)00010-7","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00010-7","url":null,"abstract":"<div><p>In this work, some of the present scenarios for the generalized uncertainty principle are reviewed and it is shown that all of them could be derived through a unified approach that guarantees the existence of both, minimal measurable length and maximal available momentum. Then, a new proposal is introduced that compensates for the defects of previous models. We also studied the effects of this modification on the energy levels and the wave function of a simple harmonic oscillator. It is shown that for the case of a harmonic oscillator, generalized uncertainty relation results in an uncertainty relation between the frequency and the mass of the oscillator.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 1","pages":"Pages 57-69"},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000107/pdfft?md5=ec5294c0bc792165889cdbcb39cd59a6&pid=1-s2.0-S0034487724000107-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139976001","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}
引用次数: 0
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