In this paper, a class of non-weight modules over the topological N = 2 super-BMS3 algebra g are completely constructed. Assume that h̄=CL0⊕CP0⊕CG0⊕CQ0 is the Cartan subalgebra of g and h=CL0⊕CP0 is a two-dimensional subalgebra of h̄. These modules over g are free of rank 2 as modules of the subalgebra h. In fact, these modules are reducible. Moreover, we give a complete classification of free U(h)-modules of rank 2 over g.
{"title":"U\u0000 (\u0000 h\u0000 )\u0000 -free modules over the topological N = 2 super-BMS3 algebra","authors":"Hao Lu, Jiancai Sun, Honglian Zhang","doi":"10.1063/5.0139069","DOIUrl":"https://doi.org/10.1063/5.0139069","url":null,"abstract":"In this paper, a class of non-weight modules over the topological N = 2 super-BMS3 algebra g are completely constructed. Assume that h̄=CL0⊕CP0⊕CG0⊕CQ0 is the Cartan subalgebra of g and h=CL0⊕CP0 is a two-dimensional subalgebra of h̄. These modules over g are free of rank 2 as modules of the subalgebra h. In fact, these modules are reducible. Moreover, we give a complete classification of free U(h)-modules of rank 2 over g.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"17 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78009628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper deals with the homogenization of a one-dimensional nonlinear non-local variable index p(x)-Laplacian operator Lɛ with a periodic structure and convolution kernel. By constructing a scale diffusive model and two corrector functions χ1 and χ2, as scale parameter ɛ → 0+, we first obtain that the limit operator L is a p-Laplacian operator with constant exponent and coefficients such that Lu=Rddx(|u′(x)|p−2u′(x)). Then, for a given function f∈Lq(R)(q=pp−1), we prove the asymptotic behavior of the solution uɛ(x) to the equation (Lɛ − I)uɛ(x) = f(x) such that uε(x)=u(x)+εχ1(xε)u′(x)+ε2χ2(xε)u″(x)+o(1)(ε→0+) in Lp(R), where u(x) is the solution of equation (L − I)u(x) = f(x).
{"title":"Homogenization of non-local nonlinear p-Laplacian equation with variable index and periodic structure","authors":"Junlong Chen, Yanbin Tang","doi":"10.1063/5.0091156","DOIUrl":"https://doi.org/10.1063/5.0091156","url":null,"abstract":"This paper deals with the homogenization of a one-dimensional nonlinear non-local variable index p(x)-Laplacian operator Lɛ with a periodic structure and convolution kernel. By constructing a scale diffusive model and two corrector functions χ1 and χ2, as scale parameter ɛ → 0+, we first obtain that the limit operator L is a p-Laplacian operator with constant exponent and coefficients such that Lu=Rddx(|u′(x)|p−2u′(x)). Then, for a given function f∈Lq(R)(q=pp−1), we prove the asymptotic behavior of the solution uɛ(x) to the equation (Lɛ − I)uɛ(x) = f(x) such that uε(x)=u(x)+εχ1(xε)u′(x)+ε2χ2(xε)u″(x)+o(1)(ε→0+) in Lp(R), where u(x) is the solution of equation (L − I)u(x) = f(x).","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"5 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85322053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We construct classes of Z2×Z2-graded Lie algebras corresponding to the classical Lie algebras in terms of their defining matrices. For the Z2×Z2-graded Lie algebra of type A, the construction coincides with the previously known class. For the Z2×Z2-graded Lie algebra of types B, C, and D, our construction is new and gives rise to interesting defining matrices closely related to the classical ones but undoubtedly different. We also give some examples and possible applications of parastatistics.
{"title":"On classical Z2×Z2-graded Lie algebras","authors":"N. I. Stoilova, J. Van der Jeugt","doi":"10.1063/5.0149175","DOIUrl":"https://doi.org/10.1063/5.0149175","url":null,"abstract":"We construct classes of Z2×Z2-graded Lie algebras corresponding to the classical Lie algebras in terms of their defining matrices. For the Z2×Z2-graded Lie algebra of type A, the construction coincides with the previously known class. For the Z2×Z2-graded Lie algebra of types B, C, and D, our construction is new and gives rise to interesting defining matrices closely related to the classical ones but undoubtedly different. We also give some examples and possible applications of parastatistics.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"19 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91304772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we define the Bartnik mass of a domain whose boundary is connected and compact, has scalar curvature bounded below −n(n − 1), and whose extensions are asymptotically hyperbolic manifolds. With this definition, we show that asymptotically hyperbolic admissible extensions of a domain that achieve the Bartnik mass must admit a static potential. Given a non-static admissible extension of a domain, we are able to construct a one-parameter family of metrics that are close to the original metric, have smaller mass, share the same bound on the scalar curvature, and contain the domain isometrically.
{"title":"Staticity of asymptotically hyperbolic minimal mass extensions","authors":"Daniel Martin","doi":"10.1063/5.0150283","DOIUrl":"https://doi.org/10.1063/5.0150283","url":null,"abstract":"In this paper, we define the Bartnik mass of a domain whose boundary is connected and compact, has scalar curvature bounded below −n(n − 1), and whose extensions are asymptotically hyperbolic manifolds. With this definition, we show that asymptotically hyperbolic admissible extensions of a domain that achieve the Bartnik mass must admit a static potential. Given a non-static admissible extension of a domain, we are able to construct a one-parameter family of metrics that are close to the original metric, have smaller mass, share the same bound on the scalar curvature, and contain the domain isometrically.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"18 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84467293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We evaluate one-dimensional representations of quantum symmetric conjugacy classes of classical matrix groups along with their quantum stabilizer subgroups.
研究了经典矩阵群及其量子稳定子群的量子对称共轭类的一维表示。
{"title":"Quantum symmetric conjugacy classes of non-exceptional groups","authors":"D. Algethami, A. Mudrov","doi":"10.1063/5.0157498","DOIUrl":"https://doi.org/10.1063/5.0157498","url":null,"abstract":"We evaluate one-dimensional representations of quantum symmetric conjugacy classes of classical matrix groups along with their quantum stabilizer subgroups.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82829774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We analyze the Cauchy problem for the Proca equation in dielectric media in a curved spacetime.
本文分析了弯曲时空介质中Proca方程的柯西问题。
{"title":"The Cauchy problem for the Proca equation in gravitating dielectric media","authors":"F. Steininger, Piotr T. Chru'sciel","doi":"10.1063/5.0156319","DOIUrl":"https://doi.org/10.1063/5.0156319","url":null,"abstract":"We analyze the Cauchy problem for the Proca equation in dielectric media in a curved spacetime.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"440 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73595038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Riemann problem for the Aw-Rascle (AR) traffic flow model with a double parameter perturbation containing flux and generalized Chaplygin gas is first solved. Then, we show that the delta-shock solution of the perturbed AR model converges to that of the original AR model as the flux perturbation vanishes alone. Particularly, it is proved that as the flux perturbation and pressure decrease, the classical solution of the perturbed system involving a shock wave and a contact discontinuity will first converge to a critical delta shock wave of the perturbed system itself and only later to the delta-shock solution of the pressureless gas dynamics (PGD) model. This formation mechanism is interesting and innovative in the study of the AR model. By contrast, any solution containing a rarefaction wave and a contact discontinuity tends to a two-contact-discontinuity solution of the PGD model, and the nonvacuum intermediate state in between tends to a vacuum state. Finally, some representatively numerical results consistent with the theoretical analysis are presented.
{"title":"Limits of solutions to the Aw-Rascle traffic flow model with generalized Chaplygin gas by flux approximation","authors":"Yu Zhang, S. Fan","doi":"10.1063/5.0140635","DOIUrl":"https://doi.org/10.1063/5.0140635","url":null,"abstract":"The Riemann problem for the Aw-Rascle (AR) traffic flow model with a double parameter perturbation containing flux and generalized Chaplygin gas is first solved. Then, we show that the delta-shock solution of the perturbed AR model converges to that of the original AR model as the flux perturbation vanishes alone. Particularly, it is proved that as the flux perturbation and pressure decrease, the classical solution of the perturbed system involving a shock wave and a contact discontinuity will first converge to a critical delta shock wave of the perturbed system itself and only later to the delta-shock solution of the pressureless gas dynamics (PGD) model. This formation mechanism is interesting and innovative in the study of the AR model. By contrast, any solution containing a rarefaction wave and a contact discontinuity tends to a two-contact-discontinuity solution of the PGD model, and the nonvacuum intermediate state in between tends to a vacuum state. Finally, some representatively numerical results consistent with the theoretical analysis are presented.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81898726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
P. M. S. Fialho, B. D. de Lima, A. Procacci, B. Scoppola
We consider a continuous system of classical particles confined in a cubic box Λ interacting through a stable and finite range pair potential with an attractive tail. We study the Mayer series of the grand canonical pressure of the system pΛω(β,λ) at inverse temperature β and fugacity λ in the presence of boundary conditions ω belonging to a very large class of locally finite particle configurations. This class of allowed boundary conditions is the basis for any probability measure on the space of locally finite particle configurations satisfying the Ruelle estimates. We show that the pΛω(β,λ) can be written as the sum of two terms. The first term, which is analytic and bounded as the fugacity λ varies in a Λ-independent and ω-independent disk, coincides with the free-boundary-condition pressure in the thermodynamic limit. The second term, analytic in a ω-dependent convergence radius, goes to zero in the thermodynamic limit. As far as we know, this is the first rigorous analysis of the behavior of the Mayer series of a non-ideal gas subjected to non-free and non-periodic boundary conditions in the low-density/high-temperature regime when particles interact through a non-purely repulsive pair potential.
{"title":"On the analyticity of the pressure for a non-ideal gas with high density boundary conditions","authors":"P. M. S. Fialho, B. D. de Lima, A. Procacci, B. Scoppola","doi":"10.1063/5.0136724","DOIUrl":"https://doi.org/10.1063/5.0136724","url":null,"abstract":"We consider a continuous system of classical particles confined in a cubic box Λ interacting through a stable and finite range pair potential with an attractive tail. We study the Mayer series of the grand canonical pressure of the system pΛω(β,λ) at inverse temperature β and fugacity λ in the presence of boundary conditions ω belonging to a very large class of locally finite particle configurations. This class of allowed boundary conditions is the basis for any probability measure on the space of locally finite particle configurations satisfying the Ruelle estimates. We show that the pΛω(β,λ) can be written as the sum of two terms. The first term, which is analytic and bounded as the fugacity λ varies in a Λ-independent and ω-independent disk, coincides with the free-boundary-condition pressure in the thermodynamic limit. The second term, analytic in a ω-dependent convergence radius, goes to zero in the thermodynamic limit. As far as we know, this is the first rigorous analysis of the behavior of the Mayer series of a non-ideal gas subjected to non-free and non-periodic boundary conditions in the low-density/high-temperature regime when particles interact through a non-purely repulsive pair potential.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"55 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76607022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gelson C. G. dos Santos, Laila C. Fontinele, Rubia G. Nascimentoa, Suellen Cristina Q. Arrudab
In this paper, we establish the existence of standing wave solutions for quasilinear Schrödinger equations involving nonlinearity with subcritical and critical growth. To apply the variational method and circumvent the “lack of compactness” of the problem, we combine the dual approach developed by Colin–Jeanjean [Nonlinear Anal. 56, 213–226 (2004)], Fang–Szulkin [J. Differ. Equations, 254, 2015–2032 (2013)], and Liu–Wang–Wang [J. Differ. Equations 187, 473–493 (2003)] with Del Pino–Felmer’s penalization technique [Calc. Var. Partial Differ. Equations 4, 121–137 (1996)], Moser’s iteration method, and an adaptation of Alves’ arguments [J. Elliptic Parabol. Equations 1, 231–241 (2015)] of the semilinear case.
{"title":"Solutions for a quasilinear Schrödinger equation: Subcritical and critical cases","authors":"Gelson C. G. dos Santos, Laila C. Fontinele, Rubia G. Nascimentoa, Suellen Cristina Q. Arrudab","doi":"10.1063/5.0142706","DOIUrl":"https://doi.org/10.1063/5.0142706","url":null,"abstract":"In this paper, we establish the existence of standing wave solutions for quasilinear Schrödinger equations involving nonlinearity with subcritical and critical growth. To apply the variational method and circumvent the “lack of compactness” of the problem, we combine the dual approach developed by Colin–Jeanjean [Nonlinear Anal. 56, 213–226 (2004)], Fang–Szulkin [J. Differ. Equations, 254, 2015–2032 (2013)], and Liu–Wang–Wang [J. Differ. Equations 187, 473–493 (2003)] with Del Pino–Felmer’s penalization technique [Calc. Var. Partial Differ. Equations 4, 121–137 (1996)], Moser’s iteration method, and an adaptation of Alves’ arguments [J. Elliptic Parabol. Equations 1, 231–241 (2015)] of the semilinear case.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"25 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79269963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The viscous–plastic equations (VPE) of Hibler [J. Geophys. Res. 82(27), 3932–3938 (1977)] are widely adopted and used in Earth system models to represent sea-ice drift due to surface winds, ocean currents, and internal stresses. However, it has been reported by various investigators, at least in one space dimension, that both Hibler’s original equations and their variant using a pressure replacement are ill posed in divergent flow regimes. Especially, Guba et al. [J. Phys. Oceanogr. 43(10), 2185–2199 (2013)] shows that both variants are ill-posed when the flow divergence exceeds a minimum threshold and their results seem to extend to two dimensions when a tensile cut-off is used. In particular, Hibler uses a Heaviside function cut-off for the viscosity coefficients of the VPE’s to avoid a singularity at infinity. Lemieux et al. [J. Comput. Phys. 231(17), 5926–5944 (2012)] regularized the Heaviside function by a hyperbolic tangent for numerical efficiency. Here, we show that, for periodic data, the linearized one-dimensional regularized VPE’s, in which the Heaviside function is replaced with a hyperbolic tangent, is well posed in the case of Hibler’s original equations. Moreover, we prove that the linearization procedure, for the regularized equations, is consistent, in the sense that the residual converges to zero that the perturbation of the solutions goes to zero, in suitable norms.
{"title":"Linear well posedness of regularized equations of sea-ice dynamics","authors":"Soufiane Chatta, B. Khouider, M. Kesri","doi":"10.1063/5.0152991","DOIUrl":"https://doi.org/10.1063/5.0152991","url":null,"abstract":"The viscous–plastic equations (VPE) of Hibler [J. Geophys. Res. 82(27), 3932–3938 (1977)] are widely adopted and used in Earth system models to represent sea-ice drift due to surface winds, ocean currents, and internal stresses. However, it has been reported by various investigators, at least in one space dimension, that both Hibler’s original equations and their variant using a pressure replacement are ill posed in divergent flow regimes. Especially, Guba et al. [J. Phys. Oceanogr. 43(10), 2185–2199 (2013)] shows that both variants are ill-posed when the flow divergence exceeds a minimum threshold and their results seem to extend to two dimensions when a tensile cut-off is used. In particular, Hibler uses a Heaviside function cut-off for the viscosity coefficients of the VPE’s to avoid a singularity at infinity. Lemieux et al. [J. Comput. Phys. 231(17), 5926–5944 (2012)] regularized the Heaviside function by a hyperbolic tangent for numerical efficiency. Here, we show that, for periodic data, the linearized one-dimensional regularized VPE’s, in which the Heaviside function is replaced with a hyperbolic tangent, is well posed in the case of Hibler’s original equations. Moreover, we prove that the linearization procedure, for the regularized equations, is consistent, in the sense that the residual converges to zero that the perturbation of the solutions goes to zero, in suitable norms.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"52 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91330067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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