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2024年, 第44卷, 第1期　刊出日期：2024-02-25 上一期    下一期

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CLASSIFICATIONS OF DUPIN HYPERSURFACES IN LIE SPHERE GEOMETRY* Thomas E. Cecil 数学物理学报(英文版). 2024 (1):  1-36.  DOI: 10.1007/s10473-024-0101-7 摘要 ( 94 )   RICH HTML PDF   收藏 This is a survey of local and global classification results concerning Dupin hypersurfaces in $S^n$ (or ${\bf R}^n$) that have been obtained in the context of Lie sphere geometry. The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres. Along with these classification results, many important concepts from Lie sphere geometry, such as curvature spheres, Lie curvatures, and Legendre lifts of submanifolds of $S^n$ (or ${\bf R}^n$), are described in detail. The paper also contains several important constructions of Dupin hypersurfaces with certain special properties. 参考文献 | 相关文章 | 计量指标

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THE RIEMANN PROBLEM FOR ISENTROPIC COMPRESSIBLE EULER EQUATIONS WITH DISCONTINUOUS FLUX* Yinzheng Sun, Aifang Qu, Hairong Yuan 数学物理学报(英文版). 2024 (1):  37-77.  DOI: 10.1007/s10473-024-0102-6 摘要 ( 96 )   RICH HTML PDF   收藏 We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux, more specifically, for pressureless flow on the left and polytropic flow on the right separated by a discontinuity $x=x(t)$. We prove that this problem admits global Radon measure solutions for all kinds of initial data. The over-compressing condition on the discontinuity $x=x(t)$ is not enough to ensure the uniqueness of the solution. However, there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve $x=x(t)+0$, in addition to the full adhesion condition on its left-side. As an application, we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas. In particular, we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas. This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field. 参考文献 | 相关文章 | 计量指标

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COMPLETE KAHLER METRICS WITH POSITIVE HOLOMORPHIC SECTIONAL CURVATURES ON CERTAIN LINE BUNDLES (RELATED TO A COHOMOGENEITY ONE POINT OF VIEW ON A YAU CONJECTURE)* Xiaoman Duan, Zhuangdan Guan 数学物理学报(英文版). 2024 (1):  78-102.  DOI: 10.1007/s10473-024-0103-5 摘要 ( 77 )   RICH HTML 收藏 In this article, we study Kähler metrics on a certain line bundle over some compact Kähler manifolds to find complete Kähler metrics with positive holomorphic sectional (or bisectional) curvatures. Thus, we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry. 参考文献 | 相关文章 | 计量指标

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THE EXACT MEROMORPHIC SOLUTIONS OF SOME NONLINEAR DIFFERENTIAL EQUATIONS* Huifang Liu, Zhiqiang Mao 数学物理学报(英文版). 2024 (1):  103-114.  DOI: 10.1007/s10473-024-0104-4 摘要 ( 46 )   RICH HTML PDF   收藏 We find the exact forms of meromorphic solutions of the nonlinear differential equations $f^n+q(z){\rm e}^{Q(z)}f^{(k)}=p_1{\rm e}^{\alpha_1 z}+p_2{\rm e}^{\alpha_2 z}, \quad n\geq3, ~k\geq1,$ where $q, Q$ are nonzero polynomials, $Q\not\equiv Const.$, and $p_1, p_2, \alpha_1, \alpha_2$ are nonzero constants with $\alpha_1\neq\alpha_2$. Compared with previous results on the equation $p(z)f^3+q(z)f''=-\sin \alpha(z)$ with polynomial coefficients, our results show that the coefficient of the term $f^{(k)}$ perturbed by multiplying an exponential function will affect the structure of its solutions. 参考文献 | 相关文章 | 计量指标

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GLOBAL CLASSICAL SOLUTIONS OF SEMILINEAR WAVE EQUATIONS ON $\mathbb{R}^{3}\times \mathbb{T}$ WITH CUBIC NONLINEARITIES* Fei Tao 数学物理学报(英文版). 2024 (1):  115-128.  DOI: 10.1007/s10473-024-0105-3 摘要 ( 55 )   RICH HTML PDF   收藏 In this paper, we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space $\mathbb{R}^3\times\mathbb{T}$. The semilinear nonlinearity is assumed to be of the cubic form. The main ingredient here is the establishment of the $L^2$-$L^\infty$ decay estimates and the energy estimates for the linear problem, which are adapted to the wave equation on the product space. The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction, the scaling technique, and the combination of the decay estimates and the energy estimates. 参考文献 | 相关文章 | 计量指标

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SOME NEW IDENTITIES OF ROGERS-RAMANUJAN TYPE* Jing GU, Zhizheng ZHANG 数学物理学报(英文版). 2024 (1):  129-142.  DOI: 10.1007/s10473-024-0106-2 摘要 ( 56 )   RICH HTML PDF   收藏 In this paper, we establish two transformation formulas for nonterminating basic hypergeometric series by using Carlitz's inversions formulas and Jackson's transformation formula. In terms of application, by specializing certain parameters in the two transformations, four Rogers-Ramanujan type identities associated with moduli 20 are obtained. 参考文献 | 相关文章 | 计量指标

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NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES* Yuecai Han, Dingwen Zhang 数学物理学报(英文版). 2024 (1):  143-160.  DOI: 10.1007/s10473-024-0107-1 摘要 ( 46 )   RICH HTML PDF   收藏 We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations. The estimates, based on either the continuously observed process or the discretely observed process, are considered. Under certain conditions, we prove the strong consistency and the asymptotic normality of the two estimators. Our method is also suitable for one-sided reflected stochastic differential equations. Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis ${et al.}$ (Stat Sin, 2021, 31: 29-51). Several real data sets of the currency exchange rate are used to illustrate our proposed methodology. 参考文献 | 相关文章 | 计量指标

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QUASIPERIODICITY OF TRANSCENDENTAL MEROMORPHIC FUNCTIONS* Xinling LIU, Kai Liu, Risto Korhonen, Galina Filipuk 数学物理学报(英文版). 2024 (1):  161-172.  DOI: 10.1007/s10473-024-0108-0 摘要 ( 41 )   RICH HTML PDF   收藏 This paper is devoted to considering the quasiperiodicity of complex differential polynomials, complex difference polynomials and complex delay-differential polynomials of certain types, and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity. 参考文献 | 相关文章 | 计量指标

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SOME PROPERTIES OF THE INTEGRATION OPERATORS ON THE SPACES ${F(p,q,s)}$* Jiale Chen 数学物理学报(英文版). 2024 (1):  173-188.  DOI: 10.1007/s10473-024-0109-z 摘要 ( 51 )   RICH HTML PDF   收藏 We study the closed range property and the strict singularity of integration operators acting on the spaces $F(p,p\alpha-2,s)$. We completely characterize the closed range property of the Volterra companion operator $I_g$ on $F(p,p\alpha-2,s)$, which generalizes the existing results and answers a question raised in [A. Anderson, Integral Equations Operator Theory, 69 (2011), no. 1, 87-99]. For the Volterra operator $J_g$, we show that, for $0<\alpha\leq1$, $J_g$ never has a closed range on $F(p,p\alpha-2,s)$. We then prove that the notions of compactness, weak compactness and strict singularity coincide in the case of $J_g$ acting on $F(p,p-2,s)$. 参考文献 | 相关文章 | 计量指标

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THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE* Yuxin Dong, Hezi Lin, Lingen Lu 数学物理学报(英文版). 2024 (1):  189-194.  DOI: 10.1007/s10473-024-0110-6 摘要 ( 67 )   RICH HTML PDF   收藏 In this note, we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature. Like the Michale-Simon Sobolev inequality, this inequality contains a term involving the mean curvature. 参考文献 | 相关文章 | 计量指标

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GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY* Shijin Ding, Yinghua Li, Yu Wang 数学物理学报(英文版). 2024 (1):  195-214.  DOI: 10.1007/s10473-024-0111-5 摘要 ( 48 )   RICH HTML PDF   收藏 This paper is concerned with the Navier-Stokes/Allen-Cahn system, which is used to model the dynamics of immiscible two-phase flows. We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form of $\eta(\rho)=\rho^\alpha$. The existence of unique global $H^{2m}$-solutions $(m\in\mathbb N)$ to the free boundary problem is proven for when $0<\alpha<\frac14$. Furthermore, we obtain the global $C^\infty$-solutions if the initial data is smooth. 参考文献 | 相关文章 | 计量指标

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ON DE FINETTI'S OPTIMAL IMPULSE DIVIDEND CONTROL PROBLEM UNDER CHAPTER 11 BANKRUPTCY* Wenyuan WANG, Ruixing MING, Yijun HU 数学物理学报(英文版). 2024 (1):  215-233.  DOI: 10.1007/s10473-024-0112-4 摘要 ( 38 )   RICH HTML PDF   收藏 Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S. bankruptcy code, in this paper we follow [44] to revisit the De Finetti dividend control problem under the reorganization process and the regulator's intervention documented in U.S. Chapter 11 bankruptcy. We do this by further accommodating the fixed transaction costs on dividends to imitate the real-world procedure of dividend payments. Incorporating the fixed transaction costs transforms the targeting optimal dividend problem into an impulse control problem rather than a singular control problem, and hence computations and proofs that are distinct from [44] are needed. To account for the financial stress that is due to the more subtle concept of Chapter 11 bankruptcy, the surplus process after dividends is driven by a piece-wise spectrally negative Lévy process with endogenous regime switching. Some explicit expressions of the expected net present values under a double barrier dividend strategy, new to the literature, are established in terms of scale functions. With the help of these expressions, we are able to characterize the optimal strategy among the set of admissible double barrier dividend strategies. When the tail of the Lévy measure is log-convex, this optimal double barrier dividend strategy is then verified as the optimal dividend strategy, solving our optimal impulse control problem. 参考文献 | 相关文章 | 计量指标

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CONVEXITY OF THE FREE BOUNDARY FOR AN AXISYMMETRIC INCOMPRESSIBLE IMPINGING JET* Xiaohui Wang 数学物理学报(英文版). 2024 (1):  234-246.  DOI: 10.1007/s10473-024-0113-3 摘要 ( 46 )   RICH HTML PDF   收藏 This paper is devoted to the study of the shape of the free boundary for a three-dimensional axisymmetric incompressible impinging jet. To be more precise, we will show that the free boundary is convex to the fluid, provided that the uneven ground is concave to the fluid. 参考文献 | 相关文章 | 计量指标

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INTERFACE BEHAVIOR AND DECAY RATES OF COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND A VACUUM* Zhenhua Guo, Xueyao Zhang 数学物理学报(英文版). 2024 (1):  247-274.  DOI: 10.1007/s10473-024-0114-2 摘要 ( 53 )   RICH HTML PDF   收藏 In this paper, we study the one-dimensional motion of viscous gas near a vacuum, with the gas connecting to a vacuum state with a jump in density. The interface behavior, the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficient $\mu(\rho)=\rho^{\alpha}$ for any $0<\alpha<1$; this includes the time-weighted boundedness from below and above. The smoothness of the solution is discussed. Moreover, we construct a class of self-similar classical solutions which exhibit some interesting properties, such as optimal estimates. The present paper extends the results in [Luo T, Xin Z P, Yang T. SIAM J Math Anal, 2000, 31(6): 1175-1191] to the jump boundary conditions case with density-dependent viscosity 参考文献 | 相关文章 | 计量指标

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MULTIPLE INTERSECTIONS OF SPACE-TIME ANISOTROPIC GAUSSIAN FIELDS* Zhenlong Chen, Weijie Yuan 数学物理学报(英文版). 2024 (1):  275-294.  DOI: 10.1007/s10473-024-0115-1 摘要 ( 27 )   RICH HTML PDF   收藏 Let $X=\{X(t)\in\mathbb{R}^{d},t\in\mathbb{R}^{N}\}$ be a centered space-time anisotropic Gaussian field with indices $H=(H_{1},\cdots ,H_{N})\in(0,1)^{N}$, where the components $X_{i}\ (i=1,\cdots ,d)$ of $X$ are independent, and the canonical metric $\sqrt{\mathbb{E}(X_{i}(t)-X_{i}(s))^{2}}\ (i=1,\cdots ,d)$ is commensurate with $\gamma^{\alpha_{i}}(\sum\limits_{j=1}^{N}|t_{j}-s_{j}|^{H_{j}})$ for $s=(s_{1},\cdots ,s_{N}), t=(t_{1},\cdots ,t_{N})\in\mathbb{R}^{N}$, $\alpha_{i}\in(0,1]$, and with the continuous function $\gamma(\cdot)$ satisfying certain conditions. First, the upper and lower bounds of the hitting probabilities of $X$ can be derived from the corresponding generalized Hausdorff measure and capacity, which are based on the kernel functions depending explicitly on $\gamma(\cdot)$. Furthermore, the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are considered. Our results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields 参考文献 | 相关文章 | 计量指标

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ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR* Jieling Chen, Mingsheng Liu 数学物理学报(英文版). 2024 (1):  295-310.  DOI: 10.1007/s10473-024-0116-0 摘要 ( 40 )   RICH HTML PDF   收藏 In this paper, we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the form $L(f)=z f_z-\bar{z} f_{\bar{z}}$, where $f$ represents normalized harmonic mappings with bounded dilation. Then, using these results, we present better estimations for the Bloch constants of certain harmonic mappings $L(f)$, where $f$ is a $K$-quasiregular harmonic or open harmonic. Finally, we establish three versions of Bloch-Landau type theorem for biharmonic mappings of the form $L(f)$. These results are sharp in some given cases and improve the related results of earlier authors. 参考文献 | 相关文章 | 计量指标

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AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVE -FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS* Safoura Rezaei Aderyani, Azam Ahadi, Reza Saadati, Hari M. Srivastava 数学物理学报(英文版). 2024 (1):  311-338.  DOI: 10.1007/s10473-024-0117-z 摘要 ( 41 )   RICH HTML PDF   收藏 In this paper, we define a new class of control functions through aggregate special functions. These class of control functions help us to stabilize and approximate a tri-additive $\boldsymbol{\psi}$-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital $C^*$-algebras and Banach algebras by the vector-valued alternative fixed point theorem. 参考文献 | 相关文章 | 计量指标

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THE INTERIOR TRANSMISSION EIGENVALUE PROBLEM FOR AN ANISOTROPIC MEDIUM BY A PARTIALLY COATED BOUNDARY* Jianli XIANG, Guozheng YAN 数学物理学报(英文版). 2024 (1):  339-354.  DOI: 10.1007/s10473-024-0118-y 摘要 ( 41 )   RICH HTML PDF   收藏 We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary $\partial\Omega$ is split into two disjoint parts and possesses different transmission conditions. Using the variational method, we obtain the well posedness of the interior transmission problem, which plays an important role in the proof of the discreteness of eigenvalues. Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that $n\equiv1$, where a fourth order differential operator is applied. In the case of $n\not\equiv1$, we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method. 参考文献 | 相关文章 | 计量指标

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ENTIRE SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENTS HAVING THE SAME ORDER* Ziheng Feng, Zhibo Huang, Yezhou Li 数学物理学报(英文版). 2024 (1):  355-368.  DOI: 10.1007/s10473-024-0119-x 摘要 ( 44 )   RICH HTML PDF   收藏 In this paper, we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order, and prove that the entire solutions are of infinite lower order. The properties on the radial distribution, the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed. 参考文献 | 相关文章 | 计量指标

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CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS* Nanbin CAO, Zunfeng LI, Heju YANG, Yuying QIAO 数学物理学报(英文版). 2024 (1):  369-385.  DOI: 10.1007/s10473-024-0120-4 摘要 ( 47 )   RICH HTML PDF   收藏 Clifford analysis is an important branch of modern analysis; it has a very important theoretical significance and application value, and its conclusions can be applied to the Maxwell equation, Yang-Mill field theory, quantum mechanics and value problems. In this paper, we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis, and get the Plemelj formula for it. Second, we discuss the Hölder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra. Finally, we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution. 参考文献 | 相关文章 | 计量指标

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THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES* Wei Ding, Yan Tang, Yueping Zhu 数学物理学报(英文版). 2024 (1):  386-404.  DOI: 10.1007/s10473-024-0121-3 摘要 ( 55 )   RICH HTML PDF   收藏 Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators, untill now, the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates. In this paper, we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition. 参考文献 | 相关文章 | 计量指标