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On De Finetti’s optimal impulse dividend control problem under Chapter 11 bankruptcy 论破产情形下De Finetti的最优脉冲股利控制问题
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0112-4
Wenyuan Wang, Ruixing Ming, Yijun Hu
{"title":"On De Finetti’s optimal impulse dividend control problem under Chapter 11 bankruptcy","authors":"Wenyuan Wang,&nbsp;Ruixing Ming,&nbsp;Yijun Hu","doi":"10.1007/s10473-024-0112-4","DOIUrl":"10.1007/s10473-024-0112-4","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"215 - 233"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473138","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}
引用次数: 0
Cauchy type integrals and a boundary value problem in a complex Clifford analysis 复数Clifford分析中的Cauchy型积分及边值问题
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0120-4
Nanbin Cao, Zunfeng Li, Heju Yang, Yuying Qiao
{"title":"Cauchy type integrals and a boundary value problem in a complex Clifford analysis","authors":"Nanbin Cao,&nbsp;Zunfeng Li,&nbsp;Heju Yang,&nbsp;Yuying Qiao","doi":"10.1007/s10473-024-0120-4","DOIUrl":"10.1007/s10473-024-0120-4","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"369 - 385"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473255","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}
引用次数: 0
The exact meromorphic solutions of some nonlinear differential equations 一类非线性微分方程的精确亚纯解
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0104-4
Huifang Liu, Zhiqiang Mao
{"title":"The exact meromorphic solutions of some nonlinear differential equations","authors":"Huifang Liu,&nbsp;Zhiqiang Mao","doi":"10.1007/s10473-024-0104-4","DOIUrl":"10.1007/s10473-024-0104-4","url":null,"abstract":"<div><p>We find the exact forms of meromorphic solutions of the nonlinear differential equations </p><div><div><span>$${f^n} + q(z){{rm{e}}^{Q(z)}}{f^{(k)}} = {p_1}{{rm{e}}^{{alpha _1}z}} + {p_2}{{rm{e}}^{{alpha _2}z}},,,,,n ge 3,,,,k ge 1,$$</span></div></div><p> where <i>q, Q</i> are nonzero polynomials, <i>Q ≡ Const.</i>, and <i>p</i><sub>1</sub>, <i>p</i><sub>2</sub>, <i>α</i><sub>1</sub>, <i>α</i><sub>2</sub> are nonzero constants with <i>α</i><sub>1</sub> ≠ <i>α</i><sub>2</sub>. Compared with previous results on the equation <i>p</i>(<i>z</i>)<i>f</i><sup>3</sup> + <i>q</i>(<i>z</i>)<i>f″</i> = − sin <i>α</i>(<i>z</i>) with polynomial coefficients, our results show that the coefficient of the term <i>f</i><sup>(<i>k</i>)</sup> perturbed by multiplying an exponential function will affect the structure of its solutions.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"103 - 114"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473073","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}
引用次数: 0
Multiple intersections of space-time anisotropic Gaussian fields 时空各向异性高斯场的多重交点
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0115-1
Zhenlong Chen, Weijie Yuan
{"title":"Multiple intersections of space-time anisotropic Gaussian fields","authors":"Zhenlong Chen,&nbsp;Weijie Yuan","doi":"10.1007/s10473-024-0115-1","DOIUrl":"10.1007/s10473-024-0115-1","url":null,"abstract":"<div><p>Let <i>X</i> = {<i>X</i>(<i>t</i>) ∈ ℝ<sup><i>d</i></sup>, <i>t</i> ∈ℝ<sup><i>N</i></sup>} be a centered space-time anisotropic Gaussian field with indices <i>H</i> = (<i>H</i><sub>1</sub>, ⋯, H<sub><i>N</i></sub>) ∈ (0, 1)<sup><i>N</i></sup>, where the components <i>X</i><sub><i>i</i></sub> (<i>i</i> = 1, ⋯, <i>d</i>) of <i>X</i> are independent, and the canonical metric <span>(sqrt {{{mathbb{E}({X_i}(t) - {X_i}(s))}^2}} ,(i = 1, cdots ,d))</span> is commensurate with <span>({gamma ^{{alpha _i}}}(sumlimits_{j = 1}^N {|{t_j} - {s_j}{|^{{H_j}}})} )</span> for <i>s</i> = (<i>s</i><sub>1</sub>, ⋯, <i>s</i><sub><i>N</i></sub>), <i>t</i> = (<i>t</i><sub>1</sub>, ⋯, <i>t</i><sub><i>N</i></sub>) ∈ ℝ<sup><i>N</i></sup>, <i>α</i><sub><i>i</i></sub> ∈ (0, 1], and with the continuous function <i>γ</i>(·) satisfying certain conditions. First, the upper and lower bounds of the hitting probabilities of <i>X</i> can be derived from the corresponding generalized Hausdorff measure and capacity, which are based on the kernel functions depending explicitly on γ (·). 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.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"275 - 294"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473074","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}
引用次数: 0
Interface behavior and decay rates of compressible Navier-Stokes system with density-dependent viscosity and a vacuum 具有密度依赖粘度和真空的可压缩Navier-Stokes体系的界面行为和衰减率
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0114-2
Zhenhua Guo, Xueyao Zhang
{"title":"Interface behavior and decay rates of compressible Navier-Stokes system with density-dependent viscosity and a vacuum","authors":"Zhenhua Guo,&nbsp;Xueyao Zhang","doi":"10.1007/s10473-024-0114-2","DOIUrl":"10.1007/s10473-024-0114-2","url":null,"abstract":"<div><p>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 <i>μ</i>(<i>ρ</i>) = <i>ρ</i><sup><i>α</i></sup> for any 0 &lt; α &lt; 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.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"247 - 274"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473279","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}
引用次数: 0
Some new identities of Rogers-Ramanujan type 罗杰斯-拉马努金型的几个新恒等式
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0106-2
Jing Gu, Zhizheng Zhang
{"title":"Some new identities of Rogers-Ramanujan type","authors":"Jing Gu,&nbsp;Zhizheng Zhang","doi":"10.1007/s10473-024-0106-2","DOIUrl":"10.1007/s10473-024-0106-2","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"129 - 142"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473254","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}
引用次数: 0
The Riemann problem for isentropic compressible Euler equations with discontinuous flux 具有不连续通量的等熵可压缩欧拉方程的黎曼问题
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0102-6
Yinzheng Sun, Aifang Qu, Hairong Yuan
{"title":"The Riemann problem for isentropic compressible Euler equations with discontinuous flux","authors":"Yinzheng Sun,&nbsp;Aifang Qu,&nbsp;Hairong Yuan","doi":"10.1007/s10473-024-0102-6","DOIUrl":"10.1007/s10473-024-0102-6","url":null,"abstract":"<div><p>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 <i>x = x</i>(<i>t</i>). We prove that this problem admits global Radon measure solutions for all kinds of initial data. The over-compressing condition on the discontinuity <i>x = x</i>(<i>t</i>) 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 <i>x = x</i>(<i>t</i>) + 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.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"37 - 77"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473278","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}
引用次数: 0
Aggregate special functions to approximate permuting tri-homomorphisms and permuting tri-derivations associated with a tri-additive ψ-functional inequality in Banach algebras 集合特殊函数以逼近Banach代数中与三加性ψ泛函不等式相关的置换三同态和置换三导数
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0117-z
Safoura Rezaei Aderyani, Azam Ahadi, Reza Saadati, Hari M. Srivastava
{"title":"Aggregate special functions to approximate permuting tri-homomorphisms and permuting tri-derivations associated with a tri-additive ψ-functional inequality in Banach algebras","authors":"Safoura Rezaei Aderyani,&nbsp;Azam Ahadi,&nbsp;Reza Saadati,&nbsp;Hari M. Srivastava","doi":"10.1007/s10473-024-0117-z","DOIUrl":"10.1007/s10473-024-0117-z","url":null,"abstract":"<div><p>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 <b><i>ψ</i></b>-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital <i>C</i>*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"311 - 338"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473316","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}
引用次数: 0
Classifications of Dupin hypersurfaces in Lie sphere geometry 李球几何中Dupin超曲面的分类
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0101-7
Thomas E. Cecil
{"title":"Classifications of Dupin hypersurfaces in Lie sphere geometry","authors":"Thomas E. Cecil","doi":"10.1007/s10473-024-0101-7","DOIUrl":"10.1007/s10473-024-0101-7","url":null,"abstract":"<div><p>This is a survey of local and global classification results concerning Dupin hypersurfaces in <i>S</i><sup><i>n</i></sup> (or <b>R</b><sup><i>n</i></sup>) 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 <i>S</i><sup><i>n</i></sup> (or <b>R</b><sup><i>n</i></sup>), are described in detail. The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"1 - 36"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473317","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}
引用次数: 1
The logarithmic Sobolev inequality for a submanifold in manifolds with asymptotically nonnegative sectional curvature 具有渐近非负截面曲率流形中的子流形的对数Sobolev不等式
4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-29 DOI: 10.1007/s10473-024-0110-6
Yuxin Dong, Hezi Lin, Lingen Lu
{"title":"The logarithmic Sobolev inequality for a submanifold in manifolds with asymptotically nonnegative sectional curvature","authors":"Yuxin Dong,&nbsp;Hezi Lin,&nbsp;Lingen Lu","doi":"10.1007/s10473-024-0110-6","DOIUrl":"10.1007/s10473-024-0110-6","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"44 1","pages":"189 - 194"},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138473336","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}
引用次数: 0
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