Convergence of an augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints

An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Löwner operator associated with a potential function for the optimization problems with inequality constraints. The favorable properties of both the Löwner operator and the corresponding augmented Lagrangian are discussed. And under some mild assumptions, the rate of convergence of the augmented Lagrange algorithm is studied in detail.     

A generalization of Carleman's uniqueness theorem and a discrete Phragmén-Lindelöf theorem

Let be a Borel measure on and be its moments. T. Carleman found sharp conditions on the magnitude of for to be uniquely determined by its moments. We show that the same conditions ensure a stronger property: if are the moments of another measure, with then the measure is supported on the interval This result generalizes both the Carleman theorem and a theorem of J. Mikusi\'{n}ski. We also present an application of this result by establishing a discrete version of a Phragmén-Lindelöf theorem.

     

Pre-B?tzinger复合体的从簇到峰放电的同步转迁及分岔机制

Pre-Bötzinger复合体是兴奋性耦合的神经元网络,通过产生复杂的放电节律和节律模式的同步转迁参与调控呼吸节律.本文选用复杂簇和峰放电节律的单神经元数学模型构建复合体模型,仿真了与生物学实验相关的多类同步节律模式及其复杂转迁历程,并利用快慢变量分离揭示了相应的分岔机制.当初值相同时,随着兴奋性耦合强度的增加,复合体模型依次表现出完全同步的“fold/homoclinic”,“subHopf/subHopf”簇放电和周期1峰放电.当初值不同时,随耦合强度增加,表现为由“fold/homoclinic”,到“fold/fold limit cycle”、到“subHopf/subHopf”与“fold/fold limit cycle”的混合簇放电、再到“subHopf/subHopf”簇放电的相位同步转迁,最后到反相同步周期1峰放电.完全(同相)同步和反相同步的周期1节律表现出了不同分岔机制.反相峰同步行为给出了与强兴奋性耦合容易诱发同相同步这一传统观念不同的新示例.研究结果给出了preBötzinger复合体的从簇到峰放电节律的同步转迁规律及复杂分岔机制,反常同步行为丰富了非线性动力学的内涵.     

非线性边界条件下拟线性瞬态方程组的Phragmén-Lindelöf型二择一结果

考虑了一类定义在三维半无穷柱体上的拟线性方程组，其中假设方程的解在柱体的有限端和侧面满足非齐次条件。定义了“能量”表达式，通过限制非线性项，利用微分不等式技术， 推导了一阶微分不等式，解此不等式得到二择一结果，即证明了“能量”随与有限端距离的增大要么呈指数式（多项式）增加，要么呈指数式（多项式）衰减。同时，在衰减情形下得到了全能量的上界。     

Theoretical investigation on optical properties of Möbius carbon nanobelts in one- and two-photon absorption

The first successful synthesis of fully fused and fully conjugated Möbius carbon nanobelts (CNBs) has attracted considerable attention. However, theoretical calculations based on such π-conjugated Möbius CNB are still insufficient. Herein, we theoretically investigated molecular spectroscopy of Möbius CNBs without and with n-butoxy groups via visualization methods. The results show that the presence of n-butoxy groups can significantly affect Möbius CNBs’ optical performance, changing electron-hole coherence and enhancing two-photon absorption cross-sections. Our work provides a deeper understanding of photophysical mechanisms of Möbius CNBs in one- and two-photon absorption and reveals possible applications on optoelectronic devices.     

Phragmén-Lindel(o)f and continuous dependence type results in a Stokes flow

This paper investigates the asymptotic behavior of end effects for a Stokes flow defined on a three-dimensional semi-infinite cylinder.With homogeneous Dirichlet conditions of the velocity on the lateral surface of the cylinder,solutions either grow or decay exponentially in the distance from the finite end of the cylinder.In the case of decay,the effect of perturbing the equation parameters is also investigated.     

On the asymptotic behavior of solutions of quasilinear elliptic equations

The asymptotic behavior of solutions of second-order quasilinear elliptic and nonhyperbolic partial differential equations defined on unbounded domains inR ⁿ contained in\(\{ x_1 ,...,x_n :\left| {x_n } \right|< \lambda \sqrt {x_1^2 + ...x_{n - 1}^2 } \) for certain sublinear functions λ is investigated when such solutions satisfy Dirichlet boundary conditions and the Dirichlet boundary data has appropriate asymptotic behavior at infinity. We prove Phragmèn-Lindelöf theorems for large classes of nonhyperbolic operators, without «lower order terms”, including uniformly elliptic operators and operators with well-definedgenre, using special barrier functions which are constructed by considering an operator associated to our original operator. We also estimate the rate at which a solution converges to its limiting function at infinity in terms of properties of the top order coefficienta _nn of the operator and the rate at which the boundary values converge to their limiting function; these results are proven using appropriate barrier functions which depend on the behavior of the coefficients of the operator and the rate of convergence of boundary values.