When null energy condition meets ADM mass

We give a conjecture on the lower bound of the ADM mass M by using the null energy condition. The conjecture includes a Penrose-like inequality $3M\geqslant \kappa { \mathcal A }/(4\pi )+\sqrt{{ \mathcal A }/4\pi }$ and the Penrose inequality $2M\geqslant \sqrt{{ \mathcal A }/4\pi }$ with ${ \mathcal A }$ the event horizon area and κ the surface gravity. Both the conjecture in the static spherically symmetric case and the Penrose inequality for a dynamical spacetime with spherical symmetry are proved by imposing the null energy condition. We then generalize the conjecture to a general dynamical spacetime. Our results raise a new challenge for the famous unsettled question in general relativity: in what general case can the null energy condition replace other energy conditions to ensure the Penrose inequality?     

Riemann-Hilbert approach and N double-pole solutions for a nonlinear Schrödinger-type equation

We investigate the inverse scattering transform for the Schrödinger-type equation under zero boundary conditions with the Riemann-Hilbert (RH) approach. In the direct scattering process, the properties are given, such as Jost solutions, asymptotic behaviors, analyticity, the symmetries of the Jost solutions and the corresponding spectral matrix. In the inverse scattering process, the matrix RH problem is constructed for this integrable equation base on analyzing the spectral problem. Then, the reconstruction formula of potential and trace formula are also derived correspondingly. Thus, N double-pole solutions of the nonlinear Schrödinger-type equation are obtained by solving the RH problems corresponding to the reflectionless cases. Furthermore, we present a single double-pole solution by taking some parameters, and it is analyzed in detail.     

Long-time asymptotics and the radiation condition with time-periodic boundary conditions for linear evolution equations on the half-line and experiment

The asymptotic Dirichlet-to-Neumann (D-N) map is constructed for a class of scalar, constant coefficient, linear, third-order, dispersive equations with asymptotically time/periodic Dirichlet boundary data and zero initial data on the half-line, modeling a wavemaker acting upon an initially quiescent medium. The large time $t$ asymptotics for the special cases of the linear Korteweg-de Vries and linear Benjamin–Bona–Mahony (BBM) equations are obtained. The D-N map is proven to be unique if and only if the radiation condition that selects the unique wave number branch of the dispersion relation for a sinusoidal, time-dependent boundary condition holds: (i) for frequencies in a finite interval, the wave number is real and corresponds to positive group velocity, and (ii) for frequencies outside the interval, the wave number is complex with positive imaginary part. For fixed spatial location $x$, the corresponding asymptotic solution is (i) a traveling wave or (ii) a spatially decaying, time-periodic wave. The linearized BBM asymptotics are found to quantitatively agree with viscous core-annular fluid experiments.     

保存条件对大鼠海马组织总RNA质量的影响

从大鼠海马组织提取总RNA后,测定了不同时间和温度下保存及3次循环冻融后RNA的浓度和纯度,并分析了其完整性;探讨了保存时间、保存温度及反复冻融对大鼠海马组织总RNA质量的影响.结果表明,不同条件下保存及冻融3次后RNA浓度较首次检测值均有所降低,4℃下保存60d标本中的RNA浓度明显低于对照组(P<0.05),其他组未见显著性差异;各组RNA的OD 260/OD280在1.8～2.0之间.在-20℃和-70℃下分别保存30d和60d,以及24h冻融3次后的样品RNA的完整性较好;但4℃下保存的两组样品的RNA发生分解.RNA在4℃和-20℃下分别保存30d和60d后,相应的RE[(不同条件下保存后的样品浓度-初始浓度)/初始浓度]值均大于15%,而-70℃下保存30d、60d以及在24h内冻融3次后的RE值均小于15%.据此可知,大鼠海马组织总RNA样品可在-70℃下保存60d,反复冻融3次后总RNA质量基本不变.     

Raman Microspectroscopic study of Iberian pottery from the La Vispesa archaeological site,Spain

Raman microspectroscopy has been employed for the characterization of 16 samples of ancient Iberian pottery. These sherds of vessels were found in the archaeological site of La Vispesa in Tamarite de Litera (Huesca, Spain) and correspond to the Iberian time. The composition of certain mineral phases such as non‐plastic inclusions has been particularly considered with a view to obtaining information on the source materials and their provenance, as well as the technological conditions of ceramic production. Typical minerals such as calcite and quartz were found in most of the samples. The presence of anatase in a group of the samples suggested the use of different clays in the production of the vessels. Furthermore, the absence of rutile in these samples, together with the identification of calcite, is indicative of a mild firing temperature. Hematite was identified in all samples, both in the ceramic body and in the decoration. Differences in the position of the bands and relative intensities characterized hematite in terms of crystallinity and origin. An attempt to assign the samples to different production centers was made according to their chemical composition and morphology. Copyright © 2011 John Wiley & Sons, Ltd.     

A note on the compactness of the index set in convex optimization. Application to metric regularity

We consider the linear quadratic optimal control problem in the infinite time horizon case for a class of discrete-time systems controlled by a continuous inputs. We show that, under certain hypothesis, the Hilbert uniqueness method can be used to determine the optimal control.     

Infinite horizon multiobjective optimal control problems in the discrete time case

This article studies multiobjective optimal control problems in the discrete time framework and in the infinite horizon case. The functions appearing in the problems satisfy smoothness conditions. This article generalizes to the multiobjective case results obtained for single-objective optimal control problems in that framework. The dynamics are governed by difference equations or difference inequations. Necessary conditions of Pareto optimality are presented, namely Pontryagin maximum principles in the weak form and in the strong form. Sufficient conditions are also provided. Other notions of Pareto optimality are defined when the infinite series do not necessarily converge.     

Understanding linear semi-infinite programming via linear programming over cones

In this article, the standard primal and dual linear semi-infinite programming (DLSIP) problems are reformulated as linear programming (LP) problems over cones. Therefore, the dual formulation via the minimal cone approach, which results in zero duality gap for the primal–dual pair for LP problems over cones, can be applied to linear semi-infinite programming (LSIP) problems. Results on the geometry of the set of the feasible solutions for the primal LSIP problem and the optimality criteria for the DLSIP problem are also discussed.     

Application of the method of multipliers to state space constrained optimal control problems with discrete time

The paper deals with convergence conditions of multiplier algorithms for solving optimal control problems with discrete time suggested by J. Bjbvonek in some earlier papers. In this approach the original state space constrained problem is converted into a control-constrained problem by introducing an additional control variable and an equality constraint which is taken into consideration by a multiplier method. Convergence conditions for the multiplier Iteration of global and local nature are given for exact and inexact solution of the subproblems.