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?     

Multimode-ultrasound and microwave assisted natural ternary deep eutectic solvent sequential pretreatments for corn straw biomass deconstruction under mild conditions

Mild and effective pretreatments are essential to deconstruct lignocellulosic biomass so as to reuse cellulose content for value-added products. In this study, sequential multimode-ultrasound and microwave with natural ternary deep eutectic solvent (NATDES) pretreatments were used to deconstruct corn straw and optimized factors such as NATDES, ultrasonic, and microwave parameters. Results indicated that the ultrasound-NATDES or microwave-NATDES pretreatment could remove 37.86% and 52.36% lignin, respectively. When using sequential multimode-ultrasound and microwave assisted NATDES pretreatment, the delignification efficiency increased to 61.50%, and the cellulose content increased from 34.70% to 76.08%. In addition, the delignification of sequential multimode-ultrasound and microwave assisted NATDES pretreatment (under the mild conditions of microwave heating at 60 °C and 60 min) increased to 57.39%, and the cellulose content increased to 59.98%, too. This highlighted the effect of the combined ultrasound and microwave technology. Finally, the microstructural changes of mercury intrusion porosimeters, scanning electron microscopy, thermogravimetric, X-ray diffraction and Fourier transform mid-infrared spectroscopy were conducted to confirm the effectiveness of this method to deconstruct corn straw. A mechanism of the deconstruction of corn straw biomass in NATDES with the assistance of the sequential multimode-ultrasound and microwave heating was proposed. This research could open a window for future use of biomass energy by deconstructing lignocellulosic biomasses using environmentally friendly pretreatment methods.     

杂双子咪唑表面活性剂的合成及其表面性能

合成了一系列以两个亚甲基为联接基的杂双子咪唑表面活性剂([C_m-2-C_nim]Br_{2, m, n}=8, 10, 12, 14, 16; m≠n). 用氢谱和质谱对其结构进行了表征. 探索了物料比、反应温度和时间对反应产率的影响. 对合成的杂双子咪唑表面活性剂的表面活性进行了研究,讨论了分子结构的不对称程度对表面活性的影响.     

Numerical study of influence of molecular diffusion in the Mild combustion regime

In this paper, the importance of molecular diffusion versus turbulent transport in the moderate or intense low-oxygen dilution (Mild) combustion mode has been numerically studied. The experimental conditions of Dally et al. [Proc. Combust. Inst. 29 (2002) 1147–1154] were used for modelling. The EDC model was used to describe the turbulence–chemistry interaction. The DRM-22 reduced mechanism and the GRI 2.11 full mechanism were used to represent the chemical reactions of an H₂/methane jet flame. The importance of molecular diffusion for various O₂ levels, jet Reynolds numbers and H₂ fuel contents was investigated. Results show that the molecular diffusion in Mild combustion cannot be ignored in comparison with the turbulent transport. Also, the method of inclusion of molecular diffusion in combustion modelling has a considerable effect on the accuracy of numerical modelling of Mild combustion. By decreasing the jet Reynolds number, decreasing the oxygen concentration in the airflow or increasing H₂ in the fuel mixture, the influence of molecular diffusion on Mild combustion increases.     

Approximate necessary conditions for locally weak Pareto optimality

Necessary conditions for a given pointx ⁰ to be a locally weak solution to the Pareto minimization problem of a vector-valued functionF=(f ₁,...,f _m ),F:XR ^m,XR ^m, are presented. As noted in Ref. 1, the classical necessary condition-conv {Df ₁(x ⁰)|i=1,...,m}T ^*(X, x ⁰) need not hold when the contingent coneT is used. We have proven, however, that a properly adjusted approximate version of this classical condition always holds. Strangely enough, the approximation form>2 must be weaker than form=2.The authors would like to thank the anonymous referee for the suggestions which led to an improved presentation of the paper.     

Robust stabilization of uncertain linear dynamical systems with time-varying delay

In this paper, the problem of the robust stabilization for a class of uncertain linear dynamical systems with time-varying delay is considered. By making use of an algebraic Riccati equation, we derive some sufficient conditions for robust stability of time-varying delay dynamical systems with unstructured or structured uncertainties. In our approach, the only restriction on the delay functionh(t) is the knowledge of its upper boundh ^–. Some analytical methods are employed to investigate these stability conditions. Since these conditions are independent of the delay, our results are also applicable to systems with perturbed time delay. Finally, a numerical example is given to illustrate the use of the sufficient conditions developed in this paper.     

Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation

Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N ²log₂ N) andO(N ²log₂log₂ N) arithmetic operations, respectively.     

Robust stabilization for a class of uncertain dynamical systems with time delay

In this paper, a new and simple approach whereby we derive several sufficient conditions on robust stabilizability for a class of uncertain dynamical systems with time delay is presented. Some analytical methods and the Bellman-Gronwall inequality are employed to investigate these sufficient conditions. The notable features of the results obtained are their simplicity in testing the stability of uncertain dynamical systems with time delay and their clarity in giving insight into system analysis. Finally, several numerical examples are given to demonstrate the utilization of the results.The authors would like to acknowledge the many helpful comments provided by the reviewer. Particularly, in the light of these comments, the proof of Theorem 3.1 has been considerably shortened.     

Dynamic complexity of optimal paths and discount factors for strongly concave problems

We study the relationship between the dynamical complexity of optimal paths and the discount factor in general infinite-horizon discrete-time concave problems. Given a dynamic systemx _t+1=h(x _t ), defined on the state space, we find two discount factors 0 < ^{* **} < 1 having the following properties. For any fixed discount factor 0 < < ^*, the dynamic system is the solution to some concave problem. For any discount factor ^** < < 1, the dynamic system is not the solution to any strongly concave problem. We prove that the upper bound ^** is a decreasing function of the topological entropy of the dynamic system. Different upper bounds are also discussed.This research was partially supported by MURST, National Group on Nonlinear dynamics in Economics and Social Sciences. The author would like to thank two anonymous referees for helpful comments and suggestions.     

开边界条件的Hubbard模型的精确解

量子杂质模型总是与边界条件有很深的联系,低维材料已经成为研究一维可解模型的动力之源.本文将研究一般形式的Hubbard模型,并推广到带有开边界条件的情况.