Hidden Symmetries for Thermodynamics and Emergence of Relativity

Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity. Though this is a beautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many other problems. In this article I will comment on some of the problems of Verlinde＇s proposal with special emphasis on the thermodynamical origin of the principle of relativity. It is found that there is a large group of hidden symmetries of thermodynamics, which contains the Poincare group of the spacetime for which space is emergent. This explains the thermodynamic origin of the principle of relativity.     

First-Principles Calculations of Atomic and Electronic Properties of T1 and In on Si（111）

The atomic and electronic structures of T1 and In on Si（111） surfaces are investigated using the firstprinciples total energy calculations. Total energy optimizations show that the energetically favored structure is 1/3 ML T1 adsorbed at the T4 sites on Si（111） surfaces. The adsorption energy difference of one T1 adatom between （√3 × √3） and （1 × 1） is less than that of each In adatom. The DOS indicates that TI 6p and Si 3p electrons play a very important role in the formation of the surface states. It is concluded that the bonding of TI adatoms on Si（111） surfaces is mainly polar covalent, which is weaker than that of In on Si（111）. So T1 atom is more easy to be migrated than In atom in the same external electric field and the structures of T1 on Si（111） is prone to switch between （√3 × √3） and （1 × 1）.     

Surface Structure and Electronic Property of InP（001）-（2×1）S Surface： A First-Principles Study

The surface structure and electronic property of InP（001）-（2 ×1）S surface under S-rich condition are investigated based on first-principles simulations. The analyses of phase transition show that the 3B model is the most stable structure and the S-S dimer is difficult to form. The geometry of the 3B structure agrees well with the experiments. It is also found that the 3B structure has a good passivation with a band gap of about 1.24eV. The results indicate that the 3B structure is the best candidate for the sulfur-rich InP（001）（2 × 1）A phase.     

Band Structures of Metal-Oxide Capped Graphene： A First Principles Study

We perform a first-principles calculation based on density functional theory to investigate the interface between single layer graphene and metal oxides. Our study reveals that the monolayer graphene becomes semiconducting by single crystal SiO2 and Al2O3 contact, with energy gaps to - 0.9 and - 1.8 eV, respectively. We find the gap originates from the breakage of π bond integrity, whose extent is related to the interface atom configuration. We believe that our results highlight a promising direction for the feasibility to apply large scale graphene layers as building blocks in future electronics devices.     

First-Principles Study of Electronic and Optical Properties of Y1-xCaxTiO3 （x=0, 0.25, 0.5, 0.75）

The full potential linearized augmented plane wave （FP-LAPW） method with the generalized gradient approximation （GGA） is applied to study the electronic and optical properties of perovskite-type compounds Y1-xCaxTiO3. The lattice parameters, magnetic moment, band structure, density of states and optical conductivity are obtained. The results show that the Ca ion plays an important role in the electronic properties and optical responses. Moreover, the optical properties including the dielectric function, absorption spectrum, extinction coefficient, energy-loss spectrum and refractive index are also discussed.     

Mindlin中厚板的辛求解方法

在Mindlin板混合能函数的基础上,通过引入混合变量及对混合能变分原理的修正,在全状态下建立了Mindlin板的Hamilton正则方程,进而采用直接法给出了两对边简支板的解析解,并通过具体例题说明了方法的有效性．     

AN EFFICIENT METHOD FOR MULTIOBJECTIVE OPTIMAL CONTROL AND OPTIMAL CONTROL SUBJECT TO INTEGRAL CONSTRAINTS

We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a ＂budget＂ remaining to satisfy each constraint; the augmented Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our approach hinges on the causality in that PDE, i.e., the monotonicity of characteristic curves in one of the newly added dimensions. A semi-Lagrangian ＂marching＂ method is used to approximate the discontinuous viscosity solution efficiently. We compare this to a recently introduced ＂weighted sum＂ based algorithm for the same problem [25]. We illustrate our method using examples from flight path planning and robotic navigation in the presence of friendly and adversarial observers.     

偶数维空间耗散波动方程解的衰减估计

研究偶数维空间带粘性的波动方程柯西问题解的逐点估计.通过对格林函数的精细分析,得到解的大时间状态.解呈现出惠更斯现象.     

A-调和方程很弱解的比较原理

应用McShane扩张定理证明了A-调和方程很弱解的比较原理.这个结果可以看作经典弱解比较原理的一个扩展.     

Dirichlet零边值问题的正解存在性

由于一些本质困难,N=3被称为具Sobolev临界指数2*的Dirichlet问题-△u=λu+|u|2*-2u,x∈ΩRN;u(x)0,x∈Ω;u=0,x∈Ω的临界维数.众所周知,N=3时,上述问题存在古典(正)解的一个充分条件是Ω为R3上的小球以及14λ1λλ1.本文考虑Ω是R3中更一般的有界光滑区域,得出了一正解存在性结论,从而肯定了沈尧天在文中提及的一个未解决的问题.