Normal approximation and fourth moment theorems for monochromatic triangles

Given a graph sequence denote by T₃(G_n) the number of monochromatic triangles in a uniformly random coloring of the vertices of G_n with colors. In this paper we prove a central limit theorem (CLT) for T₃(G_n) with explicit error rates, using a quantitative version of the martingale CLT. We then relate this error term to the well-known fourth-moment phenomenon, which, interestingly, holds only when the number of colors satisfies . We also show that the convergence of the fourth moment is necessary to obtain a Gaussian limit for any , which, together with the above result, implies that the fourth-moment condition characterizes the limiting normal distribution of T₃(G_n), whenever . Finally, to illustrate the promise of our approach, we include an alternative proof of the CLT for the number of monochromatic edges, which provides quantitative rates for the results obtained in [7].     

热光伏能量转换器件的热力学极限与优化性能预测

受不可逆损失的影响,热光伏能量转换器件在高品位热能回收与利用方面受到限制.本文揭示不可逆损失来源,提供热光伏能量转换器件性能提升方案.利用半导体物理和普朗克热辐射理论,确定热光伏能量转换器件在理想条件下的最大效率.进而考虑Auger与Shockley-Reed-Hall非辐射复合和不可逆传热损失对光伏电池的电学、光学和热学特性的影响,预测热光伏器件优化性能.确定功率密度、效率和光子截止能量的优化区间.结果表明:相比于理想热光伏器件,非理想热光伏器件的开路电压、短路电流密度和效率有所降低;优化热光伏电池电压、光子截止能量和热源温度,可提升器件的功率密度和效率.通过对比发现理论与实验结果较一致,所得结果可为实际热光伏能量转换器件的研制提供理论指导.     

Limit theorems for a class of critical superprocesses with stable branching

We consider a critical superprocess $\{X;{\mathbf{P}}_{\mu }\}$ with general spatial motion and spatially dependent stable branching mechanism with lowest stable index ${\gamma }_0>1$. We first show that, under some conditions, ${\mathbf{P}}_{\mu }(\left|X_t\right|\ne 0)$ converges to 0 as $t\to \infty$ and is regularly varying with index ${({\gamma }_0-1)}^{-1}$. Then we show that, for a large class of non-negative testing functions $f$, the distribution of $\{X_t\left(f\right);{\mathbf{P}}_{\mu }\left(\cdot \right|6X_{t}6\ne 0)\}$, after appropriate rescaling, converges weakly to a positive random variable ${\mathbf{z}}^{({\gamma }_0-1)}$ with Laplace transform $E\left[e^{-u{\mathbf{z}}^{({\gamma }_0-1)}}\right]=1-{(1+u^{-({\gamma }_0-1)})}^{-1∕({\gamma }_0-1)}.$     

Zero dissipation limit to rarefaction wave with vacuum for the one-dimensional non-isentropic micropolar equations

The zero dissipation limit of the one-dimensional non-isentropic micropolar equations is studied in this paper. If the given rarefaction wave which connects to vacuum at one side, a sequence of solution to the micropolar equations can be constructed which converge to the above rarefaction wave with vacuum as the viscosity and the heat conduction coefficient tend to zero. Moreover, the uniform convergence rate is obtained. The key point in our analysis is how to control the degeneracies in the vacuum region in the zero dissipation limit process.     

Study of the performances of an oxygen carrier: Experimental investigation of the binder's contribution and characterization of its structural modifications

The aim of this work is to investigate the contribution of the binder (NiAl₂O₄) on the performances of the oxygen carrier NiO/NiAl₂O₄. To this purpose, oxidation/reduction cycles have been performed in a fixed bed reactor using CO as a fuel. The results reveal that the binder can react with the fuel to form CO₂, and that its total reduction capacity increases with temperature. XRD characterizations performed on the binder (on the fresh and after several cycles) show a shift of the diffraction peaks of NiAl₂O₄ toward the ones of γ-alumina, which can be attributed to a progressive decomposition of NiAl₂O₄ to alumina and NiO.     

循环孔隙水压下混凝土常规三轴压缩损伤破坏特性分析

本文进行了孔隙水压不同循环次数(0次,10次,50次,100次和200次)以及不同应变速率下(10~(-5)/s,10~(-4)/s,10~(-3)/s和10~(-2)/s)混凝土常规三轴压缩试验,分析了混凝土峰值应变的变化规律、应力-应变曲线及损伤特性。结果表明:相同循环次数孔隙水压下,峰值应变随应变速率增加,整体呈现出增加的趋势;而相同应变速率下,峰值应变随孔隙水压循环次数的变化规律并不明显;在中低应变速率(10~(-5)~10~(-3)/s)下,混凝土的损伤变化受孔隙水压循环次数影响较大;当循环次数达到200次时,孔隙水压作用对混凝土产生较大的损伤。通过对循环孔隙水作用下混凝土动态损伤破坏机理的分析可知:混凝土的破坏过程实际上是内部裂纹不断形成、扩展、贯通,材料损伤不断产生、累积的过程;当损伤达到一定程度,混凝土发生宏观破坏,失去承载力。     

Controlling Decoherence Speed Limit of a Single Impurity Atom in a Bose–Einstein‐Condensate Reservoir

The decoherence speed limit (DSL) of a single impurity atom immersed in a Bose‐Einstein‐condensed (BEC) reservoir when the impurity atom is in a double‐well potential is studied. It is demonstrated how the DSL of the impurity atom can be manipulated by engineering the BEC reservoir and the impurity potential within experimentally realistic limits. It is shown that the DSL can be controlled by changing key parameters such as the condensate scattering length, the effective dimension of the BEC reservoir, and the spatial configuration of the double‐well potential imposed on the impurity. The physical mechanisms of controlling the DSL at root of the spectral density of the BEC reservoir are uncovered.