Canonical Ensemble with Temperature Limitation

Ideal Bose and Fermi systems are studied on the basis of a canonical ensemble, subject to the condition that their temperature is less than a given temperature T_max. A single new parameter (the tau-parameter, τ) is needed to keep account of the new constraint. The parameter τ is shown to be the exponential of a pseudo-chemical potential that is linearly dependent on temperature. The inclusion of the τ- parameter leads to generalizations of usual thermodynamic quantities (internal energy, heat capacity and entropy) and various particular cases are discussed. The heat capacity of a Bose system can exhibit a maximum at a temperature less than the maximum temperature T_max. The number of micro-states in the canonical ensemble is found to increase with τ. The heat capacity c_V of a Fermi system of non-interacting spins exhibits a Schottky anomaly. The peak depends on τ, and for some cases c_V/k can significantly exceed unity. The influence of τ on the entropy of the Fermi system and on the number of micro-states in the canonical ensemble is significant but not spectacular.     

Simulation of general three-body interactions in a nuclear magnetic resonance ensemble quantum computer

Three-body interaction plays an important role in many-body physics, and quantum computer is efficient in simulating many-body interactions. We have experimentally demonstrated the general three-body interactions in a three-qubit nuclear magnetic resonance ensemble quantum computer. Using a nuclear magnetic resonance computer we implemented general forms of three-body interactions including σ _x ¹ σ _z ² σ _x ³ and σ _x ¹ σ _z ² σ _y ³ The results show good agreement between theory and experiment. We have also given a concise and practical formula for a general n-body interaction in terms of one-and two-body interactions. Supported by the National Natural Science Foundation of China (Grant Nos. 10374010 and 10325521) and the National Basic Research Program of China (Grant No. 2006CB921106)     

国债发行与国民经济发展关系的定量研究

改革开发以来,中国国债发行规模逐年扩大,国债已影响到了国民经济的各个层面.国债发行规模适度问题已成为国债研究的中心问题.影响我国国债发行规模的最主要因素是什么?怎样度量中国国债的适度规模?这些问题已引起理论界的广泛注意,但迄今未有定论.本文采用现代经济计量及统计分析方法,对国债发行与国民经济发展之间的关系进行了定量分析,得出国债发行对国民经济发展的积极推动作用.希望所得结论能对国债规模管理提供参考.本文是以"实际数据蕴涵着规律"观点为基础,从三方面定量探索了国债发行与国民经济发展的关系.     

A new approach for the justification of ensembles in quantum statistical mechanics — II

The results of the first paper in this series are generalized to include spin, permutation symmetry, and time dependence. In particular, the question of time invariance of localness in the Heisenberg picture is discussed and it is conjectured that an operator that is initially local will remain local over time. In order to treat macroscopic systems, it is shown that the ensemble decomposition of the previous paper can be used to coarsegrain configuration space. Finally, a physical interpretation of the ensemble decomposition in terms of redundant macroscopic information is used to give a derivation of the generalized microcanonical average.This work was supported in part by research grants from the National Science Foundation and the U.S. Public Health Service. Some of the material in this paper is contained in a doctoral dissertation submitted by the author to the University of Oregon (1969).     

基于RNN-CNN集成深度学习模型的PM2.5小时浓度预测

针对目前大部分PM_2.5预测模型预测效果不稳定、泛化能力不强的现状,以记忆能力较强的循环神经网络（RNN）和特征表达能力较强的卷积神经网络（CNN）为基础,采取Stacking集成策略对两者进行融合,提出了RNN-CNN集成深度学习预测模型。该模型不仅充分利用时间轴上的前后关联信息去预测未来的浓度,而且在不同层次上将自动提取的高维时序数据通用特征用于预测,以保证预测结果的稳定性。最后,对集成之前的RNN、CNN和集成之后的RNN-CNN模型,以2016年中国大陆地区1 466个监测站点的空气质量数据为样本进行实例验证,结果表明,RNN-CNN在PM_2.5时间序列预测上的表现明显优于集成之前的RNN和CNN,而且泛化误差更低,在34%站点上的拟合度超过0.97,该模型可用于大范围区域的PM_2.5小时浓度预测。     

Computer-oriented approach to the ensemble theory

Computer simulation of the ensemble behavior of large interacting systems is hampered by the relative paucity of low-energy configurations. The stochastic sampling must, therefore, be guided toward the capture of configurations which, though rare, aretypical, in the sense of contributing the maximum term of the partition function, Max log . In a previous Monte Carlo study by the author, such a guidance was applied to anab initio construction of lattice configurations with a stochastic chain of steps, the transition probability at each step depending of both near and far neighbors. This study is now put on a more systematic and broader basis. It is argued that any computer study of the emergence of long-range order in large systems must be guided by Max log . Thus, lattice configurations are often constructed by a cyclic variation, which, guided by nearest-neighbor interaction, tries to relax an arbitrary initial configuration toward equilibrium (Metropolis). Such a relaxation may be also guided by Max log , with transition probabilities dependent on both near and far neighbors. Of main interest is the relevance of such a calculation for the actual relaxation behavior of the system, and this is discussed at some length.     

Tensor product composition of algebras in Bose and Fermi canonical formalism

We consider a graded algebra with two products (σ, α) over anε-factor commutation. One of the products (σ) isε-commutative, but, in general non-associative; and the other (α) is a graded Lieε-product and a gradedε-derivative with respect to the first (σ). Using the obvious mathematical condition, namely—the tensor product of two graded algebras with the sameε-factors is another with the sameε-factor, we determine the complete structure of a two-product (σ, α) graded algebra. When theε-factors are taken to be unity and the gradation structure is ignored, we recover the algebras of the physical variables of classical and quantum systems, considered by Grgin and Petersen. With the retention of the gradation structure and the possible choice of two ε-factors we recover the algebras of the canonical formalism of boson and fermion systems for the above classical and quantum theories. We also recover in this case the algebra of anticommutative classical systems considered by Martin along with its quantum analogue.     

Evaluation of anion selectivity in protic media by squaramide-Cresol Red ensembles

A new series of positively charged squaramide-ammonium compounds 1-6 bind sulfate and hydrogen phosphate in ethanol-water mixtures by a combination of electrostatic and hydrogen bonding interactions. A sensing ensemble composed of Cresol Red and an squaramide receptor signals the association events of these anions. Competitive experiments in ethanol-water mixtures (9:1) reveal a moderate selectivity for sulfate over hydrogen phosphate and suggest that squaramide 4, featuring an intermediate distance between squaramide subunits, is better suited for complexation of sulfate.     

Phase behavior of C60 by computer simulation using ab‐initio interaction potential

A first‐principles intermolecular potential recently proposed by Pacheco and Ramalho [Phys Rev Lett 1997, 79, 3873–3876] has been used with the Gibbs ensemble and Gibbs–Duhem integration Monte Carlo methods to simulate the vapor–liquid and fluid–solid coexistence properties of C₆₀. The critical properties were calculated by fitting the results to the laws of rectilinear diameters and order parameter scaling. The triple‐point properties were determined from the limiting behavior of the Gibbs ensemble vapor–liquid simulations at the lowest temperature range. A stable liquid phase is predicted for temperatures between 1570±20 and 2006±27 K and densities between 0.444±0.003 and 1.05±0.01 nm^?3. The estimated critical and triple‐point pressures are, respectively, 35±6 and 5±16 bars. We show for the first time, to our knowledge, that it is possible, strictly by computer simulation, to estimate a triple point for C₆₀ in accordance with the predictions of theoretical methods and the basic concepts of thermodynamics. The liquid and fluid radial distribution functions indicate the presence of solid or glasslike features. This may support the suggestion of a more cooperative interaction of clusters in C₆₀. A comparison of our results with the data obtained by other authors is presented and discussed. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 375–387, 2001