Zipf’s Law, Benford’s Law, and Pareto Rule

From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that Benford’s distribution fits to calculate the rank probabilities of distinguishable objects. i.e. in the distribution of words in long texts all the words in a given rank are identical, therefore, the rank distribution is Zipfian. In logarithmic tables, the objects with identical 1st digits are distinguishable as there are many different digits in the 2nd, 3rd… places, etc., and therefore the distribution is according to Benford’s law. Pareto 20 - 80 rule is shown to be an outcome of Benford’s distribution as when the number of ranks is about 10 the probability of 20% of the high probability ranks is equal to the probability of the rest of 80% low probability ranks. It is argued that all these distributions, including the central limit theorem, are outcomes of Planck’s law and are the result of the quantization of energy. This argumentation may be considered a physical origin of probability.

ENTRANCE LAWS FOR DAWSON-WATABE SUPERPROCESSES WITH NONLOCAL BRANCHING

This paper proves a 1-1 correspondence between minimal probability entrance laws for the superprocess and entrance laws for its underlying process. From this the author deduces that an infinitely divisible probability entrance law for the superprocess is uniquely determined by an infinitely divisible probability measure on the space of the underlying entrance laws. Under an additional condition, a characterization is given for all entrance laws for the superprocess, generalizing the results of Dynkin (1989). An application to immigration processes is also discussed.

Entropy Analysis of Vapor-Compression Refrigeration System by Using the Second Law of Thermodynamics

By means of the Second Law of Thermodynamics,thispaper gives out the entropy analysis method for vapor-comperession refrigeration system.The thermal irrevers-ibility of the system charged with R12 and its hopeful al-ternative refrlgerant R134a have been studied respective-ly.On the basis of all the research results of this paper,the measure used to save energy for vapor-compressionrefrigeration system has been put out.

Preliminary Study on Water Demand Law of 1-0 Rooted Cuttings of Populus szechuanica

In order to provide theoretical basis and technical support for the afforestation and artificial water supply of P.szechuanica in arid areas,the characteristics of water consumption of P.szechuanica were explored,and the law of water demand of P.szechuanica was grasped.In this paper,potted seedlings of 1-0 rooted cuttings of P.szechuanica were taken as research objects,and change situation of water consumption under different water control gradients was measured regularly by using weighing method,further analyzing dynamic change of water consumption of P.szechuanica and revealing water demand law of 1-0 rooted cuttings of P.szechuanica.The results showed that total change of water consumption of 1-0 rooted cuttings of P.szechuanica had"slow-fast-slow-fast"double-peak trend in the growth period of the current year,and corresponded with univariate linear relation(R^(2)=0.7137),with significant difference.In whole growth period,water consumption in August was the highest,which was 2.7 times of that in June and July and 1.5 times of that after September.In different water control treatments,the dynamic changes of daily and monthly water consumption were significantly different.In seven water control treatments,monthly water consumption was between(6315.95±1690.70)and(10105.28±3065.30)g/month,and mean was(8211.07±2308.23)g/month.With intensification of water control treatment,water consumption increased,but there was no seedling death due to water shortage.P.szechuanica has great plasticity in water demand,and can survive in both arid and humid environments.Meanwhile,it is revealed that P.szechuanica is the most widely distributed tree species in the region.

On the Current Situation of Basic - level Administrative Law Enforcement in China

With the development of economy and society, our country is on the road of rule by law, the legal system is progressing constantly. At the same time, we should also see that the administration according to law is not perfect, and its shortcomings exist in different degree and need to be further improved. Based on the analysis of the status quo of grass-roots administrative law enforcement in China, this paper tries to put forward corresponding countermeasures, so as to promote the work of law-based administration for the corresponding study.

LAW AND LUXURY IN AUGUSTAN ROME (TACITUS, ANNALS 3.53-4)

Introduction: Tacitus on Law and Luxury'quid enim primum prohibere et priscum ad morem recidere adgrediar? villarumne infinita spatia? familiarum numerum et nationes? argenti et auri pondus? aeris tabularumque miracula? promiscas viris et feminis vestis atque illa feminarum propria,

Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems

Scaling is an important measure of multi-scale fluctuation systems. Turbulence as the most remarkable multi-scale system possesses scaling over a wide range of scales. She-Leveque （SL） hierarchical symmetry, since its publication in 1994, has received wide attention. A number of experimental, numerical and theoretical work have been devoted to its verification, extension, and modification. Application to the understanding of magnetohydrodynamic turbulence, motions of cosmic baryon fluids, cosmological supersonic turbulence, natural image, spiral turbulent patterns, DNA anomalous composition, human heart variability are just a few among the most successful examples. A number of modified scaling laws have been derived in the framework of the hierarchical symmetry, and the SL model parameters are found to reveal both the organizational order of the whole system and the properties of the most significant fluctuation structures. A partial set of work related to these studies are reviewed. Particular emphasis is placed on the nature of the hierarchical symmetry. It is suggested that the SL hierarchical symmetry is a new form of the self-organization principle for multi-scale fluctuation systems, and can be employed as a standard analysis tool in the general multi-scale methodology. It is further suggested that the SL hierarchical symmetry implies the existence of a turbulence ensemble. It is speculated that the search for defining the turbulence ensemble might open a new way for deriving statistical closure equations for turbulence and other multi-scale fluctuation systems.

Analytical solution for the time-fractional heat conduction equation in spherical coordinate system by the method of variable separation

In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system.The method of variable separation is used to solve the timefractional heat conduction equation.The Caputo fractional derivative of the order 0 〈 α≤ 1 is used.The solution is presented in terms of the Mittag-Leffler functions.Numerical results are illustrated graphically for various values of fractional derivative.

Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

This work studies large deflections of slen- der, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed con- tinuous load and a concentrated load at the free end of the beam. The material of the cantilever is assumed to be non- linearly elastic. Different nonlinear relations between stress and strain in tensile and compressive domain are considered. The accuracy of numerical solutions is evaluated by com- paring them with results from previous studies and with a laboratory experiment.

O(t^(-β))-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS

This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical perturbations.By designing a state feedback control law and a new kind of fractional order Lyapunov functional,a new set of algebraic sufficient conditions are derived to guarantee the O(t^(-β))Synchronization and asymptotic synchronization of the considered FBAMNNs model;this can easily be evaluated without using a MATLAB LMI control toolbox.Finally,two numerical examples,along with the simulation results,illustrate the correctness and viability of the exhibited synchronization results.

Oxidation of Al_2O_3-30%TiCN-0.2%Y_2O_3 Composite

The oxidation behavior of Al2O3-30%TiCN-0.2%Y2O3 composite and its effect on high temperature bending strength was studied. The result indicates that the mass gain during static oxidation of the material under normal atmosphere follows the parabolic law. Oxide increases with increasing temperature and prolonging time. It has good oxidation resistance. The product of oxidation of the material is TiO2. Therefore, the volume of the material expands. The oxide film is destroyed because residual stress inside the oxide film is released. Proper oxidation is beneficial to the improvement of bending strength of Al2O3-30%TiCN-0.2%Y2O3 composite. The strength increase is up to 4.5%.

On the Caginalp for a Conserve Phase-Field with a Polynomial Potentiel of Order 2<i>p</i>- 1

Our aim in this paper is to study on the Caginalp for a conserved phase-field with a polynomial potentiel of order 2p - 1. In this part, one treats the conservative version of the problem of generalized phase field. We consider a regular potential, more precisely a polynomial term of the order 2p - 1 with edge conditions of Dirichlet type. Existence and uniqueness are analyzed. More precisely, we precisely, we prove the existence and uniqueness of solutions.

气象观测场在汽车试验场中的应用研究

汽车试验场作为汽车开展道路测试的重要场所,用于验证汽车产品的品质以及可靠性。除了场地道路外,气象条件作为汽车道路测试的重要一环,在《GB/T12534-1990汽车道路试验方法通则》中也有明确要求,如:试验时应是无雨无雾天气,相对湿度小于95%,气温0-40℃,风速不大于3m/s。同时气象条件也作为试验场道路管控的重要依据,实时风速、雨量、能见度等信息为场地管理者发布限速、限行、封场等通知提供必要参考依据,直接影响道路测试安全管控的及时性。因此,文章从气象观测场的建设、气象服务、异常天气道路管控等方面开展气象观测场在汽车试验场中的应用研究。

CONVERGENCERATESIN THESTRONG LAWSOFASYMPTOTICALLY NEGATIVELY ASSOCIATEDRANDOM FIELDS

In this paper, a notion of negative side ρ \|mixing ( ρ\+- \|mixing) which can be regarded as asymptotic negative association is defined, and some Rosenthal type inequalities for ρ\+- \|mixing random fields are established. The complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are also discussed for ρ\+-\| mixing random fields. The results obtained extend those for negatively associated sequences and ρ\+*\| mixing random fields.

An improved constrained steering law for SGCMGs with DPC

An improved constrained （IC） steering law for single gimbal control moment gyros （SGCMGs） with deformed pyramid configuration （DPC） is proposed, First of all, the original system with five pyramid configuration （FPC） whose two adjacent gyros are in failure state is reconfigured as a degraded system with DPC. Then, the singular angular momentum hypersurfaces of the original and the degraded systems are plotted via the singular angular momentum equa- tion of SGCMGs. Based on singular surfaces, the differences between FPC and DPC in singularity and momentum envelope are obtained directly, which provide an important reference for steering law design of DPC. Finally, an IC steering law is designed and applied to DPC. The simulation results demonstrate that the IC steering law has advantages in simplicity of calculation, avoidance of singularity and exactness of output torque, which endow the degraded system with fine controllability in a restricted workspace.

D^+→η(′)l+ν_l semileptonic decays in light-cone sum rules

We calculate the D → η transition form factor in light-cone sum rules by taking improved current correlators to avoid the pollution from the twist-3 wave function. We get consistent results of the D＋ → η^（＇）l＋νl decays with the experimental data. By comparing the difference between the results of the branching ratios of D＋ → η^（＇）l＋νl from a two-pole parameterization model and from a BZ parameterization model, we find that the two-pole model and the BZ model are comparably believable. One way is supposed for the determination of the η-η mixing angle from the dependence of the branching ratios of D＋ → η^（＇）l＋νl decays on the η-η mixing angle.

基于灰度—梯度共生矩阵的植被提取方法

在灰度共生矩阵的基础上融入梯度信息,提出灰度—梯度共生矩阵模型,再结合Laws纹理能量测度算法对植被进行提取,得到了较好的实验结果,可应用于遥感影像中的植被监测。

“入世”与南京外向型经济的发展

Nanjing’s Opening - outside Economy have made great progress, but there is stilla long distance to the rules of WTO. After China’s entering WTO, the local governments and enterprises must follow the rules of WTO. This paper gives eight suggestions and strategies aimedly with an objective analysis of Nanjing’s shortages in the opening -outside economy.

AN ADAPTIVE CONTROL STRATEGY FOR PROPER MESH DISTRI-BUTION IN LARGE EDDY SIMULATION

The Filtering Grid Scale （FGS） of sub-grid scale models does not match with the theoretical Proper FGS （PFGS） because of the improper mesh. Therefore, proper Large Eddy Simulation （LES） Mesh is very decisive for better results and more economical cost. In this work, the purpose is to provide an adaptive control strategy for proper LES mesh with turbulence theory and CFD methods. A new expression of PFGS is proposed on the basis of -5/3 law of inertial sub-range and the proper mesh of LES can be built directly from the adjustment of RANS mesh. A benchmark of the backward facing step flow at Re = 5147 is provided for application and verification. There are three kinds of mesh sizes, including the RANS mesh, LAM （LES of adaptive-control mesh）, LFM （LES of fine mesh）, employed here. The grid number of LAM is smaller than those of LFM evidently, and the results of LAM are in a good agreement with those of DNS and experiments. It is revealed that the results of LAM are very close to those of LFM. The conclusions provide positive evidences for the novel strategy.

Effect of Water Deficit on Self-thinning Line in Spring Wheat （Triticum aestivum L.） Populations

Monocultures of spring wheat （Triticum aestivum L.） were grown at overcrowded densities （10 000 and 3 000 plants per m^2） under well-watered and water-stressed conditions to investigate the effects of water deficits on self-thinning. The results showed that density reduction in water-stressed populations was delayed compared with that In well-watered populations. Populations grown In well-watered conditions conformed to the -3/2- power law. Compared with the well-watered condition, there was no significant decrease of the self-thinning line under water-stressed conditions In this experiment, although the rate of average shoot blomass accumulatlon decreased. This result Implied that the exponent of the -3/2-power equation Is not as sensitive as the rate of average shoot blomass accumulation to water stress. Further analysis indicated that, In each density treatment, the lines of the height versus shoot blomass relationships did not differ significantly between the two water conditions. However, the Intercepts of the height versus shoot blomass relationships were greater In the higher-density populations （10 000/m^2） than those In the lower-density populations （3 000/m^2）. These results showed that water deficit did not change plant geometry In this experiment. That Is to say, shoot competition for light remains constant at a given blomass, although root competition for water becomes more serious In water deficit conditions. Based on these results and previous reports we propose that, to affect the thinning line slope, changes In symmetric competition are not as efficient as changes In asymmetric competition.