Size-dependent vibration and buckling of porous functionally graded microplates based on modified couple stress theory in thermal environments by considering a dual power-law distribution of scale effects

In this study,the thermodynamic behaviors of the intrinsic frequency and buckling temperature of rectangular plates of functionally graded materials(FGMs)are explored based on the modified couple stress theory(MCST)and the novel dual powerlaw scale distribution theory.The effects of linear,homogeneous,and non-homogeneous temperature fields on the frequency and buckling temperature of FGM microplates are evaluated in detail.The results show that the porosity greatly affects the mechanical properties of FGM plates,reducing their frequency and flexural temperature compared with non-porous plates.Different temperature profiles alter plate frequencies and buckling temperatures.The presence and pattern of scale effect parameters are also shown to be crucial for the mechanical response of FGM plates.The present research aims to provide precise guidelines for the micro-electro-mechanical system(MEMS)fabrication by elucidating the complex interplay between thermal,material,and structural factors that affect the performance of FGM plates in advanced applications.

The Effectiveness of the Squared Error and Higgins-Tsokos Loss Functions on the Bayesian Reliability Analysis of Software Failure Times under the Power Law Process

Reliability analysis is the key to evaluate software’s quality. Since the early 1970s, the Power Law Process, among others, has been used to assess the rate of change of software reliability as time-varying function by using its intensity function. The Bayesian analysis applicability to the Power Law Process is justified using real software failure times. The choice of a loss function is an important entity of the Bayesian settings. The analytical estimate of likelihood-based Bayesian reliability estimates of the Power Law Process under the squared error and Higgins-Tsokos loss functions were obtained for different prior knowledge of its key parameter. As a result of a simulation analysis and using real data, the Bayesian reliability estimate under the Higgins-Tsokos loss function not only is robust as the Bayesian reliability estimate under the squared error loss function but also performed better, where both are superior to the maximum likelihood reliability estimate. A sensitivity analysis resulted in the Bayesian estimate of the reliability function being sensitive to the prior, whether parametric or non-parametric, and to the loss function. An interactive user interface application was additionally developed using Wolfram language to compute and visualize the Bayesian and maximum likelihood estimates of the intensity and reliability functions of the Power Law Process for a given data.

The Impact Analysis of New Company Law on Foreign Invested Enterprise Law

In this paper, the impact of the new company law on foreign-funded enterprise law are analyzed. Firstly. the foreign investment enterprise law is summarized, followed by a detailed introduction of the impact of the new company law and foreign-invested enterprise law . Finally. Impact on the Law of Foreign Investment Enterprises. From these researches, it is concluded thai the promotion of the new company law on the relationship between FIEs and some suggestions for the coexistence of the two.

The Impact Analysis of New Company Law on Foreign Invested Enterprise Law

In this paper, the impact of the new company law on foreign-funded enterprise law are analyzed. Firstly, the foreign investment enterprise law is summarized, followed by a detailed introduction of the impact of the new company law and foreign-invested enterprise law. Finally, Impact on the Law of Foreign Investment Enterprises. From these researches, it is concluded that the promotion of the new company law on the relationship between FIEs and some suggestions liar the coexistence of the lwo.

F-rough law and the discovery of rough law

By using function one direction S-rough sets （function one direction singular rough sets）, this article presents the concepts of F-law, F-rough law, and the relation metric of rough law; by using these concepts, this article puts forward the theorem of F-law relation metric, two orders theorem of F-rough law relation metric, the attribute theorem of F-rough law band, the extremum theorem of F-rough law relation metric, the discovery principle of F-rough law and the application of F-rough law.

Function P-sets and Mining-discovery Theorems of Unknown Information Law

Function P-sets are a set pair which are composed of function internal packetsets S F and function outer packet sets S F or (S F , S F ) are function P-sets. Function P-sets have dynamic characteristics and law characteristics. Based on function P-sets, P-information law discovery theorems which has attribute supplementing-deleting are given. Mining-discovery and mining-discovery theorems of unknown information law are proposed. Function P-sets are a new theory and new method to research dynamic information laws for information systems.

Pointwise Estimates on Travelling Wave Solution of the Scalar Viscous Conservation Laws

This paper research on the pointwise behavior of perturbations from a viscous shock solution to a scalar viscous conservation law by introducing an approximate Green’s function. The authors obtain not only the pointwise decay of the perturbation and but also the high derivative of it. Stability in anyL(p≥1) norm is a direct consequence.

Study on the Size Distribution and Similarity Law of Bubble Nuclei in Water

To study the distribution characteristics and similarity laws of nuclei under different pressures,based on the selfdesigned decompression chamber and the acoustic measuring system,the size distributions of nuclei in the degassed tap water under negative ambient pressures were measured.A number density distribution function of nuclei based on the modified Weibull distribution function was proposed and verified by the experimental measurement results and some published data of nuclei size distribution.Based on this nuclei number density distribution function,the similarity law of the nuclei size distribution was analyzed:in the scale experiment,the value of exponential in the similarity law of the nuclei number density should be determined by the nuclei size distribution of the water in the prototype experiment and the actual nuclei size distribution of the water in the model experiment.And a precondition is that the nuclei size distributions are similar.

The Equilibrium of Fractional Derivative and Second Derivative: The Mechanics of a Power-Law Visco-Elastic Solid

This paper investigates the equilibrium of fractional derivative and 2nd derivative, which occurs if the original function is damped (damping of a power-law viscoelastic solid with viscosities η of 0 ≤ η ≤ 1), where the fractional derivative corresponds to a force applied to the solid (e.g. an impact force), and the second derivative corresponds to acceleration of the solid’s centre of mass, and therefore to the inertial force. Consequently, the equilibrium satisfies the principle of the force equilibrium. Further-more, the paper provides a new definition of under- and overdamping that is not exclusively disjunctive, i.e. not either under- or over-damped as in a linear Voigt model, but rather exhibits damping phases co-existing consecutively as time progresses, separated not by critical damping, but rather by a transition phase. The three damping phases of a power-law viscoelastic solid—underdamping, transition and overdamping—are characterized by: underdamping—centre of mass oscillation about zero line;transition—centre of mass reciprocation without crossing the zero line;overdamping—power decay. The innovation of this new definition is critical for designing non-linear visco-elastic power-law dampers and fine-tuning the ratio of under- and overdamping, considering that three phases—underdamping, transition, and overdamping—co-exist consecutively if 0 < η < 0.401;two phases—transition and overdamping—co-exist consecutively if 0.401 < η < 0.578;and one phase— overdamping—exists exclusively if 0.578 < η < 1.

A LAW OF THE ITERATED LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY FUNCTION

Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f(n) for general case of d greater-than-or-equal-to 1, which gives the exact pointwise strong convergence rate of f(n).

A Comparative Analysis of the Introduction of Travel Company In China and South America

The introduction of Travel Company is a mirror which can display the culture of Travel Company and it is crucial when travelers make a choice. In order to make a better understanding of different introductions under different cultures, an analysis has been made between the introductions of two travel companies in China and South America respectively from the perspective of systemic-functional grammar(SFG).

On the Criminal Protection of the Right to Education of Chinese Citizens——With a Review on Article 32 of the Amendment to the Criminal Law(Ⅺ)

The Amendment(Ⅺ)to the Criminal Law of the People’s Republic of China responds to the institutional needs of civic education,and supplements the clause of the Criminal Law on protection of citizens’right to education nuy means of Article 32.Imposing legal responsibility in the form of internal punishments,administrative punishments,and economic compensation have failed to prevent infringements on citizens’right to education.Its role as a"secondary protection law"is the conceptual obstacle that hinders the Criminal Law from effectively intervening in the field of citizens’right to education.The equivalence between the legal interests of people to the right to education and the rights protected by the existing charges in the Criminal Law is the legitimate basis for it to intervene in disputes over the right to education.Based on Article 32 of the Amendment(Ⅺ)to the Criminal Law of the People’s Republic of China,it is suggested to further clarify the prepositional law,improve the liability provisions for the right to education,change the modest and restrained view of the Criminal Law regarding protection of the right to education,and expand the behavior types of Article 32 provided in the Amendment(Ⅺ)in due time.

Motoyosi Sugita—A “Widely Unknown” Japanese Thermodynamicist Who Explored the 4th Law of Thermodynamics for Creation of the Theory of Life

The purpose of this paper is to introduce to you, the Western people, nowadays a “widely unknown” Japanese thermodynamicist by the name of Motoyosi Sugita and his study on the thermodynamics of transient phenomena and his theory of life. This is because although he was one of the top theoretical physicists in Japan before, during and after WWII and after WWII he promoted the establishment of the biophysical society of Japan as one of the founding members, he himself and his studies themselves have seemed to be totally forgotten nowadays in spite that his study was absolutely important for the study of life. Therefore, in this paper I would like to present what kind of person he was and what he studied in physics as a review on the physics work of Motoyosi Sugita for the first time. I will follow his past studies to introduce his ideas in theoretical physics as well as in biophysics as follows: He proposed the bright ideas such as the quasi-static change in the broad sense, the virtual heat, and the field of chemical potential etc. in order to establish his own theory of thermodynamics of transient phenomena, as the generalization of the Onsager-Prigogine’s theory of the irreversible processes. By the concept of the field of chemical potential that acquired the nonlinear transport, he was seemingly successful to exceed and go beyond the scope of Onsager and Prigogine. Once he established his thermodynamics, he explored the existence of the 4th law of thermodynamics for the foundation of theory of life. He applied it to broad categories of transient phenomena including life and life being such as the theory of metabolism. He regarded the 4th law of thermodynamics as the maximum principle in transient phenomena. He tried to prove it all life long. Since I have recently found that his maximum principle can be included in more general maximum principle, which was known as the Pontryagin’s maximum principle in the theory of optimal control, I would like to explain such theories produced by Motoyosi Sugita as detailed as possible. And also I have put short history of Motoyosi Sugita’s personal life in order for you to know him well. I hope that this article helps you to know this wonderful man and understand what he did in the past, which was totally forgotten in the world and even in Japan.

Noether symmetries of discrete mechanico-electrical systems

This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electricM systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange-Maxwell equations, the discrete analogue of Noether theorems for Lagrange Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results.

Corrections to the scaling of the second-order structure function in isotropic turbulence

The approach of Obukhov assuming a constant skewness was used to obtain analytical corrections to the scaling of the second order structure function, starting from Kolmogorov＇s 4/5 law. These corrections can be used in model applications in which explicit expressions, rather than numerical solutions are needed. The comparison with an interpolation formula proposed by Batchelor, showed that the latter gives surprisingly precise results. The modification of the same method to obtain analytical corrections to the scaling law, taking into account the possible corrections induced by intermittency, is also proposed.

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.

A Numerical Verification of Self-Similar Multiplicative Theory for Small-Scale Atmospheric Turbulent Convection

The self-similar multiplicative theory(SSM theory), aims to interpret the scaling behavior of the temperature structure function. In the present paper, the author report results from a numerical simulation of atmospheric turbulent convection in order to verify this theory. The simulation was based on a shell model which was deduced from simplified atmospheric convection equations. The numerical results agreed well with the theory prediction of scaling law from the first order to the eighth order. They also showed that the prediction of this theory was better than that given by the Kolmogorov's theory in 1941, log-normal, and β model theories.

Tensile Shock Physics in Compressible Thermoviscoelastic Solid Medium

This paper addresses tensile shock physics in thermoviscoelastic (TVE) solids without memory. The mathematical model is derived using conservation and balance laws (CBL) of classical continuum mechanics (CCM), incorporating the contravariant second Piola-Kirchhoff stress tensor, the covariant Green’s strain tensor, and its rates up to order n. This mathematical model permits the study of finite deformation and finite strain compressible deformation physics with an ordered rate dissipation mechanism. Constitutive theories are derived using conjugate pairs in entropy inequality and the representation theorem. The resulting mathematical model is both thermodynamically and mathematically consistent and has closure. The solution of the initial value problems (IVPs) describing evolutions is obtained using a variationally consistent space-time coupled finite element method, derived using space-time residual functional in which the local approximations are in hpk higher-order scalar product spaces. This permits accurate description problem physics over the discretization and also permits precise a posteriori computation of the space-time residual functional, an accurate measure of the accuracy of the computed solution. Model problem studies are presented to demonstrate tensile shock formation, propagation, reflection, and interaction. A unique feature of this research is that tensile shocks can only exist in solid matter, as their existence requires a medium to be elastic (presence of strain), which is only possible in a solid medium. In tensile shock physics, a decrease in the density of the medium caused by tensile waves leads to shock formation ahead of the wave. In contrast, in compressive shocks, an increase in density and the corresponding compressive waves result in the formation of compression shocks behind of the wave. Although these are two similar phenomena, they are inherently different in nature. To our knowledge, this work has not been reported in the published literature.

Function S-rough Sets and Their Law Characteristic

Function S-rough sets(Function Singular rough sets) are defined by R-function equivalence class which has dynamic characteristic, and a function is s law, function S-rough sets have law characteristic. Function S-rough sets has these forms: function one direction S-rough sets, function two direction S-rough sets and dual of function one direction S-rough sets. This paper presents the law characteristic of function one direction S-rough sets and puts forward the theorems of law-chain-attribute and law-belt. Function S-rough sets is s new research direction of the rough sets theory.

Minority Protection in Proceedings for the Settlement of Disputes Between Shareholders

“A limited company is more than a mere judicial entity, with a personality in law of its own： Behind it, or amongst it, there are individuals, with rights, expectations and obligations inter se”. The competitive attitude of the member states of the EU （European Union）, to become the most attractive for companies results in law reforms aiming at more flexible conflict between shareholders. Besides, the economic objective of avoiding a company＇s dissolution, the English, Dutch, and Belgian exit proceedings for the settlement of disputes between shareholders set up a social objective： protecting the interests of the minority shareholder of a private limited company. The paper consists of four chapters. The introduction lays out the necessity of buy-outs for shareholders of a private limited company. The first chapter describes the different facts justifying the buy-out of a shareholder on the basis of serious grounds. The second chapter presents the findings of a comparative research of the valuation of the shares transferred in an English, Dutch, and Belgian procedure. Finally, the conclusion summarises in which way the English, Dutch, and Belgian legal system protect the interests of the minority shareholder of a private limited company.