We study the large time behavior of solutions of scalar conservation laws with periodic initial data. Under a very weak nonlinearity condition,we prove that the solutions converge to constants as time tends to infinit...We study the large time behavior of solutions of scalar conservation laws with periodic initial data. Under a very weak nonlinearity condition,we prove that the solutions converge to constants as time tends to infinity. Our results improve the earlier ones since we only require the flux to be nonlinear at the mean value of the initial data.展开更多
In this paper, we use Lax-Oleinik formula to study the asymptotic behavior for the initial problem of scalar conservation law u_t + F(u)_x = 0. First, we prove a simple but useful property of Lax-Oleinik formula(Lemma...In this paper, we use Lax-Oleinik formula to study the asymptotic behavior for the initial problem of scalar conservation law u_t + F(u)_x = 0. First, we prove a simple but useful property of Lax-Oleinik formula(Lemma 2.7). In fact, denote the Legendre transform of F(u) as L(σ), then we can prove that the quantity F(q)-′qF(q) + L(′F(q)) is a constant independent of q. As a simple application, we first give the solution of Riemann problem without using of Rankine-Hugoniot condition and entropy condition. Then we study the asymptotic behavior of the problem with some special initial data and prove that the solution contains only a single shock for t > T~*. Meanwhile, we can give the equation of the shock and an explicit value of T~*.展开更多
System behavior description using states faces problems like state explosion, lack of clear definition of state, state identification and coordination between multiple agents. The goals of this work are to ease design...System behavior description using states faces problems like state explosion, lack of clear definition of state, state identification and coordination between multiple agents. The goals of this work are to ease design activity, to reduce engineering efforts, and to mitigate project risks. The proposed way is to improve information flow during design by adding definitions and some protocols or rules for communicating a specification or design description. This work presented an objective definition of system status (way of interaction with the rest of the world) along other concepts. This work focused in definitions as mind entities and their importance to rationalize work and mitigate project risks during design. This article presented some simple examples to illustrate the advantages of each aspect of proposed definition of system status and discussed limits and exceptions for such definition. The key finding was the proposed definition which was the simplest while keeping completeness at a given product breakdown level. Such definition of status enforced formal segregation of needs and solutions, and eased the inclusion of behavior definition in specifications.展开更多
Taking into account the fact that the computer systems, as the implementations of Turing machine, are physical devices, the paper shows considerations in which hard drive behavior will be presented in terms of statist...Taking into account the fact that the computer systems, as the implementations of Turing machine, are physical devices, the paper shows considerations in which hard drive behavior will be presented in terms of statistical mechanics. Because computer is a machine, its analysis cannot be based only on mathematical models apart of physical conditions. In the paper it will be presented a very narrow part this problem – an analysis of hard drive behavior in the context of the power-law distributions. We will focus only on four selected hard drive parameters, i.e. the rate of transfer bytes to or from the disk during the read or write, the number of pending requests to the disk and the rate of read operations. Our research was performed under the Windows operating system and this allows to make a statistical analysis for the possible occurrence of power-laws representing the lack of characteristic scale for considered processes. This property will be confirmed in all analyzed cases. A presented study can help describing the behavior of the whole computer system in terms of physics of computer processing.展开更多
At present,the legal remedies in terms of the right to equal employment in China are mainly related to private law,that is,laborers seek direct legal remedies for personality rights liability and infringement liabilit...At present,the legal remedies in terms of the right to equal employment in China are mainly related to private law,that is,laborers seek direct legal remedies for personality rights liability and infringement liability according to typical private law,supplemented by indirect remedies for labor contract liability under special private law.However,there are many challenges in private law remedies for the right to equal employment,which are manifested in the misunderstanding of the general tort identification of employment discrimination,the loopholes in the regulations on discriminatory employment,the imbalance in the burden of proof,and the limitation and alienation of the functions of civil liability and private law autonomy.The root of those problems lies in the fact that the nature of anti-employment discrimination law is not private law but social law.Equal employment involves both public and private interests,and it should be based on the public interest of society and adhere to the value orientation of prioritizing fairness while taking into account efficiency.Improving the legal relief mechanism for protecting the right to equal employment,with a focus on correcting private law with social law,is the solution to the dilemma.Specific measures include establishing the special tort liability system for equal employment,the legal mechanism against discriminatory labor contracts,the public-private integrated legal responsibility system,and an essentially fair system for the responsibility of adducing evidence.展开更多
文摘We study the large time behavior of solutions of scalar conservation laws with periodic initial data. Under a very weak nonlinearity condition,we prove that the solutions converge to constants as time tends to infinity. Our results improve the earlier ones since we only require the flux to be nonlinear at the mean value of the initial data.
基金supported in part by NSFC(11671193)the Fundamental Research Funds for the Central Universities(NE2015005)supported in part by NSFC(11271182 and 11501290)
文摘In this paper, we use Lax-Oleinik formula to study the asymptotic behavior for the initial problem of scalar conservation law u_t + F(u)_x = 0. First, we prove a simple but useful property of Lax-Oleinik formula(Lemma 2.7). In fact, denote the Legendre transform of F(u) as L(σ), then we can prove that the quantity F(q)-′qF(q) + L(′F(q)) is a constant independent of q. As a simple application, we first give the solution of Riemann problem without using of Rankine-Hugoniot condition and entropy condition. Then we study the asymptotic behavior of the problem with some special initial data and prove that the solution contains only a single shock for t > T~*. Meanwhile, we can give the equation of the shock and an explicit value of T~*.
文摘System behavior description using states faces problems like state explosion, lack of clear definition of state, state identification and coordination between multiple agents. The goals of this work are to ease design activity, to reduce engineering efforts, and to mitigate project risks. The proposed way is to improve information flow during design by adding definitions and some protocols or rules for communicating a specification or design description. This work presented an objective definition of system status (way of interaction with the rest of the world) along other concepts. This work focused in definitions as mind entities and their importance to rationalize work and mitigate project risks during design. This article presented some simple examples to illustrate the advantages of each aspect of proposed definition of system status and discussed limits and exceptions for such definition. The key finding was the proposed definition which was the simplest while keeping completeness at a given product breakdown level. Such definition of status enforced formal segregation of needs and solutions, and eased the inclusion of behavior definition in specifications.
文摘Taking into account the fact that the computer systems, as the implementations of Turing machine, are physical devices, the paper shows considerations in which hard drive behavior will be presented in terms of statistical mechanics. Because computer is a machine, its analysis cannot be based only on mathematical models apart of physical conditions. In the paper it will be presented a very narrow part this problem – an analysis of hard drive behavior in the context of the power-law distributions. We will focus only on four selected hard drive parameters, i.e. the rate of transfer bytes to or from the disk during the read or write, the number of pending requests to the disk and the rate of read operations. Our research was performed under the Windows operating system and this allows to make a statistical analysis for the possible occurrence of power-laws representing the lack of characteristic scale for considered processes. This property will be confirmed in all analyzed cases. A presented study can help describing the behavior of the whole computer system in terms of physics of computer processing.
基金the research result of the Scientific Research Fund Project(supported by the Special Funds for Basic Scientific Research for Central Universities)of Renmin University of China,“Research on Solving the Dilemma of Private Law Relief for the Right to Equal Employment in Social Law”(Project Approval No.21XNH019)。
文摘At present,the legal remedies in terms of the right to equal employment in China are mainly related to private law,that is,laborers seek direct legal remedies for personality rights liability and infringement liability according to typical private law,supplemented by indirect remedies for labor contract liability under special private law.However,there are many challenges in private law remedies for the right to equal employment,which are manifested in the misunderstanding of the general tort identification of employment discrimination,the loopholes in the regulations on discriminatory employment,the imbalance in the burden of proof,and the limitation and alienation of the functions of civil liability and private law autonomy.The root of those problems lies in the fact that the nature of anti-employment discrimination law is not private law but social law.Equal employment involves both public and private interests,and it should be based on the public interest of society and adhere to the value orientation of prioritizing fairness while taking into account efficiency.Improving the legal relief mechanism for protecting the right to equal employment,with a focus on correcting private law with social law,is the solution to the dilemma.Specific measures include establishing the special tort liability system for equal employment,the legal mechanism against discriminatory labor contracts,the public-private integrated legal responsibility system,and an essentially fair system for the responsibility of adducing evidence.
