In the background of the Internet economy,a new type of intellectual property,namely,network intellectual property,has been born.It is based on the traditional intellectual property rights such as copyright and indust...In the background of the Internet economy,a new type of intellectual property,namely,network intellectual property,has been born.It is based on the traditional intellectual property rights such as copyright and industrial property,and broadens the intellectual property rights in the network environment to include areas such as databases,multimedia,electronic copyrights and computer software.This not only greatly enriches the scope of intellectual property rights,but also intensifies the risk of intellectual property infringement.In the context of the network economy,intellectual property protection faces new challenges and requirements.It has also attracted great attention from countries and international intellectual property organisations.They have conducted in-depth studies on the problems faced by intellectual property rights in the era of network economy and actively sought effective solutions to establish a complete and systematic intellectual property rights protection system to alleviate the pressure on intellectual property rights protection brought about by the complexity of the situation.In the context of network economy,IP protection faces new challenges and requirements.This has also attracted great attention from national and international IP organisations.They have conducted in-depth studies on the problems faced by IP in the era of network economy and actively sought effective solutions to establish a complete and systematic IP protection system to alleviate the pressure of IP protection brought about by complex situations.展开更多
We solve the Riemann problems for isentropic compressible Euler equations of polytropic gases in the class of Radon measures,and the solutions admit the concentration of mass.It is found that under the requirement of ...We solve the Riemann problems for isentropic compressible Euler equations of polytropic gases in the class of Radon measures,and the solutions admit the concentration of mass.It is found that under the requirement of satisfying the over-compressing entropy condition:(i)there is a unique delta shock solution,corresponding to the case that has two strong classical Lax shocks;(ii)for the initial data that the classical Riemann solution contains a shock wave and a rarefaction wave,or two shocks with one being weak,there are infinitely many solutions,each consists of a delta shock and a rarefaction wave;(iii)there are no delta shocks for the case that the classical entropy weak solutions consist only of rarefaction waves.These solutions are self-similar.Furthermore,for the generalized Riemann problem with mass concentrated initially at the discontinuous point of initial data,there always exists a unique delta shock for at least a short time.It could be prolonged to a global solution.Not all the solutions are self-similar due to the initial velocity of the concentrated point-mass(particle).Whether the delta shock solutions constructed satisfy the over-compressing entropy condition is clarified.This is the first result on the construction of singular measure solutions to the compressible Euler system of polytropic gases,that is strictly hyperbolic,and whose characteristics are both genuinely nonlinear.We also discuss possible physical interpretations and applications of these new solutions.展开更多
To professionally plan and manage the development and evolution of the Internet of Things(IoT),researchers have proposed several IoT performance measurement solutions.IoT performance measurement solutions can be very ...To professionally plan and manage the development and evolution of the Internet of Things(IoT),researchers have proposed several IoT performance measurement solutions.IoT performance measurement solutions can be very valuable for managing the development and evolution of IoT systems,as they provide insights into performance issues,resource optimization,predictive maintenance,security,reliability,and user experience.However,there are several issues that can impact the accuracy and reliability of IoT performance measurements,including lack of standardization,complexity of IoT systems,scalability,data privacy,and security.While previous studies proposed several IoT measurement solutions in the literature,they did not evaluate any individual one to figure out their respective measurement strengths and weaknesses.This study provides a novel scheme for the evaluation of proposed IoT measurement solutions using a metrology-coverage evaluation based on evaluation theory,metrology principles,and software measurement best practices.This evaluation approach was employed for 12 IoT measure categories and 158 IoT measurement solutions identified in a Systematic Literature Review(SLR)from 2010 to 2021.The metrology coverage of these IoT measurement solutions was analyzed from four perspectives:across IoT categories,within each study,improvement over time,and implications for IoT practitioners and researchers.The criteria in this metrology-coverage evaluation allowed for the identification of strengths and weaknesses in the theoretical and empirical definitions of the proposed IoT measurement solutions.We found that the metrological coverage varies significantly across IoT measurement solution categories and did not show improvement over the 2010–2021 timeframe.Detailed findings can help practitioners understand the limitations of the proposed measurement solutions and choose those with stronger designs.These evaluation results can also be used by researchers to improve current IoT measurement solution designs and suggest new solutions with a stronger metrology base.展开更多
With the rapid development of electrical automation system, the factors that affect its internal operation safety are gradually increasing. Relevant professionals should make use of the rational use of relay protectio...With the rapid development of electrical automation system, the factors that affect its internal operation safety are gradually increasing. Relevant professionals should make use of the rational use of relay protection devices to strengthen the professional control of the system, and effectively solve the problems encountered. After clarifying the working principle of such devices, the application scope of relay protection devices can be effectively enhanced. Next, the article focuses on the analysis of influencing factors and solutions of relay protection safety of electrical automation system.展开更多
Elevator is widely used in high-rise buildings, which is a common means of transportation and brings great convenience to peoples lives. In the daily operation of elevators, the speed limiter plays a very important ro...Elevator is widely used in high-rise buildings, which is a common means of transportation and brings great convenience to peoples lives. In the daily operation of elevators, the speed limiter plays a very important role. For example, the speed limiter can protect the elevator from speeding or rope breaking in the running process. Therefore, the inspection of the speed limiter is directly related to the safe operation of the elevator, so it is very important to inspect the speed limiter of the elevator. However, there are often many problems in the actual elevator speed limiter inspection work, which requires the relevant personnel to conduct in-depth research and analysis, and put forward corresponding solutions to ensure the safe operation of the elevator.展开更多
Driven by social economy and science and technology, centralized accounting emerges at the historic moment, and its characteristics of "three separate and one open" meet the current market demand and develop...Driven by social economy and science and technology, centralized accounting emerges at the historic moment, and its characteristics of "three separate and one open" meet the current market demand and development needs. State-owned enterprises need new driving forces and new ideas in adapting to the new era, so as to better fit the market and obtain new growth opportunities. Centralized accounting is one of the key points of financial management. In order to ensure the quality of work, it is necessary to ensure the accuracy and integrity of information data first, and then combine with modern management concept to provide impetus for the development of contemporary state-owned enterprises. State-owned enterprises in the process of financial accounting, by establishing a perfect accounting concentration accounting information system, implement the financial management level of state-owned enterprises, but at present accounting information management of the enterprise and the financial department accounting aspects there are still many problems, in this paper, the problems that exist in the state-owned enterprises accounting concentration accounting application again was summarized and analyzed, and tries to seek for the corresponding solutions, strive to the centralized accounting can be successfully implemented and play the due utility.展开更多
With the development of the socialist market economy, a large number of civil engineering projects are emerging in China. This is not only the result of the improvement of China's scientific and technological leve...With the development of the socialist market economy, a large number of civil engineering projects are emerging in China. This is not only the result of the improvement of China's scientific and technological level, but also a great help to improve people's quality of life. However, in recent years, adverse events have frequently occurred in the construction site management of civil engineering in our country, which makes people pay more and more attention to them. In the new era, how to better manage the construction site of civil engineering is something we should explore. This paper is divided into five parts: The first part gives a brief overview of the construction of migrant workers. The second part discusses the significance of strengthening on-site construction management of civil engineering. The third part tells the importance of construction management of civil engineering. The fourth part analyzes the problems existing in the construction management of civil engineering construction site at the present stage. The fifth part puts forward the measures to strengthen the construction management of civil engineering site based on the problem analysis.展开更多
At present, there are still many problems in the specific treatment of industrial sewage in our country. In order to enhance the treatment quality of industrial sewage, relevant sewage treatment units should pay atten...At present, there are still many problems in the specific treatment of industrial sewage in our country. In order to enhance the treatment quality of industrial sewage, relevant sewage treatment units should pay attention to improving the treatment level of environmental engineering sewage, strengthening the standardization of sewage treatment market system and strengthening the innovation of sewage management form. Based on the characteristics of industrial wastewater treatment, reasonable and effective treatment strategies are applied to effectively improve the wastewater treatment technology, which is helpful to improve the quality of wastewater treatment. This paper makes an in-depth exploration and analysis of the common problems in industrial sewage treatment for reference.展开更多
We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separat...We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x=x(t).We prove that this problem admits global Radon measure solutions for all kinds of initial data.The over-compressing condition on the discontinuity x=x(t)is not enough to ensure the uniqueness of the solution.However,there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve x=x(t)+0,in addition to the full adhesion condition on its left-side.As an application,we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas.In particular,we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas.This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field.展开更多
Under the background of rapid economic development, more and more high-rise buildings have appeared. As a means of transportation, elevators have emerged as the times require and are widely used in high-rise buildings...Under the background of rapid economic development, more and more high-rise buildings have appeared. As a means of transportation, elevators have emerged as the times require and are widely used in high-rise buildings. Elevator brings great convenience to life, but at the same time, safety accidents frequently occur. This makes the quality problem and safe operation of elevators get great attention from people. Not only the construction department starts to pay attention to the safety of elevators, but also the users start to pay attention to the safety in the process of elevator operation. This paper is based on the analysis of matters needing attention in the process of elevator installation, and puts forward corresponding countermeasures for matters needing attention, so as to ensure the high-quality completion of elevator installation, thus ensuring the safe operation of the elevator.展开更多
As trust becomes increasingly important in software domain, software trustworthiness--as a complex high- composite concept, has developed into a big challenge people have to face, especially in the current open, dynam...As trust becomes increasingly important in software domain, software trustworthiness--as a complex high- composite concept, has developed into a big challenge people have to face, especially in the current open, dynamic and ever-changing Internet environment. Furthermore, how to recognize and define trust problem from its nature and how to measure software trustworthiness correctly and effectively play a key role in improving users＇ trust in choosing software. Based on trust theory in the field of humanities and sociology, this paper proposes a measurable S2S （Social-to-Software） software trustworthiness framework, introduces a generalized indicator loss to unify three parts of trustworthiness result, and presents a whole metric solution for software trustworthiness, including the advanced J-M model based on power function and time-loss rate for ability trustworthiness measurement, the fuzzy comprehensive evaluation advanced-model considering effect of multiple short boards for basic standard trustworthiness, and the identity trustworthiness measurement method based on the code homology detecting tools. Finally, it provides a case study to verify that the solution is applicable and effective.展开更多
In this paper,the Riemann problem of the 1-D reduced model for the 2-D Euler equations is considered and the Riemann solutions are obtained.It is proved that,as the pressure vanishes,they converge to two kinds of Riem...In this paper,the Riemann problem of the 1-D reduced model for the 2-D Euler equations is considered and the Riemann solutions are obtained.It is proved that,as the pressure vanishes,they converge to two kinds of Riemann solutions to the 1D reduced model for the 2-D transport equations:one contains δ-shocks,the other contains vacuum.展开更多
We give some extensions of Monch-Harton inequalities with respect to measures of noncompactness. As an example of the application, we obtain two existencetheorems of solutions for Cauchy problems of differential equat...We give some extensions of Monch-Harton inequalities with respect to measures of noncompactness. As an example of the application, we obtain two existencetheorems of solutions for Cauchy problems of differential equations on closed setsunder weaker compactness conditions.展开更多
The notion of bridge is introduced for systems of coupled forward-backward doubly stochastic differential equations （FBDSDEs）. It is proved that if two FBDSDEs are linked by a bridge, then they have the same unique ...The notion of bridge is introduced for systems of coupled forward-backward doubly stochastic differential equations （FBDSDEs）. It is proved that if two FBDSDEs are linked by a bridge, then they have the same unique solvability. Consequently, by constructing appropriate bridges, we obtain several classes of uniquely solvable FBDSDEs. Finally, the probabilistie interpretation for the solutions to a class of quasilinear stochastic partial differential equations （SPDEs） combined with algebra equations is given. One distinctive character of this result is that the forward component of the FBDSDEs is coupled with the backvzard variable.展开更多
For stationary hypersonic-limit Euler flows passing a solid body in three-dimensional space,the shock-front coincides with the upwind surface of the body,hence there is an infinite-thin layer of concentrated mass,in w...For stationary hypersonic-limit Euler flows passing a solid body in three-dimensional space,the shock-front coincides with the upwind surface of the body,hence there is an infinite-thin layer of concentrated mass,in which all particles hitting the body move along its upwind surface.By proposing a concept of Radon measure solutions of boundary value problems of the multi-dimensional compressible Euler equations,which incorporates the large-scale of three-dimensional distributions of upcoming hypersonic flows and the small-scale of particles moving on two-dimensional surfaces,the authors derive the compressible Euler equations for flows in concentration layers,which is a stationary pressureless compressible Euler system with source terms and independent variables on curved surface.As a by-product,they obtain a formula for pressure distribution on surfaces of general obstacles in hypersonic flows,which is a generalization of the classical Newton-Busemann law for drag/lift in hypersonic aerodynamics.展开更多
This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, w...This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, where U is a control set, and x satisfies the ordinary equation x（s） = f（x（s）, u（x（s）, s））.It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation：Vt（t, x） ＋ sup u∈U = 0,V（0, x） = Φ0（x）.展开更多
文摘In the background of the Internet economy,a new type of intellectual property,namely,network intellectual property,has been born.It is based on the traditional intellectual property rights such as copyright and industrial property,and broadens the intellectual property rights in the network environment to include areas such as databases,multimedia,electronic copyrights and computer software.This not only greatly enriches the scope of intellectual property rights,but also intensifies the risk of intellectual property infringement.In the context of the network economy,intellectual property protection faces new challenges and requirements.It has also attracted great attention from countries and international intellectual property organisations.They have conducted in-depth studies on the problems faced by intellectual property rights in the era of network economy and actively sought effective solutions to establish a complete and systematic intellectual property rights protection system to alleviate the pressure on intellectual property rights protection brought about by the complexity of the situation.In the context of network economy,IP protection faces new challenges and requirements.This has also attracted great attention from national and international IP organisations.They have conducted in-depth studies on the problems faced by IP in the era of network economy and actively sought effective solutions to establish a complete and systematic IP protection system to alleviate the pressure of IP protection brought about by complex situations.
基金supported by the National Natural Science Foundation of China under Grants No.11871218,No.12071298the Science and Technology Commission of Shanghai Municipality under Grant No.18dz2271000.
文摘We solve the Riemann problems for isentropic compressible Euler equations of polytropic gases in the class of Radon measures,and the solutions admit the concentration of mass.It is found that under the requirement of satisfying the over-compressing entropy condition:(i)there is a unique delta shock solution,corresponding to the case that has two strong classical Lax shocks;(ii)for the initial data that the classical Riemann solution contains a shock wave and a rarefaction wave,or two shocks with one being weak,there are infinitely many solutions,each consists of a delta shock and a rarefaction wave;(iii)there are no delta shocks for the case that the classical entropy weak solutions consist only of rarefaction waves.These solutions are self-similar.Furthermore,for the generalized Riemann problem with mass concentrated initially at the discontinuous point of initial data,there always exists a unique delta shock for at least a short time.It could be prolonged to a global solution.Not all the solutions are self-similar due to the initial velocity of the concentrated point-mass(particle).Whether the delta shock solutions constructed satisfy the over-compressing entropy condition is clarified.This is the first result on the construction of singular measure solutions to the compressible Euler system of polytropic gases,that is strictly hyperbolic,and whose characteristics are both genuinely nonlinear.We also discuss possible physical interpretations and applications of these new solutions.
基金supported by the University of South Africa under Grant No.409000.
文摘To professionally plan and manage the development and evolution of the Internet of Things(IoT),researchers have proposed several IoT performance measurement solutions.IoT performance measurement solutions can be very valuable for managing the development and evolution of IoT systems,as they provide insights into performance issues,resource optimization,predictive maintenance,security,reliability,and user experience.However,there are several issues that can impact the accuracy and reliability of IoT performance measurements,including lack of standardization,complexity of IoT systems,scalability,data privacy,and security.While previous studies proposed several IoT measurement solutions in the literature,they did not evaluate any individual one to figure out their respective measurement strengths and weaknesses.This study provides a novel scheme for the evaluation of proposed IoT measurement solutions using a metrology-coverage evaluation based on evaluation theory,metrology principles,and software measurement best practices.This evaluation approach was employed for 12 IoT measure categories and 158 IoT measurement solutions identified in a Systematic Literature Review(SLR)from 2010 to 2021.The metrology coverage of these IoT measurement solutions was analyzed from four perspectives:across IoT categories,within each study,improvement over time,and implications for IoT practitioners and researchers.The criteria in this metrology-coverage evaluation allowed for the identification of strengths and weaknesses in the theoretical and empirical definitions of the proposed IoT measurement solutions.We found that the metrological coverage varies significantly across IoT measurement solution categories and did not show improvement over the 2010–2021 timeframe.Detailed findings can help practitioners understand the limitations of the proposed measurement solutions and choose those with stronger designs.These evaluation results can also be used by researchers to improve current IoT measurement solution designs and suggest new solutions with a stronger metrology base.
文摘With the rapid development of electrical automation system, the factors that affect its internal operation safety are gradually increasing. Relevant professionals should make use of the rational use of relay protection devices to strengthen the professional control of the system, and effectively solve the problems encountered. After clarifying the working principle of such devices, the application scope of relay protection devices can be effectively enhanced. Next, the article focuses on the analysis of influencing factors and solutions of relay protection safety of electrical automation system.
文摘Elevator is widely used in high-rise buildings, which is a common means of transportation and brings great convenience to peoples lives. In the daily operation of elevators, the speed limiter plays a very important role. For example, the speed limiter can protect the elevator from speeding or rope breaking in the running process. Therefore, the inspection of the speed limiter is directly related to the safe operation of the elevator, so it is very important to inspect the speed limiter of the elevator. However, there are often many problems in the actual elevator speed limiter inspection work, which requires the relevant personnel to conduct in-depth research and analysis, and put forward corresponding solutions to ensure the safe operation of the elevator.
文摘Driven by social economy and science and technology, centralized accounting emerges at the historic moment, and its characteristics of "three separate and one open" meet the current market demand and development needs. State-owned enterprises need new driving forces and new ideas in adapting to the new era, so as to better fit the market and obtain new growth opportunities. Centralized accounting is one of the key points of financial management. In order to ensure the quality of work, it is necessary to ensure the accuracy and integrity of information data first, and then combine with modern management concept to provide impetus for the development of contemporary state-owned enterprises. State-owned enterprises in the process of financial accounting, by establishing a perfect accounting concentration accounting information system, implement the financial management level of state-owned enterprises, but at present accounting information management of the enterprise and the financial department accounting aspects there are still many problems, in this paper, the problems that exist in the state-owned enterprises accounting concentration accounting application again was summarized and analyzed, and tries to seek for the corresponding solutions, strive to the centralized accounting can be successfully implemented and play the due utility.
文摘With the development of the socialist market economy, a large number of civil engineering projects are emerging in China. This is not only the result of the improvement of China's scientific and technological level, but also a great help to improve people's quality of life. However, in recent years, adverse events have frequently occurred in the construction site management of civil engineering in our country, which makes people pay more and more attention to them. In the new era, how to better manage the construction site of civil engineering is something we should explore. This paper is divided into five parts: The first part gives a brief overview of the construction of migrant workers. The second part discusses the significance of strengthening on-site construction management of civil engineering. The third part tells the importance of construction management of civil engineering. The fourth part analyzes the problems existing in the construction management of civil engineering construction site at the present stage. The fifth part puts forward the measures to strengthen the construction management of civil engineering site based on the problem analysis.
文摘At present, there are still many problems in the specific treatment of industrial sewage in our country. In order to enhance the treatment quality of industrial sewage, relevant sewage treatment units should pay attention to improving the treatment level of environmental engineering sewage, strengthening the standardization of sewage treatment market system and strengthening the innovation of sewage management form. Based on the characteristics of industrial wastewater treatment, reasonable and effective treatment strategies are applied to effectively improve the wastewater treatment technology, which is helpful to improve the quality of wastewater treatment. This paper makes an in-depth exploration and analysis of the common problems in industrial sewage treatment for reference.
基金supported by the National Natural Science Foundation of China(11871218,12071298)in part by the Science and Technology Commission of Shanghai Municipality(21JC1402500,22DZ2229014)。
文摘We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x=x(t).We prove that this problem admits global Radon measure solutions for all kinds of initial data.The over-compressing condition on the discontinuity x=x(t)is not enough to ensure the uniqueness of the solution.However,there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve x=x(t)+0,in addition to the full adhesion condition on its left-side.As an application,we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas.In particular,we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas.This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field.
文摘Under the background of rapid economic development, more and more high-rise buildings have appeared. As a means of transportation, elevators have emerged as the times require and are widely used in high-rise buildings. Elevator brings great convenience to life, but at the same time, safety accidents frequently occur. This makes the quality problem and safe operation of elevators get great attention from people. Not only the construction department starts to pay attention to the safety of elevators, but also the users start to pay attention to the safety in the process of elevator operation. This paper is based on the analysis of matters needing attention in the process of elevator installation, and puts forward corresponding countermeasures for matters needing attention, so as to ensure the high-quality completion of elevator installation, thus ensuring the safe operation of the elevator.
基金This work was supported by the National Natural Science Foundation of China under Grant No. 90818021, the HeGaoJi Program of China under Grant No. 2012zx01039-004-46, and the Information Security Program of National Development and Reform Commission of China under Grant No. 2012-1424.
文摘As trust becomes increasingly important in software domain, software trustworthiness--as a complex high- composite concept, has developed into a big challenge people have to face, especially in the current open, dynamic and ever-changing Internet environment. Furthermore, how to recognize and define trust problem from its nature and how to measure software trustworthiness correctly and effectively play a key role in improving users＇ trust in choosing software. Based on trust theory in the field of humanities and sociology, this paper proposes a measurable S2S （Social-to-Software） software trustworthiness framework, introduces a generalized indicator loss to unify three parts of trustworthiness result, and presents a whole metric solution for software trustworthiness, including the advanced J-M model based on power function and time-loss rate for ability trustworthiness measurement, the fuzzy comprehensive evaluation advanced-model considering effect of multiple short boards for basic standard trustworthiness, and the identity trustworthiness measurement method based on the code homology detecting tools. Finally, it provides a case study to verify that the solution is applicable and effective.
文摘In this paper,the Riemann problem of the 1-D reduced model for the 2-D Euler equations is considered and the Riemann solutions are obtained.It is proved that,as the pressure vanishes,they converge to two kinds of Riemann solutions to the 1D reduced model for the 2-D transport equations:one contains δ-shocks,the other contains vacuum.
文摘We give some extensions of Monch-Harton inequalities with respect to measures of noncompactness. As an example of the application, we obtain two existencetheorems of solutions for Cauchy problems of differential equations on closed setsunder weaker compactness conditions.
基金supported by National Natural Science Foundation of China (Grant Nos. 10771122, 11071145, 10921101 and 11231005)Natural Science Foundation of Shandong Province of China(Grant No. Y2006A08)+1 种基金National Basic Research Program of China (973 Program) (Grant No. 2007CB814900)Independent Innovation Foundation of Shandong University (Grant No. 2010JQ010)
文摘The notion of bridge is introduced for systems of coupled forward-backward doubly stochastic differential equations （FBDSDEs）. It is proved that if two FBDSDEs are linked by a bridge, then they have the same unique solvability. Consequently, by constructing appropriate bridges, we obtain several classes of uniquely solvable FBDSDEs. Finally, the probabilistie interpretation for the solutions to a class of quasilinear stochastic partial differential equations （SPDEs） combined with algebra equations is given. One distinctive character of this result is that the forward component of the FBDSDEs is coupled with the backvzard variable.
基金supported by the National Natural Science Foundation of China(Nos.11871218,12071298)the Science and Technology Commission of Shanghai Municipality(No.18dz2271000)。
文摘For stationary hypersonic-limit Euler flows passing a solid body in three-dimensional space,the shock-front coincides with the upwind surface of the body,hence there is an infinite-thin layer of concentrated mass,in which all particles hitting the body move along its upwind surface.By proposing a concept of Radon measure solutions of boundary value problems of the multi-dimensional compressible Euler equations,which incorporates the large-scale of three-dimensional distributions of upcoming hypersonic flows and the small-scale of particles moving on two-dimensional surfaces,the authors derive the compressible Euler equations for flows in concentration layers,which is a stationary pressureless compressible Euler system with source terms and independent variables on curved surface.As a by-product,they obtain a formula for pressure distribution on surfaces of general obstacles in hypersonic flows,which is a generalization of the classical Newton-Busemann law for drag/lift in hypersonic aerodynamics.
文摘This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, where U is a control set, and x satisfies the ordinary equation x（s） = f（x（s）, u（x（s）, s））.It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation：Vt（t, x） ＋ sup u∈U = 0,V（0, x） = Φ0（x）.
