Since the specifications of most of the existing context-sensitive graph grammars tend to be either too intricate or not intuitive, a novel context-sensitive graph grammar formalism, called context-attributed graph gr...Since the specifications of most of the existing context-sensitive graph grammars tend to be either too intricate or not intuitive, a novel context-sensitive graph grammar formalism, called context-attributed graph grammar（CAGG）, is proposed. In order to resolve the embedding problem, context information of a graph production in the CAGG is represented in the form of context attributes of the nodes involved. Moreover, several properties of a set of confluent CAGG productions are characterized, and then an algorithm based on them is developed to decide whether or not a set of productions is confluent, which provides the foundation for the design of efficient parsing algorithms. It can also be shown through the comparison of CAGG with several typical context-sensitive graph grammars that CAGG is more succinct and, at the same time, more intuitive than the others, making it more suitably and effortlessly applicable to the specification of visual languages.展开更多
A systematic approach for end-to-end QoS qualitative diagnosis and quantitative guarantee is proposed to support quality of service （QoS） management on current Internet. An automatic unwatched discretization algorit...A systematic approach for end-to-end QoS qualitative diagnosis and quantitative guarantee is proposed to support quality of service （QoS） management on current Internet. An automatic unwatched discretization algorithm for discretizing continuous numeric-values is brought forth to reshape these QoS metrics and contexts into their discrete forms. For QoS qualitative diagnosis, causal relationships between a QoS metric and its contexts are exploited with K2 Bayesian network （BN） structure learning by treating QoS metrics and contexts as BN nodes. A QoS metric node is qualitatively diagnosed to be causally related to its parent context nodes. To guarantee QoS quantitatively, those causal relationships are next modeled quantitatively by BN parameter learning. Then, BN inference can be carried out on the BN. Finally, the QoS metric is guaranteed to a specific value with certain probability by tuning its causal contexts to suitable values suggested by the BN inference. Our approach is validated to be sound and effective by simulations on a peer-to-peer （P2P） network.展开更多
In this paper,we propose a systemic architecture of network selection based on context-awareness services,which gathers contextual information that includes such network information,user information and local informat...In this paper,we propose a systemic architecture of network selection based on context-awareness services,which gathers contextual information that includes such network information,user information and local information.This network selection strategy considers the Quality of Service(QoS) and user preferences.Also,it perceives contexts such as speed,coverage percentage and location,etc.,and it eventually performs network selection decision making and network execution based on multiple factors.From the perspective of network decision,it presents two network selection algorithms,namely the fuzzy mathematics evaluation method and multiple attribute decision making using the TOPSIS evaluation method.System simulations suggest that network selection based on the mathematics evaluation method is much faster than the TOPSIS evaluation method.However,the TOPSIS evaluation method is practically more efficient.The network selection method based on context-awareness provides an effective and flexible network vertical handover strategy,and ensures a good accuracy and efficiency.展开更多
In this paper,we study the asymptotic dynamics of a single-species model with resource-dependent dispersal in one dimension.To overcome the analytical difficulties brought by the resource-dependent dispersal,we use th...In this paper,we study the asymptotic dynamics of a single-species model with resource-dependent dispersal in one dimension.To overcome the analytical difficulties brought by the resource-dependent dispersal,we use the idea of changing variables to transform the model into a uniform dispersal one.Then the existence and uniqueness of positive stationary solution to the model can be verified by the squeezing argument,where the solution plays a crucial role in later analyses.Moreover,the asymptotic behavior of solutions to the model is obtained by the upper-lower solutions method.The result indicates that the solutions of the model converge to the corresponding positive stationary solution locally uniformly in one dimension as time goes to infinity.展开更多
This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.
According to Kripke, traditional approaches to presupposition and anaphora do not work in some compound sentences because traditionally, they have been thought to assign presuppositions to each clause in isolation. I ...According to Kripke, traditional approaches to presupposition and anaphora do not work in some compound sentences because traditionally, they have been thought to assign presuppositions to each clause in isolation. I agree with this criticism, but also think that context is required in order to determine the presupposition included in a complex sentence. To show the context role in fixing the utterance truth-conditions in those cases, this paper introduces the Kripkean anaphoric account on presuppositions （section 2）, and then criticizes this approach because it is very restrictive （section 3）. The paper concludes that to solve those difficulties, one should appeal to a two-dimensional framework, including a new parameter that focuses on the sentence according to the concrete features of the context： the speaker＇s point of view （section 4）.展开更多
In order to avoid the discretization in the classical rough set theory, a generlization rough set theory is proposed. At first, the degree of general importance of an attribute and attribute subsets are presented. The...In order to avoid the discretization in the classical rough set theory, a generlization rough set theory is proposed. At first, the degree of general importance of an attribute and attribute subsets are presented. Then, depending on the degree of general importance of attribute, the space distance can be measured with weighted method. At last, a generalization rough set theory based on the general near neighborhood relation is proposed. The proposed theory partitions the universe into the tolerant modules, and forms lower approximation and upper approximation of the set under general near neighborhood relationship, which avoids the discretization in Pawlak's rough set theory.展开更多
This paper describes an equation discovery approach based on machine learning using LAGRAMGE as an equation discovery tool, with two sources of input, a dataset and model presented in context-free grammar. The approac...This paper describes an equation discovery approach based on machine learning using LAGRAMGE as an equation discovery tool, with two sources of input, a dataset and model presented in context-free grammar. The approach is searching a large range of po- tential equations by a specific inodel. The parameters of the equation are fitted to find the best equations. The experiments are illustratedwith commodity prices from the London Metal Exchange for the period of January-October 2009. The outputs of the experiments are a large mumber of equations; some of the equations display that the predicted prices are following the market trends in perfect patterns.展开更多
The presented paper puts in discussion the dilemma of the linear supports of formal teaching and learning processes of regular school, coexisting with an inter and transdisciplinarity of the process mentioned above. I...The presented paper puts in discussion the dilemma of the linear supports of formal teaching and learning processes of regular school, coexisting with an inter and transdisciplinarity of the process mentioned above. In this perspective, the author wonders about the subjectivity of the students＇ apprenticeship and about the way they can change, according to the methodological variants, as well as the context. So, he intents to explore the C.P.M.P.S （Creative and Participative Method of Problem Solution） in the development of Portuguese written language competence, through the art subject. In this paper, we can see the increase of different variables from the perspective of students and teachers which validates in some manner of the teaching methodology.展开更多
Medialization has become like digitalization, rationalization, dynamization, globalization, pluralization, hybridization, and differentialization and is one of the buzzwords of modern Western industrialized societies,...Medialization has become like digitalization, rationalization, dynamization, globalization, pluralization, hybridization, and differentialization and is one of the buzzwords of modern Western industrialized societies, which are all together essentially responsible for structural change in communication. Medialization means the adaption of producers to media logics, media formats, and media routines ＆ workflows. There are consequently and logically influences because of the dynamic process of medialization to legal discourse and genres, law, media, and social power. It has to be discussed if the logics, data formats, and routines ＆ workflows of new media and information and communication technologies （ICTs） like social media are creating also a new generation of genres and novel form of legal discourses. Also, if social media will replace or complete old classic media （law of Riepl）, the question of the relevance of law concerning new ＆ social media has to be answered in close future. Lastly, if to the fore of social power, these new novel resources are actually framing for problem-based inquiries in law. There are big chances but also serious risks in cyberworld, their realities, and dangers. There actually exists an urgent call of action to theory building, development of methodologies, and empirical research.展开更多
Harmonization of tax policy at European level is the result of compromise that must be achieved between member states＇ sovereignty and obstacles that create differences in legal regime for different categories of tax...Harmonization of tax policy at European level is the result of compromise that must be achieved between member states＇ sovereignty and obstacles that create differences in legal regime for different categories of taxes. The current level of harmonization achieved by the member states clearly shows that the process of reconciliation of taxes will not be a spontaneous, nor will evolve rapidly. With the occasion of European Union [EU] enlargement in 2004 and 2007, disparities in income levels matter between nationals of member states have put more pressure on the cooperation between member states, but some progress has been made including in this area. The idea of harmonization of taxes in the European plan is not new. Context of pertinent and uniform EU position has occurred since the first treaties concluded between member states. The free movements of goods, persons, services and capital, without any obstruction became absolute values. Creating a European tax, set and charged uniformly to all and by all member states, would be possible only if the criteria of budgetary requirements, criteria of efficiency and equity criteria are taken into consideration. Ruling a uniform level of charging would lead to establishing a single tax, mission almost impossible as long as the legal framework on taxation and civil duties remains under the responsibility of each member of EU. This analysis seems to greatly restrict the area of taxes that may meet all requirements listed. EU is still far from time to harmonize VAT （value added tax） levels perceived, but it is noted that the value added tax, income tax and tax on benefits eventually could meet the characteristics of a uniform European tax, achieving unanimous agreement among member states.展开更多
Mistreatment and violation of international laws are recurrent events during Second World War （WWII） and torture is a frequent method used in the Algerian War. This paper investigates the escalation of violence whi...Mistreatment and violation of international laws are recurrent events during Second World War （WWII） and torture is a frequent method used in the Algerian War. This paper investigates the escalation of violence which, in some cases, degenerates into torture and offers a comparison between the situation of Axis Prisoners of War （1943-1946） and the imprisonment’s conditions in Algeria （1954-1962）. In spite of the temporal interval and different political contexts, in some cases there’s a strange “continuity”.展开更多
As former Fermatist, the author tried many times to prove Fermat＇s Last Theorem in an elementary way. Just few insights of the proposed schemes partially passed the peer-reviewing and they motivated the subsequent fr...As former Fermatist, the author tried many times to prove Fermat＇s Last Theorem in an elementary way. Just few insights of the proposed schemes partially passed the peer-reviewing and they motivated the subsequent fruitful collaboration with Prof. Mario De Paz. Among the author＇s failures, there is an unpublished proof emblematic of the FLT＇s charming power for the suggestive circumstances it was formulated. As sometimes happens with similar erroneous attempts, containing out-of-context hints, it provides a germinal approach to power sums yet to be refined.展开更多
We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analys...We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analysis is rather subtle and it is inadequate to apply the powerful theory of monotone dynamical systems. By using the method of super-sub solutions, combined with the careful analysis of the kernel function in the nonlocal term, we prove nonexistence, existence and uniqueness of positive steady states of the model.Moreover, due to the mature individuals do not diffuse, the solution semiflow to the model is not compact. To overcome the difficulty of non-compactness in describing the global asymptotic stability of the unique positive steady state, we first establish an appropriate comparison principle. With the help of the comparison principle,we can employ the theory of dissipative systems to obtain the global asymptotic stability of the unique positive steady state. The main results are illustrated with the nonlocal Nicholson's blowflies equation and the nonlocal Mackey-Glass equation.展开更多
Objective： To investigate the neurobiological mechanism of depression pathogenesis and reveal the mechanism of acupuncture treatment of depression. Methods： Wistar rats were selected for subjects. A rat model of dep...Objective： To investigate the neurobiological mechanism of depression pathogenesis and reveal the mechanism of acupuncture treatment of depression. Methods： Wistar rats were selected for subjects. A rat model of depression was made by individually housing with unpredicted chronic moderate stimuli. Changes in behavior and hypothalamus-pituitaryadrenocortical axis were examined in rat models of stress-induced depression. Meanwhile, the intervening effect of acupuncture was evaluated and the curative effects of different acupuncture methods compared. Results： CORT and ACTH contents of serum were significantly higher in the model and normal saline groups than in the control group （P〈0.05）, significantly lower in the hand acupuncture and electroacupuncture groups than in the model group （P〈0.05） and significantly lower in the medication group than in the normal saline group （P〈0.05）. There were no significant differences between the hand acupuncture, electroacupuncture and medication groups. Conclusion： Acupuncture of Baihui（GV 20） and Taichong （LR 3） has a marked antidepressant effect. Its mechanism may be related to the regulation of HPA axis by acupuncture.展开更多
We introduce some ways to compute the lower and upper bounds of the Laplace eigenvalue problem.By using the special nonconforming finite elements,i.e.,enriched Crouzeix-Raviart element and extended Q1ro t,we get the l...We introduce some ways to compute the lower and upper bounds of the Laplace eigenvalue problem.By using the special nonconforming finite elements,i.e.,enriched Crouzeix-Raviart element and extended Q1ro t,we get the lower bound of the eigenvalue.Additionally,we use conforming finite elements to do the postprocessing to get the upper bound of the eigenvalue,which only needs to solve the corresponding source problems and a small eigenvalue problem if higher order postprocessing method is implemented.Thus,we can obtain the lower and upper bounds of the eigenvalues simultaneously by solving eigenvalue problem only once.Some numerical results are also presented to demonstrate our theoretical analysis.展开更多
In this paper,a multiscale problem arising in material science is considered.The problem involves a random coefficient which is assumed to be a perturbation of a deterministic coefficient,in a sense made precisely in ...In this paper,a multiscale problem arising in material science is considered.The problem involves a random coefficient which is assumed to be a perturbation of a deterministic coefficient,in a sense made precisely in the body of the text.The homogenized limit is then computed by using a perturbation approach.This computation requires repeatedly solving a corrector-like equation for various configurations of the material.For this purpose,the reduced basis approach is employed and adapted to the specific context.The authors perform numerical tests that demonstrate the efficiency of the approach.展开更多
基金The National Natural Science Foundation of China(No.60571048,60673186,60736015)the National High Technology Researchand Development Program of China(863Program)(No.2007AA01Z178)
文摘Since the specifications of most of the existing context-sensitive graph grammars tend to be either too intricate or not intuitive, a novel context-sensitive graph grammar formalism, called context-attributed graph grammar（CAGG）, is proposed. In order to resolve the embedding problem, context information of a graph production in the CAGG is represented in the form of context attributes of the nodes involved. Moreover, several properties of a set of confluent CAGG productions are characterized, and then an algorithm based on them is developed to decide whether or not a set of productions is confluent, which provides the foundation for the design of efficient parsing algorithms. It can also be shown through the comparison of CAGG with several typical context-sensitive graph grammars that CAGG is more succinct and, at the same time, more intuitive than the others, making it more suitably and effortlessly applicable to the specification of visual languages.
基金Supported by the National High Technology Research and Development Program of China （No. 2007AA010302, 2009AA012404） the National Basic Research Program of China （No. 2007CB307103）+1 种基金 the National Natural Science Foundation of China （No. 60432010, 60802034） the Specialized Research Fund for the Doctoral Program of Higher Education （No. 20070013026）.
文摘A systematic approach for end-to-end QoS qualitative diagnosis and quantitative guarantee is proposed to support quality of service （QoS） management on current Internet. An automatic unwatched discretization algorithm for discretizing continuous numeric-values is brought forth to reshape these QoS metrics and contexts into their discrete forms. For QoS qualitative diagnosis, causal relationships between a QoS metric and its contexts are exploited with K2 Bayesian network （BN） structure learning by treating QoS metrics and contexts as BN nodes. A QoS metric node is qualitatively diagnosed to be causally related to its parent context nodes. To guarantee QoS quantitatively, those causal relationships are next modeled quantitatively by BN parameter learning. Then, BN inference can be carried out on the BN. Finally, the QoS metric is guaranteed to a specific value with certain probability by tuning its causal contexts to suitable values suggested by the BN inference. Our approach is validated to be sound and effective by simulations on a peer-to-peer （P2P） network.
基金supported by the National Basic Research Program of China(973 Program)under Grant No.2012CB315805supported by the National Natural Science Foundation of China under Grants No.71172135,No.71231002,No.71201011,No.71271099the Ministry of Education of the People's Republic of China under Grant No.20120005120001
文摘In this paper,we propose a systemic architecture of network selection based on context-awareness services,which gathers contextual information that includes such network information,user information and local information.This network selection strategy considers the Quality of Service(QoS) and user preferences.Also,it perceives contexts such as speed,coverage percentage and location,etc.,and it eventually performs network selection decision making and network execution based on multiple factors.From the perspective of network decision,it presents two network selection algorithms,namely the fuzzy mathematics evaluation method and multiple attribute decision making using the TOPSIS evaluation method.System simulations suggest that network selection based on the mathematics evaluation method is much faster than the TOPSIS evaluation method.However,the TOPSIS evaluation method is practically more efficient.The network selection method based on context-awareness provides an effective and flexible network vertical handover strategy,and ensures a good accuracy and efficiency.
基金supported by the National Natural Science Foundation of China (Nos.12301101,12101121)the Guangdong Basic and Applied Basic Research Foundation (Nos.2022A1515110019,2020A1515110585)。
文摘In this paper,we study the asymptotic dynamics of a single-species model with resource-dependent dispersal in one dimension.To overcome the analytical difficulties brought by the resource-dependent dispersal,we use the idea of changing variables to transform the model into a uniform dispersal one.Then the existence and uniqueness of positive stationary solution to the model can be verified by the squeezing argument,where the solution plays a crucial role in later analyses.Moreover,the asymptotic behavior of solutions to the model is obtained by the upper-lower solutions method.The result indicates that the solutions of the model converge to the corresponding positive stationary solution locally uniformly in one dimension as time goes to infinity.
文摘This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.
文摘According to Kripke, traditional approaches to presupposition and anaphora do not work in some compound sentences because traditionally, they have been thought to assign presuppositions to each clause in isolation. I agree with this criticism, but also think that context is required in order to determine the presupposition included in a complex sentence. To show the context role in fixing the utterance truth-conditions in those cases, this paper introduces the Kripkean anaphoric account on presuppositions （section 2）, and then criticizes this approach because it is very restrictive （section 3）. The paper concludes that to solve those difficulties, one should appeal to a two-dimensional framework, including a new parameter that focuses on the sentence according to the concrete features of the context： the speaker＇s point of view （section 4）.
基金Natural Science Foundation of Jiangsu Province of China ( No.BK2006176)High-Tech Key Laboratory of Jiangsu,China (No.BM2007201)
文摘In order to avoid the discretization in the classical rough set theory, a generlization rough set theory is proposed. At first, the degree of general importance of an attribute and attribute subsets are presented. Then, depending on the degree of general importance of attribute, the space distance can be measured with weighted method. At last, a generalization rough set theory based on the general near neighborhood relation is proposed. The proposed theory partitions the universe into the tolerant modules, and forms lower approximation and upper approximation of the set under general near neighborhood relationship, which avoids the discretization in Pawlak's rough set theory.
文摘This paper describes an equation discovery approach based on machine learning using LAGRAMGE as an equation discovery tool, with two sources of input, a dataset and model presented in context-free grammar. The approach is searching a large range of po- tential equations by a specific inodel. The parameters of the equation are fitted to find the best equations. The experiments are illustratedwith commodity prices from the London Metal Exchange for the period of January-October 2009. The outputs of the experiments are a large mumber of equations; some of the equations display that the predicted prices are following the market trends in perfect patterns.
文摘The presented paper puts in discussion the dilemma of the linear supports of formal teaching and learning processes of regular school, coexisting with an inter and transdisciplinarity of the process mentioned above. In this perspective, the author wonders about the subjectivity of the students＇ apprenticeship and about the way they can change, according to the methodological variants, as well as the context. So, he intents to explore the C.P.M.P.S （Creative and Participative Method of Problem Solution） in the development of Portuguese written language competence, through the art subject. In this paper, we can see the increase of different variables from the perspective of students and teachers which validates in some manner of the teaching methodology.
文摘Medialization has become like digitalization, rationalization, dynamization, globalization, pluralization, hybridization, and differentialization and is one of the buzzwords of modern Western industrialized societies, which are all together essentially responsible for structural change in communication. Medialization means the adaption of producers to media logics, media formats, and media routines ＆ workflows. There are consequently and logically influences because of the dynamic process of medialization to legal discourse and genres, law, media, and social power. It has to be discussed if the logics, data formats, and routines ＆ workflows of new media and information and communication technologies （ICTs） like social media are creating also a new generation of genres and novel form of legal discourses. Also, if social media will replace or complete old classic media （law of Riepl）, the question of the relevance of law concerning new ＆ social media has to be answered in close future. Lastly, if to the fore of social power, these new novel resources are actually framing for problem-based inquiries in law. There are big chances but also serious risks in cyberworld, their realities, and dangers. There actually exists an urgent call of action to theory building, development of methodologies, and empirical research.
文摘Harmonization of tax policy at European level is the result of compromise that must be achieved between member states＇ sovereignty and obstacles that create differences in legal regime for different categories of taxes. The current level of harmonization achieved by the member states clearly shows that the process of reconciliation of taxes will not be a spontaneous, nor will evolve rapidly. With the occasion of European Union [EU] enlargement in 2004 and 2007, disparities in income levels matter between nationals of member states have put more pressure on the cooperation between member states, but some progress has been made including in this area. The idea of harmonization of taxes in the European plan is not new. Context of pertinent and uniform EU position has occurred since the first treaties concluded between member states. The free movements of goods, persons, services and capital, without any obstruction became absolute values. Creating a European tax, set and charged uniformly to all and by all member states, would be possible only if the criteria of budgetary requirements, criteria of efficiency and equity criteria are taken into consideration. Ruling a uniform level of charging would lead to establishing a single tax, mission almost impossible as long as the legal framework on taxation and civil duties remains under the responsibility of each member of EU. This analysis seems to greatly restrict the area of taxes that may meet all requirements listed. EU is still far from time to harmonize VAT （value added tax） levels perceived, but it is noted that the value added tax, income tax and tax on benefits eventually could meet the characteristics of a uniform European tax, achieving unanimous agreement among member states.
文摘Mistreatment and violation of international laws are recurrent events during Second World War （WWII） and torture is a frequent method used in the Algerian War. This paper investigates the escalation of violence which, in some cases, degenerates into torture and offers a comparison between the situation of Axis Prisoners of War （1943-1946） and the imprisonment’s conditions in Algeria （1954-1962）. In spite of the temporal interval and different political contexts, in some cases there’s a strange “continuity”.
文摘As former Fermatist, the author tried many times to prove Fermat＇s Last Theorem in an elementary way. Just few insights of the proposed schemes partially passed the peer-reviewing and they motivated the subsequent fruitful collaboration with Prof. Mario De Paz. Among the author＇s failures, there is an unpublished proof emblematic of the FLT＇s charming power for the suggestive circumstances it was formulated. As sometimes happens with similar erroneous attempts, containing out-of-context hints, it provides a germinal approach to power sums yet to be refined.
基金supported by National Natural Science Foundation of China(Grant Nos.11031002 and 11371107)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20124410110001)
文摘We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analysis is rather subtle and it is inadequate to apply the powerful theory of monotone dynamical systems. By using the method of super-sub solutions, combined with the careful analysis of the kernel function in the nonlocal term, we prove nonexistence, existence and uniqueness of positive steady states of the model.Moreover, due to the mature individuals do not diffuse, the solution semiflow to the model is not compact. To overcome the difficulty of non-compactness in describing the global asymptotic stability of the unique positive steady state, we first establish an appropriate comparison principle. With the help of the comparison principle,we can employ the theory of dissipative systems to obtain the global asymptotic stability of the unique positive steady state. The main results are illustrated with the nonlocal Nicholson's blowflies equation and the nonlocal Mackey-Glass equation.
文摘Objective： To investigate the neurobiological mechanism of depression pathogenesis and reveal the mechanism of acupuncture treatment of depression. Methods： Wistar rats were selected for subjects. A rat model of depression was made by individually housing with unpredicted chronic moderate stimuli. Changes in behavior and hypothalamus-pituitaryadrenocortical axis were examined in rat models of stress-induced depression. Meanwhile, the intervening effect of acupuncture was evaluated and the curative effects of different acupuncture methods compared. Results： CORT and ACTH contents of serum were significantly higher in the model and normal saline groups than in the control group （P〈0.05）, significantly lower in the hand acupuncture and electroacupuncture groups than in the model group （P〈0.05） and significantly lower in the medication group than in the normal saline group （P〈0.05）. There were no significant differences between the hand acupuncture, electroacupuncture and medication groups. Conclusion： Acupuncture of Baihui（GV 20） and Taichong （LR 3） has a marked antidepressant effect. Its mechanism may be related to the regulation of HPA axis by acupuncture.
基金supported by National Science Foundations of China (Grant Nos. 11001259,11031006)Croucher Foundation of Hong Kong Baptist University
文摘We introduce some ways to compute the lower and upper bounds of the Laplace eigenvalue problem.By using the special nonconforming finite elements,i.e.,enriched Crouzeix-Raviart element and extended Q1ro t,we get the lower bound of the eigenvalue.Additionally,we use conforming finite elements to do the postprocessing to get the upper bound of the eigenvalue,which only needs to solve the corresponding source problems and a small eigenvalue problem if higher order postprocessing method is implemented.Thus,we can obtain the lower and upper bounds of the eigenvalues simultaneously by solving eigenvalue problem only once.Some numerical results are also presented to demonstrate our theoretical analysis.
基金Project supported by EOARD(European Office of Aerospace Research and Development) (No.FA865510-C-4002)
文摘In this paper,a multiscale problem arising in material science is considered.The problem involves a random coefficient which is assumed to be a perturbation of a deterministic coefficient,in a sense made precisely in the body of the text.The homogenized limit is then computed by using a perturbation approach.This computation requires repeatedly solving a corrector-like equation for various configurations of the material.For this purpose,the reduced basis approach is employed and adapted to the specific context.The authors perform numerical tests that demonstrate the efficiency of the approach.
