In this paper,we study the Bowen entropy of stable sets in positive entropy G-system of amenable group actions.The lower bound of the Bowen entropy of these sets are estimated.
In this paper, the definition of weak dominance is proposed for a NTU game and two new solution concepts of NTU games are introduced: the refined core and weakly stable set. The relationship is explored among the core...In this paper, the definition of weak dominance is proposed for a NTU game and two new solution concepts of NTU games are introduced: the refined core and weakly stable set. The relationship is explored among the core, the weakly stable set and the refined core.展开更多
Objective:This study aimed to develop a core outcome set(COS)for use in future studies of stable angina pectoris(SAP)in traditional Chinese medicine(TCM).Methods:Systematic literature reviews and qualitative interview...Objective:This study aimed to develop a core outcome set(COS)for use in future studies of stable angina pectoris(SAP)in traditional Chinese medicine(TCM).Methods:Systematic literature reviews and qualitative interviews with cardiologists and patients with SAP treated using TCM were conducted to generate a set of outcomes.Outcomes were prioritized by stakeholders via two rounds of an online Delphi survey and face-to-face consensus meetings.Following the final consensus meeting,a final COS was generated.Results:An initial set of 324 outcomes was identified.A preliminary list of 65 outcomes was employed in the Delphi study.In total,223 participants from seven stakeholder groups were invited to score outcomes in the first Delphi round:87 completed round 1 and 47 completed round 2.Thirty-one participants attended the consensus meeting and agreed on a final core set of outcomes comprising six items across four domains:frequency of angina attack,duration of angina attack,Seattle angina questionnaire,total exercise duration in the exercise treadmill test,cardiovascular events,and QT interval on electrocardiography.Conclusions:The COS developed in this study provides the minimum requirements for measurement and reporting in future TCM clinical trials for the treatment of SAP.The employment of this COS may reduce heterogeneity across trials and facilitate evidencebased decision-making for stakeholders.展开更多
In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a C^r（r 〉 1） conservative par...In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism is stably ergodic if it is robustly weakly ergodic and has positive （or negative） central exponents on a positive measure set. Furthermore, if the condition of robust weak ergodicity is replaced by weak ergodicity, then the diffeomophism is an almost stably ergodic system. Additionally, we show in dimension three, a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism can be approximated by stably ergodic systems if it is robustly weakly ergodic and robustly has non-zero central exponents.展开更多
The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear function...The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.展开更多
Let M^n be an n-dimensional complete noncompact oriented weakly stable constant mean curvature hypersurface in an （n ＋ 1）-dimensional Riemannian manifold N^n＋1 whose （n - 1）th Ricci curvature satisfying Ric^N（...Let M^n be an n-dimensional complete noncompact oriented weakly stable constant mean curvature hypersurface in an （n ＋ 1）-dimensional Riemannian manifold N^n＋1 whose （n - 1）th Ricci curvature satisfying Ric^N（n-1） （n - 1）c. Denote by H and φ the mean curvature and the trace-free second fundamental form of M respectively. If ｜φ｜^2 - （n- 2）√n（n- 1）｜H｜｜φ｜＋ n（2n - 1）（H^2＋ c） 〉 0, then M does not admit nonconstant bounded harmonic functions with finite Dirichlet integral. In particular, if N has bounded geometry and c ＋ H^2 〉 0, then M must have only one end.展开更多
In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 4...In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.展开更多
Agriculture is an important foundation of China’s socio-economic development. To secure the sound development of modern agriculture in the 21st century, the supply of fertilizers such as potassium is a key factor. Ow...Agriculture is an important foundation of China’s socio-economic development. To secure the sound development of modern agriculture in the 21st century, the supply of fertilizers such as potassium is a key factor. Owing to the limited arable land in China, a vital measure to feed the country’s increasing population is the augmentation of fertilizers so as to gain higher per unit area grain yields. At present, for a fairly long time to come, additional fertilizer resources will mainly come from nitrogen, phosphorus and potassium fertilizers. But there is a severe application disproportion between nitroge-展开更多
In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend t...In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.展开更多
In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS are studied. Firstly, it is proved that the category GIFS has all topoi properties except that ...In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS are studied. Firstly, it is proved that the category GIFS has all topoi properties except that it has no subobject classifiers, Secondly, it is proved that the category GIFS has middle object and consequently GIFS is a weak topos. Thirdly, by the use of theory of weak topos GIFS, the power object of an object in GIFS is studied.展开更多
When the bi-stable stochastic resonance method was applied to enhance weak thruster fault for autonomous underwater vehicle(AUV), the enhancement performance could not satisfy the detection requirement of weak thruste...When the bi-stable stochastic resonance method was applied to enhance weak thruster fault for autonomous underwater vehicle(AUV), the enhancement performance could not satisfy the detection requirement of weak thruster fault. As for this problem, a fault feature enhancement method based on mono-stable stochastic resonance was proposed. In the method, in order to improve the enhancement performance of weak thruster fault feature, the conventional bi-stable potential function was changed to mono-stable potential function which was more suitable for aperiodic signals. Furthermore, when particle swarm optimization was adopted to adjust the parameters of mono-stable stochastic resonance system, the global convergent time would be long. An improved particle swarm optimization method was developed by changing the linear inertial weighted function as nonlinear function with cosine function, so as to reduce the global convergent time. In addition, when the conventional wavelet reconstruction method was adopted to detect the weak thruster fault, undetected fault or false alarm may occur. In order to successfully detect the weak thruster fault, a weak thruster detection method was proposed based on the integration of stochastic resonance and wavelet reconstruction. In the method, the optimal reconstruction scale was determined by comparing wavelet entropies corresponding to each decomposition scale. Finally, pool-experiments were performed on AUV with thruster fault. The effectiveness of the proposed mono-stable stochastic resonance method in enhancing fault feature and reducing the global convergent time was demonstrated in comparison with particle swarm optimization based bi-stochastic resonance method. Furthermore, the effectiveness of the proposed fault detection method was illustrated in comparison with the conventional wavelet reconstruction.展开更多
Four massive brecciated, chimney-like, and slender pipe network carbonate samples(JA-4, JA-5, JX-8 and BG-12) were collected from southwestern Taiwan, which were suggested to have formed as a result of anaerobic oxidi...Four massive brecciated, chimney-like, and slender pipe network carbonate samples(JA-4, JA-5, JX-8 and BG-12) were collected from southwestern Taiwan, which were suggested to have formed as a result of anaerobic oxidization of methane(AOM). Considering that the environmental conditions of the carbonates precipitation and the sources of carbon and organic matter need to be further declared, molecular fossils and compound-specific carbon isotopic investigations of the carbonates were conducted in this study. According to lipid biomarkers of 2,6,10,15,19-pentamethyleicosane(PMI) and squalane diagnostic to methanotrophic archaea, as well as the extremely low δ^(13)C values(as low as -1^(13).4‰) detected in samples JA-4, JA-5 and JX-8, these carbonates were revealed to be a result of AOM. Based on the varied δ^(13)C values of characteristic archaea biomarkers in specific samples, biogenic methane was proposed to be responsible for the formation of samples JA-4 and JA-5, whereas a mixed carbon source of ^(13)C-depleted methane and ^(13)C-enriched residual CO_2 from methanogenesis was suggested for the carbonate of JX-8 due to the co-occurrence of a highly positive δ^(13) C_(carb) value(+8‰) and a moderate ^(13)C depletion of PMI. The low content of AOM-related biomarkers and the absence of indicators for ANME-2 suggested that these carbonates were formed in weak seep settings. By comparison, no typical lipid biomarkers for methanotrophic archaea was detected in carbonate BG-12. The short-chain and long-chain n-alkanes accounted for 30% and 45% of all hydrocarbons, respectively, with a CPI value of 1.2, suggesting that the n-alkanes were derived from both marine organisms and terrestrial inputs. A low thermal maturity could be revealed by the incomplete equilibrium value of the C^(31)αβ 22S/(22S+22R) ratio(0.5), and the carbonate BG-12 was probably deposited in a suboxic condition indicated by a value of Pr/Ph ratio(2.5).展开更多
In this article, we investigate the global behavior of weak solutions of a simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals in time in a bounded three-dimension domain-arbitrary forc...In this article, we investigate the global behavior of weak solutions of a simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals in time in a bounded three-dimension domain-arbitrary forces. By adapting the arguments for the compressible Navier-Stokes equations, and carefully analyzing the direction field of liquid crystals in the equations of angular momentum, we show the existence of bounded absorbing sets, global bounded trajectories, and global attractors to weak solutions of compressible flows of nematic liquid crystals with the adiabatic constant γ〉5/3.展开更多
1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved....1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X).展开更多
In brder to study the contradiction problem of multilayer multidimensional complex systems, the concepts of extension field and stable field of intersection and union of multilayer multidimensional extension set are g...In brder to study the contradiction problem of multilayer multidimensional complex systems, the concepts of extension field and stable field of intersection and union of multilayer multidimensional extension set are given. Then the related operations and properties are discussed. The results of study expand the concepts of intersection and union of extension set to a general situation, and provide the theoretical basis for production of the concepts of intersection and union of multilayer multidimensional matter element system extension set. In this way, it will be possible that matter element system theory is used to creative designs of complex systems.展开更多
J. Mather and A. Fathi defined Mané set and Aubry set, which are the important invariant sets in positive definite Lagrangian system, in different ways. They use variational principle and Weak KAM theory respecti...J. Mather and A. Fathi defined Mané set and Aubry set, which are the important invariant sets in positive definite Lagrangian system, in different ways. They use variational principle and Weak KAM theory respectively. In this paper we provide a proof of the equivalence between the two kinds of definitions, and generalize A. Fathi＇s definition. In the end of the paper, we calculate the Mane set and Aubry set for a single pendulum system.展开更多
1 IntroductionIn this paper we study the existence of pullback attractors for multivalued nonautonomous and multivalued random semiflow. In [1] and [2], the authors have proved the existence of pullback attractors of ...1 IntroductionIn this paper we study the existence of pullback attractors for multivalued nonautonomous and multivalued random semiflow. In [1] and [2], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow （random semiflow） under the assumption of the existence of compact absorbing set. In [3], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow and random semiflow under the assumptions of uniformly pullback asymptotically upper semicompact and closed graph. In [4], the authors consider the existence of pullback attractor of singlevalued nonautonomous semiflow and random semiflow under the assumption of pullback asymptotic compactness. Instead of these assumptions, we consider multivalued nonautonomous semiflow and multivalued random semiflow with weak pullback asymptotic upper semi-compactness and prove the existence of pullback attractors.展开更多
基金Supported by NSFC(No.11861010),also supported by NSFC(No.12171175),also supported by NSFC(No.12261006)NSF of Guangxi Province(No.2018GXNSFFA281008)Project of Guangxi First Class Disciplines of Statistics(No.GJKY-2022-01)。
文摘In this paper,we study the Bowen entropy of stable sets in positive entropy G-system of amenable group actions.The lower bound of the Bowen entropy of these sets are estimated.
文摘In this paper, the definition of weak dominance is proposed for a NTU game and two new solution concepts of NTU games are introduced: the refined core and weakly stable set. The relationship is explored among the core, the weakly stable set and the refined core.
基金supported by the National Natural Science Foundation of China(No.81473544).
文摘Objective:This study aimed to develop a core outcome set(COS)for use in future studies of stable angina pectoris(SAP)in traditional Chinese medicine(TCM).Methods:Systematic literature reviews and qualitative interviews with cardiologists and patients with SAP treated using TCM were conducted to generate a set of outcomes.Outcomes were prioritized by stakeholders via two rounds of an online Delphi survey and face-to-face consensus meetings.Following the final consensus meeting,a final COS was generated.Results:An initial set of 324 outcomes was identified.A preliminary list of 65 outcomes was employed in the Delphi study.In total,223 participants from seven stakeholder groups were invited to score outcomes in the first Delphi round:87 completed round 1 and 47 completed round 2.Thirty-one participants attended the consensus meeting and agreed on a final core set of outcomes comprising six items across four domains:frequency of angina attack,duration of angina attack,Seattle angina questionnaire,total exercise duration in the exercise treadmill test,cardiovascular events,and QT interval on electrocardiography.Conclusions:The COS developed in this study provides the minimum requirements for measurement and reporting in future TCM clinical trials for the treatment of SAP.The employment of this COS may reduce heterogeneity across trials and facilitate evidencebased decision-making for stakeholders.
基金supported by National Natural Science Foundation of China(11001284)Natural Science Foundation Project of CQ CSTC(cstcjjA00003)Fundamental Research Funds for the Central Universities(CQDXWL2012008)
文摘In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism is stably ergodic if it is robustly weakly ergodic and has positive （or negative） central exponents on a positive measure set. Furthermore, if the condition of robust weak ergodicity is replaced by weak ergodicity, then the diffeomophism is an almost stably ergodic system. Additionally, we show in dimension three, a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism can be approximated by stably ergodic systems if it is robustly weakly ergodic and robustly has non-zero central exponents.
基金supported by the National Natural Science Foundation of China(11471043,11671271)the Beijing Natural Science Foundation(1172004)
文摘The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.
基金Supported by the National Natural Science Foundation of China (10771187 10671087)+1 种基金Trans-Century Training Programme Foundation for Talents by the Ministry of Education of ChinaJiangxi Province Natural Science Foundation (2008GZS0060)
文摘Let M^n be an n-dimensional complete noncompact oriented weakly stable constant mean curvature hypersurface in an （n ＋ 1）-dimensional Riemannian manifold N^n＋1 whose （n - 1）th Ricci curvature satisfying Ric^N（n-1） （n - 1）c. Denote by H and φ the mean curvature and the trace-free second fundamental form of M respectively. If ｜φ｜^2 - （n- 2）√n（n- 1）｜H｜｜φ｜＋ n（2n - 1）（H^2＋ c） 〉 0, then M does not admit nonconstant bounded harmonic functions with finite Dirichlet integral. In particular, if N has bounded geometry and c ＋ H^2 〉 0, then M must have only one end.
文摘In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.
文摘Agriculture is an important foundation of China’s socio-economic development. To secure the sound development of modern agriculture in the 21st century, the supply of fertilizers such as potassium is a key factor. Owing to the limited arable land in China, a vital measure to feed the country’s increasing population is the augmentation of fertilizers so as to gain higher per unit area grain yields. At present, for a fairly long time to come, additional fertilizer resources will mainly come from nitrogen, phosphorus and potassium fertilizers. But there is a severe application disproportion between nitroge-
基金supported by National Natural Science Foundation of China (10901054)
文摘In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.
文摘In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS are studied. Firstly, it is proved that the category GIFS has all topoi properties except that it has no subobject classifiers, Secondly, it is proved that the category GIFS has middle object and consequently GIFS is a weak topos. Thirdly, by the use of theory of weak topos GIFS, the power object of an object in GIFS is studied.
基金Project(51279040)supported by the National Natural Science Foundation of China
文摘When the bi-stable stochastic resonance method was applied to enhance weak thruster fault for autonomous underwater vehicle(AUV), the enhancement performance could not satisfy the detection requirement of weak thruster fault. As for this problem, a fault feature enhancement method based on mono-stable stochastic resonance was proposed. In the method, in order to improve the enhancement performance of weak thruster fault feature, the conventional bi-stable potential function was changed to mono-stable potential function which was more suitable for aperiodic signals. Furthermore, when particle swarm optimization was adopted to adjust the parameters of mono-stable stochastic resonance system, the global convergent time would be long. An improved particle swarm optimization method was developed by changing the linear inertial weighted function as nonlinear function with cosine function, so as to reduce the global convergent time. In addition, when the conventional wavelet reconstruction method was adopted to detect the weak thruster fault, undetected fault or false alarm may occur. In order to successfully detect the weak thruster fault, a weak thruster detection method was proposed based on the integration of stochastic resonance and wavelet reconstruction. In the method, the optimal reconstruction scale was determined by comparing wavelet entropies corresponding to each decomposition scale. Finally, pool-experiments were performed on AUV with thruster fault. The effectiveness of the proposed mono-stable stochastic resonance method in enhancing fault feature and reducing the global convergent time was demonstrated in comparison with particle swarm optimization based bi-stochastic resonance method. Furthermore, the effectiveness of the proposed fault detection method was illustrated in comparison with the conventional wavelet reconstruction.
基金supported by Qingdao National Laboratory for Marine Science and Technology(No.QNLM2016ORP0210)the NSF of China(No.41473080 and 41673029)
文摘Four massive brecciated, chimney-like, and slender pipe network carbonate samples(JA-4, JA-5, JX-8 and BG-12) were collected from southwestern Taiwan, which were suggested to have formed as a result of anaerobic oxidization of methane(AOM). Considering that the environmental conditions of the carbonates precipitation and the sources of carbon and organic matter need to be further declared, molecular fossils and compound-specific carbon isotopic investigations of the carbonates were conducted in this study. According to lipid biomarkers of 2,6,10,15,19-pentamethyleicosane(PMI) and squalane diagnostic to methanotrophic archaea, as well as the extremely low δ^(13)C values(as low as -1^(13).4‰) detected in samples JA-4, JA-5 and JX-8, these carbonates were revealed to be a result of AOM. Based on the varied δ^(13)C values of characteristic archaea biomarkers in specific samples, biogenic methane was proposed to be responsible for the formation of samples JA-4 and JA-5, whereas a mixed carbon source of ^(13)C-depleted methane and ^(13)C-enriched residual CO_2 from methanogenesis was suggested for the carbonate of JX-8 due to the co-occurrence of a highly positive δ^(13) C_(carb) value(+8‰) and a moderate ^(13)C depletion of PMI. The low content of AOM-related biomarkers and the absence of indicators for ANME-2 suggested that these carbonates were formed in weak seep settings. By comparison, no typical lipid biomarkers for methanotrophic archaea was detected in carbonate BG-12. The short-chain and long-chain n-alkanes accounted for 30% and 45% of all hydrocarbons, respectively, with a CPI value of 1.2, suggesting that the n-alkanes were derived from both marine organisms and terrestrial inputs. A low thermal maturity could be revealed by the incomplete equilibrium value of the C^(31)αβ 22S/(22S+22R) ratio(0.5), and the carbonate BG-12 was probably deposited in a suboxic condition indicated by a value of Pr/Ph ratio(2.5).
文摘In this article, we investigate the global behavior of weak solutions of a simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals in time in a bounded three-dimension domain-arbitrary forces. By adapting the arguments for the compressible Navier-Stokes equations, and carefully analyzing the direction field of liquid crystals in the equations of angular momentum, we show the existence of bounded absorbing sets, global bounded trajectories, and global attractors to weak solutions of compressible flows of nematic liquid crystals with the adiabatic constant γ〉5/3.
文摘1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X).
基金Sponsored bythe National Natural Science Foundation of China(60375014) the Shandong Province Natural Science Foundation(Y2002G16)
文摘In brder to study the contradiction problem of multilayer multidimensional complex systems, the concepts of extension field and stable field of intersection and union of multilayer multidimensional extension set are given. Then the related operations and properties are discussed. The results of study expand the concepts of intersection and union of extension set to a general situation, and provide the theoretical basis for production of the concepts of intersection and union of multilayer multidimensional matter element system extension set. In this way, it will be possible that matter element system theory is used to creative designs of complex systems.
文摘J. Mather and A. Fathi defined Mané set and Aubry set, which are the important invariant sets in positive definite Lagrangian system, in different ways. They use variational principle and Weak KAM theory respectively. In this paper we provide a proof of the equivalence between the two kinds of definitions, and generalize A. Fathi＇s definition. In the end of the paper, we calculate the Mane set and Aubry set for a single pendulum system.
文摘1 IntroductionIn this paper we study the existence of pullback attractors for multivalued nonautonomous and multivalued random semiflow. In [1] and [2], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow （random semiflow） under the assumption of the existence of compact absorbing set. In [3], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow and random semiflow under the assumptions of uniformly pullback asymptotically upper semicompact and closed graph. In [4], the authors consider the existence of pullback attractor of singlevalued nonautonomous semiflow and random semiflow under the assumption of pullback asymptotic compactness. Instead of these assumptions, we consider multivalued nonautonomous semiflow and multivalued random semiflow with weak pullback asymptotic upper semi-compactness and prove the existence of pullback attractors.
