Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying som...Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.展开更多
In this paper,using inhomogeneous Calderon’s reproducing formulas and the space of test functions associated with a para-accretive function,the inhomogeneous Besov and TriebelLizorkin spaces are established.As applic...In this paper,using inhomogeneous Calderon’s reproducing formulas and the space of test functions associated with a para-accretive function,the inhomogeneous Besov and TriebelLizorkin spaces are established.As applications,pointwise multiplier theorems are also obtained.展开更多
In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Su...In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.展开更多
Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator i...Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated.展开更多
The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamenta...The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.展开更多
The Three Gorges Reservoir Area(TGRA)is an important ecological barrier in the Yangtze River Basin,China.Therefore,it is of great importance to understand the spatio-temporal variation and the driving factors of produ...The Three Gorges Reservoir Area(TGRA)is an important ecological barrier in the Yangtze River Basin,China.Therefore,it is of great importance to understand the spatio-temporal variation and the driving factors of production-living-ecological spaces for sustainable and high-quality development in the TGRA.This study investigated the dynamic variation of production-living-ecological spaces in the TGRA by employing land use data in 2000,2005,2010,2015,and 2018,and detected the influencing factors by using the Geographic detector(GeoDetector).Results implied that the structure and dynamic trajectories of production-living-ecological spaces in the TGRA varied in both horizontal and vertical directions,and the study area was dominated by ecological space.A spatial orientation towards the northeast was detected in the evolution of production-living-ecological spaces during 2000-2018.In terms of quantity,the transition from ecological space(grassland and woodland)to agriculture land accounted for the largest proportion from 2000 to 2018.However,the reverse transition from agriculture land to ecological space has increased since 2000 with the efforts of“Grain for Green”.In terms of temporal scale,there was a fluctuating trend in production space with the continuous expansion of living space,while ecological space showed an inverted U-shaped trend during 2000-2018.The dynamic pattern of production-living-ecological spaces in the TGRA was influenced by both physical and socio-economic variables as basic determinants and dominant driving factors,respectively.Finally,the harmonization and protection of production-living-ecological spaces still require policy-makers’efforts.This work may have potential in advancing our understanding about land use conflicts,and provide a reference for rational layout of spatial functions and the realization of sustainable development in the TGRA.展开更多
The aim of this study was to carry out a dynamic simulation of the energy and environmental performance of a built space system, with a view to assessing its energy and environmental class. The use of a simulation and...The aim of this study was to carry out a dynamic simulation of the energy and environmental performance of a built space system, with a view to assessing its energy and environmental class. The use of a simulation and modeling tool, supported by various methodological references, formed the basis of our approach. Adopting a systemic perspective, we described the structural and functional aspects of the systems making up built spaces, as well as the associated energy flows. Our approach was also based on a typology, taking into account typical days, structural and functional configurations at different scales and angles of observation. The analysis tool we developed in Java was applied to the built space system of the Patte d’Oie university campus in Ouagadougou. Annual electricity consumption was measured at 124387.34 kWh, closely aligned with the average annual electricity bill (125224.31 kWh), with a maximum relative deviation of 1%, followed by a carbon emission balance of 58337.66 kg eq CO<sub>2</sub> per year. This validation confirmed the effectiveness of our tool. In addition, following the analysis of electricity consumption using our tool, the university campus was classified in energy class B and environmental class C. These results will be based on the emission factors of the energy mix of the West African Economic and Monetary Union (WAEMU) territory, with particular emphasis on Burkina Faso.展开更多
AIM:To investigate effects of perirenal space blocking(PSB)on gastrointestinal function in patients with severe acute pancreatitis(SAP).METHODS:Forty patients with SAP were randomly allocated to receive PSB or no PSB(...AIM:To investigate effects of perirenal space blocking(PSB)on gastrointestinal function in patients with severe acute pancreatitis(SAP).METHODS:Forty patients with SAP were randomly allocated to receive PSB or no PSB(NPSB).All the SAP patients received specialized medical therapy(SMT).Patients in the PSB group received PSB+SMT when hospitalized and after diagnosis,whereas patients in the NPSB group only received SMT.A modifed gastrointestinal failure(GIF)scoring system was used to assess the gastrointestinal function in SAP patients after admission.Pain severity(visual analog scale,0 to100)was monitored every 24 h for 72 h.RESULTS:Modified GIF score decreased in both groups during the 10-d study period.The median score decrease was initially significantly greater in the PSB group than in the NPSB group after PSB was per-formed.During the 72-h study period,pain intensity decreased in both groups.The median pain decrease was significantly greater in the PSB group than in the NPSB group at single time points.Patients in the PSB group had significantly lower incidences of hospital mortality,multiple organ dysfunction syndrome,systemic inflammatory response syndrome,and pancreatic infection,and stayed in the intensive care unit for a shorter duration.However,no difference in terms of operation incidence was found between the two groups.CONCLUSION:PSB could ameliorate gastrointestinal dysfunction or failure during the early stage of SAP.Moreover,PSB administration could improve prognosis and decrease the mortality of SAP patients.展开更多
In this article we introduce the paranormed sequence spaces (f,A, Am,p), c0(f,A,Am,p) and L00(f,A, Am,p), associated with the multiplier sequence ∧ = (hk), defined by a modulus function f. We study their diff...In this article we introduce the paranormed sequence spaces (f,A, Am,p), c0(f,A,Am,p) and L00(f,A, Am,p), associated with the multiplier sequence ∧ = (hk), defined by a modulus function f. We study their different properties like solidness, symmetricity, completeness etc. and prove some inclusion results.展开更多
Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years...Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are (weak) Asplund spaces.展开更多
This article is devoted to presenting a recapitulative introduction for the theory of Besov-type and Triebel-Lizorkin-type spaces developed in recent years.
In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.
Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f(p∑i=1xi+q∑j=1yj+2d∑k=1zk/2)=p∑i=1f(xi)+q∑j=1f(yj)+2d∑k=1f(zk...Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f(p∑i=1xi+q∑j=1yj+2d∑k=1zk/2)=p∑i=1f(xi)+q∑j=1f(yj)+2d∑k=1f(zk),where p, q, d are integers greater than 1, in non-Archimedean normed spaces.展开更多
We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applic...We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.展开更多
Reliability-based design optimization (RBDO) is intrinsically a double-loop procedure since it involves an overall optimization and an iterative reliability assessment at each search point. Due to the double-loop pr...Reliability-based design optimization (RBDO) is intrinsically a double-loop procedure since it involves an overall optimization and an iterative reliability assessment at each search point. Due to the double-loop procedure, the computational expense of RBDO is normally very high. Current RBDO research focuses on problems with explicitly expressed performance functions and readily available gradients. This paper addresses a more challenging type of RBDO problem in which the performance functions are computation intensive. These computation intensive functions are often considered as a "black-box" and their gradients are not available or not reliable. On the basis of the reliable design space (RDS) concept proposed earlier by the authors, this paper proposes a Reliable Space Pursuing (RSP) approach, in which RDS is first identified and then gradually refined while optimization is performed. It fundamentally avoids the nested optimization and probabilistic assessment loop. Three well known RBDO problems from the literature are used for testing and demonstrating the effectiveness of the proposed RSP method.展开更多
In this paper,We mainly discuss some subclasses of analytic functions for operators onac, and determine a representation formula and sufficient condition for the class 4;(a.p,r,E,7) and prove a sufficient and necessar...In this paper,We mainly discuss some subclasses of analytic functions for operators onac, and determine a representation formula and sufficient condition for the class 4;(a.p,r,E,7) and prove a sufficient and necessary condition.coefficient estimates and distortiontheorem for the subclass O;o (a,p,Y,e,9) of the class ac;(a,p,y,c,V).Furthermore,the analogues also are true for operators on Hilbert space.展开更多
In this article, we introduce some double sequence spaces of fuzzy real numbers defined by Orlicz function, study some of their properties like solidness, symmetricity, completeness etc, and prove some inclusion results.
In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k (w) for 0〈k〈...In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k (w) for 0〈k〈 1 and w ∈ A1.展开更多
基金supported by the National Key Research and Development Program of China(2020YFA0712900)the National Natural Science Foundation of China(12371093,12071197,12122102 and 12071431)+2 种基金the Key Project of Gansu Provincial National Science Foundation(23JRRA1022)the Fundamental Research Funds for the Central Universities(2233300008 and lzujbky-2021-ey18)the Innovative Groups of Basic Research in Gansu Province(22JR5RA391).
文摘Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.
基金supported by the National Natural Science Foundation of China(11901495)Hunan Provincial NSF Project(2019JJ50573)the Scientific Research Fund of Hunan Provincial Education Department(22B0155)。
文摘In this paper,using inhomogeneous Calderon’s reproducing formulas and the space of test functions associated with a para-accretive function,the inhomogeneous Besov and TriebelLizorkin spaces are established.As applications,pointwise multiplier theorems are also obtained.
文摘In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.
文摘Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated.
文摘The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.
基金the National Natural Science Foundation of China(41971215,42371205)the Youth Innovation Promotion Association of Chinese Academy of Sciences(2022317).
文摘The Three Gorges Reservoir Area(TGRA)is an important ecological barrier in the Yangtze River Basin,China.Therefore,it is of great importance to understand the spatio-temporal variation and the driving factors of production-living-ecological spaces for sustainable and high-quality development in the TGRA.This study investigated the dynamic variation of production-living-ecological spaces in the TGRA by employing land use data in 2000,2005,2010,2015,and 2018,and detected the influencing factors by using the Geographic detector(GeoDetector).Results implied that the structure and dynamic trajectories of production-living-ecological spaces in the TGRA varied in both horizontal and vertical directions,and the study area was dominated by ecological space.A spatial orientation towards the northeast was detected in the evolution of production-living-ecological spaces during 2000-2018.In terms of quantity,the transition from ecological space(grassland and woodland)to agriculture land accounted for the largest proportion from 2000 to 2018.However,the reverse transition from agriculture land to ecological space has increased since 2000 with the efforts of“Grain for Green”.In terms of temporal scale,there was a fluctuating trend in production space with the continuous expansion of living space,while ecological space showed an inverted U-shaped trend during 2000-2018.The dynamic pattern of production-living-ecological spaces in the TGRA was influenced by both physical and socio-economic variables as basic determinants and dominant driving factors,respectively.Finally,the harmonization and protection of production-living-ecological spaces still require policy-makers’efforts.This work may have potential in advancing our understanding about land use conflicts,and provide a reference for rational layout of spatial functions and the realization of sustainable development in the TGRA.
文摘The aim of this study was to carry out a dynamic simulation of the energy and environmental performance of a built space system, with a view to assessing its energy and environmental class. The use of a simulation and modeling tool, supported by various methodological references, formed the basis of our approach. Adopting a systemic perspective, we described the structural and functional aspects of the systems making up built spaces, as well as the associated energy flows. Our approach was also based on a typology, taking into account typical days, structural and functional configurations at different scales and angles of observation. The analysis tool we developed in Java was applied to the built space system of the Patte d’Oie university campus in Ouagadougou. Annual electricity consumption was measured at 124387.34 kWh, closely aligned with the average annual electricity bill (125224.31 kWh), with a maximum relative deviation of 1%, followed by a carbon emission balance of 58337.66 kg eq CO<sub>2</sub> per year. This validation confirmed the effectiveness of our tool. In addition, following the analysis of electricity consumption using our tool, the university campus was classified in energy class B and environmental class C. These results will be based on the emission factors of the energy mix of the West African Economic and Monetary Union (WAEMU) territory, with particular emphasis on Burkina Faso.
文摘AIM:To investigate effects of perirenal space blocking(PSB)on gastrointestinal function in patients with severe acute pancreatitis(SAP).METHODS:Forty patients with SAP were randomly allocated to receive PSB or no PSB(NPSB).All the SAP patients received specialized medical therapy(SMT).Patients in the PSB group received PSB+SMT when hospitalized and after diagnosis,whereas patients in the NPSB group only received SMT.A modifed gastrointestinal failure(GIF)scoring system was used to assess the gastrointestinal function in SAP patients after admission.Pain severity(visual analog scale,0 to100)was monitored every 24 h for 72 h.RESULTS:Modified GIF score decreased in both groups during the 10-d study period.The median score decrease was initially significantly greater in the PSB group than in the NPSB group after PSB was per-formed.During the 72-h study period,pain intensity decreased in both groups.The median pain decrease was significantly greater in the PSB group than in the NPSB group at single time points.Patients in the PSB group had significantly lower incidences of hospital mortality,multiple organ dysfunction syndrome,systemic inflammatory response syndrome,and pancreatic infection,and stayed in the intensive care unit for a shorter duration.However,no difference in terms of operation incidence was found between the two groups.CONCLUSION:PSB could ameliorate gastrointestinal dysfunction or failure during the early stage of SAP.Moreover,PSB administration could improve prognosis and decrease the mortality of SAP patients.
文摘In this article we introduce the paranormed sequence spaces (f,A, Am,p), c0(f,A,Am,p) and L00(f,A, Am,p), associated with the multiplier sequence ∧ = (hk), defined by a modulus function f. We study their different properties like solidness, symmetricity, completeness etc. and prove some inclusion results.
文摘Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are (weak) Asplund spaces.
基金supported by the National Natural Science Foundation of China(11171027and 11101038)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20120003110003)+1 种基金the Fundamental Research Funds for Central Universities of China(2012LYB26)supported by the Alexander von Humboldt Foundation
文摘This article is devoted to presenting a recapitulative introduction for the theory of Besov-type and Triebel-Lizorkin-type spaces developed in recent years.
文摘In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.
文摘Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f(p∑i=1xi+q∑j=1yj+2d∑k=1zk/2)=p∑i=1f(xi)+q∑j=1f(yj)+2d∑k=1f(zk),where p, q, d are integers greater than 1, in non-Archimedean normed spaces.
文摘We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.
基金supported by Natural Science and Engineering Research Council (NSERC) of Canada
文摘Reliability-based design optimization (RBDO) is intrinsically a double-loop procedure since it involves an overall optimization and an iterative reliability assessment at each search point. Due to the double-loop procedure, the computational expense of RBDO is normally very high. Current RBDO research focuses on problems with explicitly expressed performance functions and readily available gradients. This paper addresses a more challenging type of RBDO problem in which the performance functions are computation intensive. These computation intensive functions are often considered as a "black-box" and their gradients are not available or not reliable. On the basis of the reliable design space (RDS) concept proposed earlier by the authors, this paper proposes a Reliable Space Pursuing (RSP) approach, in which RDS is first identified and then gradually refined while optimization is performed. It fundamentally avoids the nested optimization and probabilistic assessment loop. Three well known RBDO problems from the literature are used for testing and demonstrating the effectiveness of the proposed RSP method.
文摘In this paper,We mainly discuss some subclasses of analytic functions for operators onac, and determine a representation formula and sufficient condition for the class 4;(a.p,r,E,7) and prove a sufficient and necessary condition.coefficient estimates and distortiontheorem for the subclass O;o (a,p,Y,e,9) of the class ac;(a,p,y,c,V).Furthermore,the analogues also are true for operators on Hilbert space.
文摘In this article, we introduce some double sequence spaces of fuzzy real numbers defined by Orlicz function, study some of their properties like solidness, symmetricity, completeness etc, and prove some inclusion results.
文摘In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k (w) for 0〈k〈 1 and w ∈ A1.