In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly sm...In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.展开更多
Most relatively high-level radioactive sandstone(HRSS)reservoir has considerable oil(or gas)resource potential.HRSS is often wrongly identified due to its similar logging response characteristics as mudstone,which lea...Most relatively high-level radioactive sandstone(HRSS)reservoir has considerable oil(or gas)resource potential.HRSS is often wrongly identified due to its similar logging response characteristics as mudstone,which leads to the omission of effective reservoirs.In this paper,a quantitative identification method for HRSS is proposed after the analyzing of the response characteristics and relationship between spontaneous potential log and natural gamma-ray log in conventional sandstone and mudstone strata.Take the Upper Triassic Yanchang Formation in Ordos Basin as an example:the responses of spontaneous potential log and the responses of natural gamma-ray log are synchronized and positively correlated in conventional sandstone and mudstone strata,but they are not synchronized in HRSS.Quantitative identification of HRSS was realized based on this synchronization feature,and a"virtual compensation"of natural gamma-ray log was performed.At the same time,logging evaluation method about HRSS has been discussed.The final results shows that this identification method work effectively,and can reduce the misjudgment and omission of effective reservoirs.展开更多
Interruption,as a linguistic phenomenon,can be see everywhere.And talk show programs are common setting for interruptions.So in this thesis three questions are addressed as followed:What function does the interruption...Interruption,as a linguistic phenomenon,can be see everywhere.And talk show programs are common setting for interruptions.So in this thesis three questions are addressed as followed:What function does the interruption have in these two kinds of talk shows(relatively formal and informal) respectively;what are the similarities of relatively formal and informal talk show programs;what are the differences between relatively formal and informal talk shows.展开更多
In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-stro...In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then, we show that the sequence converges strongly to a common element of the two sets. Our results improve and extend the corresponding results reported by many others.展开更多
In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in ...In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.展开更多
In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real...In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real uniformly smooth and uniformly convex Banach space are proposed. Some weak convergence theorems are obtained, which extend and complement some previous work.展开更多
It is given in Weil and Rosenlicht ([1], p. 15) that (resp. 2) for all non-negative integers m and n with m≠n if c is any even (resp. odd) integer. In the present paper we generalize this. Our purpose is to give othe...It is given in Weil and Rosenlicht ([1], p. 15) that (resp. 2) for all non-negative integers m and n with m≠n if c is any even (resp. odd) integer. In the present paper we generalize this. Our purpose is to give other integral sequences such that G.C.D.(ym,yn)=1 for all positive integers m and n with m≠n. Roughly speaking we show the following 1) and 2). 1) There are infinitely many polynomial sequences such that G.C.D.(fm(a),fn(a))=1 for all positive integers m and n with with m≠n and infinitely many rational?integers a. 2) There are polynomial sequences such that G.C.D.(gm(a,b),gn(a,b))=1 for all positive integers m and n with m≠n and arbitrary (rational or odd) integers a and b with G.C.D.(a,b)=1. Main results of the present paper are Theorems 1 and 2, and Corollaries 3, 4 and 5.展开更多
This article is about the structure of expanding universe. Here I am trying to create a structural model of universe according to my thoughts. Studies showthat universe is accelerating its rate of expansion. Here I am...This article is about the structure of expanding universe. Here I am trying to create a structural model of universe according to my thoughts. Studies showthat universe is accelerating its rate of expansion. Here I am trying to get some conclusions according to my thoughts. In my opinion, our universe is under a gravitational frame with all the matters in it. In this gravitational frame of universe we can consider our universe as a closed system and the empty space outside the frame as an open system. There are two possibilities we can find. One is relative motion of the objects inside the frame. By this way we can feel the universe is accelerating its expansion, but it is not. Another one is the vacuum energy absorption and negative pressure inside the frame. According to this thought, we can say that universe is accelerating and it can continue its motion at present conditions on it, even the force created by the big bang is decreasing. The other point is that, once the absorbed vacuum can create a negative pressure inside the frame, there is no need for the concept of dark energy in our universe [1]. According to this model, negative pressure inside the frame will be created by the absorbed vacuum from the space. So the existence of dark energy can be questioned. In this model, dark energy doesn't play any role in the expansion or rate of acceleration on the expansion of universe. So the dark energy doesn’t exist in this model. During the absorption of vacuum to the frame, it will increase the volume of the frame. It will create free spaces inside the frame to accommodate the vacuum inside the frame. The rest of the absorbed vacuum will move to the center of the frame by the action against gravity and the force created by the big bang. It will increase the density of the absorbed vacuum in the center and can create the negative pressure on the frame to pull it outside to the empty space. It will cause the acceleration on expansion of universe. These things are explained deeply in this article. And here it also explains the destiny of universe according to the frame and expansion of universe.展开更多
On the basis of expounding the status quo of rural residents' residence, the thesis notes that influenced by the weak foundation of rural economy, the characteristic of mountain landscape, smallholder consciousnes...On the basis of expounding the status quo of rural residents' residence, the thesis notes that influenced by the weak foundation of rural economy, the characteristic of mountain landscape, smallholder consciousness, shortage of capital and other factors, the rural residents in Chongqing City mainly live scattered. In addition to opportunities of the expansion and drive of city, rural market development, rural resources development, rural industrial development, and rural ecological migration, the model of urban development promotion, the model of market development drive, the model of land development drive, the model of rural industry construction and the model of resettlement and reconstruction are advocated in order to guide the rural residents to adopt relative centralized residence. The suggestions concerning guiding rural residents' relative centralized residence are put forward as follows: firstly, act according to circumstances and conduct scientific planning and design; secondly, propagate extensively and activate famers' willingness; thirdly, first experiment and exert the exemplary guide; fourthly, perfect policy and guarantee farmers' benefit; fifthly, strengthen leadership and decrease the risk of centralized residence; sixthly, boost gradually and realize moderate centralized residence.展开更多
Nonconvex–nonconcave saddle-point optimization in machine learning has triggered lots of research for studying non-monotone variational inequalities(VIs).In this work,we introduce two mirror frameworks,called mirror ...Nonconvex–nonconcave saddle-point optimization in machine learning has triggered lots of research for studying non-monotone variational inequalities(VIs).In this work,we introduce two mirror frameworks,called mirror extragradient method and mirror extrapolation method,for approximating solutions to relatively Lipschitz and monotone-like VIs.The former covers the well-known Nemirovski’s mirror prox method and Nesterov’s dual extrapolation method,and the recently proposed Bregman extragradient method;all of them can be reformulated into a scheme that is very similar to the original form of extragradient method.The latter includes the operator extrapolation method and the Bregman extrapolation method as its special cases.The proposed mirror frameworks allow us to present a unified and improved convergence analysis for all these existing methods under relative Lipschitzness and monotone-like conditions that may be the currently weakest assumptions guaranteeing(sub)linear convergence.展开更多
The key parameters that characterize the morphological quality of multi-layer and multi-pass metal laser deposited parts are the surface roughness and the error between the actual printing height and the theoretical m...The key parameters that characterize the morphological quality of multi-layer and multi-pass metal laser deposited parts are the surface roughness and the error between the actual printing height and the theoretical model height.The Taguchi method was employed to establish the correlations between process parameter combinations and multi-objective characterization of metal deposition morphology(height error and roughness).Results show that using the signal-to-noise ratio and grey relational analysis,the optimal parameter combination for multi-layer and multi-pass deposition is determined as follows:laser power of 800 W,powder feeding rate of 0.3 r/min,step distance of 1.6 mm,and scanning speed of 20 mm/s.Subsequently,a Genetic Bayesian-back propagation(GB-BP)network is constructed to predict multi-objective responses.Compared with the traditional back propagation network,the GB-back propagation network improves the prediction accuracy of height error and surface roughness by 43.14%and 71.43%,respectively.This network can accurately predict the multi-objective characterization of morphological quality of multi-layer and multi-pass metal deposited parts.展开更多
The aim of this paper is to investigate relatively flat envelopes. A necessary and sufficient condition is given for a relatively-finitely presented module to have a (mono-morphic or epic) relatively flat envelope. Th...The aim of this paper is to investigate relatively flat envelopes. A necessary and sufficient condition is given for a relatively-finitely presented module to have a (mono-morphic or epic) relatively flat envelope. Then those rings are characterized whose every relatively-finitely presented module has a relatively flat envelope which coincides with its in-jective envelope. Some known results are obtained as corollaries.展开更多
In this paper, we have proved that for a relatively complemented distributive lattice L,there exists one and only one completion ? of L such that for every ξ∈?, there exists afamily {S_α}_(α∈△) of non-vacuous su...In this paper, we have proved that for a relatively complemented distributive lattice L,there exists one and only one completion ? of L such that for every ξ∈?, there exists afamily {S_α}_(α∈△) of non-vacuous subsets of L satisfying ξ= ∨[∧f(S_α)]. Such a completion? is called the entire completion of L. We have in this paper extended the homomorphic extension theorem of a generalizedBoolean lattice to that of a relatively complemented distributive lattice and proved that the lat-tice of the congruences on a relatively complemented distributive lattice is isomorphicwith the lattice of the convex sublattices containing a fixed element and that the entire comple-tion of a relatively complemented distributive lattice L, the lattice of the completable con-gruences on L and the lattice of the completable convex sublattices of L containing a fixed ele-ment are isomorphic.展开更多
In this note, we obtain a sufficient and necessary condition for a set in an abstract Winner space （X, H, μ） to be relatively compact in L^2（X, μ）. Meanwhile, we give a sufficient condition for relative compactn...In this note, we obtain a sufficient and necessary condition for a set in an abstract Winner space （X, H, μ） to be relatively compact in L^2（X, μ）. Meanwhile, we give a sufficient condition for relative compactness in L^P（X, μ） for p〉1. We also provide an example of Da Prato-Malliavin Nualart to show the result.展开更多
Matsushita, Takahashi[4] proved a strong convergence theorem for relatively nonex- pansive mappings in a Banach space by using the hybrid method (CQ method) in mathematical programming. The purpose of this paper is to...Matsushita, Takahashi[4] proved a strong convergence theorem for relatively nonex- pansive mappings in a Banach space by using the hybrid method (CQ method) in mathematical programming. The purpose of this paper is to modify the hybrid method of Matsushita, Taka- hashi by monotone CQ method, and to prove strong convergence theorems for weak relatively nonexpansive mappings and maximal monotone operators in Banach spaces. The convergence rate of monotone CQ method is faster than the hybrid method of Matsushi...展开更多
We prove that for a relatively hyperbolic group,there is a sequence of relatively hyperbolic proper quotients such that their growth rates converge to the growth rate of the group.Under natural assumptions,a similar r...We prove that for a relatively hyperbolic group,there is a sequence of relatively hyperbolic proper quotients such that their growth rates converge to the growth rate of the group.Under natural assumptions,a similar result holds for the critical exponent of a cusp-uniform action of the group on a hyperbolic metric space.As a corollary,we obtain that the critical exponent of a torsion-free geometrically finite Kleinian group can be arbitrarily approximated by those of proper quotient groups.This resolves a question of Dal’bo–Peigné–Picaud–Sambusetti.Our approach is based on the study of Patterson–Sullivan measures on Bowditch boundary of a relatively hyperbolic group and gives a series of results on growth functions of balls and cones.展开更多
In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-stro...In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges weakly to a common element of two sets.展开更多
Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algeb...Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.展开更多
Aging,mitochondria,and neurodegenerative diseases:Aging is often viewed as the buildup of changes that lead to the gradual transformations associated with getting older,along with a rising likelihood of disease and mo...Aging,mitochondria,and neurodegenerative diseases:Aging is often viewed as the buildup of changes that lead to the gradual transformations associated with getting older,along with a rising likelihood of disease and mortality.Although organis m-wide deterioration is observed during aging,organs with high metabolic demand,such as the brain,are more vulnerable.展开更多
BACKGROUND While varices and variceal bleeds are well-known and feared complications of advanced cirrhosis and portal hypertension,omental variceal bleed are a rare sequala even in patients with known esophageal or ga...BACKGROUND While varices and variceal bleeds are well-known and feared complications of advanced cirrhosis and portal hypertension,omental variceal bleed are a rare sequala even in patients with known esophageal or gastric varices.While rare,omental varices pose a risk for hemoperitoneum if ruptured,which is a lifethreatening complication with high mortality rates despite surgical intervention.CASE SUMMARY This report reviews the case of a patient 36-year-old female with alcohol related cirrhosis decompensated by ascites,but no history of varices admitted for hemorrhagic shock from spontaneous rupture of omental varices requiring emergency surgery.She underwent the first documented successful orthotopic liver transplantation the same admission.CONCLUSION This case report and literature review stresses the importance of early consideration and identification of intraabdominal variceal sources in cirrhotic patients with refractory shock.展开更多
基金the National Natural Science Foundation of China (10771050)
文摘In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.
基金supported by the National "863" program of China(No.2012AA050103)
文摘Most relatively high-level radioactive sandstone(HRSS)reservoir has considerable oil(or gas)resource potential.HRSS is often wrongly identified due to its similar logging response characteristics as mudstone,which leads to the omission of effective reservoirs.In this paper,a quantitative identification method for HRSS is proposed after the analyzing of the response characteristics and relationship between spontaneous potential log and natural gamma-ray log in conventional sandstone and mudstone strata.Take the Upper Triassic Yanchang Formation in Ordos Basin as an example:the responses of spontaneous potential log and the responses of natural gamma-ray log are synchronized and positively correlated in conventional sandstone and mudstone strata,but they are not synchronized in HRSS.Quantitative identification of HRSS was realized based on this synchronization feature,and a"virtual compensation"of natural gamma-ray log was performed.At the same time,logging evaluation method about HRSS has been discussed.The final results shows that this identification method work effectively,and can reduce the misjudgment and omission of effective reservoirs.
文摘Interruption,as a linguistic phenomenon,can be see everywhere.And talk show programs are common setting for interruptions.So in this thesis three questions are addressed as followed:What function does the interruption have in these two kinds of talk shows(relatively formal and informal) respectively;what are the similarities of relatively formal and informal talk show programs;what are the differences between relatively formal and informal talk shows.
文摘In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then, we show that the sequence converges strongly to a common element of the two sets. Our results improve and extend the corresponding results reported by many others.
文摘In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.
基金Supported by the National Natural Science Foundation of China(10771050)the Natural Science Foun-dation of Hebei Province(A2010001482)
文摘In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real uniformly smooth and uniformly convex Banach space are proposed. Some weak convergence theorems are obtained, which extend and complement some previous work.
文摘It is given in Weil and Rosenlicht ([1], p. 15) that (resp. 2) for all non-negative integers m and n with m≠n if c is any even (resp. odd) integer. In the present paper we generalize this. Our purpose is to give other integral sequences such that G.C.D.(ym,yn)=1 for all positive integers m and n with m≠n. Roughly speaking we show the following 1) and 2). 1) There are infinitely many polynomial sequences such that G.C.D.(fm(a),fn(a))=1 for all positive integers m and n with with m≠n and infinitely many rational?integers a. 2) There are polynomial sequences such that G.C.D.(gm(a,b),gn(a,b))=1 for all positive integers m and n with m≠n and arbitrary (rational or odd) integers a and b with G.C.D.(a,b)=1. Main results of the present paper are Theorems 1 and 2, and Corollaries 3, 4 and 5.
文摘This article is about the structure of expanding universe. Here I am trying to create a structural model of universe according to my thoughts. Studies showthat universe is accelerating its rate of expansion. Here I am trying to get some conclusions according to my thoughts. In my opinion, our universe is under a gravitational frame with all the matters in it. In this gravitational frame of universe we can consider our universe as a closed system and the empty space outside the frame as an open system. There are two possibilities we can find. One is relative motion of the objects inside the frame. By this way we can feel the universe is accelerating its expansion, but it is not. Another one is the vacuum energy absorption and negative pressure inside the frame. According to this thought, we can say that universe is accelerating and it can continue its motion at present conditions on it, even the force created by the big bang is decreasing. The other point is that, once the absorbed vacuum can create a negative pressure inside the frame, there is no need for the concept of dark energy in our universe [1]. According to this model, negative pressure inside the frame will be created by the absorbed vacuum from the space. So the existence of dark energy can be questioned. In this model, dark energy doesn't play any role in the expansion or rate of acceleration on the expansion of universe. So the dark energy doesn’t exist in this model. During the absorption of vacuum to the frame, it will increase the volume of the frame. It will create free spaces inside the frame to accommodate the vacuum inside the frame. The rest of the absorbed vacuum will move to the center of the frame by the action against gravity and the force created by the big bang. It will increase the density of the absorbed vacuum in the center and can create the negative pressure on the frame to pull it outside to the empty space. It will cause the acceleration on expansion of universe. These things are explained deeply in this article. And here it also explains the destiny of universe according to the frame and expansion of universe.
基金Supported by the Research on the Mechanism and System of Guiding Farmers' Relatively Centralized Residence (0106002442003)Research Program of the Comprehensive Matching Reform Subject of Coordinating City and Village in 2009
文摘On the basis of expounding the status quo of rural residents' residence, the thesis notes that influenced by the weak foundation of rural economy, the characteristic of mountain landscape, smallholder consciousness, shortage of capital and other factors, the rural residents in Chongqing City mainly live scattered. In addition to opportunities of the expansion and drive of city, rural market development, rural resources development, rural industrial development, and rural ecological migration, the model of urban development promotion, the model of market development drive, the model of land development drive, the model of rural industry construction and the model of resettlement and reconstruction are advocated in order to guide the rural residents to adopt relative centralized residence. The suggestions concerning guiding rural residents' relative centralized residence are put forward as follows: firstly, act according to circumstances and conduct scientific planning and design; secondly, propagate extensively and activate famers' willingness; thirdly, first experiment and exert the exemplary guide; fourthly, perfect policy and guarantee farmers' benefit; fifthly, strengthen leadership and decrease the risk of centralized residence; sixthly, boost gradually and realize moderate centralized residence.
基金supported by the National Natural Science Foundation of China(No.11971480)the Natural Science Fund of Hunan for Excellent Youth(No.2020JJ3038)+2 种基金the Fund for NUDT Young Innovator Awards(No.20190105)supported by the National Natural Science Foundation of China(Nos.11991020,11631013,12021001,11971372 and 11991021)the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDA27000000).
文摘Nonconvex–nonconcave saddle-point optimization in machine learning has triggered lots of research for studying non-monotone variational inequalities(VIs).In this work,we introduce two mirror frameworks,called mirror extragradient method and mirror extrapolation method,for approximating solutions to relatively Lipschitz and monotone-like VIs.The former covers the well-known Nemirovski’s mirror prox method and Nesterov’s dual extrapolation method,and the recently proposed Bregman extragradient method;all of them can be reformulated into a scheme that is very similar to the original form of extragradient method.The latter includes the operator extrapolation method and the Bregman extrapolation method as its special cases.The proposed mirror frameworks allow us to present a unified and improved convergence analysis for all these existing methods under relative Lipschitzness and monotone-like conditions that may be the currently weakest assumptions guaranteeing(sub)linear convergence.
基金National Natural Science Foundation of China(52175237)。
文摘The key parameters that characterize the morphological quality of multi-layer and multi-pass metal laser deposited parts are the surface roughness and the error between the actual printing height and the theoretical model height.The Taguchi method was employed to establish the correlations between process parameter combinations and multi-objective characterization of metal deposition morphology(height error and roughness).Results show that using the signal-to-noise ratio and grey relational analysis,the optimal parameter combination for multi-layer and multi-pass deposition is determined as follows:laser power of 800 W,powder feeding rate of 0.3 r/min,step distance of 1.6 mm,and scanning speed of 20 mm/s.Subsequently,a Genetic Bayesian-back propagation(GB-BP)network is constructed to predict multi-objective responses.Compared with the traditional back propagation network,the GB-back propagation network improves the prediction accuracy of height error and surface roughness by 43.14%and 71.43%,respectively.This network can accurately predict the multi-objective characterization of morphological quality of multi-layer and multi-pass metal deposited parts.
基金Project supported by the National Natural Science Foundation of China.
文摘The aim of this paper is to investigate relatively flat envelopes. A necessary and sufficient condition is given for a relatively-finitely presented module to have a (mono-morphic or epic) relatively flat envelope. Then those rings are characterized whose every relatively-finitely presented module has a relatively flat envelope which coincides with its in-jective envelope. Some known results are obtained as corollaries.
文摘In this paper, we have proved that for a relatively complemented distributive lattice L,there exists one and only one completion ? of L such that for every ξ∈?, there exists afamily {S_α}_(α∈△) of non-vacuous subsets of L satisfying ξ= ∨[∧f(S_α)]. Such a completion? is called the entire completion of L. We have in this paper extended the homomorphic extension theorem of a generalizedBoolean lattice to that of a relatively complemented distributive lattice and proved that the lat-tice of the congruences on a relatively complemented distributive lattice is isomorphicwith the lattice of the convex sublattices containing a fixed element and that the entire comple-tion of a relatively complemented distributive lattice L, the lattice of the completable con-gruences on L and the lattice of the completable convex sublattices of L containing a fixed ele-ment are isomorphic.
基金supported by NSF(No.10301011)of China Project 973
文摘In this note, we obtain a sufficient and necessary condition for a set in an abstract Winner space （X, H, μ） to be relatively compact in L^2（X, μ）. Meanwhile, we give a sufficient condition for relative compactness in L^P（X, μ） for p〉1. We also provide an example of Da Prato-Malliavin Nualart to show the result.
基金the National Natural Science Foundation of China (No.10771050)
文摘Matsushita, Takahashi[4] proved a strong convergence theorem for relatively nonex- pansive mappings in a Banach space by using the hybrid method (CQ method) in mathematical programming. The purpose of this paper is to modify the hybrid method of Matsushita, Taka- hashi by monotone CQ method, and to prove strong convergence theorems for weak relatively nonexpansive mappings and maximal monotone operators in Banach spaces. The convergence rate of monotone CQ method is faster than the hybrid method of Matsushi...
文摘We prove that for a relatively hyperbolic group,there is a sequence of relatively hyperbolic proper quotients such that their growth rates converge to the growth rate of the group.Under natural assumptions,a similar result holds for the critical exponent of a cusp-uniform action of the group on a hyperbolic metric space.As a corollary,we obtain that the critical exponent of a torsion-free geometrically finite Kleinian group can be arbitrarily approximated by those of proper quotient groups.This resolves a question of Dal’bo–Peigné–Picaud–Sambusetti.Our approach is based on the study of Patterson–Sullivan measures on Bowditch boundary of a relatively hyperbolic group and gives a series of results on growth functions of balls and cones.
文摘In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges weakly to a common element of two sets.
基金Supported by the Science and Technology Program of Guizhou Province(Grant No.QKHJC QN[2025]362)the National Natural Science Foundation of China(Grant No.12361005).
文摘Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.
文摘Aging,mitochondria,and neurodegenerative diseases:Aging is often viewed as the buildup of changes that lead to the gradual transformations associated with getting older,along with a rising likelihood of disease and mortality.Although organis m-wide deterioration is observed during aging,organs with high metabolic demand,such as the brain,are more vulnerable.
文摘BACKGROUND While varices and variceal bleeds are well-known and feared complications of advanced cirrhosis and portal hypertension,omental variceal bleed are a rare sequala even in patients with known esophageal or gastric varices.While rare,omental varices pose a risk for hemoperitoneum if ruptured,which is a lifethreatening complication with high mortality rates despite surgical intervention.CASE SUMMARY This report reviews the case of a patient 36-year-old female with alcohol related cirrhosis decompensated by ascites,but no history of varices admitted for hemorrhagic shock from spontaneous rupture of omental varices requiring emergency surgery.She underwent the first documented successful orthotopic liver transplantation the same admission.CONCLUSION This case report and literature review stresses the importance of early consideration and identification of intraabdominal variceal sources in cirrhotic patients with refractory shock.
