Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.
E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixe...E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.展开更多
The purpose of this article is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive ma...The purpose of this article is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this article extend and improve the corresponding results of [1, 2, 4-9, 11-15].展开更多
In this paper,we introduce the concepts of I-covering mappings and 1-I-covering mappings,discuss the difference between sequence-covering and I-covering mappings by some examples.With those concepts,we get some intere...In this paper,we introduce the concepts of I-covering mappings and 1-I-covering mappings,discuss the difference between sequence-covering and I-covering mappings by some examples.With those concepts,we get some interesting properties of I-covering(1-I-covering)mappings and some characterizations of I-covering(1-I-covering)and compact mapping images of metric spaces.展开更多
Building compact 3D maps of the environment models has become an important research topic. This paper presented an efficient stream decimation algorithm of massive meshes. The algorithm adapted the pre-processing step...Building compact 3D maps of the environment models has become an important research topic. This paper presented an efficient stream decimation algorithm of massive meshes. The algorithm adapted the pre-processing step leading to lower in-corn memory consumption. This algorithm is applied to reconstructing compact terrain with mobile robot, achieving satisfying results.展开更多
The characterization of kerogen nanopores is crucial for predicting the geostorage capacity and recoverability of natural gas in unconventional gas shale reservoirs.Towards this end,a powerful technique is presented w...The characterization of kerogen nanopores is crucial for predicting the geostorage capacity and recoverability of natural gas in unconventional gas shale reservoirs.Towards this end,a powerful technique is presented which integrates 2D NMR T_(1)-T_(2) relaxation measurements with molecular dynamics(MD)simulations of hydrocarbons confined in the nanopores of kerogen.The integrated NMR-MD technique is demonstrated using T_(1)-T_(2) measurements of kerogen isolates and organic-rich chalks saturated with heptane,together with MD simulations of heptane completely dissolved in a realistic kerogen model.The NMR-MD results are used to extract the swelling ratio and nanopore size distribution of kerogen as a function of depth in the reservoir.The effects of organic nanoconfinement on the T_(1) relaxation dispersion and T_(2) residual dipolar coupling of heptane are investigated,as well as the effect of downhole effective stress on the kerogen nanopore size as a function of depth and compaction.Potential applications in partially depleted gas shale reservoirs are discussed,including CO_(2) utilization/geostorage,geostorage of green H2,and integration of the NMR-MD technique with thermodynamic models for predicting the competitive sorption of gas mixtures in kerogen.展开更多
This paper gives internal characterizations of some sequence covering compact images and compact covering compact images of paracompact locally compact spaces, which improve some results on compact images of locally...This paper gives internal characterizations of some sequence covering compact images and compact covering compact images of paracompact locally compact spaces, which improve some results on compact images of locally compact metric spaces.展开更多
Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continu...Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.展开更多
The main purpose of the present work is to introduce necessary conditions for a map on a non-metric space, defined by using a map on a metric space, to have a fixed point.
Our purpose is to introduce new necessary conditions for a fixed point of maps on non-metric spaces. We use a contraction map on a metric topological space and a lately published definition of limit of a function betw...Our purpose is to introduce new necessary conditions for a fixed point of maps on non-metric spaces. We use a contraction map on a metric topological space and a lately published definition of limit of a function between the metric topological space and the non-metric topological space. Then we show that we can create a function h on the non-metric space Y, h :Y →Y and present necessary conditions for a fixed point of this map on this map on Y. Therefore, this gives an opportunity to take a best conclusion in some sense, when non-metrizable matter is under consideration.展开更多
Topological entropy can be an indicator of complicated behavior in dynamical systems. It is first introduce by Adler, Konheim and McAndrew by using open covers in 1965. After that it is still an active research by man...Topological entropy can be an indicator of complicated behavior in dynamical systems. It is first introduce by Adler, Konheim and McAndrew by using open covers in 1965. After that it is still an active research by many researchers to produce more properties and applications up to nowadays. The purpose of this paper is to review and explain most important concepts and results of topological entropies of continuous self-maps for dynamical systems on compact and non-compact topological and metric spaces. We give proofs for some of its elementary properties of the topological entropy. Slight modification on Adler＇s topological entropy is also presented.展开更多
文摘Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.
基金Supported in part by Education Ministry,Anhui Province,China(No:2003kj047zd)
文摘E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.
基金The present studies were supported by the Natural Science Foundation of Zhe-jiang Province (Y605191)the Natural Science Foundation of Heilongjiang Province (A0211)the Key Teacher Creating Capacity Fund of Heilongjiang General College (1053G015)the Scientific Research Foundation from Zhejiang Province Education Committee (20051897)the Starting Foundation of Scientific Research from Hangzhou Teacher's College.
文摘The purpose of this article is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this article extend and improve the corresponding results of [1, 2, 4-9, 11-15].
基金Supported by the National Natural Science Foundation of China(Grant No.11801254)the Ningde Normal University(Grant No.2017T01)
文摘In this paper,we introduce the concepts of I-covering mappings and 1-I-covering mappings,discuss the difference between sequence-covering and I-covering mappings by some examples.With those concepts,we get some interesting properties of I-covering(1-I-covering)mappings and some characterizations of I-covering(1-I-covering)and compact mapping images of metric spaces.
文摘Building compact 3D maps of the environment models has become an important research topic. This paper presented an efficient stream decimation algorithm of massive meshes. The algorithm adapted the pre-processing step leading to lower in-corn memory consumption. This algorithm is applied to reconstructing compact terrain with mobile robot, achieving satisfying results.
基金Vinegar Technologies LLC,Chevron Energy Technology Company,Rice University Consortium for Processes in Porous Media,and the American Chemical Society Petroleum Research Fund(No.ACS PRF 58859-ND6)for their financial support。
文摘The characterization of kerogen nanopores is crucial for predicting the geostorage capacity and recoverability of natural gas in unconventional gas shale reservoirs.Towards this end,a powerful technique is presented which integrates 2D NMR T_(1)-T_(2) relaxation measurements with molecular dynamics(MD)simulations of hydrocarbons confined in the nanopores of kerogen.The integrated NMR-MD technique is demonstrated using T_(1)-T_(2) measurements of kerogen isolates and organic-rich chalks saturated with heptane,together with MD simulations of heptane completely dissolved in a realistic kerogen model.The NMR-MD results are used to extract the swelling ratio and nanopore size distribution of kerogen as a function of depth in the reservoir.The effects of organic nanoconfinement on the T_(1) relaxation dispersion and T_(2) residual dipolar coupling of heptane are investigated,as well as the effect of downhole effective stress on the kerogen nanopore size as a function of depth and compaction.Potential applications in partially depleted gas shale reservoirs are discussed,including CO_(2) utilization/geostorage,geostorage of green H2,and integration of the NMR-MD technique with thermodynamic models for predicting the competitive sorption of gas mixtures in kerogen.
文摘This paper gives internal characterizations of some sequence covering compact images and compact covering compact images of paracompact locally compact spaces, which improve some results on compact images of locally compact metric spaces.
基金Project supported by D.G.E.S. Pb 96-1338-CO 2-01 and the Junta de Andalucia
文摘Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.
文摘The main purpose of the present work is to introduce necessary conditions for a map on a non-metric space, defined by using a map on a metric space, to have a fixed point.
文摘Our purpose is to introduce new necessary conditions for a fixed point of maps on non-metric spaces. We use a contraction map on a metric topological space and a lately published definition of limit of a function between the metric topological space and the non-metric topological space. Then we show that we can create a function h on the non-metric space Y, h :Y →Y and present necessary conditions for a fixed point of this map on this map on Y. Therefore, this gives an opportunity to take a best conclusion in some sense, when non-metrizable matter is under consideration.
文摘Topological entropy can be an indicator of complicated behavior in dynamical systems. It is first introduce by Adler, Konheim and McAndrew by using open covers in 1965. After that it is still an active research by many researchers to produce more properties and applications up to nowadays. The purpose of this paper is to review and explain most important concepts and results of topological entropies of continuous self-maps for dynamical systems on compact and non-compact topological and metric spaces. We give proofs for some of its elementary properties of the topological entropy. Slight modification on Adler＇s topological entropy is also presented.
