In Orlicz-Bochner sequence spaces endowed with Orlicz norm and Luxemburg norm, points of lower monotonicity, upper monotonicity, lower local uniform monotonicity and upper local uniform monotonicity are characterized.
In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup...In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of e1（S） are equivalent. We use this to give a direct proof of the approximate amenability of e1 （S） for a Brandt semigroup S. Moreover, we characterize the approximate amenability of e1（S）, where S is a uniformly locally finite band semigroup.展开更多
A new method for targeted heating of deep tissue was developed by using an ultrasound phased-array system which can generate various multiple loci patterns by electronically changing its amplitude or phase pattern. Th...A new method for targeted heating of deep tissue was developed by using an ultrasound phased-array system which can generate various multiple loci patterns by electronically changing its amplitude or phase pattern. This method involves using a technique of combining switching and rotating of multiple foei patterns to create a uniform temperature over tissue volumes in various size. Using this method, the target tissue deep in the body can be heated to a specified temperature, which gives conditions for thermo-sensi- tive liposomes release. A simulation study for a 108-element, spherically sectioned array was performed to determine an optimal heating scheme from a set of multiple focus fields which were produced by inputting different combinations of phases and amplitudes. Comparisons of a static multiple foei field, the switched fields and the switched-rotated fields indicated that the technique of combining switching and rotating of multiple foei patterns has advantages of both lowering the peak temperature and evening the temperature distribution. The simulation results also show that the therapeutic heating zones in various size （ Φ5mm ～40mm） with uniform temperature distributions can be obtained employing the combined method. These results offer significant data for desisting thermotherapy equipment for tumor-specific drug release with thermo-sensitive liposomes.展开更多
First we prove that the approximative compactness of a nonempty set C in a normed linear space can be reformulated equivalently in another way.It is known that if C is a semi-Chebyshev closed and approximately compact...First we prove that the approximative compactness of a nonempty set C in a normed linear space can be reformulated equivalently in another way.It is known that if C is a semi-Chebyshev closed and approximately compact set in a Banach space X,then the metric projectorπC from X onto C is continuous.Under the assumption that X is midpoint locally uniformly rotund,we prove that the approximative compactness of C is also necessary for the continuity of the projectorπC by the method of geometry of Banach spaces.Using this general result we find some necessary and sufficient conditions for T to have a continuous Moore-Penrose metric generalized inverse T^+,where T is a bounded linear operator from an approximative compact and a rotund Banach space X into a midpoint locally uniformly rotund Banach space Y.展开更多
Hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stabi...Hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stability and continuity for such best approximation problems are discussed.展开更多
We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k...We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k + 1)-convex, and in the second case, the k-Hessian equations are uniformly elliptic with respect to that solution. Based on this classification, we obtain the existence of C∞local solution for nonhomogeneous term f without sign assumptions.展开更多
A series of convex functions on a Banach space is studied. The generalizations of the Moreau-Rockafellar theorem are given. As its application, the partial generalization of the Kuhn- Tucker theorem is obtained.
Longtime behavior of degenerate equations with the nonlinearity of polynomial growth of arbitrary order on the whole space RN is considered. By using-tra jectories methods, we proved that weak solutions generated by d...Longtime behavior of degenerate equations with the nonlinearity of polynomial growth of arbitrary order on the whole space RN is considered. By using-tra jectories methods, we proved that weak solutions generated by degenerate equations possess an（LU^2（R^N）, Lloc^2（R^N））-global attractor.Moreover, the upper bounds of the Kolmogorov ε-entropy for such global attractor are also obtained.展开更多
We establish the moderate deviation for the density process of the single point catalytic super-Brownian motion. The main tools are the abstract Gaertner-Ellis theorem, Dawson-Gaertner the- orem and the contraction pr...We establish the moderate deviation for the density process of the single point catalytic super-Brownian motion. The main tools are the abstract Gaertner-Ellis theorem, Dawson-Gaertner the- orem and the contraction principle. The rate function is expressed by the Fenchel-Legendre transform of log-exponential moment generation function.展开更多
文摘In Orlicz-Bochner sequence spaces endowed with Orlicz norm and Luxemburg norm, points of lower monotonicity, upper monotonicity, lower local uniform monotonicity and upper local uniform monotonicity are characterized.
文摘In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of e1（S） are equivalent. We use this to give a direct proof of the approximate amenability of e1 （S） for a Brandt semigroup S. Moreover, we characterize the approximate amenability of e1（S）, where S is a uniformly locally finite band semigroup.
基金the National Natural Science Foundation of China(No.30500124)Shanghai Key Technologies R&D Program of China(No.05DZ19509)
文摘A new method for targeted heating of deep tissue was developed by using an ultrasound phased-array system which can generate various multiple loci patterns by electronically changing its amplitude or phase pattern. This method involves using a technique of combining switching and rotating of multiple foei patterns to create a uniform temperature over tissue volumes in various size. Using this method, the target tissue deep in the body can be heated to a specified temperature, which gives conditions for thermo-sensi- tive liposomes release. A simulation study for a 108-element, spherically sectioned array was performed to determine an optimal heating scheme from a set of multiple focus fields which were produced by inputting different combinations of phases and amplitudes. Comparisons of a static multiple foei field, the switched fields and the switched-rotated fields indicated that the technique of combining switching and rotating of multiple foei patterns has advantages of both lowering the peak temperature and evening the temperature distribution. The simulation results also show that the therapeutic heating zones in various size （ Φ5mm ～40mm） with uniform temperature distributions can be obtained employing the combined method. These results offer significant data for desisting thermotherapy equipment for tumor-specific drug release with thermo-sensitive liposomes.
基金the State Committee for Scientific Research,Poland (Grant No.1P03A1127)the National Nature Science Foundation of China (Grant Nos.10471032,10671049)
文摘First we prove that the approximative compactness of a nonempty set C in a normed linear space can be reformulated equivalently in another way.It is known that if C is a semi-Chebyshev closed and approximately compact set in a Banach space X,then the metric projectorπC from X onto C is continuous.Under the assumption that X is midpoint locally uniformly rotund,we prove that the approximative compactness of C is also necessary for the continuity of the projectorπC by the method of geometry of Banach spaces.Using this general result we find some necessary and sufficient conditions for T to have a continuous Moore-Penrose metric generalized inverse T^+,where T is a bounded linear operator from an approximative compact and a rotund Banach space X into a midpoint locally uniformly rotund Banach space Y.
基金Supported by National Natural Science Foundation of China, Grant (10471032)
文摘Hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stability and continuity for such best approximation problems are discussed.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171339 and 11171261)National Center for Mathematics and Interdisciplinary Sciences
文摘We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k + 1)-convex, and in the second case, the k-Hessian equations are uniformly elliptic with respect to that solution. Based on this classification, we obtain the existence of C∞local solution for nonhomogeneous term f without sign assumptions.
文摘A series of convex functions on a Banach space is studied. The generalizations of the Moreau-Rockafellar theorem are given. As its application, the partial generalization of the Kuhn- Tucker theorem is obtained.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.NS2014075)
文摘Longtime behavior of degenerate equations with the nonlinearity of polynomial growth of arbitrary order on the whole space RN is considered. By using-tra jectories methods, we proved that weak solutions generated by degenerate equations possess an（LU^2（R^N）, Lloc^2（R^N））-global attractor.Moreover, the upper bounds of the Kolmogorov ε-entropy for such global attractor are also obtained.
基金Supported by National Natural Science Foundation of China (Grant No. 11071021)
文摘We establish the moderate deviation for the density process of the single point catalytic super-Brownian motion. The main tools are the abstract Gaertner-Ellis theorem, Dawson-Gaertner the- orem and the contraction principle. The rate function is expressed by the Fenchel-Legendre transform of log-exponential moment generation function.
