Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defin...Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionaUy differentiable functions are derived. Furthermore, the mean-value theorem for a directionaUy differentiable function is demonstrated.展开更多
We classify a generalized coupled singular Emden-Fowler type system ＋a（t）vn=0,v＋b（t）um=0 with respect to the standard first-order Lagrangian according to the Noether point symmetries which it admits.First integr...We classify a generalized coupled singular Emden-Fowler type system ＋a（t）vn=0,v＋b（t）um=0 with respect to the standard first-order Lagrangian according to the Noether point symmetries which it admits.First integrals of the various cases which admit Noether point symmetries are then obtained.This system was discussed in the literature from the view-point of existence and uniqueness of positive solutions.展开更多
This is the second paper in a series following Tian and Xu(2015), on the construction of a mathematical theory of the gauged linear σ-model(GLSM). In this paper, assuming the existence of virtual moduli cycles and th...This is the second paper in a series following Tian and Xu(2015), on the construction of a mathematical theory of the gauged linear σ-model(GLSM). In this paper, assuming the existence of virtual moduli cycles and their certain properties, we define the correlation function of GLSM for a fixed smooth rigidified r-spin curve.展开更多
Let E be a cookie-cutter set with dimH E =s. It is known that the Hausdorff s-measure and the packing s-measure of the set E are positive and finite. In this paper, we prove that for a gauge function g the set E has p...Let E be a cookie-cutter set with dimH E =s. It is known that the Hausdorff s-measure and the packing s-measure of the set E are positive and finite. In this paper, we prove that for a gauge function g the set E has positive and finite Hausdorff g-measure if and only if 0 〈 liminft→0 g（t）/ts 〈 ∞. Also, we prove that for a doubling gauge function g the set E has positive and finite packing g-measure if and only if 0 〈 lim supt→0 g（t）/ts 〈 ∞.展开更多
In the framework of reflexive Banach spaces satisfying a weakly continuous duality map, the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many a...In the framework of reflexive Banach spaces satisfying a weakly continuous duality map, the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many asymptotically nonexpansive mappings. The main results obtained in this paper improve and extend some recent results.展开更多
In this paper, the relationship between the s-dimensional Hausdorff measures and the g-measures in Rd is discussed, where g is a gauge function which is equivalent to ts and 0 < s≤d. It shows that if s=d, then Hg ...In this paper, the relationship between the s-dimensional Hausdorff measures and the g-measures in Rd is discussed, where g is a gauge function which is equivalent to ts and 0 < s≤d. It shows that if s=d, then Hg = c1Hd, Cg = c2Cd and Pg = c3Pd on Rd, where constants c1, c2 and c3 are determined by where Wg, Cg and Pg are the g-Hausdorff, g-central Hausdorff and g-packing measures on Rd respectively. In the case 0<s<d, some examples are given to show that the above conclusion may fail. However, there is always some s-set F (?) Rd such that Hg|F=C1HS|F, Cg|F = c2Cs|F and Pg|F = c3Ps|F, where the constants c1, c2 and c3 depend not only on g and s, but also on F. A criterion is presented for judging whether an s-set has the above properties.展开更多
Massless quark pair production in SU(2) gauge chromoelectric field is investigated by solving the Wigner function with back reaction. The temporal evolution of specific field and its current are obtained self consiste...Massless quark pair production in SU(2) gauge chromoelectric field is investigated by solving the Wigner function with back reaction. The temporal evolution of specific field and its current are obtained self consistently. For the quark distribution function, both its time and momentum dependence are studied. In particular, some interesting phenomena are found, for example, the more abundant symmetry or/and antisymmetry characteristics, the existence of the attractive basin structure and the existence of the momentum "gap" in the quark distribution and so on. All the phenomena are associated with the quark-gluon plasma oscillation, which due to the back reaction effect. The study and analysis qualitatively about the components of the Wigner function are expected to be helpful to deepen the understanding of the QCD vacuum.展开更多
文摘Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionaUy differentiable functions are derived. Furthermore, the mean-value theorem for a directionaUy differentiable function is demonstrated.
文摘We classify a generalized coupled singular Emden-Fowler type system ＋a（t）vn=0,v＋b（t）um=0 with respect to the standard first-order Lagrangian according to the Noether point symmetries which it admits.First integrals of the various cases which admit Noether point symmetries are then obtained.This system was discussed in the literature from the view-point of existence and uniqueness of positive solutions.
基金supported by National Science Foundation of USA(Grant No.DMS-1309359)National Natural Science Foundation of China(Grant No.11331001)
文摘This is the second paper in a series following Tian and Xu(2015), on the construction of a mathematical theory of the gauged linear σ-model(GLSM). In this paper, assuming the existence of virtual moduli cycles and their certain properties, we define the correlation function of GLSM for a fixed smooth rigidified r-spin curve.
基金Supported by NSFC (Grant Nos.10571063,10771164)HuBei JiaoYuTing (Grant No.D20061001)
文摘Let E be a cookie-cutter set with dimH E =s. It is known that the Hausdorff s-measure and the packing s-measure of the set E are positive and finite. In this paper, we prove that for a gauge function g the set E has positive and finite Hausdorff g-measure if and only if 0 〈 liminft→0 g（t）/ts 〈 ∞. Also, we prove that for a doubling gauge function g the set E has positive and finite packing g-measure if and only if 0 〈 lim supt→0 g（t）/ts 〈 ∞.
文摘In the framework of reflexive Banach spaces satisfying a weakly continuous duality map, the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many asymptotically nonexpansive mappings. The main results obtained in this paper improve and extend some recent results.
文摘In this paper, the relationship between the s-dimensional Hausdorff measures and the g-measures in Rd is discussed, where g is a gauge function which is equivalent to ts and 0 < s≤d. It shows that if s=d, then Hg = c1Hd, Cg = c2Cd and Pg = c3Pd on Rd, where constants c1, c2 and c3 are determined by where Wg, Cg and Pg are the g-Hausdorff, g-central Hausdorff and g-packing measures on Rd respectively. In the case 0<s<d, some examples are given to show that the above conclusion may fail. However, there is always some s-set F (?) Rd such that Hg|F=C1HS|F, Cg|F = c2Cs|F and Pg|F = c3Ps|F, where the constants c1, c2 and c3 depend not only on g and s, but also on F. A criterion is presented for judging whether an s-set has the above properties.
基金Supported by the National Natural Science Foundation of China under Grant No.11475026
文摘Massless quark pair production in SU(2) gauge chromoelectric field is investigated by solving the Wigner function with back reaction. The temporal evolution of specific field and its current are obtained self consistently. For the quark distribution function, both its time and momentum dependence are studied. In particular, some interesting phenomena are found, for example, the more abundant symmetry or/and antisymmetry characteristics, the existence of the attractive basin structure and the existence of the momentum "gap" in the quark distribution and so on. All the phenomena are associated with the quark-gluon plasma oscillation, which due to the back reaction effect. The study and analysis qualitatively about the components of the Wigner function are expected to be helpful to deepen the understanding of the QCD vacuum.
