一类压缩型映射的不动点定理

在完备的度量空间中,讨论了一类新型的非线性压缩映射ρ(Tx,Ty)≤a(ρ(x,y))ρ(x,Tx)+b(ρ(x,y))ρ(y,Ty)+c(ρ(x,y))ρ(x,y)通过构造迭代序列,指出该映射的不动点的存在性和唯一性,并给出相应的误差估计式,拓展和改进了有关文献的范围.     

p-Adic函数空间上Hardy型算子的多线性交换子估计

在p-adic域上研究分数次Hardy型算子与CMO(Q_p~n)函数生成的多线性交换子,建立了交换子在Lebesgue空间和Herz空间上的有界性.对Hardy算子的多线性交换子也得到了相应的结果.     

Boundedness of commutators on homogeneous Herz spaces

The boundedness on homogeneous Herz spaces is established for a large class of linear commutators generated by BMO(R ⁿ ) functions and linear operators of rough kernels which include the Calderón-Zygmund operators and the Ricci-Stein oRfiUatory singular integrals with rough kernels. Project supponed in pan by the National h’atural Science Foundation of China (Grant No. 19131080) and the NEDF of China.     

Integral Kernel Operators on Fock Space – Generalizations and Applications to Quantum Dynamics

A general theory of operators on Boson Fock space is discussed in terms of the white noise distribution theory on Gaussian space (white noise calculus). An integral kernel operator is generalized from two aspects: (i) The use of an operator-valued distribution as an integral kernel leads us to the Fubini type theorem which allows an iterated integration in an integral kernel operator. As an application a white noise approach to quantum stochastic integrals is discussed and a quantum Hitsuda–Skorokhod integral is introduced. (ii) The use of pointwise derivatives of annihilation and creation operators assures the partial integration in an integral kernel operator. In particular, the particle flux density becomes a distribution with values in continuous operators on white noise functions and yields a representation of a Lie algebra of vector fields by means of such operators.     

Improving the rate of convergence of Newton methods on Banach spaces with a convergence structure and applications

In this note, we use inexact Newton-like methods to find solutions of nonlinear operator equations on Banach spaces with a convergence structure. Our technique involves the introduction of a generalized norm as an operator from a linear space into a partially ordered Banach space. In this way, the metric properties of the examined problem can be analyzed more precisely. Moreover, this approach allows us to derive from the same theorem, on the one hand, semilocal results of Kantorovich-type, and on the other hand, global results based on monotonicity considerations. By imposing very general Lipschitz-like conditions on the operators involved, on the one hand, we cover a wider range of problems, and on the other hand, by choosing our operators appropriately, we can find sharper error bounds on the distances involved than before. Furthermore, we show that special cases of our results reduce to the corresponding ones already in the literature. Finally, several examples are being provided where our results compare favorably with earlier ones.     

Convex functions, subdifferentiability and renormings

This paper through discussing subdifferentiability and convexity of convex functions shows that a Banach space admits an equivalent uniformly [locally uniformly, strictly] convex norm if and only if there exists a continuous uniformly [locally uniformly, strictly] convex function on some nonempty open convex subset of the space and presents some characterizations of super-reflexive Banach spaces. Supported by NSFC     

Exploiting the diversity of time scales in the immune system: A B-cell antibody model

Using the continuous shape space formalism, we develop an immune system model involving both B lymphocytes and antibody molecules. The binding and cross-linking of receptors on B cells stimulates the cells to divide and, with a lag, to secrete antibody. Using the method of multiple scales, we show how to correctly formulate long-time-scale equations for the population dynamics of B cells, the total antibody concentration, and rate of antibody secretion. We compare our model with previous phenomenological formulations.