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.     

CONCEPTUAL DESIGN STUDIES OF AN 84 GHz, 500 kW, CW GYROTRON

The feasibility of an 84 GHz, 500 kW, CW gyrotron for ECRH on an experimental tokamak will be presented in this paper. Mode competition and mode selection procedures are carefully investigated by considering various candidate modes and the TE_10,4 mode is chosen as the operating mode. A conventional cylindrical cavity resonator with weak input and output tapers and parabolic roundings is considered for interaction studies. Self-consistent, both single mode and time-dependent, calculations are carried out and power and efficiencies are computed for a typical set of beam parameters. The results show that an output power of well over 500 kW, CW and efficiency around 40% can be reached without a depressed collector.     

Banach空间二阶非线性微分方程的弱Carathéodory解

本文定义了二阶微分方程的弱 Carathéodory解 ,在不涉及紧型条件的情形下 ,直接用迭代法证明了 Banach空间二阶非线性常微分方程两点边值问题存在唯一解 ,并给出逼近解迭代序列的误差估计 ,对周期边值问题得到类似的结果     

一类含参广义集值拟变分包含组的解的灵敏性分析

本文引入了一类新的含参广义集值拟变分包含组,应用隐预解算子技巧,建立了该类变分包含组与一类不动点问题的等价性,在适当的条件下,分析了含参广义集值拟变分包含组的解的灵敏性,所得结果推广改进了最新文献中的许多结果．     

The AB2-XA1 electronic transition of NO2: A rovibronic survey covering 14 300-18 000 cm

More than 250 rotationally resolved vibrational bands of the A²B₂-X²A₁ electronic transition of ¹⁵NO₂ have been observed in the 14 300-18 000 cm⁻¹ range. The bands have been recorded in a recently constructed setup designed for high resolution spectroscopy of jet cooled molecules by combining time gated fluorescence spectroscopy and molecular beam techniques. The majority of the observed bands has been rotationally assigned and can be identified as transitions starting from the vibrational ground state or from vibrationally excited (hot band) states. An exceptionally strong band is located at 14 851 cm⁻¹ and studied in more detail as a typical benchmark transition to monitor ¹⁵NO₂ in atmospheric remote sensing experiments. Standard rotational fit routines provide band origins, rotational and spin rotation constants. A subset of 177 vibronic levels of ²B₂ vibronic symmetry has been analyzed in the energy range between 14 300 and 17 250 cm⁻¹, in terms of integrated density and using Next Neighbor Distribution. It is found that the overall statistical properties and polyad structure of ¹⁵NO₂ are comparable to those of ¹⁴NO₂ but that the internal structures of the polyads are completely different. This is a direct consequence of the X²A₁-A²B₂ vibronic mixing.