Scattering theory without large-distance asymptotics

In conventional scattering theory, to obtain an explicit result, one imposes a precondition that the distance between target and observer is infinite. With the help of this precondition, one can asymptotically replace the Hankel function and the Bessel function with the sine functions so that one can achieve an explicit result. Nevertheless, after such a treatment, the information of the distance between target and observer is inevitably lost. In this paper, we show that such a precondition is not necessary: without losing any information of distance, one can still obtain an explicit result of a scattering rigorously. In other words, we give an rigorous explicit scattering result which contains the information of distance between target and observer. We show that at a finite distance, a modification factor --- the Bessel polynomial --- appears in the scattering amplitude, and, consequently, the cross section depends on the distance, the outgoing wave-front surface is no longer a sphere, and, besides the phase shift, there is an additional phase (the argument of the Bessel polynomial) appears in the scattering wave function

Personal Characteristics, Job Characteristics, Job Satisfaction, and Organizational Commitment of Taiwanese Expatriates Working in Mainland China

With a population of 1.2 billion, mainland China has become a major target country for many foreign companies looking to expand their businesses because of its inexpensive labor and its large market. Since 1987, many manufacturers in Taiwan have moved to mainland China to reduce labor costs. In 2006, there were 70,256 companies from Taiwan operating in mainland China with fiscal expenditures exceeding US $42.8 1 billion dollars (Ministry of Commerce of the People\u27s Republic of China, 2006). If Taiwan\u27s foreign direct investment (FDI) and offshore investment expenditures were included, Taiwan would have had the second largest FDI in mainland China (Department of Investment Services Ministry of Economic Affairs, 2006). The purpose of this correlational (explanatory), causal comparative (exploratory) study is to investigate the relationships among personal characteristics, job characteristics, job satisfaction, and organizational commitment, and the mediating effects of job characteristics on job satisfaction and organizational commitment of Taiwanese expatriates working in mainland China. The entire accessible population of 6,156 Taiwanese expatriates was invited to participate by e-mail - resulting in a valid sample of 389 responses. The survey was translated into Traditional Chinese. To answer the research questions and examine the hypotheses, all responses obtained through the online survey were analyzed by the Statistical Package from Social Sciences (SPSS) version 14.0. The methods of data analysis used in this study consisted of exploratory data analysis (EDA), exploratory factor analysis (EFA), internal consistency reliability, one-way analysis of variance (ANOVA) with post hoc comparison tests, two-tailed independent t-tests, hierarchical regression, and moderated multiple regression (MMR). Findings indicated that (a) the variables of job characteristics, job satisfaction, and organizational commitment were significantly different according to variables of personal characteristics; (b) personal characteristics, job characteristics, and job satisfaction were significant explanatory variables of affective commitment, normative commitment, and continuance commitment; (c) job characteristics mediated the positive impact of intrinsic job satisfaction on affective commitment; (d) job characteristics mediated the negative impact of extrinsic job satisfaction on affective commitment and normative commitment. Further study to replicate the research in different countries in order to explore the relationships among personal characteristics, job characteristics, job satisfaction, and organizational commitment of expatriates was recommended

Probability Thermodynamics and Probability Quantum Field

In this paper, we introduce probability thermodynamics and probability quantum fields. By probability we mean that there is an unknown operator, physical or nonphysical, whose eigenvalues obey a certain statistical distribution. Eigenvalue spectra define spectral functions. Various thermodynamic quantities in thermodynamics and effective actions in quantum field theory are all spectral functions. In the scheme, eigenvalues obey a probability distribution, so a probability distribution determines a family of spectral functions in thermodynamics and in quantum field theory. This leads to probability thermodynamics and probability quantum fields determined by a probability distribution. There are two types of spectra: lower bounded spectra, corresponding to the probability distribution with nonnegative random variables, and the lower unbounded spectra, corresponding to probability distributions with negative random variables. For lower unbounded spectra, we use the generalized definition of spectral functions. In some cases, we encounter divergences. We remove the divergence by a renormalization procedure. Moreover, in virtue of spectral theory in physics, we generalize some concepts in probability theory. For example, the moment generating function in probability theory does not always exist. We redefine the moment generating function as the generalized heat kernel, which makes the concept definable when the definition in probability theory fails. As examples, we construct examples corresponding to some probability distributions. Thermodynamic quantities, vacuum amplitudes, one-loop effective actions, and vacuum energies for various probability distributions are presented

Non-canonical statistics of finite quantum system

The canonical statistics describes the statistical properties of an open system by assuming its coupling with the heat bath infinitesimal in comparison with the total energy in thermodynamic limit. In this paper, we generally derive a non-canonical distribution for the open system with a finite coupling to the heat bath, which deforms the energy shell to effectively modify the conventional canonical way. The obtained non-canonical distribution reflects the back action of system on the bath, and thus depicts the statistical correlations through energy fluctuations