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

Local Protectionism and Regional Specialization: Evidence from China’s Industries

This paper uses a dynamic panel estimation method to investigate the determinants of regional specialization in China’s industries, paying particular attention to local protectionism. Less geographic concentration is found in industries where the past tax-plus-profit margins and the shares of state ownership are high, re- flecting stronger local government protection of these industries. The evidence also supports the scale-economies theory of regional specialization. Finally, the overall time trend of regional specialization of China’s industries is found to have reversed an early drop in the mid 1980s, and registered a significant increase in the later years.http://deepblue.lib.umich.edu/bitstream/2027.42/39951/3/wp565.pd

A new method for overconvergence of {{(φ,Γ)(\varphi ,\Gamma)}}-modules

We show all Laurent $F$-crystals over $p$-adic fields are overconvergent.Comment: 15 pages. Comments welcom

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

Measurements of the instantaneous velocity difference and local velocity with a fiber-optic coupler

New optical arrangements with two single-mode input fibers and a fiber-optic coupler are devised to measure the instantaneous velocity difference and local velocity. The fibers and the coupler are polarization-preserving to guarantee a high signal-to-noise ratio. When the two input fibers are used to collect the scattered light with the same momentum transfer vector but from two spatially separated regions in a flow, the obtained signals interfere when combined via the fiber-optic coupler. The resultant light received by a photomultiplier tube contains a cross-beat frequency proportional to the velocity difference between the two measuring points. If the two input fibers are used to collect the scattered light from a common scattering region but with two different momentum transfer vectors, the resultant light then contains a self-beat frequency proportional to the local velocity at the measuring point. The experiment shows that both the cross-beat and self-beat signals are large and the standard laser Doppler signal processor can be used to measure the velocity difference and local velocity in real time. The new technique will have various applications in the general area of fluid dynamics.Comment: Patent number: 67437 for associated information on the hardware, see http://karman.phyast.pitt.edu/horvath