The harmonic decomposition reconstruction for the exponential radon transform

The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads to the harmonic decomposition reconstruction. The results are similar results of Tretiak and Metz. Foundation item: Supported by the National Natural Science Foundation of China (No. 19971064), Key Project of Science and Technology of Hubei Province Education Committee. Biography: Wang Jin-ping (1963-), male, Ph.D. candidate, research direction: numberical solution of singular integral equation and integral transformation etc.     

Resource Search in Unstructured Peer-to-Peer System Based on Multiple-Tree Overlay Structure

We propose a multiple-tree overlay structure for resource discovery in unstructured P2P systems. Peers that have similar interests or hold similar type of resources will be grouped into a tree-like cluster. We exploit the heterogeneity of peers in each cluster by connecting peers with more capacities closer to the root of the tree. The capacity of a peer can be defined in different ways （e.g. higher network bandwidth, larger disk space, more data items of a certain type etc.） according to different needs of users or applications.     

On the verge of <Emphasis Type="Italic">Umdeutung</Emphasis> in Minnesota: Van Vleck and the correspondence principle. Part one

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Using Bohr’s correspondence principle and Einstein’s quantum theory of radiation along with advanced techniques from classical mechanics, Van Vleck showed that quantum formulae for emission, absorption, and dispersion of radiation merge with their classical counterparts in the limit of high quantum numbers. For modern readers Van Vleck’s paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg’s Umdeutung paper. This makes Van Vleck’s paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself. This paper was written as part of a joint project in the history of quantum physics of the Max Planck Institut für Wissenschaftsgeschichte and the Fritz-Haber-Institut in Berlin.     

The Response of Debris-Flow Events to Solar Proton Flares （Ⅰ）

By analyzing the observation data from Dongchuan Debris Flow Observation and Research Station and historical data from year 1965 to 1990 gotten from National Astronomical Ob-servatories/Yunnan Observatory,the responding of debris flow in Jiangjia Ravine to Solar Proton Flare is studied. The following conclusion can be drawn. Solar Proton Flare,as one of most im-portant astronomical factors,affects the activity of debris flow in Yunnan. Generally,from 1965 to1990,the more active Solar Pro-ton Flare is,the greater the probability of high frequency and large runoff of debris flow is. On the contrary,the less active Solar Pro-ton Flare is,the greater the probability of low frequency,small runoff,and low sediment transport of debris flow is.     

Bang bang control of unified chaotic system

The unified chaotic system contains the Lorenz system and the Chen system as two dual systems at the two extremes of its parameter spectrum. This paper presents the design of bang bang controller for unified system and multitude of numerical experiments under various control parameters. Numerical experiments meet the theoretic proof perfectly and convincingly demonstrated the controller can be effectively used for unified systems with uncertainty of the equilibrium points. The method enriches the applications of chaotic control. Foundation item: Supported by the National Natural Science Foundation of China(50209012) Biography: Deng Xiao-ming (1980-), male, Master candidate, research direction: chaos control.     

Quantal transmitter secretion from myocytes loaded with acetylcholine.

It is well known that transmitter secretion requires specialized secretory organelles, the synaptic vesicles, for the packaging, storage and exocytotic release of the transmitter. Here we report that when acetylcholine (ACh) is loaded into an isolated Xenopus myocyte, there is spontaneous quantal release of ACh from the myocyte which results in activation of its own surface ACh channels and the appearance of membrane currents resembling miniature endplate currents. This myocyte secretion probably reflects Ca(2+)-regulated exocytosis of ACh-filled cytoplasmic compartments. Furthermore, step depolarization of the myocyte membrane triggers evoked ACh release from the myocyte with a weak excitation-secretion coupling. These findings suggest that quantal transmitter secretion does not require secretory pathways unique to neurons and that the essence of presynaptic differentiation may reside in the provision of transmitter supply and modification of the preexisting secretion pathway.     

新型全固态铁离子敏感电极研究

采用稀土电极材料六硼化镧制备了一种新的全固态铁离子敏感电极。研究了该敏感电极在常见介质中对Ｆｅ３＋的响应行为。结果表明，该铁离子敏感电极在１．５ｍｏｌ／ＬＨ３ＰＯ４介质中的线性响应范围、检测下限和响应斜率分别为１．０×１０－５～１．０×１０－１ｍｏｌ／ＬＦｅ３＋，６．０×１０－６ｍｏｌ／ＬＦｅ３＋和６０ｍＶ／ｐＣ，且具有较好的选择性。     

A calcium sensor in the sodium channel modulates cardiac excitability.

Sodium channels are principal molecular determinants responsible for myocardial conduction and maintenance of the cardiac rhythm. Calcium ions (Ca2+) have a fundamental role in the coupling of cardiac myocyte excitation and contraction, yet mechanisms whereby intracellular Ca2+ may directly modulate Na channel function have yet to be identified. Here we show that calmodulin (CaM), a ubiquitous Ca2+-sensing protein, binds to the carboxy-terminal 'IQ' domain of the human cardiac Na channel (hH1) in a Ca2+-dependent manner. This binding interaction significantly enhances slow inactivation-a channel-gating process linked to life-threatening idiopathic ventricular arrhythmias. Mutations targeted to the IQ domain disrupted CaM binding and eliminated Ca2+/CaM-dependent slow inactivation, whereas the gating effects of Ca2+/CaM were restored by intracellular application of a peptide modelled after the IQ domain. A naturally occurring mutation (A1924T) in the IQ domain altered hH1 function in a manner characteristic of the Brugada arrhythmia syndrome, but at the same time inhibited slow inactivation induced by Ca2+/CaM, yielding a clinically benign (arrhythmia free) phenotype.     

Ruin Probability with Variable Premium Rate and Disturbed by Diffusion in a Markovian Environment

We consider a risk model with a premium rate which varies with the level of free reserves. In this model, the occurrence of claims is described by a Cox process with Markov intensity process, and the influence of stochastic factors is considered by adding a diffusion process. The integro-differential equation for the ruin probability is derived by a infinitesimal method.     

Newton's Easy Quadratures ``Omitted for the Sake of Brevity'

In the 1687 Principia, Newton gave a solution to the direct problem (given the orbit and center of force, find the central force) for a conic-section with a focal center of force (answer: a reciprocal square force) and for a spiral orbit with a polar center of force (answer: a reciprocal cube force). He did not, however, give solutions for the two corresponding inverse problems (given the force and center of force, find the orbit). He gave a cryptic solution to the inverse problem of a reciprocal cube force, but offered no solution for the reciprocal square force. Some take this omission as an indication that Newton could not solve the reciprocal square, for, they ask, why else would he not select this important problem? Others claim that ``it is child's play' for him, as evidenced by his 1671 catalogue of quadratures (tables of integrals). The answer to that question is obscured for all who attempt to work through Newton's published solution of the reciprocal cube force because it is done in the synthetic geometric style of the 1687 Principia rather than in the analytic algebraic style that Newton employed until 1671. In response to a request from David Gregory in 1694, however, Newton produced an analytic version of the body of the proof, but one which still had a geometric conclusion. Newton's charge is to find both ``the orbit' and ``the time in orbit.' In the determination of the dependence of the time on orbital position, t(r), Newton evaluated an integral of the form ∫dx/x <sup>n</sup> to calculate a finite algebraic equation for the area swept out as a function of the radius, but he did not write out the analytic expression for time t = t(r), even though he knew that the time t is proportional to that area. In the determination of the orbit, θ (r), Newton obtained an integral of the form ∫dx/√(1−x<sup>2</sup>) for the area that is proportional to the angle θ, an integral he had shown in his 1669 On Analysis by Infinite Equations to be equal to the arcsin(x). Since the solution must therefore contain a transcendental function, he knew that a finite algebraic solution for θ=θ(r) did not exist for ``the orbit' as it had for ``the time in orbit.' In contrast to these two solutions for the inverse cube force, however, it is not possible in the inverse square solution to generate a finite algebraic expression for either ``the orbit' or ``the time in orbit.' In fact, in Lemma 28, Newton offers a demonstration that the area of an ellipse cannot be given by a finite equation. I claim that the limitation of Lemma 28 forces Newton to reject the inverse square force as an example and to choose instead the reciprocal cube force as his example in Proposition 41. (Received August 14, 2002) Published online March 26, 2003 Communicated by G. Smith