LINEAR ISOMETRIC NON-ANTICIPATIVE TRANSFORMATIONS OF WIENER PROCESS

ThispaperisanoutcomeofnumerousdiscusionsandexchangeofideaswithlatePredragPerunicic,whosedeepandprofoundmathematicalknowledgeandhumanvaluesgaveusaninspirationandmotivationtofinalizeourjointideas.1.Wereferto[3,4]forthenotionofspectralmultiplicitytheoryintheseparableHilbertspace.LetHbeacyclicHilbertspacewiththeresolutionoftheidentity{p(t)}ofthemaximalspectraltypelIP(dt)ll'~dt-ordinaryLebesguemeasure.Anon-anticipativelineartransformationsisdefinedbyVolterrakernelg(t,u),uSt,ajsf'g(t)u)p(du),t>0…     

求强非线性系统次谐共振解的MLP方法

定义了一个新的参数变换α=α(ε,nω₀/m,ω₁),扩展了改进的LP方法的应用范围,使该方法能够求强非线性系统的次谐共振解.研究了Duffing方程的1/3亚谐和3次超谐共振解以及Vander Pol-Mathieu方程1/2亚谐共振解,这些例子说明近似解和数值解相当吻合.     

GLn(k)和SLn(k)的阶

本文利用矩阵行的初等变换 ,采用递推的方法 ,求出了有限域 k上 n次一般线性群 GLn(k)和 n次特殊线性群 SLn(k)的阶 .     

Containerless rapid solidification of undercooled Cu-Co peritectic alloys

Droplets of Co-16%Cu and Co-71.6%Cu peritectic alloys were solidified during containerless processing in a 3_m drop tube. The microstructures of Co-16%Cu alloy droplets were characterized by dendritic or equiaxed α-Co phase with a small amount of Cu-rich solid solution distributed on α-Co phase boundaries. Two thresholds of droplet diameter were observed for Co-16%Cu alloy at which "equiaxed-dendritic-equiaxed" morphological transitions occur to primary α-Co phase. This conspicuous refinement of primary α-Co grains results from the fragmentation of α-Co dendrites caused by recalescence effect. For Co-71.6%Cu alloy, the primary α-Co phase forms as coarse columnar dendrites in large droplets and equiaxed dendrites in small droplets. Theoretical calculations indicate that Marangoni migration contributes more to the growth of disperse Co-rich spheres by stimulating collision and coalescence than Stokes motion caused by the residual gravity in the falling Co-71.6%Cu alloy droplets.     

Bcklund transformation, non-local symmetry and exact solutions for (2+1)-dimensional variable coefficient generalized KP equations

IntroductionDuring the study of water wave, many completely iategrable models were derived, such as(1+1)-dimensional KdV equation, MKdV equation, (2+1)-dimensional KdV equation, Boussinesq equation and WBK equations etc. Many properties of these models had been researched,such as BAcklund transformation (BT), converse rules, N-soliton solutions and Painleve property etc.II--8]. In this paper, we would like to consider (2+1)-dimensional variable coefficientgeneralized KP equation which …     

Rapid crystal growth without inherent supersaturation induced by nanoscale fluid flows?

Crystal growth is a process that only takes place under non‐equilibrium conditions and a necessary prerequisite is that the crystal is exposed to a phase that is supersaturated in the material the crystal is composed of, be it a solution, a vapour or a supercooled melt. In industrial mass crystallization the growth rate for a population of crystals (in suspension growth processes [1]) rarely exceeds mean linear velocities of 10^‐7 ms^‐1. Here we present a mass crystallization process which is accompanied by rapid crystal growth several orders of magnitude faster and into a region of solution that is without inherent supersaturation. The material investigated is a solid hydrate that exhibits a solution mediated phase transition to its anhydrous form in the presence of methanol [2]. The phase transition is initiated simply by placing an amount of hydrate crystals into the solvent and is characterized by the rapid emergence of needle‐shaped crystals. The needles emanate from the crystal faces of the hydrate crystals and grow into the solution, which is nominally free of the substance to be crystallized. The high growth rate of the crystals, which of the order of up to 10^‐4 ms^‐1 is surprising. Although rapid needle growth has been observed before [3‐9], to date a satisfactory explanation for needles growing under the abovementioned conditions is still outstanding. Based upon the topology of the crystals we propose a tentative mechanism for this phenomenon capable of explaining the unusually rapid growth and highlight those questions that need addressing in order to verify this mechanism. X‐ray powder diffraction is used to characterize the crystal phase of the needles; confocal fluorescence microscopy reveals that the needles are hollow. The width of these needles is between 0.5 and 5 μm, their length appears to be limited only by the amount of hydrate available for their formation. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Probabilistic Teleportation of an Arbitrary Two-Particle State and Its Quantum Circuits

Two simple schemes for probabilistic teleportation of an arbitrary unknown two-particle state using a non-maximally entangled EPR pair and a non-maximally entangled GHZ state as quantum channels are proposed. After receiving Alice's Bell state measurement results, Bob performs a collective unitary transformation on his inherent particles without introducing the auxiliary qubit. The original state can be probabilistically teleported. Meanwhile, quantum circuits for realization of successful teleportation are also presented.     

Entanglement dynamics in two-component Bose--Einstein condensates

Based on the exact solution of the time-dependent Schr\"{o}dinger equation for two-species Bose--Einstein condensates (BECs) consisting of two hyperfine states of the atoms coupled by a tuned adiabatic and time-varying Raman coupling, we obtain analytically the entanglement dynamics of the system with various initial states, particularly the SU(2) coherent state, for both of cases with and without the nonlinear interactions. It is shown that the effect of nonlinear interaction on the entanglement appears only in a longer time period depending on the BEC parameters.     

Probabilistic teleportation of a non-symmetric three-particle state

This paper proposes a scheme for teleporting a kind of essential three-particle non-symmetric entangled state, which is much more valuable than a GHZ and W state for some applications in quantum information processing. In comparison with previous proposal of teleportation, the resources of entangled states as quantum channel and the number of classical messages required by our scheme can be cut down. Moreover, it is shown that there exists a class of transformations which ensure the success of this scheme, because the two-particle transformation performed by the receiver in the course of teleportation may be a generic two-particle operation instead of a control-NOT (CNOT) operation. In addition, all kinds of transformations performed by sender and receiver are given in detail.     

Unitary Transformation in Quantum Teleportation

In the well-known treatment of quantum teleportation, the receiver should convert the state of his EPR particle into the replica of the unknown quantum state by one of four possible unitary transformations. However, the importance of these unitary transformations must be emphasized. We will show in this paper that the receiver cannot transform the state of his particle into an exact replica of the unknown state which the sender wants to transfer if he has not a proper implementation of these unitary transformations. In the procedure of converting state, the inevitable coupling between EPR particle and environment which is needed by the implementation of unitary transformations will reduce the accuracy of the replica.