Determining Modes for Continuous Data Assimilation in 2D Turbulence

We study the number of determining modes necessary for continuous data assimilation in the two-dimensional incompressible Navier–Stokes equations. Our focus is on how the spatial structure of the body forcing affects the rate of continuous data assimilation and the number of determining modes. We treat this problem analytically by proving a convergence result depending on the H ^–1 norm of f and computationally by considering a family of forcing functions with identical Grashof numbers that are supported on different annuli in Fourier space. The rate of continuous data assimilation and the number of determining modes is shown to depend strongly on the length scales present in the forcing.     

Indexing text using the Ziv–Lempel trie

Let a text of u characters over an alphabet of size σ be compressible to n phrases by the LZ78 algorithm. We show how to build a data structure based on the Ziv–Lempel trie, called the LZ-index, that takes 4nlog₂n(1+o(1)) bits of space (that is, 4 times the entropy of the text for ergodic sources) and reports the R occurrences of a pattern of length m in worst case time O(m³logσ+(m+R)logn). We present a practical implementation of the LZ-index, which is faster than current alternatives when we take into consideration the time to report the positions or text contexts of the occurrences found.     

Local Existence and Continuation Criterion for Solutions of the Spherically Symmetric Einstein-Vlasov-Maxwell System

Using the iterative scheme we prove the local existence and uniqueness of solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data. We prove a continuation criterion to global in-time solutions.     

未确知数学方法处理物理实验数据

介绍未确知数学方法，并用未确知数学方法分析处理物理实验数据，与传统的数据处理方法比较，未确知数学方法不必对数据作任何假设，因此更合理，也更符合实际。     

The Existence of Periodic Orbits for Higher Dimensional Autonomous Systemswith Small Perturbations

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Maslov-type index and brake orbits in nonlinear Hamiltonian systems

In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian systems.     

Asymptotic analysis of a large closed queueing network with discriminatory processor sharing

In this paper the steady-state behavior of a closed queueing network with multiple classes and large populations is investigated. One of the two nodes of the network simply introduces random delays and the discipline in the other node is discriminatory processor sharing. The network is not product-form, so not even the steady-state behavior is known. We assume that the usage is moderately heavy, and obtain two-term asymptotic approximations to the mean number of jobs, and the mean sojourn time, of each class of jobs in the processor node. We also obtain the leading term in the asymptotic approximation to the joint distribution of the number of jobs in the processor node, which is a zero-mean multivariate Gaussian distribution around a line through the origin.     

Solitary wave solutions of nonlinear financial markets :data-modeling-concept-practicing

This paper seeks to solve the difficult nonlinear problem in financial markets on the complex system theory and the nonlinear dynamics principle, with the data-model-concept-practice issue-oriented reconstruction of the phase space by the high frequency trade data. In theory, we have achieved the differentiable manifold geometry configuration, discovered the Yang-Mills functional in financial markets, obtained a meaningful conserved quantity through corresponding space-time non-Abel localization gauge symmetry transformation, and derived the financial solitons, which shows that there is a strict symmetry between manifold fiber bundle and guage field in financial markets. In practical applications of financial markets, we have repeatedly carried out experimental tests in a fluctuant evolvement, directly simulating and validating the existence of solitons by researching the price fluctuations (society phenomena) using the same methods and criterion as in natural science and in actual trade to test the stock Guangzhou Proprietary and the futures Fuel Oil in China. The results demonstrate that the financial solitons discovered indicates that there is a kind of new substance and form of energy existing in financial trade markets, which likely indicates a new science paradigm in the economy and society domains beyond physics.      

Local algorithms in exterior tomography

Exterior tomographic data are taken over lines outside a central region, and such data occur in the industrial nondestructive evaluation of large objects such as rockets. We explain, using microlocal analysis, which singularities are well reconstructed from exterior data, and we explain how this phenomenon is reflected in the singular value decomposition for the exterior transform [E.T. Quinto, Singular value decompositions and inversion methods for the exterior Radon transform and a spherical transform, J. Math. Anal. Appl. 95 (1983) 437–448]. We extend Lambda Tomography to exterior data and to limited angle exterior data. The algorithm is tested on industrial data from Perceptics, Inc.     

Excess enthalpy of ternary mixture for diamine+heptane+cyclohexan

The excess molar enthalpy of ternary mixture for 3-diethylaminopropylamine+heptane+cyclohexane were measured using a Calvet microcalorimeter at 303.15 K. Empirical equations, Redlich-Kister, Tsao-Smith, and Kohler and group contribution models, UNIFAC (modified version) and DISQUAC have been applied. A reasonable representation of ternary data is obtained. This revised version was published online in August 2006 with corrections to the Cover Date.