CATALYTIC DEBROMINATION OF DIPHENYL BROMOMETHANE UNDER HETEROPHASE CONDITIONS USING POLYMERS WITH VIOLOGEN STRUCTURE

The debromination of diphenyl bromomethane (Ph_2CHBr) using polymers with viologen structure as electron--transfer catalyst (ETC) afforded tetraphenylethane in good yields under het- erophase conditions.

Entropy Formulation for Triply Nonlinear Degenerate Elliptic-Parabolic-Hyperbolic Equation with Zero-Flux Boundary Condition

In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.

Structured condition numbers and statistical condition estimation for the LDU factorization

In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of LDU factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments.

Fluorescence Properties and Crystal Structures of Metal-organic Coordination Complexes Based on the 2,6-Naphthalenedicarboxylic Acid

Two metal-organic coordination complexes, [Zn（2,6-ndc）（1,2-bix）]n（1） and [Zn（2,6-ndc）（1,3-bix）]n（2）（2,6-H2ndc = 2,6-naphthalenedicarboxylic acid, 1,2-bix = 1,2-bis（imidazole-1-ylmethyl）-benzene and 1,3-bix = 1,3-bis（imidazole-1-ylmethyl）-benzene） have been synthesized by the hydrothermal method. Though the two complexes both crystallize in a triclinic system, space group P1 and show similar two-dimensional structures, weak intermolecular interactions（π-π packing interactions） only exist in complex 2. They are characterized by single-crystal X-ray diffraction analysis, fluorescence measurement, IR spectroscopy and TGA. Moreover, the solid-state fluorescence spectra of two complexes show maximal emission peaks at 365（λ（ex） = 329 nm） and 367 nm（λex = 344 nm）, respectively.

THE EFFECT OF THE NEGATIVE ENTROPY FLOW ON THE ORGANIZATION OF ATMOSPHERIC DISSIPATIVE STRUCTURES IN NON-EQUILIBRIUM CONDITIONS

The entropy balance equation that describes the entropy budget of atmospheric systems is derived from the Gibbs relation.The distribution of the entropy flows of a west-Pacific typhoon and a Bengal-Bay cyclone is calculated and thus the dissipativity of the atmospheric systems is revealed.

Structure condition under initial enlargement of filtration

We address the question of how the structure condition is affected when one possesses some additional information at the very beginning of the investment period.The structure condition represents essentially an alternative to non-arbitrage conditions for the Markowitz’s portfolio optimization framework,and is crucial for the existence of the optimal portfolio in quadratic utility settings.Herein,we provide practical assumption on the initial market model and the additional information to preserve the structure condition.The stochastic tools that drive this result are a generalization of the Lazaro-Yor representation by Lazaro and Yor(1978)and optional stochastic integral.

Towards Fast and Efficient Algorithm for Learning Bayesian Network

Learning Bayesian network structure is one of the most exciting challenges in machine learning. Discovering a correct skeleton of a directed acyclic graph（DAG） is the foundation for dependency analysis algorithms for this problem. Considering the unreliability of high order condition independence（CI） tests, and to improve the efficiency of a dependency analysis algorithm, the key steps are to use few numbers of CI tests and reduce the sizes of conditioning sets as much as possible. Based on these reasons and inspired by the algorithm PC, we present an algorithm, named fast and efficient PC（FEPC）, for learning the adjacent neighbourhood of every variable. FEPC implements the CI tests by three kinds of orders, which reduces the high order CI tests significantly. Compared with current algorithm proposals, the experiment results show that FEPC has better accuracy with fewer numbers of condition independence tests and smaller size of conditioning sets. The highest reduction percentage of CI test is 83.3% by EFPC compared with PC algorithm.

Application of Moore-Penrose Inverse in Deciding the Minimal Martingale Measure

The Moore-Penrose inverse is an important tool in algebra.This paper shows that the MoorePenrose inverse is also an effcient technique in determining the minimal martingale measure if a security price follows a semi-martingale which satisfies some structure condition.We extend a result of Dzhaparidze and Spreij concerning the Moore-Penrose inverse to the case that the Moore-Penrose inverse of any matrix-valued predictable process is still predictable.Furthermore,we obtain an explicit formula of the minimal martingale measure by employing the Moore-Penrose inverse.Specifically,the minimal martingale measure in a generalized Black-Scholes model is found.

STRUCTURED CONDITION NUMBERS FOR THE TIKHONOV REGULARIZATION OF DISCRETE ILL-POSED PROBLEMS

The possibly most popular regularization method for solving the least squares problem rain ‖Ax - b‖2 with a highly ill-conditioned or rank deficient coefficient matrix A is the x Tikhonov regularization method. In this paper we present the explicit expressions of the normwise, mixed and componentwise condition numbers for the Tikhonov regularization when A has linear structures. The structured condition numbers in the special cases of nonlinear structure i.e. Vandermonde and Cauchy matrices are also considered. Some comparisons between structured condition numbers and unstructured condition numbers are made by numerical experiments. In addition, we also derive the normwise, mixed and componentwise condition numbers for the Tikhonov regularization when the coefficient matrix, regularization matrix and right-hand side vector are all perturbed, which generalize the results obtained by Chu et al. [Numer. Linear Algebra Appl., 18 （2011）, 87-103].

Markov branching processes with immigration-migration and resurrection

We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are obtained. An explicit expression for the equilibrium distribution is also presented. As a preparation, the criteria for regularity and uniqueness for such structure are firstly established.