CONSTRUCTIVE KISSING NUMBERS IN HIGH-DIMENSIONAL SPACES

In the present paper, we focus on constructive spherical codes. By employing algebraic geometry codes, we give an explicit construction of spherical code sequences. By making use of the idea involved in the proof of the Gilbert-Varshamov bound in coding theory, we construct a spherical code sequence in exponential time which meets the best-known asymptotic bound by Shamsiev and Wyner.     

On the Meromorphic Solutions of Linear Differential Equations

In this paper, we investigate the growth of meromorphic solutions of higher order linear differential equation f^（k） ＋Ak-1 （z）e^Pk-1^（z） f^（k-1） ＋…＋A1 （z）e^P1（z） f′ ＋Ao（z）e^Po（z） f = 0 （k ≤ 2）, where Pj（z） （j = 0, 1,..., k - 1） are nonconstant polynomials such that deg Pj = n （j = 0, 1,..., k - 1） and Aj（z）（≠ 0） （j = 0, 1,..., k - 1） are meromorphic functions with order p（Aj） 〈 n （j = 0, 1,..., k - 1）.     

EXPLORATION/EXPLOITATION TRADEOFF WITH CELL-SHIFT AND HEURISTIC CROSSOVER FOR EVOLUTIONARY ALGORITHMS

In order to tradeoff exploration/exploitation and inspired by cell genetic algorithm a cellshift crossover operator for evolutionary algorithm （EA） is proposed in this paper. The definition domain is divided into n-dimension cubic sub-domains （cell） and each individual locates at an ndimensional cube. Cell-shift crossover first exchanges the cell numbers of the crossover pair if they are in the different cells （exploration） and subsequently shift the first individual from its initial place to the other individual＇s cell place. If they are already in the same cell heuristic crossover （exploitation） is used. Cell-shift/heuristic crossover adaptively executes exploration/exploitation search with the vary of genetic diversity. The cell-shift EA has excellent performance in terms of efficiency and efficacy on ten usually used optimization benchmarks when comparing with the recent well-known FEP evolutionary algorithm.     

EXISTENCE AND UNIQUENESS AND STABILITY OF SOLUTIONS FOR STOCHASTIC IMPULSIVE SYSTEMS

This paper studies the existence, uniqueness, and stability of solutions for stochastic impulsive systems. By employing Lyapunov-like functions, some sufficient conditions of the global existence, uniqueness, and stability of solutions for stochastic impulsive systems are established. Furthermore, the results are specialized to the case of linear stochastic impulsive systems. Finally, some examples are given to illustrate the applications of our theory.     

AN EXPONENTIAL INEQUALITY FOR AUTOREGRESSIVE PROCESSES IN ADAPTIVE TRACKING

A wide range of literature concerning classical asymptotic properties for linear models with adaptive control is available, such as strong laws of large numbers or central limit theorems. Unfortunately, in contrast with the situation without control, it appears to be impossible to find sharp asymptotic or nonasymptotic properties such as large deviation principles or exponential inequalities. Our purpose is to provide a first step towards that direction by proving a very simple exponential inequality for the standard least squares estimator of the unknown parameter of Gaussian autoregressive process in adaptive tracking.     

INFORMATION CHARACTERIZATION OF COMMUNICATION CHANNELS FOR SYSTEM IDENTIFICATION

This paper studies identification of systems in which the system output is quantized, transmitted through a digital communication channel, and observed afterwards. The concept of the CR Ratio is introduced to characterize impact of communication channels on identification. The relationship between the CR Ratio and Shannon channel capacity is discussed. Identification algorithms are further developed when the channel error probability is unknown.     

PEAK COVARIANCE STABILITY OF A RANDOM RICCATI EQUATION ARISING FROM KALMAN FILTERING WITH OBSERVATION LOSSES

We consider the stability of a random Riccati equation with a Markovian binary jump coefficient. More specifically, we are concerned with the boundedness of the solution of a random Riccati difference equation arising from Kalman filtering with measurement losses. A sufficient condition for the peak covariance stability is obtained which has a simpler form and is shown to be less conservative in some cases than a very recent result in existing literature. Furthermore, we show that a known sufficient condition is also necessary when the observability index equals one.     

ROLE OF α-PSEUDO-UNIVEX FUNCTIONS IN VECTOR VARIATIONAL-LIKE INEQUALITY PROBLEMS

In this paper, we introduce a new class of generalized convex function, namely, a-pseudounivex function, by combining the concepts of pseudo-univex and α-invex functions. Further, we establish some relationships between vector variational-like inequality problems and vector optimization problems under the assumptions of α-pseudo-univex functions. Results obtained in this paper present a refinement and improvement of previously known results.     

Research on catalysis of sodium-metallochlorophylls in Ni/MH battery

The effects of sodium-metallochlorophylls including sodium-iron chlorophyllin, sodium-copper chlorophyllin and sodium-magnesium chlorophyllin on performance of Ni/MH battery were investigated. The results show that sodium-iron chlorophyllin can effectively activate the gases produced during charge in Ni/MH battery, therefore reducing the reduction potential of oxygen and the oxidation potential of hydrogen, and the increased speed of inner pressure of battery is decreased significantly. With the aid of DMol3 software, the activation process of oxygen and hydrogen by sodiummetallochlorophylls was simulated and analyzed. It was found that the catalysis behavior is in agreement with the experimental results, and the activation process also gets a reasonable explanation from the calculated results.     

New crystal structure of molecular complex 1-piperidine carboxylate-piperidinium-H<Subscript>2</Subscript>O studied by X-ray single crystal diffraction

Piperidine absorbs CO2 and H2O in air to form a molecular complex： piperidium-l-piperidinecarboxylate-H2O. The structure of the complex was characterized by X-ray single crystal diffraction. The crystal structure was determined to be triclinic, space group P1^-with a=0.648 6（8） nm, b=0.809 200） nm, c= 1.357 1（16） nm, a=96.96706）°, β =102.506（15）°,γ=104.202 05）°, Z=2. The complex is stabilized via five hydrogen bonds between the three components, N-O electrostatic interaction and O-O interaction （electron transfer） betweenl-piperidinecarboxylate and H2O. Due to electron transference of carbamate ion, the oxygen atom in water molecule is strongly negatively charged and the O-H bond is considerably shorter than that of the free molecule of water. The formation of the molecular complex is a reversible process and will decompose upon heating. The mechanism of formation and stabilization is further investigated herein.