The characterization of binary constant weight codes meeting the bound of Fu and Shen

Fu and Shen gave an upper bound on binary constant weight codes. In this paper, we present a new proof for the bound of Fu and Shen and characterize binary constant weight codes meeting this bound. It is shown that binary constant weight codes meet the bound of Fu and Shen if and only if they are generated from certain symmetric designs and quasi-symmetric designs in combinatorial design theory. In particular, it turns out that the existence of binary codes with even length meeting the Grey–Rankin bound is equivalent to the existence of certain binary constant weight codes meeting the bound of Fu and Shen. Furthermore, some examples are listed to illustrate these results. Finally, we obtain a new upper bound on binary constant weight codes which improves on the bound of Fu and Shen in certain case. This research is supported in part by the DSTA research grant R-394-000-025-422 and the National Natural Science Foundation of China under the Grant 60402031, and the NSFC-GDSF joint fund under the Grant U0675001     

一类可调转股价可转债的定价分析与计算

1 引言可转换债券以其独特的风险受益特性逐渐为投、融资者所接受并得到了广泛的欢迎．如今,无论在广度还是深度上,全球范围的可转债市场都已经发生了质的变化,并且日趋成熟和繁荣．中国的可转债市场在经历了十余年的沉寂之后,近两年也正进入一个高速发     

Sufficient Conditions for Global Optimality of Bivalent Nonconvex Quadratic Programs with Inequality Constraints

We present sufficient conditions for the global optimality of bivalent nonconvex quadratic programs involving quadratic inequality constraints as well as equality constraints. By employing the Lagrangian function, we extend the global subdifferential approach, developed recently in Jeyakumar et al. (J. Glob. Optim., 2007, to appear; Math. Program. Ser. A, 2007, to appear) for studying bivalent quadratic programs without quadratic constraints, and derive global optimality conditions. The authors are grateful to the referees for constructive comments and suggestions which have contributed to the final preparation of the paper. Z.Y. Wu’s current address: School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Victoria, Australia. The work of this author was completed while at the Department of Applied Mathematics, University of New South Wales, Sydney, Australia.     

Binary fuzzy goal programming

Goal programming is an important technique for solving many decision/management problems. Fuzzy goal programming involves applying the fuzzy set theory to goal programming, thus allowing the model to take into account the vague aspirations of a decision-maker. Using preference-based membership functions, we can define the fuzzy problem through natural language terms or vague phenomena. In fact, decision-making involves the achievement of fuzzy goals, some of them are met and some not because these goals are subject to the function of environment/resource constraints. Thus, binary fuzzy goal programming is employed where the problem cannot be solved by conventional goal programming approaches. This paper proposes a new idea of how to program the binary fuzzy goal programming model. The binary fuzzy goal programming model can then be solved using the integer programming method. Finally, an illustrative example is included to demonstrate the correctness and usefulness of the proposed model.     

A NEW FAMILY OF BINARY SEQUENCES WITH OPTIMAL AUTOCORRELATION VALUES AND NICE PSEUDO-RANDOM PROPERTIES

In this paper we present a series of binary sequences which is a generalization of GMW sequences constructed by Scholtz and Welch. Our sequences have optimal autocorrelation values as m -sequences, and nice pseudo-random property. The number of such sequences is counted and the linear span of such sequences is evaluated.     

Generating 2-Gray codes for ballot sequences in constant amortized time

We present a simple algorithm that generates a cyclic 2-Gray code for ballot sequences. The algorithm generates each ballot sequence in constant amortized time using a linear amount of space. This is the first known cyclic 2-Gray code for ballot sequences that achieves this time bound. In addition, the algorithm can be easily modified to output ballot sequences in binary reflected Gray code order in constant amortized time per string using a linear amount of space.     

Evaluation of an activated carbon from olive stones used as an adsorbent for heavy metal removal from aqueous phases

The performance of a microporous activated carbon prepared chemically from olive stones for removing Cu(II), Cd(II) and Pb(II) from single and binary aqueous solutions was investigated via the batch technique. The activated carbon sample was characterized using N₂ adsorption–desorption isotherms, SEM, XRD, FTIR, and Boehm titration. The effect of initial pH and contact time were studied. Adsorption kinetic rates were found to be fast and kinetic experimental data fitted very well the pseudo-second-order equation. The adsorption isotherms fit the Redlich–Peterson model very well and maximum adsorption amounts of single metal ions solutions follow the trend Pb(II) > Cd(II) > Cu(II). The adsorption behavior of binary solution systems shows a relatively high affinity to Cu(II) at the activated carbon surface of the mixture with Cd(II) or Pb(II). An antagonistic competitive adsorption phenomenon was observed. Desorption experiments indicated that about 59.5% of Cu(II) and 23% of Cd(II) were desorbed using a diluted sulfuric acid solution.     

A novel particle tracking algorithm using polar coordinate system similarity

A new algorithm using polar coordinate system similarity (PCSS) for tracking particle in particle tracking velocimetry (PTV) is proposed. The essence of the algorithm is to consider simultaneously the changes of the distance and angle of surrounding particles relative to the object particle. Monte Carlo simulations of a solid body rotational flow and a parallel shearing flow are used to investigate flows measurable by PCSS and the influences of experimental parameters on the implementation of the new algorithm. The results indicate that the PCSS algorithm can be applied to flows subjected to strong rotation and is not sensitive to experimental parameters in comparison with the conventional binary image cross-correlation (BICC) algorithm. Finally, PCSS is applied to images of a real experiment. The project supported by the National Natural Science Foundation of China (50206019) The English text was polished by Yunming Chen.     

Intermolecular hydrogen bonding in the binary mixture [(C2H5)2CO + CH3OH] probed by polarized Raman measurements and DFT calculations

The Raman spectra of neat (C₂H₅)₂CO (pentanone) and its binary mixtures with hydrogen donor solvent (CH₃OH), [(C₂H₅)₂CO + CH₃OH] having different mole fractions of the reference system, (C₂H₅)₂CO in the range 0.1-0.9 at a regular interval of 0.1 were recorded in the CO stretching region. In neat liquid, the Raman peak appears asymmetric. The asymmetric nature of the peak has been attributed to the CO stretching mode of the two conformers of (C₂H₅)₂CO having C₂ and C_2v point groups and the corresponding bands at ∼1711 and ∼1718 cm⁻¹, respectively. A careful analysis of the I_iso (isotropic component of the Raman scattered intensity) at different concentrations reveals that upon dilution with methanol, at mole fraction C = 0.6, an additional peak in the CO stretching region is observed at ∼1703 cm⁻¹ which is attributed to the hydrogen bonding with methanol. A peculiar feature in this study is that upon dilution, the peak at ∼1718 cm⁻¹ shows a minimum at C = 0.6, but on further dilution it shows a blue shift. However, the other peak at ∼1711 cm⁻¹ shows a continuous red shift with dilution as well as a maximum at C = 0.7 in the linewidth vs. concentration plot, which is essentially due to competition between motional narrowing and diffusion phenomena. A significant amount of narrowing in the Raman band at ∼1718 cm⁻¹ can be understood in terms of caging effect of the reference molecule by the solvent molecules at high dilution. A density functional theoretic (DFT) calculation on optimized geometries and vibrational frequencies of two conformers of neat (C₂H₅)₂CO in C₂ ad C_2v forms and the complexes with one and two CH₃OH molecules with both the conformers was performed. The experimental results and theoretical calculations together indicate a co-existence of two conformers as well as hydrogen bonded complex with methanol in the binary mixture, [(C₂H₅)₂CO + CH₃OH] at intermediate concentrations.     

High-dimensional generation of Bernoulli random vectors

The objective of this paper is to explore different modeling strategies to generate high-dimensional Bernoulli vectors. We discuss the multivariate Bernoulli (MB) distribution, probe its properties and examine three models for generating random vectors. A latent multivariate normal model whose bivariate distributions are approximated with Plackett distributions with univariate normal distributions is presented. A conditional mean model is examined where the conditional probability of success depends on previous history of successes. A mixture of beta distributions is also presented that expresses the probability of the MB vector as a product of correlated binary random variables. Each method has a domain of effectiveness. The latent model offers unpatterned correlation structures while the conditional mean and the mixture model provide computational feasibility for high-dimensional generation of MB vectors.