Cooperative games of choosing partners and forming coalitions in the marketplace

Two games of interacting between a coalition of players in a marketplace and the residual players acting there are discussed, along with two approaches to fair imputation of gains of coalitions in cooperative games that are based on the concepts of the Shapley vector and core of a cooperative game. In the first game, which is an antagonistic one, the residual players try to minimize the coalition's gain, whereas in the second game, which is a noncooperative one, they try to maximize their own gain as a coalition. A meaningful interpretation of possible relations between gains and Nash equilibrium strategies in both games considered as those played between a coalition of firms and its surrounding in a particular marketplace in the framework of two classes of n-person games is presented. A particular class of games of choosing partners and forming coalitions in which models of firms operating in the marketplace are those with linear constraints and utility functions being sums of linear and bilinear functions of two corresponding vector arguments is analyzed, and a set of maximin problems on polyhedral sets of connected strategies which the problem of choosing a coalition for a particular firm is reducible to are formulated based on the firm models of the considered kind.     

Simultaneous Measurement of Particle Size and Particle Velocity by the Spatial Filtering Technique

The objective of this study was to compare the measuring results of a fiber‐optical probe based on a modified spatial filtering technique with given size distributions of different test powders and also with particle velocity values of laser Doppler measurements. Fiber‐optical spatial filtering velocimetry was modified by fiber‐optical spot scanning in order to determine simultaneously the size and the velocity of particles. The fiber‐optical probe system can be used as an in‐line measuring device for sizing of particles in different technical applications. Spherical test particles were narrow‐sized glass beads in the range 30–100 μm and irregularly shaped test particles were limestone particles in the range 10–600 μm. Particles were dispersed by a brush disperser and the measurements were carried out at a fixed position in a free particle‐laden air stream. Owing to the measurement of chord lengths and to the influence of diffraction and divergent angle, the probe results show differences from the given test particle sizes. Owing to the particle‐probe collisions, the mean velocity determined by the probe is smaller than the laser Doppler mean velocity.     

Solutions in Sobolev spaces of vector refinement equations with a general dilation matrix

In this paper, we present a necessary and sufficient condition for the existence of solutions in a Sobolev space W_p^k(ℝ^s) (1≤p≤∞) to a vector refinement equation with a general dilation matrix. The criterion is constructive and can be implemented. Rate of convergence of vector cascade algorithms in a Sobolev space W_p^k(ℝ^s) will be investigated. When the dilation matrix is isotropic, a characterization will be given for the L_p (1≤p≤∞) critical smoothness exponent of a refinable function vector without the assumption of stability on the refinable function vector. As a consequence, we show that if a compactly supported function vector φ∈L_p(ℝ^s) (φ∈C(ℝ^s) when p=∞) satisfies a refinement equation with a finitely supported matrix mask, then all the components of φ must belong to a Lipschitz space Lip(ν,L_p(ℝ^s)) for some ν>0. This paper generalizes the results in R.Q. Jia, K.S. Lau and D.X. Zhou (J. Fourier Anal. Appl. 7 (2001) 143–167) in the univariate setting to the multivariate setting. Dedicated to Professor Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 42C20, 41A25, 39B12. Research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC Canada) under Grant G121210654.     

Degree distribution of the greatest common divisor of polynomials over 𝔽q

We study the degree distribution of the greatest common divisor of two or more random polynomials over a finite field ??_q. We provide estimates for several parameters like number of distinct common irreducible factors, number of irreducible factors counting repetitions, and total degree of the gcd of two or more polynomials. We show that the limiting distribution of a random variable counting the total degree of the gcd is geometric and that the distributions of random variables counting the number of common factors (with and without repetitions) are very close to Poisson distributions when q is large. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

f(R) theories of gravity in the Palatini approach matched with observations

We investigate the viability of f(R) theories in the framework of the Palatini approach as solutions to the problem of the observed accelerated expansion of the universe. Two physically motivated popular choices for f(R) are considered,: power law, f(R) = β R ⁿ , and logarithmic, f(R) = α ln R. Under the Palatini approach, both Lagrangians give rise to cosmological models comprising only standard matter and undergoing a present phase of accelerated expansion. We use the Hubble diagram of type Ia Supernovae and the data on the gas mass fraction in relaxed galaxy clusters to see whether these models are able to reproduce what is observed and to constrain their parameters. It turns out that they are indeed able to fit the data with values of the Hubble constant and of the matter density parameter in agreement with some model independent estimates, but the today deceleration parameter is higher than what is measured in the concordance ΛCDM model.     

An Alternative Approach to Obtain the Exact Wave Functions of Time-Dependent Hamiltonian Systems Involving Quadratic, Inverse Quadratic, and (1/x)p+p(1/x) Terms

By using the Lewis-Riesenfeld theory and algebraic method, we present an alternative approach to obtain the exact solution of time-dependent Hamiltonian systems involving quadratic, inverse quadratic and (1/x)p+p(1/x) terms. This solution is discussed and compared with that obtained by Choi, J. R. (2003). International Journal of Theoretical Physics 42, 853]. PACS: 03.65Ge; 03.65Fd; 03.65Bz     

The Role of a Specific Response of Media in the Vavilov-Cherenkov Effect

It is shown that the condition υ > υ_p (ω), which is necessary in order to trigger the Vavilov-Cherenkov effect, determines the interval of radiated frequencies and it alone cannot establish a strong restriction to the velocity of the particle. It is exhibited that it is possible to define a general lower bound for the velocity of the particle, which does not depend on the frequency when both, a specific response of the medium is taken into account and the mentioned condition is considered. The minimum value of the phase velocity of light in the medium determines the existence of such general lower bound.     

关于Z-空间的对偶空间的讨论

本文以自然的方式定义了从Z-空间X到Z-空间Y的有界线性算子的和以及它们的数乘.从而得到了与赋范空间的对偶空间理论类似的一系列结论.     

溶胶-凝胶VO2薄膜转换特性研究

利用溶胶凝胶法在SiO2Si衬底上沉积高取向的V2O5薄膜,在压强低于2Pa,温度高于400℃的条件下,对V2O5薄膜进行真空烘烤,获得了电阻率变化3个数量级以上、弛豫宽度为62℃的VO2多晶薄膜.以X射线衍射(XRD)、扫描电子显微镜(SEM)图和电阻率转换特性等实验结果为依据,详细分析了溶胶凝胶薄膜在真空烘烤时从V2O5向VO2的转化,它经历了从VnO2n+1(n=2,3,4,6)到VO2的过程.实验证明,根据选择合适的成膜热处理条件和真空烘烤条件是实现溶胶凝胶V2O5结构向VO2结构成功转换的关键 关键词： 溶胶-凝胶法 氧化钒薄膜 VO2膜转换特性     

Game of two cars: Case of variable speed

A stochastic version of Isaacs's (Ref. 1) game of two cars is dealt with here. In this version, the pursuer, owing to thrust and drag forces, has a variable speed, whereas the evader's speed is constant. Also, the pursuer can maneuver as long as his speed is bounded by some lower and upper limits. The probability of interception, corresponding to optimal (saddle-point) feedback strategies, is computed and serves as a reference for evaluating the performance of four different versions of the proportional navigation pursuit law as well as two other strategies.