Periodic solutions for a Lotka–Volterra mutualism system with several delays

In the present paper, a Lotka–Volterra type mutualism system with several delays is studied. Some new and interesting sufficient conditions are obtained for the global existence of positive periodic solutions of the mutualism system. Our method is based on Mawhin’s coincidence degree and novel estimation techniques for the a priori bounds of unknown solutions. Our results are different from the existing ones such as those in of Yang et al. [F. Yang, D. Jiang, A. Ying, Existence of positive solution of multidelays facultative mutualism system, J. Eng. Math. 3 (2002) 64–68] and Chen et al. [F. Chen, J. Shi, X. Chen, Periodicity in a Lotka–Volterra facultative mutualism system with several delays, J. Eng. Math. 21 (3) (2004) 403–409].     

The inverse scattering problem for Schrödinger and Klein–Gordon equations with a nonlocal nonlinearity

We study the inverse scattering problem for the nonlinear Schrödinger equation and for the nonlinear Klein–Gordon equation with the generalized Hartree type nonlinearity. We reconstruct the nonlinearity from knowledge of the scattering operator, which improves the known results.     

用板式电势差计测量电池的电动势和内阻实验的改进

分析了在“用板式电势差计测量电池的电动势和内阻”实验中 ,由于待测干电池的电动势和内阻在实验过程中均不为恒定值而引起的误差 ,依据电化学理论和电阻构成解释了实验现象 ,并给出了实验改进方案 .     

On Romanoff's constant

In 1934, Romanoff proved that there are a positive proportion natural numbers which can be expressed as the sum of a prime and a power of 2. In this paper, a quantitative version of this theorem is given. We show that the proportion is larger than 0.0868 and for a positive proportion of odd integers the number of such representations is between 1 and 16.     

The solvable radical of Sylow factorizable groups

Let G be a finite group. A complete Sylow product of G is a product of Sylow subgroups of G, one for each prime divisor of |G|. We shall call G a Sylow factorizable group if it is equal to at least one of its complete Sylow products. We prove that if G is a Sylow factorizable group then the intersection of all complete Sylow products of G is equal to the solvable radical of G. We generalize the concepts and the result to Sylow products which involve an arbitrary subset of the prime divisors of |G|. Received: 26 January 2005     

Random Walks And The Colored Jones Function

It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system. We give two curious formulas for the weight system of a colored Jones function: one in terms of the permanent of a matrix associated to a chord diagram, and another in terms of counting paths of intersecting chords. Electronic supplementary material to this article is available at and is accessible to authorized users. * S. G. was partially supported by an NSF and by an Israel-US BSF grant. † M. L. was partly supported by GAUK 158 grant and by the Project LN00A056 of the Czech Ministry of Education.     

纵横扩张的优化

得到了最小折数纵横扩张的判别准则．针对4-正则图的平面嵌入的纵横扩张的特殊性，给出了它的最小折数纵横扩张判别准则．     

短脉冲强激光在稀薄等离子体中传播时的电磁类孤立子

 采用二维粒子模拟方法，研究了短脉冲强激光在稀薄等离子体中传播时电磁类孤立子的产生和时空演化过程。通过分析电磁场与等离子体波的非线性能量交换和激光场的频率谱结构等，给出了电磁类孤立子形成的基本物理图像，讨论了等离子体参数对电磁类孤立子形成的影响。模拟结果表明：类孤立子的形成是由于局部电磁波振荡频率减小至等离子体频率引起的，初始等离子体密度越高越容易形成空间局域结构。