MULTIPLE PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS VIA CONLEY INDEX THEORY

In this paper we study the existence of periodic solutions of asymptotically linear Hamiltonian systems which may not satisfy the Palais-Smale condition. By using the Conley index theory and the Galerkin approximation methods, we establish the existence of at least two nontrivial periodic solutions for the corresponding systems.

Linearization Method and Linear Complexity

We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N ( 2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.

linear cryptanalysis of nush block cipher

IEEE Computer Society

Interaction of linear waves with an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth

The linear water wave scattering and radiation by an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth is investigated by use of the multipole expansion method. The diffracted and radiated potentials are expressed as a linear combination of infinite multipoles placed at the centre of each cylinder with unknown coefficients to be determined by the cylinder boundary conditions. Analytical expressions for wave forces, hydrodynamic coefficients, reflection and transmission coefficients and energies are derived. Comparisons are made between the present analytical results and those obtained by the boundary element method, and some examples are presented to illustrate the hydrodynamic behavior of multiple horizontal circular cylinders in a two-layer fluid. It is found that for two submerged circular cylinders the influence of the fluid density ratio on internal-mode wave forces is more appreciable than surface-mode wave forces, and the periodic oscillations of hydrodynamic results occur with the increase of the distance between two cylinders; for four submerged circular cylinders the influence of adding two cylinders on the wave forces of the former cylinders is small in low and high wave frequencies, but the influence is appreciable in intermediate wave frequencies.

Interaction of linear waves with infinitely long horizontal cylinders studied by boundary element method

The two-dimensional problems concerning the interaction of linear water waves with cylinders of arbitrary shape in two-layer deep water are investigated by use of the Boundary Integral Equation method (BIEM). Simpler new expressions for the Green functions are derived, and verified by comparison of results obtained by BIEM with these by an analytical method. Examined are the radiation and scattering of linear waves by two typical configurations of cylinders in two-layer deep water. Hydrodynamic behaviors including hydrodynamic coefficients, wave forces, reflection and transmission coefficients and energies are analyzed in detail, and some interesting physical phenomena are observed.

On the radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas

The radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas of finite depth is investigated. The analytical expressions for the radiated and diffracted potentials are derived as infinite series by use of the method of separation of variables. The unknown coefficients in the series are determined by the eigenfunction expansion matching method. The expressions for wave forces, hydrodynamic coefficients and reflection and transmission coefficients are given and verified by the boundary element method. Using the present analytical solution, the hydrodynamic influences of the angle of incidence, the submergence, the width and the thickness of the structure on the wave forces, hydrodynamic coefficients, and reflection and transmission coefficients are discussed in detail.

Scattering of linear water waves by a fixed and infinitely long rectangular structure parallel to a vertical wall in oblique seas

The scattering of linear water waves by an infinitely long rectangular structure parallel to a vertical wall in oblique seas is investigated. Analytical expressions for the diffracted potentials are derived using the method of separation of variables. The unknown coefficients in the expressions are determined through the application of the eigenfunction expansion matching method. The expressions for wave forces on the structure are given. The calculated results are compared with those obtained by the boundary element method. In addition, the influences of the wall, the angle of wave incidence, the width of the structure, and the distance between the structure and the wall on wave forces are discussed. The method presented here can be easily extended to the study of the diffraction of obliquely incident waves by multiple rectangular structures.

茂金属线性低密度聚乙烯的光氧化和热力学降解研究

聚乙烯是广泛应用的合成高分子材料之一，工业化己有几十年历史，为适应不断扩展的加工及应用的要求，氧化降解反应一直是较活跃的研究领域。目前为止，一些氧化降解的规律和机理已经确定，某些还在积极地研究探索之中。茂金属线性低密度聚乙烯（m-LLDPE）是进入九十年代以后才出现的采用新型茂金属催化剂催化合成的树脂，与传统 Ziegler-Natta线性低密度聚乙烯（LLDPE）相比，其具有分子量分布窄，共聚单体在主链中分布均匀的特点，决定了它具有比传统LLDPE更加优异的使用性能，因而在生产生活中得到广泛应用。目前对其氧化降解的研究较少，因此对m-LLDPE的氧化及稳定性的研究对指导其应用有着积极的意义。本论文选择催化剂和共聚单体类型不同的三种m-LLDPE和两种传统LLDPE对比研究了m-LLDPE的光氧化和热力学降解稳定性，而且研究了过渡金属化合物光敏化剂对它的热力学降解的影响，热力学降解和光敏化剂对m-LLDPE的光、热氧化稳定性的影响。化测试方法表征m-LLDPE的光氧俐反应，长时间光氧化后支化度和结晶度都有不同程度的上升，光氧化速率主要受亚乙烯基双链浓度的影响，受支化度的影响不明显。因此在合成m-LLDPE的过程中应该合理设计茂金属催化剂，降低聚合产品中亚乙烯基双键的浓度，提高它的光氧化稳定性。采用熔体流动速率、流变法和红外光谱法研究了m-LLDPE和传统LLDPE在密炼过程中的热力学降解反应，和光敏化剂对热力学降解反应的影响，利用氧化诱导温度法快速表征热力学降解对m-LLDPE和LLDPE的氧化稳定性的影响，并利用自然光曝晒测试碳基指数和力学性能的变化和热氧化观察脆化时间的方法研究了热力学降解对它们的光、热氧化稳定性的影响，为m-LLDPE在气候条件下应用提供理论依据。共聚单体类型相同的m-LLDPEI和m-LLDPEZ相比较，m-LLDPEI在热力学降解过程中生成更多的氧化产物，光敏化剂硬脂酸钻和乙酰基丙酮钻对m-LLDPEI热力学降解生成氧化产物的敏化作用更强，也更显著地降低了密炼后样品的氧化诱导温度。流变法不仅表征了m-LLDPEI热力学降解过程中的分子结构的变化，也反映了样品的热稳定性。共聚单体类型不同的m-LLDPE3和LLDPEZ相比较，热力学降解后熔体流动速率下降得多，但拨基指数上升较少，这是m-LLDPE3密炼过程中熔融粘度较高的原因。光敏化剂更强烈得增强了LLDPE2的热力学降解过程中氧化产物的形成。热力学降解明显的降低了 LLDPE2的光氧化稳定性而没有对m-LLDPE3的光氧化稳定性产生明显作用，同时敏化剂对LLDPE2的光氧化敏化作用也更强烈一些。本文还研究了光敏化剂硬脂酸钻和硬脂酸铁对三种共聚单体类型不同的传统LLDPE和LDPE的光敏化效果，发现光敏化剂对不同链结构的聚乙烯的光敏化效果存在很大的差异，光敏化作用的顺序为：乙烯一辛烯共聚LLDPE＜乙烯一丁烯共聚LLDPE＜LDPE，光敏化效果并不随敏化剂浓度的增大而增强。从红外光谱可以分析聚乙烯中亚乙烯基浓度越高，光照过程中形成的氢过氧化物浓度越高，光敏化剂的敏化效果越强。

Linear polarization of photoluminescence in quantum wires

The linear character of the polarization of the luminescence in porous Si is studied experimentally, and the corresponding luminescence characteristics in quantum wires are studied theoretically using a quantum cylindrical model in the framework of the effective-mass theory. From the experimental and theoretical results it is concluded that there is a stronger linear polarization parallel to the wire direction than there is perpendicular to the wire, and that it is connected with the valence band structure in quantum confinement in two directions. The theoretical photoluminescence spectra of the parallel and perpendicular polarization directions, and the degree of polarization as functions of the radius of the wire and the temperature are obtained for In0.53Ga0.47As quantum wires and porous silicon. From the theory, we demonstrated that the degree of polarization decreases with increasing temperature and radius, and that this effect is more apparent for porous Si. The theoretical results are in good agreement with the experimental results for the InGaAs quantum wires, and in qualitative agreement with those for the porous silicon.

Linear-Polarization Optical Property of CdSe Quantum Rods

The linear-polarization optical property of CdSe quantum rods is studied in the framework of effective-mass envelope function theory.The effects of shape and magnetic field on the linear polarization factors are investigated.It is found that CdSe quantum spheres have negative polarization factors (xy-polarized emission)and quantum long rods with small radius have positive linear polarization factors (z-polarized emission).The z-direction is the direction of the c axis.Quantum long rods with large radius have negative linear polarization factors,due to the hexagonal crystal symmetry and the crystal field splitting energy.The linear polarization factors decrease and may change from a positive value to a negative value;i.e.,the z-polarized emissions decrease relative to xy-polarized emissions as the magnetic field applied along the z direction increases.