Based on noncommutative differential calculus, we present a theory of prolongation structure for semidiscrete non/inear evolution equations. As an illustrative example, a semi-discrete model of the non/inear SchrSding...Based on noncommutative differential calculus, we present a theory of prolongation structure for semidiscrete non/inear evolution equations. As an illustrative example, a semi-discrete model of the non/inear SchrSdinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.展开更多
At very high energies, pair production formation (γ + N → e<sup>+</sup>e<sup>-</sup>) exhibits a variety of intriguing properties. Analytically and quantitatively, the formation of Electron-P...At very high energies, pair production formation (γ + N → e<sup>+</sup>e<sup>-</sup>) exhibits a variety of intriguing properties. Analytically and quantitatively, the formation of Electron-Positron pairs in the Electro-Magnetic field of light nuclei has been calculated. In Ultra-Relativistic (UR) areas of incident photon energy, applying the resulting formulas to the energy distribution of the (e<sup>-</sup>, e<sup>+</sup>) operation. When we compare the results, we can observe that the Magnetic field of the target nucleus is more efficacious than the Electric field of the nucleus in the (e<sup>-</sup>, e<sup>+</sup>) operation. Furthermore, we can show that in Pair Production operation, the Differential Cross Section (DCS) owing to the target nucleus’s Electric Quadrupole (EQ) and Magnetic Octupole (MO) are bigger than the Differential Cross Section (DCS) attributable to the target nucleus’s Electric Charge (EC) distribution and Magnetic Dipole (MD).展开更多
为了提高电连接器在承载信号传递及高速互连方面的质量及可靠性,以高速背板连接器作为研究对象,建立了该电连接器的结构模型,通过仿真分析了影响其信号完整性的重要参数,进行结构优化后实现了参数的调整,使得时域反射阻抗提高了22Ω,回...为了提高电连接器在承载信号传递及高速互连方面的质量及可靠性,以高速背板连接器作为研究对象,建立了该电连接器的结构模型,通过仿真分析了影响其信号完整性的重要参数,进行结构优化后实现了参数的调整,使得时域反射阻抗提高了22Ω,回波损耗降低了6.54 d B,说明了经优化后的参数能够满足性能指标要求。再结合参数测试分析,对仿真结果和测试结果进行了比较,结果表明:仅回波损耗的测试结果存在一定偏差,其余参数的仿真结果与测试结果相吻合,同时也验证了信号完整性分析方法合理有效。所得结论可是电连接器设计、测试以及可靠性评估的参考依据。展开更多
A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability ...A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectie map and a completely integrable tinite-dimensionai Hamiltonian system.展开更多
基金The project supported by Tianyuan Foundation for Mathematics under Grant No. 10626016 of National Natural Science Foundation of China, China Postdoctoral Science Foundation, Beijing Jiao-Wei Key Project under Grant No. KZ 200310028010, and National Natural Science Foundation of China under Grant No. 10375038
文摘Based on noncommutative differential calculus, we present a theory of prolongation structure for semidiscrete non/inear evolution equations. As an illustrative example, a semi-discrete model of the non/inear SchrSdinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.
文摘At very high energies, pair production formation (γ + N → e<sup>+</sup>e<sup>-</sup>) exhibits a variety of intriguing properties. Analytically and quantitatively, the formation of Electron-Positron pairs in the Electro-Magnetic field of light nuclei has been calculated. In Ultra-Relativistic (UR) areas of incident photon energy, applying the resulting formulas to the energy distribution of the (e<sup>-</sup>, e<sup>+</sup>) operation. When we compare the results, we can observe that the Magnetic field of the target nucleus is more efficacious than the Electric field of the nucleus in the (e<sup>-</sup>, e<sup>+</sup>) operation. Furthermore, we can show that in Pair Production operation, the Differential Cross Section (DCS) owing to the target nucleus’s Electric Quadrupole (EQ) and Magnetic Octupole (MO) are bigger than the Differential Cross Section (DCS) attributable to the target nucleus’s Electric Charge (EC) distribution and Magnetic Dipole (MD).
文摘为了提高电连接器在承载信号传递及高速互连方面的质量及可靠性,以高速背板连接器作为研究对象,建立了该电连接器的结构模型,通过仿真分析了影响其信号完整性的重要参数,进行结构优化后实现了参数的调整,使得时域反射阻抗提高了22Ω,回波损耗降低了6.54 d B,说明了经优化后的参数能够满足性能指标要求。再结合参数测试分析,对仿真结果和测试结果进行了比较,结果表明:仅回波损耗的测试结果存在一定偏差,其余参数的仿真结果与测试结果相吻合,同时也验证了信号完整性分析方法合理有效。所得结论可是电连接器设计、测试以及可靠性评估的参考依据。
基金Supported by the Science and Technology Plan Projects of the Educational Department of Shandong Province of China under GrantNo. J08LI08
文摘A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectie map and a completely integrable tinite-dimensionai Hamiltonian system.
