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191.
Apparently, no rigorous results exist for the dynamics of a classical point particle interacting with the electromagnetic field, as described by the standard Maxwell-Lorentz equations. Some results are given here for the corresponding linearized system (dipole approximation) in the presence of a mechanical linear restoring force. We consider a regularization of the system (Pauli-Fierz model), and explicitly solve the Cauchy problem in terms of normal modes. Then we study the limit of the particle's motion as the regularization is removed. We prove that the particle's motion corresponding to smooth initial data for the field has a well-defined limit if mass is renormalized, while the motion is trivial (i.e. the particle does not move at all) if mass is not renormalized. Moreover, the limit particle's motion corresponding to an interesting class of initial data satifies exactly the Abraham-Lorentz-Dirac equation. Finally, for generic initial data the limit motion is runaway. 相似文献
192.
Summary The preparation of the dinucleoside phosphonate GpCH2U, starting from the isosteric phosphonate analogue of uridine (3) and the guanosine derivative5 is described.
Eintopfsynthese des Dinucleosidphosphonats GpCH2U
Zusammenfassung Die Herstellung des Dinucleosidphosphonats GpCH2U aus dem isosteren Phosphonatanalogen von Uridin (3) und dem Guanosinderivat5 wird beschrieben.相似文献
193.
This paper develops an efficient particle tracking algorithm to be used in fluid simulations approximated by a high-order multidomain discretization of the Navier–Stokes equations. We discuss how to locate a particle's host subdomain, how to interpolate the flow field to its location, and how to integrate its motion in time. A search algorithm for the nearest subdomain and quadrature point, tuned to a typical quadrilateral isoparametric spectral subdomain, takes advantage of the inverse of the linear blending equation. We show that to compute particle-laden flows, a sixth-order Lagrangian polynomial that uses points solely within a subdomain is sufficiently accurate to interpolate the carrier phase variables to the particle position. Time integration of particles with a lower-order Adams–Bashforth scheme, rather than the fourth-order Runge–Kutta scheme often used for the integration of the carrier phase, increases computational efficiency while maintaining engineering accuracy. We verify the tracking algorithm with numerical tests on a steady channel flow and an unsteady backward-facing step flow. 相似文献
194.
Cheman Cheng Xiaoqing Jin Vaikuong Sin 《高等学校计算数学学报(英文版)》2007,16(1):28-36
A matrix is said to be stable if the real parts of all the eigenvalues are negative. In this paper, for any matrix An, we discuss the stability properties of T. Chan's preconditioner cU(An) from the viewpoint of the numerical range. An application in numerical ODEs is also given. 相似文献
195.
杨丕文 《数学物理学报(A辑)》2006,(Z1)
This article studies the inhomogeneous Moisil-Theodorsco system in the space R3, gives the integral expression of its solution, proves the Holder continuity of the solution. Moreover the author studies the Riemann-Hilbert boundary value problem for the Moisil-Theodorsco system in a cylindrical domain of R3, and gives the solvability conditions and the integral expressions of solutions. The Holder continuity of the solutions is proved. 相似文献
196.
We consider a massless scalar Bose field interacting with two particles, one of them infinitely heavy. Neither an infrared nor an ultraviolet cutoff is imposed. In case the charge of the particles is of the same sign and sufficiently small, we prove the existence of a ground state. 相似文献
197.
李冰 《数学的实践与认识》2002,32(3):519-523
本文讨论并提出数字技术与数学科学的内在联系 .并根据实际的分析和研究 ,认为数字化技术只是信息化促进科技发展的一个阶段 ,尽管数字技术已经并将继续推动科技和生产力的发展速度 相似文献
198.
Harm Derksen 《Journal of Pure and Applied Algebra》2007,209(1):91-98
The vanishing ideal I of a subspace arrangement V1∪V2∪?∪Vm⊆V is an intersection I1∩I2∩?∩Im of linear ideals. We give a formula for the Hilbert polynomial of I if the subspaces meet transversally. We also give a formula for the Hilbert series of the product ideal J=I1I2?Im without any assumptions about the subspace arrangement. It turns out that the Hilbert series of J is a combinatorial invariant of the subspace arrangement: it only depends on the intersection lattice and the dimension function. The graded Betti numbers of J are determined by the Hilbert series, so they are combinatorial invariants as well. We will also apply our results to generalized principal component analysis (GPCA), a tool that is useful for computer vision and image processing. 相似文献
199.
Seong Cho Dana Jones Wilburn E. Reddick Robert J. Ogg R.Grant Steen 《Magnetic resonance imaging》1997,15(10):1133-1143
The goal of this study was to determine the expected normal range of variation in spin-lattice relaxation time (T1) of brain tissue in vivo, as a function of age. A previously validated precise and accurate inversion recovery method was used to map T1 transversely, at the level of the basal ganglia, in a study population of 115 healthy subjects (ages 4 to 72; 57 male and 58 female). Least-squares regression analysis shows that T1 varied as a function of age in pulvinar nucleus (R2 = 56%), anterior thalamus (R2 = 51%), caudate (R2 = 50%), frontal white matter (R2 = 47%), optic radiation (R2 = 39%), putamen (R2 = 36%), genu (R2 = 22%), occipital white matter (R2 = 20%) (all p < 0.0001), and cortical gray matter (R2 = 53%) (p < 0.001). There were no significant differences in T1 between men and women. T1 declines throughout adolescence and early adulthood, to achieve a minimum value in the fourth to sixth decade of life, then T1 begins to increase. Quantitative magnetic resonance imaging provides evidence that brain tissue continues to change throughout the lifespan among healthy subjects with no neurologic deficits. Age-related changes follow a strikingly different schedule in different brain tissues; white matter tracts tend to reach a minimum T1 value, and to increase again, sooner than do gray matter tracts. Such normative data may prove useful for the early detection of brain pathology in patients. 相似文献
200.