Methods of Celestial Mechanics

Singular-spectrum analysis: a toolkit for short, noisy chaotic signals

Summary) The abstract should follow the structure of the article (relevance, degree of exploration of the problem, the goal, the main results, conclusion) and characterize the theoretical and practical significance of the study results. The abstract should not contain wording echoing the title, cumbersome grammatical structures and abbreviations. The text should be written in scientific style. The volume of abstracts (summaries) depends on the content of the article, but should not be less than 250 words. All abbreviations must be disclosed in the summary (in spite of the fact that they will be disclosed in the main text of the article), references to the numbers of publications from reference list should not be made. The sentences of the abstract should constitute an integral text, which can be made by use of the words “consequently”, “for example”, “as a result”. Avoid the use of unnecessary introductory phrases (eg, “the author of the article considers...”, “The article presents...” and so on.)

/pdf/ministry-of-education-and-science-of-the-russian-federation-7m2jn0xnm1.pdf

Ministry of Education and Science of the Russian Federation

The relation between the solutions of the time‐independent Schrodinger equation and the periodic orbits of the corresponding classical system is examined in the case where neither can be found by the separation of variables. If the quasiclassical approximation for the Green's function is integrated over the coordinates, a response function for the system is obtained which depends only on the energy and whose singularities give the approximate eigenvalues of the energy. This response function is written as a sum over all periodic orbits where each term has a phase factor containing the action integral and the number of conjugate points, as well as an amplitude factor containing the period and the stability exponent of the orbit. In terms of the approximate density of states per unit interval of energy, each stable periodic orbit is shown to yield a series of δ functions whose locations are given by a simple quantum condition: The action integral differs from an integer multiple of h by half the stability angle times ℏ. Unstable periodic orbits give a series of broadened peaks whose half‐width equals the stability exponent times ℏ, whereas the location of the maxima is given again by a simple quantum condition. These results are applied to the anisotropic Kepler problem, i.e., an electron with an anisotropic mass tensor moving in a (spherically symmetric) Coulomb field. A class of simply closed, periodic orbits is found by a Fourier expansion method as in Hill's theory of the moon. They are shown to yield a well‐defined set of levels, whose energy is compared with recent variational calculations of Faulkner on shallow bound states of donor impurities in semiconductors. The agreement is good for silicon, but only fair for the more anisotropicgermanium.

Periodic orbits and classical quantization conditions

http://ieeexplore.ieee.org/iel5/4768668/4784008/04784017.pdf

TanDEM-X: A satellite formation for high-resolution SAR interferometry

This paper asks how complexity theory informs the role of leadership in organizations. Complexity theory is a science of complexly interacting systems; it explores the nature of interaction and adaptation in such systems and how they influence such things as emergence, innovation, and fitness. We argue that complexity theory focuses leadership efforts on behaviors that enable organizational effectiveness, as opposed to determining or guiding effectiveness. Complexity science broadens conceptualizations of leadership from perspectives that are heavily invested in psychology and social psychology (e.g., human relations models) to include processes for managing dynamic systems and interconnectivity. We develop a definition of organizational complexity and apply it to leadership science, discuss strategies for enabling complexity and effectiveness, and delve into the relationship between complexity theory and other currently important leadership theories. The paper concludes with a discussion of possible implications for research strategies in the social sciences.

/pdf/leadership-in-complex-organizations-rvcmh71x39.pdf

Methods of Celestial Mechanics

Citations

Singular-spectrum analysis: a toolkit for short, noisy chaotic signals

Ministry of Education and Science of the Russian Federation

Periodic orbits and classical quantization conditions

TanDEM-X: A satellite formation for high-resolution SAR interferometry

Leadership in complex organizations

Related Papers (5)

Solar system dynamics

Theory of satellite geodesy

Secular perturbations of asteroids with high inclination and eccentricity

Theory of Orbits.

Mathematical Methods of Classical Mechanics