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Mathematical Terms (mathematical + term)
Selected AbstractsDimensional analysis of the earthquake-induced pounding between adjacent structuresEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 7 2009Elias Dimitrakopoulos Abstract In this paper the dynamic response of two and three pounding oscillators subjected to pulse-type excitations is revisited with dimensional analysis. Using Buckingham's ,-theorem the number of variables that govern the response of the system is reduced by three. When the response is presented in the dimensionless ,-terms remarkable order emerges. It is shown that regardless of the acceleration level and duration of the pulse all response spectra become self-similar and follow a single master curve. This is true despite the realization of finite duration contacts with increasing durations as the excitation level increases. All physically realizable contacts (impacts, continuous contacts, and detachments) are captured via a linear complementarity approach. The study confirms the existence of three spectral regions. The response of the most flexible among the two oscillators amplifies in the low range of the frequency spectrum (flexible structures); whereas, the response of the most stiff among the two oscillators amplifies at the upper range of the frequency spectrum (stiff structures). Most importantly, the study shows that pounding structures such as colliding buildings or interacting bridge segments may be most vulnerable for excitations with frequencies very different from their natural eigenfrequencies. Finally, by applying the concept of intermediate asymptotics, the study unveils that the dimensionless response of two pounding oscillators follows a scaling law with respect to the mass ratio, or in mathematical terms, that the response exhibits an incomplete self-similarity or self-similarity of the second kind with respect to the mass ratio. Copyright © 2008 John Wiley & Sons, Ltd. [source] Lie Theory for Quantum ControlGAMM - MITTEILUNGEN, Issue 1 2008G. Dirr Abstract One of the main theoretical challenges in quantum computing is the design of explicit schemes that enable one to effectively factorize a given final unitary operator into a product of basic unitary operators. As this is equivalent to a constructive controllability task on a Lie group of special unitary operators, one faces interesting classes of bilinear optimal control problems for which efficient numerical solution algorithms are sought for. In this paper we give a review on recent Lie-theoretical developments in finite-dimensional quantum control that play a key role for solving such factorization problems on a compact Lie group. After a brief introduction to basic terms and concepts from quantum mechanics, we address the fundamental control theoretic issues for bilinear control systems and survey standard techniques fromLie theory relevant for quantum control. Questions of controllability, accessibility and time optimal control of spin systems are in the center of our interest. Some remarks on computational aspects are included as well. The idea is to enable the potential reader to understand the problems in clear mathematical terms, to assess the current state of the art and get an overview on recent developments in quantum control-an emerging interdisciplinary field between physics, control and computation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Rules-of-thumb of implementing short electric band heaters (length to diameter ratio <1.5) for external heating of pipe flowsINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 2 2002X. D. Chen Abstract Short electric band heaters (L/Di<1.5) are constructed for the ease of implementation in small scale heating applications. They are usually mounted side-by-side in series along the external wall of a pipe for heating the fluid within the pipe. There are no rules-of-thumb available about designing such a system to achieve good uniformity of the temperature profile at the pipe inner surface beforehand. Non-uniformity can cause preferential fouling at hotter spots. This study focuses on the axial uniformity of heating along a pipe inside which the heated fluid if flowing. The situation has been simplified a great deal in mathematical terms from the corresponding conventional conjugate problem considered previously due to the small temperature rise in the fluid flow through one section of the pipe which is heated by one band heater. Similarity parameter sets have been deduced and verified by numerical simulations. The worst scenario of non-uniformity for such short band heaters, that is when L/Di=1.5, is presented in this paper. This may be used for designing a system to minimize the non-uniformity in terms of choosing the right pipe material, percentage of heater wire coverage in the band heater, etc. Copyright © 2002 John Wiley & Sons, Ltd. [source] Which truth values in fuzzy logics are definable?INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 10 2003Hung T. Nguyen In fuzzy logic, every word or phrase describing uncertainty is represented by a real number from the interval [0, 1]. There are only denumerable many words and phrases and continuum many real numbers; thus, not every real number corresponds to some common sense degree of uncertainty. In this article, for several fuzzy logics, we describe which numbers are describing such degrees, i.e., in mathematical terms, which real numbers are definable in the corresponding fuzzy logic. © 2003 Wiley Periodicals, Inc. [source] Principle of organization: a dynamic-systems view of the archetype-as-suchTHE JOURNAL OF ANALYTICAL PSYCHOLOGY, Issue 4 2001Maxson J. McDowell The personality is a dynamic system. Like all other dynamic systems, it must be self-organized. In this paper I focus upon the archetype-as-such, that is, upon the essential core around which both an archetypal image and a complex are organized. I argue that an archetype-as-such is a pre-existing principle of organization. Within the personality that principle manifests itself as a psychological vortex (a complex) into which we are drawn. The vortex is impersonal. We mediate it through myths and rituals or through consciousness. In this paper I show that Jung's intuition about the archetype-as-such is supported by recent science. I evaluate other concepts of the archetype. My concept is different from that proposed recently by Saunders and Skar. My concept allows each archetype-as-such to be defined precisely in mathematical terms. It suggests a new interpretation of mythology. It also addresses our spiritual experience of an archetype. Because the archetypes-as-such are fundamental to the personality, the better we understand them the better we understand our patients. The paper is grounded with clinical examples. [source] | ||||||||||