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Mathematical Structure (mathematical + structure)

Distribution by Scientific Domains

Chemistry	25%

Selected Abstracts

Preliminary evaluation of electroencephalographic entrainment using thalamocortical modelling

EXPERT SYSTEMS, Issue 4 2009
Dean Cvetkovic
Abstract: The concept of linked oscillators in biological control systems has long been established. Frequency entrainment is a predominant explanation behind many biological rhythms. In this paper a preliminary examination of electroencephalographic entrainment is made to survey the possibility and methods of achieving signal entrainment at the highest level of neurological organization and function. A model of the thalamocortical system is employed to generate simulated electroencephalographic signals and is tested in various configurations in the search for entrainment under very simple conditions. Additionally, an analysis of the coupled Van der Pol model of the circadian rhythm controller is performed to identify the possibility of affecting that system with a drastically different coupling input signal. We were able to conclude that overall signal shape can have a significant impact on the entrainment characteristics of the system. Due to the nature of the underlying mathematical structure of the model, by examining the circadian rhythm controller, we found that it is unsuitable for entrainment to an incident entraining signal of much higher frequency. [source]

From the Hagedoorn imaging technique to Kirchhoff migration and inversion

GEOPHYSICAL PROSPECTING, Issue 6 2001
Norman Bleistein
The seminal 1954 paper by J.G. Hagedoorn introduced a heuristic for seismic reflector imaging. That heuristic was a construction technique , a ,string construction' or ,ruler and compass' method , for finding reflectors as an envelope of equal traveltime curves defined by events on a seismic trace. Later, Kirchhoff migration was developed. This method is based on an integral representation of the solution of the wave equation. For decades Kirchhoff migration has been one of the most popular methods for imaging seismic data. Parallel with the development of Kirchhoff wave-equation migration has been that of Kirchhoff inversion, which has as its objectives both structural imaging and the recovery of angle-dependent reflection coefficients. The relationship between Kirchhoff migration/inversion and Hagedoorn's constructive technique has only recently been explored. This paper addresses this relationship, presenting the mathematical structure that the Kirchhoff approach adds to Hagedoorn's constructive method and showing the relationship between the two. [source]

Foundation of quantum similarity measures and their relationship to QSPR: Density function structure, approximations, and application examples

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2005
Ramon Carbó-Dorca
Abstract This work presents a schematic description of the theoretical foundations of quantum similarity measures and the varied usefulness of the enveloping mathematical structure. The study starts with the definition of tagged sets, continuing with inward matrix products, matrix signatures, and vector semispaces. From there, the construction and structure of quantum density functions become clear and facilitate entry into the description of quantum object sets, as well as into the construction of atomic shell approximations (ASA). An application of the ASA is presented, consisting of the density surfaces of a protein structure. Based on this previous background, quantum similarity measures are naturally constructed, and similarity matrices, composed of all the quantum similarity measures on a quantum object set, along with the quantum mechanical concept of expectation value of an operator, allow the setup of a fundamental quantitative structure,activity relationship (QSPR) equation based on quantum descriptors. An application example is presented based on the inhibition of photosynthesis produced by some naphthyridinone derivatives, which makes them good herbicide candidates. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source]

A Simpler Approach to Population Balance Modeling in Predicting the Performance of Ziegler-Natta Catalyzed Gas-Phase Olefin Polymerization Reactor Systems

MACROMOLECULAR REACTION ENGINEERING, Issue 2-3 2009
Randhir Rawatlal
Abstract In this work, an alternative formulation of the Population Balance Model (PBM) is proposed to simplify the mathematical structure of the reactor model. The method is based on the segregation approach applied to the recently developed unsteady state residence time distribution (RTD). It is shown that the model can predict the performance of a reactor system under unsteady flow and composition conditions. Case studies involving time-varying catalyst flowrates, reactor temperature and reactor pressure were simulated and found to predict reactor performance with reasonable accuracy. The model was used to propose a grade transition strategy that could reduce transition time by as much as two hours. [source]

Manifestly covariant classical correlation dynamics I. General theory

ANNALEN DER PHYSIK, Issue 10-11 2009
C. Tian
Abstract In this series of papers we substantially extend investigations of Israel and Kandrup on nonequilibrium statistical mechanics in the framework of special relativity. This is the first one devoted to the general mathematical structure. Based on the action-at-a-distance formalism we obtain a single-time Liouville equation. This equation describes the manifestly covariant evolution of the distribution function of full classical many-body systems. For such global evolution the Bogoliubov functional assumption is justified. In particular, using the Balescu-Wallenborn projection operator approach we find that the distribution function of full many-body systems is completely determined by the reduced one-body distribution function. A manifestly covariant closed nonlinear equation satisfied by the reduced one-body distribution function is rigorously derived. We also discuss extensively the generalization to general relativity especially an application to self-gravitating systems. [source]

Manifestly covariant classical correlation dynamics I. General theory

Transfer of Mathematical Knowledge: The Portability of Generic Instantiations

CHILD DEVELOPMENT PERSPECTIVES, Issue 3 2009
Jennifer A. Kaminski
Abstract, Mathematical concepts are often difficult to acquire. This difficulty is evidenced by failure of knowledge to transfer to novel analogous situations. One approach to this challenge is to present the learner with a concrete instantiation of the to-be-learned concept. Concrete instantiations communicate more information than their abstract, generic counterparts and, in doing so, they may facilitate initial learning. However, this article argues that extraneous information in concrete instantiations may distract the learner from the relevant mathematical structure and, as a result, hinder transfer. At the same time, generic instantiations, such as traditional mathematical notation, can be learned by both children and adults and can, in turn, allow for transfer, suggesting that generic instantiations result in a portable knowledge representation. [source]

Multiresolution of quasicrystal diffraction spectra

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 6 2009
Avi Elkharrat
A method for analyzing and classifying two-dimensional pure point diffraction spectra (i.e. a set of Bragg peaks) of certain self-similar structures with scaling factor , > 1, such as quasicrystals, is presented. The two-dimensional pure point diffraction spectrum , is viewed as a point set in the complex plane in which each point is assigned a positive number, its Bragg intensity. Then, by using a nested sequence of self-similar subsets called ,-lattices, we implement a multiresolution analysis of the spectrum ,. This analysis yields a partition of , simultaneously in geometry, in scale and in intensity (the `fingerprint' of the spectrum, not of the diffracting structure itself). The method is tested through numerical explorations of pure point diffraction spectra of various mathematical structures and also with the diffraction pattern of a realistic model of a quasicrystal. [source]