scholarly journals On the Angular Density of Three Dimensional Scattering Resonances

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Lung-Hui Chen
Keyword(s):  
Angular Distribution ◽  
Complex Plane ◽  
Function Theory ◽  
Counting Function ◽  
Quantitative Description ◽  
Three Dimensional ◽  
Mathematical Physics ◽  
Integral Function ◽  
Angular Density ◽  
Scattering Resonances

We apply Cartwright’s theory in integral function theory to describe the angular distribution of scattering resonances in mathematical physics. A quantitative description on the counting function along rays in complex plane is obtained.

scholarly journals Machine-readable Yin–Yang imbalance: traditional Chinese medicine syndrome computer modeling based on three-dimensional noninvasive cardiac electrophysiology imaging

2019 ◽  
Vol 47 (4) ◽  
pp. 1580-1591 ◽  
Author(s):  
Wei Cen ◽  
Ralph Hoppe ◽  
Aiwu Sun ◽  
Hongyan Ding ◽  
Ning Gu
Keyword(s):  
Chinese Medicine ◽  
Traditional Chinese Medicine ◽  
Electrical Activity ◽  
Computer Modeling ◽  
Cardiac Electrophysiology ◽  
Three Dimensional ◽  
Mathematical Physics ◽  
Syndrome Differentiation ◽  
Physics Model ◽  
Machine Readable

Objectives The principal diagnostic methods of traditional Chinese medicine (TCM) are inspection, auscultation and olfaction, inquiry, and pulse-taking. Treatment by syndrome differentiation is likely to be subjective. This study was designed to provide a basic theory for TCM diagnosis and establish an objective means of evaluating the correctness of syndrome differentiation. Methods We herein provide the basic theory of TCM syndrome computer modeling based on a noninvasive cardiac electrophysiology imaging technique. Noninvasive cardiac electrophysiology imaging records the heart’s electrical activity from hundreds of electrodes on the patient’s torso surface and therefore provides much more information than 12-lead electrocardiography. Through mathematical reconstruction algorithm calculations, the reconstructed heart model is a machine-readable description of the underlying mathematical physics model that reveals the detailed three-dimensional (3D) electrophysiological activity of the heart. Results From part of the simulation results, the imaged 3D cardiac electrical source provides dynamic information regarding the heart’s electrical activity at any given location within the 3D myocardium. Conclusions This noninvasive cardiac electrophysiology imaging method is suitable for translating TCM syndromes into a computable format of the underlying mathematical physics model to offer TCM diagnosis evidence-based standards for ensuring correct evaluation and rigorous, scientific data for demonstrating its efficacy.

scholarly journals THE RESIDUE THEOREM AND AN ANALOG OF P. APPELL’S FORMULA FOR FINITE RIEMANN SURFACES

2016 ◽  
pp. 40-45
Author(s):  
Viktor Chueshev ◽  
Viktor Chueshev ◽  
Aleksandr Chueshev ◽  
Aleksandr Chueshev
Keyword(s):  
Riemann Surfaces ◽  
Meromorphic Functions ◽  
Function Theory ◽  
Mathematical Physics ◽  
General Function ◽  
Multiplicative Functions ◽  
Residue Theorem ◽  
Equations Of Mathematical Physics ◽  
Compact Riemann Surfaces ◽  
Integral Order

A theory of multiplicative functions and Prym differentials for the case of special characters on compact Riemann surfaces has found applications in geometrical function theory of complex variable, analytical number theory and in equations of mathematical physics. Theory of functions on compact Riemann surfaces differs from the theory of functions on finite Riemann surfaces even for the class of single meromorphic functions and Abelian differentials. In this article we continue the construction of the general function theory on finite Riemann surfaces for multiplicative meromorphic functions and differentials. We have proved analogues of the theorem on the full sum of residues for Prym differentials of every integral order and P. Appell's formula on expansion of the multiplicative function with poles of arbitrary multiplicity in the sum of elementary Prym integrals.

Three-Dimensional Topological Insulators: The Case of Inverse Heusler Compound Lu2FePb

2014 ◽  
Vol 926-930 ◽  
pp. 440-443
Author(s):  
Ning Ding ◽  
Xi Feng Liu ◽  
Xiao Tian Wang ◽  
Wen Yuan
Keyword(s):  
Function Theory ◽  
Three Dimensional ◽  
Density Function Theory ◽  
Full Potential ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Wave Method ◽  
Heusler Compound ◽  
Plane Wave Method ◽  
Band Inversion

Using the full-potential linerized augumented plane-wave method based on the density function theory, we theoretically predict the Heusler compound Lu2FePb is a new three-dimensional topological insulator system. We also point out that the spin-orbit coupling is not the leading cause but an account can add further fuel to the band inversion.

The Simulation and Modelling of the Crack Path of Biomaterials

2011 ◽  
Vol 465 ◽  
pp. 141-144
Author(s):  
Sebastian Stach
Keyword(s):  
Fracture Surface ◽  
Spanning Tree ◽  
Crack Path ◽  
Quantitative Description ◽  
Three Dimensional ◽  
Minimal Spanning Tree ◽  
Simulation And Modelling ◽  
Metallic Biomaterial ◽  
Cracking Process

Analysis of issues related to the cracking process of materials requires a quantitative description of the problem which frequently, due to its complexity, is difficult or impossible to solve. In a number of cases, the deficiencies of a quantitative description made using classical methods are compensated for by such unconventional tools as percolation, which requires creating an appropriate model. The aim of the study was to use a three-dimensional minimal spanning tree (3DMST) to create a model of the crack path, based on an example of a metallic biomaterial. For this purpose, a stereometric file, obtained as a result of measuring its fracture surface, was applied.

scholarly journals CORRELATIONS WEAK AND STRONG: DIVERS GUISES OF THE TWO-DIMENSIONAL ELECTRON GAS

1999 ◽  
Vol 13 (05n06) ◽  
pp. 447-459
Author(s):  
A. H. MACDONALD
Keyword(s):  
Quantum Wells ◽  
Electron Gas ◽  
Quantitative Description ◽  
Three Dimensional ◽  
Electronic Systems ◽  
Strongly Correlated ◽  
Dimensional Electron ◽  
Many Body ◽  
Many Body Theory ◽  
Dimensional Electron Gas

The three-dimensional electron-gas model has been a major focus for many-body theory applied to the electronic properties of metals and semiconductors. Because the model neglects band effects, whereas electronic systems are generally more strongly correlated in narrow band systems, it is most widely used to describe the qualitative physics of weakly correlated metals with unambiguous Fermi liquid properties. The model is more interesting in two space dimensions because it provides a quantitative description of electrons in quantum wells and because these can form strongly correlated many-particle states. We illustrate the range of possible many-particle behaviors by discussing the way correlations are manifested in 2D tunneling spectroscopy experiments.

ELLIPTIC AND AUTOMORPHIC DYNAMICAL SYSTEMS ON SURFACES

2006 ◽  
Vol 16 (04) ◽  
pp. 911-923 ◽  
Author(s):  
S. P. BANKS ◽  
SONG YI
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Half Plane ◽  
Complex Plane ◽  
Fundamental Domain ◽  
Function Theory ◽  
Theta Series ◽  
The Hyperbolic Metric ◽  
Upper Half Plane ◽  
Definition Of

We derive explicit differential equations for dynamical systems defined on generic surfaces applying elliptic and automorphic function theory to make uniform the surfaces in the upper half of the complex plane with the hyperbolic metric. By modifying the definition of the standard theta series we will determine general meromorphic systems on a fundamental domain in the upper half plane the solution trajectories of which "roll up" onto an appropriate surface of any given genus.

scholarly journals The asymptotic expansion of integral functions defined by Taylor series

1940 ◽  
Vol 238 (795) ◽  
pp. 423-451 ◽  
Keyword(s):  
Asymptotic Expansion ◽  
Complex Plane ◽  
Taylor Series ◽  
Asymptotic Expansions ◽  
Integral Function ◽  
The Other ◽  
General Integral ◽  
Other Hand

1.1. Considerable attention has been devoted to the behaviour of the general integral function for large values of the variable, and many important theorems have been proved in this field. On the other hand, the behaviour of a large number of particular integral functions has been studied in detail and their asymptotic expansions for certain regions of the plane obtained. There is, however, a substantial gap between the two theories. For example, much of the most interesting work on the general integral function deals with the distribution of its zeroes and other values; but many of the asymptotic expansions obtained for particular functions are not valid in the regions in which these functions have zeroes. In this paper and its sequels I propose to study several fairly wide classes of functions defined by Taylor series; from the properties of the coefficients I deduce asymptotic expansions of the function defined by the series. For the sort of functions I consider we can usually divide the whole complex plane, with the exception of certain “ barrier regions” , into a number of regions R , in each of which the function is given asymptotically by an equation of the form

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