scholarly journals A measurable map with analytic domain and metrizable range is quotient

1970 ◽  
Vol 76 (5) ◽  
pp. 1112-1118 ◽  
Author(s):  
Zdeněk Frolík
Keyword(s):  
Measurable Map ◽  
Analytic Domain

scholarly journals DISCRETENESS WITHOUT SYMMETRY BREAKING: A THEOREM

2009 ◽  
Vol 24 (32) ◽  
pp. 2579-2587 ◽  
Author(s):  
LUCA BOMBELLI ◽  
JOE HENSON ◽  
RAFAEL D. SORKIN
Keyword(s):  
Symmetry Breaking ◽  
Lorentz Invariance ◽  
Minkowski Spacetime ◽  
Dispersion Relations ◽  
Poisson Processes ◽  
Discrete Structure ◽  
Preferred Frame ◽  
Modified Dispersion Relations ◽  
Measurable Map

This paper concerns random sprinklings of points into Minkowski spacetime (Poisson processes). It proves that there exists no equivariant measurable map from sprinklings to spacetime directions (even locally). Therefore, if a discrete structure is associated to a sprinkling in an intrinsic manner, then the structure will not pick out a preferred frame, locally or globally. This implies that the discreteness of a sprinkled causal set will not give rise to "Lorentz breaking" effects like modified dispersion relations. Another consequence is that there is no way to associate a finite-valency graph to a sprinkling consistently with Lorentz invariance.

scholarly journals Analytic-domain lens design with proximate ray tracing

2010 ◽  
Vol 27 (8) ◽  
pp. 1791 ◽  
Author(s):  
Nan Zheng ◽  
Nathan Hagen ◽  
David J. Brady
Keyword(s):  
Ray Tracing ◽  
Lens Design ◽  
Analytic Domain

scholarly journals Counting nodal lines which touch the boundary of an analytic domain

2009 ◽  
Vol 81 (3) ◽  
pp. 649-686 ◽  
Author(s):  
John A. Toth ◽  
Steve Zelditch
Keyword(s):  
Nodal Lines ◽  
Analytic Domain

Feynman averaging of semigroups generated by Schrödinger operators

2018 ◽  
Vol 21 (02) ◽  
pp. 1850010 ◽  
Author(s):  
Leonid A. Borisov ◽  
Yuriy N. Orlov ◽  
Vsevolod Zh. Sakbaev
Keyword(s):  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Linear Operators ◽  
Evolutionary Equation ◽  
Coordinate Space ◽  
Initial Value ◽  
Semigroups Of Linear Operators ◽  
Measurable Map ◽  
Translation Operators ◽  
Complex Valued

The extension of averaging procedure for operator-valued function is defined by means of the integration of measurable map with respect to complex-valued measure or pseudomeasure. The averaging procedure of one-parametric semigroups of linear operators based on Chernoff equivalence for operator-valued functions is constructed. The initial value problem solutions are investigated for fractional diffusion equation and for Schrödinger equation with relativistic Hamiltonian of free motion. It is established that in these examples the solution of evolutionary equation can be obtained by applying the constructed averaging procedure to the random translation operators in classical coordinate space.

scholarly journals Mappings by the complex exponential function

2020 ◽  
Vol 1674 (1) ◽  
pp. 012006
Author(s):  
J G Triana ◽  
J A Fuentes ◽  
P Ramirez
Keyword(s):  
Exponential Function ◽  
Complex Plane ◽  
Conformal Mappings ◽  
Complex Functions ◽  
Complex Exponential ◽  
Analytic Domain

Abstract In mathematics, engineering, and physics, some problems can be solved through complex functions; in many cases, with geometric inconveniences or complicated domains. Conformal mappings are essential to transform a complicated analytic domain onto a simple domain. Physical approaches to visualization of complex functions can be used to represent conformal mappings, here we use the transformation of regions of the complex plane. This paper provides a graphical overview of the transformation of a set of regions by the complex exponential function.

scholarly journals Big by blocks: modular analytics

2016 ◽  
Vol 58 (4) ◽  
Author(s):  
Martin Hahmann ◽  
Claudio Hartmann ◽  
Lars Kegel ◽  
Dirk Habich ◽  
Wolfgang Lehner
Keyword(s):  
Big Data ◽  
Data Analytics ◽  
Big Data Analytics ◽  
Building Blocks ◽  
High Demand ◽  
Effective Application ◽  
Major Interest ◽  
Interest In Research ◽  
Analytic Domain ◽  
Do So

AbstractBig Data and Big Data analytics have attracted major interest in research and industry and continue to do so. The high demand for capable and scalable analytics in combination with the ever increasing number and volume of application scenarios and data has lead to a large and intransparent landscape full of versions, variants and individual algorithms. As this zoo of methods lacks a systematic way of description, understanding is almost impossible which severely hinders effective application and efficient development of analytic algorithms. To solve this issue we propose our concept of modular analytics that abstracts the essentials of an analytic domain and turns them into a set of universal building blocks. As arbitrary algorithms can be created from the same set of blocks, understanding is eased and development benefits from reusability.

scholarly journals A CAT(0)-VALUED POINTWISE ERGODIC THEOREM

2011 ◽  
Vol 03 (02) ◽  
pp. 145-152 ◽  
Author(s):  
TIM AUSTIN
Keyword(s):  
Compact Group ◽  
Ergodic Theorem ◽  
Haar Measure ◽  
Probability Space ◽  
Invariant Function ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Pointwise Ergodic Theorem ◽  
Measurable Map ◽  
Compact Subsets

This note proves a version of the pointwise ergodic theorem for functions taking values in a separable complete CAT(0)-space. The precise setting consists of an amenable locally compact group G with left Haar measure mG, a jointly measurable, probability-preserving action [Formula: see text] of G on a probability space, and a separable complete CAT(0)-space (X, d) with barycentre map b. In this setting we show that if (Fn)n ≥ 1 is a tempered Følner sequence of compact subsets of G and f : Ω → X is a measurable map such that for some (and hence any) fixed x ∈ X, we have [Formula: see text] then as n → ∞ the functions of empirical barycentres [Formula: see text] converge pointwise for almost every ω to a T-invariant function [Formula: see text].

scholarly journals The Analytic Domain of Multiple- Intelligence and Its Relation to English Objective Test

2019 ◽  
Vol 12 (5) ◽  
pp. 161
Author(s):  
Baan Jafar Sadiq
Keyword(s):  
Multiple Intelligence ◽  
Objective Test ◽  
Response Format ◽  
Free Response ◽  
Objective Tests ◽  
Analytic Domain

The current research aims at identifying the analytic domain of multiple -intelligence and English objective test. The research is trying to answer that if there is a correlation between the analytic domain of multiple- intelligence and the English objective tests. Thus, the research has adopted a close questionnaire for diagnosing analytic domain (logical, rhythmic, and naturalistic) of multiple- intelligence of Iraqi students at Baghdad University, and an objective English test to achieve the aim of the research. Nine colleges at Baghdad University are randomly chosen to represent the sample of the research which is 511 students. The results of the research have shown that there are weak significant correlation between the analytic domain of multiple intelligent and the objective English test. Thus, from the results of the research Baghdad University could modify the objective tests with alternative ones that based on students’ ability and intelligence not guessing tests. Continuous long-term assessment, untimed, free- response format, individualized test and creative answers based on multiple- intelligence are recommended.

Mathematical modeling of building structures and nonlinear differential equations

2020 ◽  
Vol 11 (03) ◽  
pp. 2050026
Author(s):  
Victor Orlov ◽  
Yulia Zheglova
Keyword(s):  
Mathematical Modeling ◽  
Approximate Solution ◽  
Differential Equations ◽  
Numerical Experiment ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Singular Points ◽  
Building Structures ◽  
Approximate Methods ◽  
Analytic Domain

Nonlinear differential equations with moving singular points require emergence and development of new approximate methods of solution. In this paper, we give a solution to one of the problems of the analytical approximate method for solving nonlinear differential equations with moving singular points, and study the influence of the perturbation of the initial conditions on the analytical approximate solution in the analytic domain. Theoretical material was tested using a numerical experiment confirming its reliability. The theoretical material presented in this paper allows researchers to use nonlinear differential equations with moving singular points when designing mathematical models of building structures.

Sign in / Sign up

Export Citation Format

Share Document