Search results for "TOPOLOGY"
showing 10 items of 2892 documents
General Theory: Topological Aspects
2009
In Chapter 1, we have analyzed the structure of pip-spaces from the algebraic point of view only, (i.e., the compatibility relation). Here we will discuss primarily the topological structure given by the partial inner product itself. The aim is to tighten the definitions so as to eliminate as many pathologies as possible. The picture that emerges is reassuringly simple: Only two types of pip-spaces seem sufficiently regular to have any practical use, namely lattices of Hilbert spaces (LHS) or Banach spaces (LBS), that we have introduced briefly in the Introduction. Our standard reference on locally convex topological vector spaces (LCS) will be the textbook of Kothe [Kot69]. In addition, fo…
Hadronic light-by-light contribution to $(g-2)_\mu$ from lattice QCD with SU(3) flavor symmetry
2020
We perform a lattice QCD calculation of the hadronic light-by-light contribution to $(g-2)_\mu$ at the SU(3) flavor-symmetric point $m_\pi=m_K\simeq 420\,$MeV. The representation used is based on coordinate-space perturbation theory, with all QED elements of the relevant Feynman diagrams implemented in continuum, infinite Euclidean space. As a consequence, the effect of using finite lattices to evaluate the QCD four-point function of the electromagnetic current is exponentially suppressed. Thanks to the SU(3)-flavor symmetry, only two topologies of diagrams contribute, the fully connected and the leading disconnected. We show the equivalence in the continuum limit of two methods of computin…
A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising
2015
Variational methods are commonly used to solve noise removal problems. In this paper, we present an augmented Lagrangian-based approach that uses a discrete form of the L1-norm of the mean curvature of the graph of the image as a regularizer, discretization being achieved via a finite element method. When a particular alternating direction method of multipliers is applied to the solution of the resulting saddle-point problem, this solution reduces to an iterative sequential solution of four subproblems. These subproblems are solved using Newton’s method, the conjugate gradient method, and a partial solution variant of the cyclic reduction method. The approach considered here differs from ex…
Determining the number of sources in high-density EEG recordings of event-related potentials by model order selection
2011
To high-density electroencephalography (EEG) recordings, determining the number of sources to separate the signal and the noise subspace is very important. A mostly used criterion is that percentage of variance of raw data explained by the selected principal components composing the signal space should be over 90%. Recently, a model order selection method named as GAP has been proposed. We investigated the two methods by performing independent component analysis (ICA) on the estimated signal subspace, assuming the number of selected principal components composing the signal subspace is equal to the number of sources of brain activities. Through examining wavelet-filtered EEG recordings (128…
Synchronization of hidden chaotic attractors on the example of radiophysical oscillators
2017
In the present paper we consider the problem of synchronization of hidden and self-excited attractors in the context of application to a system of secure communication. The system of two coupled Chua models was studied. Complete synchronization was observed as for self-excited, as hidden attractors. Beside it for hidden attractors some special type of dynamic was revealed.
‘Knowing Development, Developing Knowledge?’ Introduction to a Special Issue
2014
The articles in this special issue give a flavor of the overall theme ‘Knowing development, developing knowledge’, the title of the second Nordic Conference for Development Research held in Finland...
The N-dimensional N-person chesslike game strategy analysis model
2016
In this research a mathematical, symmetric n-player game model, based on chess is designed. Symmetry in this context refers to players' positions with respect to each other. While the order of move naturally violates the symmetry, this problem may also be solved. The motivation for building this kind of game model stems from the difficulty of finding mathematical solutions for multi-player games in general. The number of varying factors is so huge, that finding optimal strategies is mathematically almost impossible. The best way to attempt this is to use simulation. Once the model has been built, it can be applied in many ways by using computational algorithms based on the created model. Ch…
New Insights into Segmental Packing, Chain Dynamics and Thermomechanical Performance of Aliphatic Polyurea Composites: Comparison between Silica Oxid…
2021
Polyurea (PU) is intrinsically reinforced by its microphase-separated morphology, giving its excellent mechanical properties. In this study, it is shown how a high-index PU formulation applies easy diffusion of hard segments into the soft phase of the PU matrix and tune its chain mobility. Moreover, the interaction of micro (>100 nm), nano (<100 nm) fillers with the microdomains and their thermomechanical properties are unraveled. Herein, nanosilica oxide (NS) and micro titanium (III) oxide (Ti2O3) are incorporated at low loadings into a solvent-free two-component aliphatic PU via insitu polymerization. While NS achieves an interfacial interaction with urea groups and forms a tight ha…
Measurement of the top quark charge in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector
2013
A measurement of the top quark electric charge is carried out in the ATLAS experiment at the Large Hadron Collider using 2.05 fb[superscript −1] of data at a centre-of-mass energy of 7 TeV. In units of the elementary electric charge, the top quark charge is determined to be 0.64 ± 0.02 (stat.) ± 0.08 (syst.) from the charges of the top quark decay products in single lepton t[¯ over t] candidate events. This excludes models that propose a heavy quark of electric charge −4/3, instead of the Standard Model top quark, with a significance of more than 8σ.
Some Remarks about Product Spaces
2018
Summary This article covers some technical aspects about the product topology which are usually not given much of a thought in mathematics and standard literature like [7] and [6], not even by Bourbaki in [4]. Let {Ti}i∈I be a family of topological spaces. The prebasis of the product space T = ∏ i∈I Ti is defined in [5] as the set of all π −1 i (V) with i ∈ I and V open in Ti . Here it is shown that the basis generated by this prebasis consists exactly of the sets ∏ i∈I Vi with Vi open in Ti and for all but finitely many i ∈ I holds Vi = Ti . Given I = {a} we have T ≅ Ta , given I = {a, b} with a≠ b we have T ≅ Ta ×Tb . Given another family of topological spaces {Si}i∈I such that Si ≅ Ti fo…