Search results for " spaces"

Exploring the Virchow-Robin spaces function: A unified theory of brain diseases.

2016

Background: Cerebrospinal fluid (CSF) transport across the central nervous system (CNS) is no longer believed to be on the conventional lines. The Virchow-Robin space (VRS) that facilitates CSF transport from the basal cisterns into the brain interstitial fluid (ISF) has gained interest in a whole new array of studies. Moreover, new line of evidence suggests that VRS may be involved in different pathological mechanisms of brain diseases. Methods: Here, we review emerging studies proving the feasible role of VRS in sleep, Alzheimer's disease, chronic traumatic encephalopathy, and traumatic brain injury (TBI). Results: In this study, we have outlined the possible role of VRS in different path…

Pattern-Recognition: a Foundational Approach

2015

This paper aims at giving a contribution to the ongoing attempt to turn the theory of pattern-recognition into a rigorous science. In this article we address two problems which lie at the foundations of pattern-recognition theory: (i) What is a pattern? and (ii) How do we come to know patterns? In so doing much attention will be paid to tracing a non-arbitrary connection between (i) and (ii), a connection which will be ultimately based on considerations relating to Darwin’s theory of evolution.

The Variational Mcshane Integral in Locally Convex Spaces

2009

The variational McShane integral for functions taking values in a locally convex space is defined, and it is characterized by means of the p-variation of the indefinite Pettis integral

A Birkhoff type integral and the Bourgain property in a locally convex space

2007

An integral, called the $Bk$-integral, for functions taking values in a locally convex space is defined. Properties of $Bk$-integrable functions are considered and the relations with other integrals are studied. Moreover the $Bk$-integrability of bounded functions is compared with the Bourgain property.

Generation of Frames

2004

It is well known that, given a generic frame, there exists a unique frame operator which satisfies, together with its adjoint, a double operator inequality. In this paper we start considering the inverse problem, that is how to associate a frame to certain operators satisfying the same kind of inequality. The main motivation of our analysis is the possibility of using frame theory in the discussion of some aspects of the quantum time evolution, both for open and for closed physical systems.

Electronic Processes in Solid State: Dirac Framework

2019

The present paper proposes canonical Dirac framework adapted for application to the electronic processes in solid state. The concern is a spatially periodic structure of atoms distinguished by birth and annihilation of particle states excited due to interaction with the electromagnetic field. This implies replacing the conventional energy-momentum relation specific of the canonical Dirac framework and permissible for particle physics by a case specific relation available for the solid state. The advancement is a unified and consistent mathematical framework incorporating the Hilbert space, the quantum field, and the special relativity. Essential details of the birth and annihilation of the …

Finding Electron-Hole Interaction in Quantum Kinetic Framework

2018

The present research has been supported by the Institute of Solid State Physics, the University of Latvia within the framework of National Research Program IMIS2. [Grant numbers VPPI IMIS2, IMIS4].

A Remark on an Overdetermined Problem in Riemannian Geometry

2016

Let (M, g) be a Riemannian manifold with a distinguished point O and assume that the geodesic distance d from O is an isoparametric function. Let \(\varOmega \subset M\) be a bounded domain, with \(O \in \varOmega \), and consider the problem \(\varDelta _p u = -1\ \mathrm{in}\ \varOmega \) with \(u=0\ \mathrm{on}\ \partial \varOmega \), where \(\varDelta _p\) is the p-Laplacian of g. We prove that if the normal derivative \(\partial _{\nu }u\) of u along the boundary of \(\varOmega \) is a function of d satisfying suitable conditions, then \(\varOmega \) must be a geodesic ball. In particular, our result applies to open balls of \(\mathbb {R}^n\) equipped with a rotationally symmetric metr…

Re-Building Public (Plural) Spaces Through Inclusionary Participative Processes in 'Tresholds' Places

2010

Metabolic Impacts of Confinement during the COVID-19 Pandemic Due to Modified Diet and Physical Activity Habits

2020

While the detrimental effects of a chronic positive energy balance due to a sedentary lifestyle have been well established, the impacts of a short period of abruptly reduced physical activity and overeating arising from strict confinement due to the COVID-19 pandemic will soon start to emerge. To reasonably anticipate major consequences according to the available evidence, we hereby review the literature for studies that have explored the health impacts of several weeks of a reduction in physical activity and daily step-count combined with modified eating habits. These studies identify as main metabolic consequences increases in insulin resistance, total body fat, abdominal fat and inflamma…