Search results for "Mathematica"

Left braces and the quantum Yang-Baxter equation

2019

[EN] Braces were introduced by Rump in 2007 as a useful tool in the study of the set-theoretic solutions of the Yang¿Baxter equation. In fact, several aspects of the theory of finite left braces and their applications in the context of the Yang¿Baxter equation have been extensively investigated recently. The main aim of this paper is to introduce and study two finite brace theoretical properties associated with nilpotency, and to analyse their impact on the finite solutions of the Yang¿Baxter equation.

Target point calculation in the computerized tomography. Comparison of different stereotactic methods

1995

The adaptation of computerized tomography for stereotactic operations requires the transformation of the coordinates of the target point from the CT image space into the stereotactic frame space. Two basic solutions for this transformation are realized in the most of the contemporary stereotactical systems. The indirect geometric method adjusts the frame coordinate system mechanically and identifies its origin in the CT image. There are 6 degrees of freedom: 3 of rotation and 3 of translation which have to be taken into consideration. The second method is a based on direct algebraic coordinate transformation and is independent of the explicite knowledge of the relationship between the image…

Influence of the scalp thickness on the intracranial contribution to rheoencephalography

2004

In spite of the great efforts made by the scientific community, up to now there is no agreement about the rheoencephalography (REG) capability to reflect cerebral blood flow (CBF). Moreover, a standard procedure and the optimal electrode arrangement have not been established yet. In a previous study, we found, using a classical four-shell spherical model of the head and solving it by numerical methods that, theoretically, there could exist an electrode arrangement to register an REG II free of extracranial contribution. In this paper, we have studied the influence of scalp thickness on the intracranial contribution to REG II. The study has been performed by solving the head model, using in …

Mutual Information Analysis of Brain-Body Interactions during different Levels of Mental stress

2019

In this work, we analyze brain-heart interactions during different mental states computing mutual information (MI) between the dynamic activity of different physiological systems. In 18 healthy subjects monitored in a relaxed resting state and during a mental arithmetic and a serious game task, multichannel EEG, one lead ECG, respiration and blood volume pulse were collected via wireless non-invasive biosensors. From these signals, synchronous 300-second time series were extracted measuring brain activity via the δ, θ, α, and β EEG power, and activity of the body district via the ECG R-R interval η, the respiratory amplitude ϱ and the pulse arrival time π. MI was computed using a linear est…

Subharmonic and homoclinic bifurcations in the driven and damped sine-Gordon system

1999

Abstract Chaotic responses induced by an applied biharmonic driven signal on the sine-Gordon (sG) system influenced by a constant dc-driven and the damping fields are investigated using a collective coordinate approach for the motion of the breather in the system. For this biharmonic signal, one term has a large amplitude at low frequency. Thus, the classical Melnikov method does not apply to such a system; however, we use the modified version of the Melnikov method to homoclinic bifurcations of the perturbed sG system. Additionally resonant breathers are studied using the modified subharmonic Melnikov theory. This dynamic behavior is illustrated by some numerical computations.

The validity of the “liminf” formula and a characterization of Asplund spaces

2014

Abstract We show that for a given bornology β on a Banach space X the following “ lim inf ” formula lim inf x ′ ⟶ C x T β ( C ; x ′ ) ⊂ T c ( C ; x ) holds true for every closed set C ⊂ X and any x ∈ C , provided that the space X × X is ∂ β -trusted. Here T β ( C ; x ) and T c ( C ; x ) denote the β-tangent cone and the Clarke tangent cone to C at x. The trustworthiness includes spaces with an equivalent β-differentiable norm or more generally with a Lipschitz β-differentiable bump function. As a consequence, we show that for the Frechet bornology, this “ lim inf ” formula characterizes in fact the Asplund property of X. We use our results to obtain new characterizations of T β -pseudoconve…

The Rise and Fall of Business Firms: A Stochastic Framework on Innovation, Creative

2021

Theoretical study of a Bénard Marangoni problem

2011

[EN] In this paper we prove the existence of strong solutions for the stationary Benard-Marangoni problem in a finite domain flat on the top, bifurcating from the basic heat conductive state. The Benard-Marangoni problem is a physical phenomenon of thermal convection in which the effects of buoyancy and surface tension are taken into account. This problem is modelled with a system of partial differential equations of the type Navier-Stokes and heat equation. The boundary conditions include crossed boundary conditions involving tangential derivatives of the temperature and normal derivatives of the velocity field. To define tangential derivatives at the boundary, intended in the trace sense,…

A COMPARATIVE STUDY BETWEEN ´ BIHARMONIC BEZIER SURFACES AND BIHARMONIC EXTREMAL SURFACES

2009

AbstractGiven a prescribed boundary of a Bezier surface, we compare the Bezier surfaces generated by two different methods, i.e., the Bezier surface minimising the biharmonic functional and the unique Bezier surface solution of the biharmonic equation with prescribed boundary. Although often the two types of surfaces look visually the same, we show that they are indeed different. In this paper, we provide a theoretical argument showing why the two types of surfaces are not always the same.

Two -methods to generate Bézier surfaces from the boundary

2009

Two methods to generate tensor-product Bezier surface patches from their boundary curves and with tangent conditions along them are presented. The first one is based on the tetraharmonic equation: we show the existence and uniqueness of the solution of @D^4x->=0 with prescribed boundary and adjacent to the boundary control points of a nxn Bezier surface. The second one is based on the nonhomogeneous biharmonic equation @D^2x->=p, where p could be understood as a vectorial load adapted to the C^1-boundary conditions.