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Weak Sense (weak + sense)

Distribution by Scientific Domains
Mathematics and Statistics57%

Selected Abstracts

Coherence in consciousness: Paralimbic gamma synchrony of self-reference links conscious experiences

HUMAN BRAIN MAPPING, Issue 2 2010
Hans C. Lou
Abstract A coherent and meaningful percept of the world is essential for human nature. Consequently, much speculation has focused on how this is achieved in the brain. It is thought that all conscious experiences have reference to the self. Self-reference may either be minimal or extended, i.e., autonoetic. In minimal self-reference subjective experiences are self-aware in the weak sense that there is something it feels like for the subject to experience something. In autonoetic consciousness, consciousness emerges, by definition, by retrieval of memories of personally experienced events (episodic memory). It has been shown with transcranial magnetic stimulation (TMS) that a medial paralimbic circuitry is critical for self-reference. This circuitry includes anterior cingulate/medial prefrontal and posterior cingulate/medial parietal cortices, connected directly and via thalamus. We here hypothesized that interaction in the circuitry may bind conscious experiences with widely different degrees of self-reference through synchrony of high frequency oscillations as a common neural event. This hypothesis was confirmed with magneto-encephalography (MEG). The observed coupling between the neural events in conscious experience may explain the sense of unity of consciousness and the severe symptoms associated with paralimbic dysfunction. Hum Brain Mapp, 2010. © 2009 Wiley-Liss, Inc. [source]

hp -Mortar boundary element method for two-body contact problems with friction

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2008
Alexey Chernov
Abstract We construct a novel hp -mortar boundary element method for two-body frictional contact problems for nonmatched discretizations. The contact constraints are imposed in the weak sense on the discrete set of Gauss,Lobatto points using the hp -mortar projection operator. The problem is reformulated as a variational inequality with the Steklov,Poincaré operator over a convex cone of admissible solutions. We prove an a priori error estimate for the corresponding Galerkin solution in the energy norm. Due to the nonconformity of our approach, the Galerkin error is decomposed into the approximation error and the consistency error. Finally, we show that the Galerkin solution converges to the exact solution as ,,((h/p)1/4) in the energy norm for quasiuniform discretizations under mild regularity assumptions. We solve the Galerkin problem with a Dirichlet-to-Neumann algorithm. The original two-body formulation is rewritten as a one-body contact subproblem with friction and a one-body Neumann subproblem. Then the original two-body frictional contact problem is solved with a fixed point iteration. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Elements of a theory of Ukrainian ethno-national identities

NATIONS AND NATIONALISM, Issue 1 2002
Andrew Wilson
Despite winning independence in 1991, Ukraine remains an amorphous society with a weak sense of national identity. One possible explanation is ,late' nation-creation, but in this article emphasis is laid on a continuing plurality of identity projects and the legacy of the ,failed' identity-building projects of the past. Ukraine's most important distinguishing feature , the existence of a substantial middle ground between Ukrainian and Russian identities , has considerable capacity to resist the logic of consolidating statehood. [source]

The boundary element method with Lagrangian multipliers,

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2009
Gabriel N. Gatica
Abstract On open surfaces, the energy space of hypersingular operators is a fractional order Sobolev space of order 1/2 with homogeneous Dirichlet boundary condition (along the boundary curve of the surface) in a weak sense. We introduce a boundary element Galerkin method where this boundary condition is incorporated via the use of a Lagrangian multiplier. We prove the quasi-optimal convergence of this method (it is slightly inferior to the standard conforming method) and underline the theory by a numerical experiment. The approach presented in this article is not meant to be a competitive alternative to the conforming method but rather the basis for nonconforming techniques like the mortar method, to be developed. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source]

On the mixed finite element method with Lagrange multipliers

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2003
Ivo Babu
Abstract In this note we analyze a modified mixed finite element method for second-order elliptic equations in divergence form. As a model we consider the Poisson problem with mixed boundary conditions in a polygonal domain of R2. The Neumann (essential) condition is imposed here in a weak sense, which yields the introduction of a Lagrange multiplier given by the trace of the solution on the corresponding boundary. This approach allows to handle nonhomogeneous Neumann boundary conditions, theoretically and computationally, in an alternative and usually easier way. Then we utilize the classical Babu,ka-Brezzi theory to show that the resulting mixed variational formulation is well posed. In addition, we use Raviart-Thomas spaces to define the associated finite element method and, applying some elliptic regularity results, we prove the stability, unique solvability, and convergence of this discrete scheme, under appropriate assumptions on the mesh sizes. Finally, we provide numerical results illustrating the performance of the algorithm for smooth and singular problems. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 192,210, 2003 [source]

Embedded Stochastic Runge-Kutta Methods

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
Andreas Rößler
We present some new embedded explicit stochastic Runge-Kutta methods for the approximation of Stratonovich stochastic differential equations in the weak sense with different orders of convergence. The presented methods yield an estimate of the local error which can be used for a step size control algorithm. [source]

Mathematical analysis of vortex sheets

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2006
Sijue Wu
We consider the motion of the interface separating two domains of the same fluid that moves with different velocities along the tangential direction of the interface. The evolution of the interface (the vortex sheet) is governed by the Birkhoff-Rott (BR) equations. We consider the question of the weakest possible assumptions such that the Birkhoff-Rott equation makes sense. This leads us to introduce chord-arc curves to this problem. We present three results. The first can be stated as the following: Assume that the Birkhoff-Rott equation has a solution in a weak sense and that the vortex strength is bounded away from 0 and ,. Moreover, assume that the solution gives rise to a vortex sheet curve that is chord-arc. Then the curve is automatically smooth, in fact analytic, for fixed time. The second and third results demonstrate that the Birkhoff-Rott equation can be solved if and only if only half the initial data is given. © 2005 Wiley Periodicals, Inc. [source]