Search results for "bundle"
showing 10 items of 257 documents
Quasi *-Algebras of Operators in Rigged Hilbert Spaces
2002
In this chapter, we will study families of operators acting on a rigged Hilbert space, with a particular interest in their partial algebraic structure. In Section 10.1 the notion of rigged Hilbert space D[t] ↪ H ↪ D × [t ×] is introduced and some examples are presented. In Section 10.2, we consider the space.L(D, D ×) of all continuous linear maps from D[t] into D × [t ×] and look for conditions under which (L(D, D ×), L +(D)) is a (topological) quasi *-algebra. Moreover the general problem of introducing in L(D, D ×) a partial multiplication is considered. In Section 10.3 representations of abstract quasi *-algebras into quasi*-algebras of operators are studied and the GNS-construction is …
Vulnerability of different nerves to intrafascicular injection by different needle types and at different approach angles: a mathematical model
2019
Background and objectivesWe assume that intrafascicular spread of a solution can only occur if a large enough portion of the distal needle orifice is placed inside the fascicle. Our aim is to present and evaluate a mathematical model that can calculate the theoretical vulnerability of fascicles, analyzing the degree of occupancy of the needle orifice in fascicular tissue by performing simulations of multiple positions that a needle orifice can take inside a cross-sectional nerve area.MethodsWe superimposed microscopic images of two routinely used nerve block needles (22-gauge, 15° needle and 22-gauge, 30° needle) over the microscopic images of cross-sections of four nerve types photographed…
Nucleus incertus—An emerging modulatory role in arousal, stress and memory
2011
A major challenge in systems neuroscience is to determine the underlying neural circuitry and associated neurotransmitters and receptors involved in psychiatric disorders, such as anxiety and depression. A focus of many of these studies has been specific brainstem nuclei that modulate levels of arousal via their ascending monoaminergic projections (e.g. the serotonergic dorsal raphe, noradrenergic locus ceruleus and cholinergic laterodorsal tegmental nucleus). After years of relative neglect, the subject of recent studies in this context has been the GABAergic nucleus incertus,1 which is located in the midline periventricular central gray in the ‘prepontine’ hindbrain, with broad projection…
The effect of rewarding hypothalamic stimulation on behavioral and neural hippocampal responses during trace eyeblink conditioning in rabbit (Oryctol…
2005
Rabbits were trace-conditioned with a tone as a conditioned stimulus and an airpuff as an unconditioned stimulus. Electrical stimulation to the medial forebrain bundle in the lateral hypothalamus was delivered either before or after the tone-airpuff pair. The purpose of the present study was to test whether the effect of post-trial hypothalamic stimulation differed from the effect of pre-trial hypothalamic stimulation on trace conditioning in the same subjects. Additionally, hippocampal responses were measured during sessions to see if hypothalamic stimulation activated dopaminergic fibres and affected hippocampal cell functioning and thus learning. The results showed that behavioral nictit…
Normal Coulomb Frames in $${\mathbb{R}}^{4}$$
2012
Now we consider two-dimensional surfaces immersed in Euclidean spaces \({\mathbb{R}}^{n+2}\) of arbitrary dimension. The construction of normal Coulomb frames turns out to be more intricate and requires a profound analysis of nonlinear elliptic systems in two variables. The Euler–Lagrange equations of the functional of total torsion are identified as non-linear elliptic systems with quadratic growth in the gradient, and, more exactly, the nonlinearity in the gradient is of so-called curl-type, while the Euler–Lagrange equations appear in a div-curl-form. We discuss the interplay between curvatures of the normal bundles and torsion properties of normal Coulomb frames. It turns out that such …
Uniform fibre Bragg gratings with an embedded perturbed section for multiple applications
1999
The interest in fibre Bragg gratings has been increased with the development of flexible fabrication techniques which are able to make gratings with any non-uniform characteristic (chirped, apodised, sampled, phase-shifted, etc.) required for an specific application [1].
On the volume of unit vector fields on spaces of constant sectional curvature
2004
A unit vector field X on a Riemannian manifold determines a submanifold in the unit tangent bundle. The volume of X is the volume of this submanifold for the induced Sasaki metric. It is known that the parallel fields are the trivial minima.
Purification of Lindblad dynamics, geometry of mixed states and geometric phases
2015
We propose a nonlinear Schr\"odinger equation in a Hilbert space enlarged with an ancilla such that the partial trace of its solution obeys to the Lindblad equation of an open quantum system. The dynamics involved by this nonlinear Schr\"odinger equation constitutes then a purification of the Lindbladian dynamics. This nonlinear equation is compared with other Schr\"odinger like equations appearing in the theory of open systems. We study the (non adiabatic) geometric phases involved by this purification and show that our theory unifies several definitions of geometric phases for open systems which have been previously proposed. We study the geometry involved by this purification and show th…
Presymplectic manifolds and conservation laws
2008
In this paper we make use of a new structure called seeded fibre bundle. This allows us to combine the symplectic formalism and general relativity. A theorem of existence is obtained and some examples and properties are studied.
One-Loop Effective Lagrangian in QED
2020
Our main goal in this section is the derivation of an expression for the effective Lagrangian in one-loop approximation. So let’s start with the vacuum persistence amplitude in presence of an external field: $$\displaystyle \langle 0_+\vert 0_-\rangle ^A = e^{ iW^{(1)}[A]} = e^{i \int d^4x\mathcal {L}^{(1)}(x)} $$