Search results for "fiber"

Distribution of Eigenvalues for Semi-classical Elliptic Operators with Small Random Perturbations, Results and Outline

2019

In this chapter we will state a result asserting that for elliptic semi-classical (pseudo-)differential operators the eigenvalues are distributed according to Weyl’s law “most of the time” in a probabilistic sense. The first three sections are devoted to the formulation of the results and in the last section we give an outline of the proof that will be carried out in Chaps. 16 and 17.

Bifurcations of Regular Limit Periodic Sets

1998

In this chapter, (X λ ) will be a smooth or analytic (in Section 3) family of vector fields on a phase space S, with parameter λ ∈ P, as in Chapter 1. Periodic orbits and elliptic singular points which are limits of sequences of limit cycles are called regular limit periodic sets. The reason for this terminology is that for such a limit periodic set Γ one can define local return maps on transversal segments, which are as smooth as the family itself. The limit cycles near Γ will be given by a smooth equation and the theory of bifurcations of limit cycles from Γ will reduce to the theory of unfoldings of differentiable functions. In fact, we will just need the Preparation Theorem and not the …

Invariants of equivariant algebraic vector bundles and inequalities for dominant weights

1998

Steady-state radiation heat transfer problem

1996

In Section 8.2, we shall see that the steady-state radiative heat transfer problem can be transformed to minimization of a smooth nonquadratic functional J over a convex and closed subset of a Banach space V. To this end we firstly shortly recall some basic definitions concerning differentiability of J, because these sometimes differ in the literature.

An Approach to a Version of the S(M, g)-pseudo-differential Calculus on Manifolds

2003

For appropriate triples (M,g,M), where M is an (in general non-compact) manifold, g is a metric on T* M, and M is a weight function on T* M, we develop a pseudo-differential calculus on.A4 which is based on the S(M,g))-calculus of L. Hormander [27] in local models. In order to do so, we generalize the concept of E. Schrohe [41] of so-called SG-compatible manifolds. In the final section we give an outlook onto topological properties of the algebras of pseudo-differential operators. We state the existence of “order reducing operators” and that the algebra of operators of order zero is a submultiplicative Ψ*-algebra in the sense of B. Gramsch [18] in \( \mathcal{L}\left( {{L^2}\left( M \right)…

*-Representations of Partial *-Algebras

2002

This chapter is devoted to *-representations of partial *-algebras. We introduce in Section 7.1 the notions of closed, fully closed, self-adjoint and integrable *-representations. In Section 7.2, the intertwining spaces of two *-representations of a partial *-algebra are defined and investigated, and using them we define the induced extensions of a *-representation. Section 7.3 deals with vector representations for a *-representation of a partial *-algebra, which are the appropriate generalization to a *-representation of the notion of generalized vectors described in Chapter 5. Regular and singular vector representations are defined and characterized by the properties of the commutant, and…

Self-Organization of Polarization State in Optical Fibers

2017

Conductive polycaprolactone/gelatin/polyaniline nanofibres as functional scaffolds for cardiac tissue regeneration

2022

Abstract The endorsement of functional features such as biocompatibility, mechanical integrity, or electrical conductivity to tissue engineering (TE) scaffolds is essential to stimulate cell adhesion and proliferation. In this study, electrospun nanofibers based on polycaprolactone (PCL) and gelatin (Ge) (ratios 60/40, 50/50, and 40/60), and polyaniline (PAni) particles (0.25, 0.50, and 1.00%wt) were prepared. The time of dissolution in an acid solvent mixture before electrospinning allowed for obtaining nanofibers with controlled features. Changes in the molar mass (Mn from 90·103 to 15·103 g·mol−1), in the crystalline microstructure (Xc from 60 to 25%) and the surface morphology (diameter…

Fiber-Optic Aqueous Dipping Sensor Based on Coaxial-Michelson Modal Interferometers

2009

Fiber-optic modal interferometers with a coaxial-Michelson configuration can be used to monitor aqueous solutions by simple dipping of few centimeters of a fiber tip. The fabrication of these sensors to work around 850 nm enables the use of compact, robust, and low-cost optical spectrum analyzers. The use of this type of portable sensor system to monitor sewage treatment plants is shown.

Fast response vibration sensor based on Bragg gratings written in tapered core fibres

2007

Bragg gratings written in tapered core fibres permit a direct measure of mechanical vibrations with a time response better than 10 µs. The intrinsic properties of the sensors lead to a simple interrogation technique and wavelength multiplexing capacity. The sensor system is operated at 800 nm and is compact and low-cost.