Search results for "Vector"

Existence and stability of periodic solutions in a neural field equation

2017

We study the existence and linear stability of stationary periodic solutions to a neural field model, an intergo-differential equation of the Hammerstein type. Under the assumption that the activation function is a discontinuous step function and the kernel is decaying sufficiently fast, we formulate necessary and sufficient conditions for the existence of a special class of solutions that we call 1-bump periodic solutions. We then analyze the stability of these solutions by studying the spectrum of the Frechet derivative of the corresponding Hammerstein operator. We prove that the spectrum of this operator agrees up to zero with the spectrum of a block Laurent operator. We show that the no…

MR3667002 Reviewed Vogt, Dietmar(D-BUW) Hadamard operators on D′(Ω). (English summary) Math. Nachr. 290 (2017), no. 8-9, 1374–1380. 46F10 (46F12 47B3…

2017

In this paper, the Hadamard operators, i.e. a particular class of continuous linear operators on D′(Ω) whose set of eigenvectors is the class of monomials, are considered on an open set Ω⊂Rd. Specifically, Hadamard operators L are characterized by the multiplicative convolution, that is, there exists a distribution T such that L(S)=S⋆T, where the multiplicative convolution ⋆ is defined by (S⋆T)ϕ=Sy(Txϕ(xy)). To obtain this characterization, the author defines a particular extension to D(Ω˜), where Ω˜:=⋃a∈RdaΩ, of the transpose of Hadamard operators. This result is a generalization of a previous work of the author where only the case Ω=Rd was considered.

Identification and expression of the 11β‐steroid hydroxylase from Cochliobolus lunatus in Corynebacterium glutamicum

2019

Hydroxylation of steroids has acquired special relevance for the pharmaceutical industries. Particularly, the 11β-hydroxylation of steroids is a reaction of biotechnological importance currently carried out at industrial scale by the fungus Cochliobolus lunatus. In this work, we have identified the genes encoding the cytochrome CYP103168 and the reductase CPR64795 of C. lunatus responsible for the 11β-hydroxylase activity in this fungus, which is the key step for the preparative synthesis of cortisol in industry. A recombinant Corynebacterium glutamicum strain harbouring a plasmid expressing both genes forming a synthetic bacterial operon was able to 11β-hydroxylate several steroids as subs…

Individual Differences in Working Memory Capacity Are Unrelated to the Magnitude of Benefits from Object- and Dimension-Based Retro-Cues

2021

Vector π pulse soliton in coherent optical amplifiers

2007

We found a novel type of vector soliton pulse in a medium with linear loss and nonlinear gain from the coherent resonant interaction of light with two-level atoms exhibiting a degenerate upper state.

Design of an FBG based-on sensor device for large displacement deformation

2013

This article deals with the modeling of a strain-displacement transducer conceived for extending the FBG measurement range. The intrinsic fragility of the optical fiber limits their application to cases characterized by relatively small deformations. To extend the employ to the large displacement field (i.e. morphing applications), a dedicated device was conceived, constituted by a circular ring connected to the structure and laterally integrated with a FBG sensor. This device was mathematically modeled minimizing the potential energy this way arriving at a description of the displacement and deformation field along the curvilinear abscissa. The theoretical predictions were then validated t…

Generalized modulational instability in multimode fibers: Wideband multimode parametric amplification

2015

In this paper intermodal modulational instability (IM-MI) is analyzed in a multimode fiber where several spatial and polarization modes propagate. The coupled nonlinear Schr\"odinger equations describing the modal evolution in the fiber are linearized and reduced to an eigenvalue problem. As a result, the amplification of each mode can be described by means of the eigenvalues and eigenvectors of a matrix that stores the information about the dispersion properties of the modes and the modal power distribution of the pump. Some useful analytical formulas are also provided that estimate the modal amplification as function of the system parameters. Finally, the impact of third-order dispersion …

Wave Propagation in a 3-D Optical Waveguide

2003

In this paper we study the problem of wave propagation in a 3-D optical fiber. The goal is to obtain a solution for the time-harmonic field caused by a source in a cylindrically symmetric waveguide. The geometry of the problem, corresponding to an open waveguide, makes the problem challenging. To solve it, we construct a transform theory which is a nontrivial generalization of a method for solving a 2-D version of this problem given by Magnanini and Santosa.\cite{MS} The extension to 3-D is made complicated by the fact that the resulting eigenvalue problem defining the transform kernel is singular both at the origin and at infinity. The singularities require the investigation of the behavio…

Orientation of199mHg by optical pumping detected by ?-radiation anisotropy

1975

199mHg was produced and mass separated at the ISOLDE facility (CERN). Nuclear orientation achieved by optical pumping via the resonance line 6s21S0→6s6p3P1,λ=2537A was monitored by means of the anisotropy of theγ-radiation emitted in the cascade199mHg(I=13/2+) $${}^{199m}Hg(I = 13/2^ + )\xrightarrow[{M4}]{}{}^{199*}Hg(I = 5/2^ - )\xrightarrow[{E2}]{}{}^{199}Hg(I = 1/2^ - ).$$ 199*Hg(I=5/2−)199Hg(I=1/2−).

Simultaneous remote extraction of multiple speech sources and heart beats from secondary speckles pattern

2009

The ability of dynamic extraction of remote sounds is very appealing. In this manuscript we propose an optical approach allowing the extraction and the separation of remote sound sources. The approach is very modular and it does not apply any constraints regarding the relative position of the sound sources and the detection device. The optical setup doing the detection is very simple and versatile. The principle is to observe the movement of the secondary speckle patterns that are generated on top of the target when it is illuminated by a spot of laser beam. Proper adaption of the imaging optics allows following the temporal trajectories of those speckles and extracting the sound signals ou…