Improvement on peak-to-trough ratio of sampled fiber Bragg gratings with multiple phase shifts

Via a cascaded structure, the peak-to-trough ratio is considerably improved for sampled fiber Bragg gratings （SFBGs） based on multiple-phase-shift （MPS） technique. This cascaded filter is composed of two identical SFBGs which are inserted with the increasing or decreasing arrangement of phase shifts. With this inverse arrangement of MPS in grating design, the phase fluctuation of individual SFBG can be compensated, and as a result an excellent phase matching condition is realized. In this way, the peak-to- trough ratio in reflection spectra is improved from 6 to 12 dB when multiplication factor m = 4, and from 5dBto 10dBwhenm=8.     

Analysis of visual perception of light emitting diode brightness in dense fog with various droplet sizes

Road signs must provide a conspicuous signal to a wide variety of drivers over a broad range of environmental and geometric conditions. Recently, there are an increasing number of applications in which light emitting diodes (LEDs) are used as the light source, including critical transportation signaling. In the presence of fog, the resulting visual signal is disturbed due to light scattering by airborne water droplets. By measuring LED brightness with human spectral sensitivity in various densities and various droplet sizes (10, 30, 50, and 100 μm), it is understood that the particle size distribution (fog droplet size) and density of fog does affect visibility in fog. The colored LEDs that contain a yellow component had high brightness evaluation, blue component had low brightness evaluation in all densities and different droplet sizes. The result in this paper can contribute to air and land traffic safety and the prevention of accidents.     

Newton's method on Riemannian manifolds and a geometric model for the human spine

To study a geometric model of the human spine we are led tofinding a constrained minimum of a real valued function definedon a product of special orthogonal groups. To take advantgeof its Lie group structure we consider Newton's method on thismanifold. Comparisons between measured spines and computed spinesshow the pertinence of this approach.     

Cyclic Designs with Block Size 4 and Related Optimal Optical Orthogonal Codes

We prove the existence of a cyclic (4p, 4, 1)-BIBD—and hence, equivalently, that of a cyclic (4, 1)-GDD of type 4 ^p —for any prime such that (p–1)/6 has a prime factor q not greater than 19. This was known only for q=2, i.e., for . In this case an explicit construction was given for . Here, such an explicit construction is also realized for .We also give a strong indication about the existence of a cyclic (4p 4, 1)-BIBD for any prime , p>7. The existence is guaranteed for p>(2q ³–3q ²+1)²+3q ² where q is the least prime factor of (p–1)/6.Finally, we prove, giving explicit constructions, the existence of a cyclic (4, 1)-GDD of type 6 ^p for any prime p>5 and the existence of a cyclic (4, 1)-GDD of type 8 ^p for any prime . The result on GDD's with group size 6 was already known but our proof is new and very easy.All the above results may be translated in terms of optimal optical orthogonal codes of weight four with =1.     

On the Right-Definite and Left-Definite Spectral Theory of the Legendre Polynomials

In this paper, we further develop the left-definite and right-definite spectral theory associated with the self-adjoint differential operator A in L²(-1,1), generated from the classical second-order Legendre differential equation, having the sequence of Legendre polynomials as eigenfunctions. Specifically, we determine the first three left-definite spaces associated with the pair (L²(-1,1),A). As a consequence of these results, we determine the explicit domain of both the associated left-definite operator A₁, first observed by Everitt, and the self-adjoint operator A^1/2. In addition, we give a new characterization of the domain D(A) of A and, as a corollary, we present a new proof of the Everitt-Mari result which gives optimal global smoothness of functions in D(A).     

Group Representation of Waves in Gyrotropic Crystals

A new group (linear) representation of the propagation of waves in properly and naturally gyrotropic crystals in the general case where the nonreciprocity effect takes place has been developed. Simple expressions of the dependence of ray (group) velocities and polarization vectors of isonormal waves on the complex vector of principal velocities dual to the unitary tensor by which the optical properties of crystals are directly characterized have been obtained. The relationship between gyrotropy and anisotropy and the dipole moment and displacement current induced by the radiation in the crystal has been established. It is shown that the presence of gyrotropy and nonlinear polarization of radiation together with the elimination of conical points entails a phase ambiguity of the ray velocity of the quantummechanical type and a smearing and layering of the wave surface, as well as a discreteness of the spectrum of velocity values of isonormal waves.     

Conservative Means of Orthogonal Series and the Spaces $$L^p [0;1] $$ , $$p \in (1;\infty ) $$

Necessary and sufficient conditions for an orthogonal series to be the Fourier series of a function in the space , , are obtained. In the special case of regular summation methods we recover the classical results of Orlicz and Lomnicki.     

Confocal Microscopy Studies of Trypsin Immobilization on Porous Glycidyl Methacrylate Beads

The immobilization of trypsin on porous glycidyl methacrylate (GMA–GDMA) beads has been investigated. In particular, the distribution within the beads of trypsin and of dextran used for hydrophilizing the bead surface prior to protein immobilization was investigated with confocal microscopy. For the system investigated, the fluorescence intensity profiles obtained when using borate buffer as an ambient solution displayed a distinct minimum at the center of the beads, irrespective of the observation depth. However, by reduction of the refractive index difference between the solution and the beads through the addition of glucose to the aqueous solution, artifacts relating to optical length differences could be reduced. For both low molecular weight fluorescein isothiocyanate (FITC), FITC-labeled trypsin, and FITC-labeled dextran, an essentially homogeneous distribution throughout the beads was observed. This simple “contrast matching” method seems therefore to be an interesting tool when investigating the distribution of immobilized protein in porous chromatography media.     

On the Relation Between Orthogonal,Symplectic and Unitary Matrix Ensembles

For the unitary ensembles of N×N Hermitian matrices associated with a weight function w there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For the orthogonal and symplectic ensembles of Hermitian matrices there are 2×2 matrix kernels, usually constructed using skew-orthogonal polynomials, which play an analogous role. These matrix kernels are determined by their upper left-hand entries. We derive formulas expressing these entries in terms of the scalar kernel for the corresponding unitary ensembles. We also show that whenever w/w is a rational function the entries are equal to the scalar kernel plus some extra terms whose number equals the order of w/w. General formulas are obtained for these extra terms. We do not use skew-orthogonal polynomials in the derivations