Theory of a FIR optical digital differentiator

Abstract

An optical realization of a proposed family of the finite impulse response (FIR) qth-order mth-derivative digital differentiators (under coherent operation), whose transfer functions are derived from the well-known numerical differentiation scheme (namely, the backward Taylor series expansion), using the amplified fiber optic transversal filters is presented. Several input pulse shapes, such as polynomials of various orders and the Gaussian and exponential pulses, are chosen as examples for illustration of the accuracy of the proposed optically realized differentiators. A mathematical model describing the dynamic (or transient) response of any optical discrete-time systems using the z-transform technique is proposed. The real-time performances of the proposed differentiators have been analyzed using both the steady-state and the dynamic analyses, Although the analysis is directed at fiber optic systems, the methodology and the results are applicable to other physical systems.     

On projectively flat Finsler spaces

First we present a short overview of the long history of projectively flat Finsler spaces. We give a simple and quite elementary proof of the already known condition for the projective flatness, and we give a criterion for the projective flatness of a special Lagrange space (Theorem 1). After this we obtain a second-order PDE system, whose solvability is necessary and sufficient for a Finsler space to be projectively flat (Theorem 2). We also derive a condition in order that an infinitesimal transformation takes geodesics of a Finsler space into geodesics. This yields a Killing type vector field (Theorem 3). In the last section we present a characterization of the Finsler spaces which are projectively flat in a parameter-preserving manner (Theorem 4), and we show that these spaces over ${\mathbb {R}}^{n}$ are exactly the Minkowski spaces (Theorems 5 and 6).     

The influence of nitrogen vacancies on the magnetic behaviour of rare-earth nitrides

The rare-earth nitrides are ferromagnetic semiconductors with promise for spintronic devices. Their most common dopants are nitrogen vacancies (V_N), with a small enough energy of formation that they exist at of order 1% in epitaxial films. Here we report preliminary investigations of their effect on the magnetic states of two of them in the series, GdN and EuN. In the former we find an enhanced Curie temperature at very high V_N concentration, and the Eu²⁺ ions associated with V_N in the latter show strong exchange with their Eu³⁺ neighbours that might form the basis of a diluted magnetic semiconductor.     

Processus simultane d'évaporation libre et de diffusion de surface

If a conical metal tip is annealed in vacuum, the radius at the apex increases with time by surface diffusion. This was calculated by Nichols and Mullins and recently verified by the authors. This phenomenon is now calculated in case of a simultaneous action of evaporation and surface diffusion. By evaporation the blunting rate should be lowered until it becomes zero for a critical value of the curvature radius. Numerical data for different temperatures and cone angles are calculated for some metals (W, Mo, Pt, Ni, Cu). Measured are profile changes of Mo tips during annealing. The lowering of the blunting rate and the existence of a limit radius are confirmed. An evaporation can also occur as a consequence of a surface reaction. The measured radius changes of tungsten tips annealled in 1.5 × 10^?5 torr and 2.5 × 10^?5 torr of oxygen agree fairly well with the predictions. Surface self-diffusion measurements at high temperatures may be erroneous if evaporation is not considered, an example for Mo at 2150°K is given.     

Sanglifehrin-cyclophilin interaction: degradation work,synthetic macrocyclic analogues,X-ray crystal structure,and binding data

Sanglifehrin A (SFA) is a novel immunosuppressive natural product isolated from Streptomyces sp. A92-308110. SFA has a very strong affinity for cyclophilin A (IC(50) = 6.9 +/- 0.9 nM) but is structurally different from cyclosporin A (CsA) and exerts its immunosuppressive activity via a novel mechanism. SFA has a complex molecular structure consisting of a 22-membered macrocycle, bearing in position 23 a nine-carbon tether terminated by a highly substituted spirobicyclic moiety. Selective oxidative cleavage of the C(26)=C(27) exocyclic double bond affords the spirolactam containing fragment 1 and macrolide 2. The affinity of 2 for cyclophilin (IC(50) = 29 +/- 2.1 nM) is essentially identical to SFA, which indicates that the interaction between SFA and cyclophilin A is mediated exclusively by the macrocyclic portion of the molecule. This observation was confirmed by the X-ray crystal structure resolved at 2.1 A of cyclophilin A complexed to macrolide 16, a close analogue of 2. The X-ray crystal structure showed that macrolide 16 binds to the same deep hydrophobic pocket of cyclophilin A as CsA. Additional valuable details of the structure-activity relationship were obtained by two different chemical approaches: (1) degradation work on macrolide 2 or (2) synthesis of a library of macrolide analogues using the ring-closing metathesis reaction as the key step. Altogether, it appears that the complex macrocyclic fragment of SFA is a highly optimized combination of multiple functionalities including an (E,E)-diene, a short polypropionate fragment, and an unusual tripeptide unit, which together provide an extremely strong affinity for cyclophilin A.     

The effect of pressure on the dissociation of boric acid and sodium borate ion pairs at 25°C

A high pressure UV-visible spectrophotometer was used to determine the dissociation constant of boric acid using an indicator technique. The measurements were made at 25°C and at ionic strengths of 0.1 and 1.0m over a pressure range of 1 to 2000 atm. Extrapolation to I=0 gave a thermodynamic dissociation constant of 5.16×10^–10 at 1 atm. The pressure dependence yielded a partial molal volume change of –28.9 and –31.8 cm³-mol^–1 and a compressibility change of –3.1 and –4.8×10^–3 cm³-mol^–1-atm^–1 for the dissociation at I=0.1 and 1.0m, respectively. The association constant for the formation of the sodium borate ion pair was determined by comparing the acid constants in tetramethylammonium chloride to those in sodium chloride solutions. Extrapolation to I=0 yielded a K_A for [NaB(OH)₄] of 0.64 at 1 atm. The pressure dependence of K_A gave and for the formation of the ion pair.