Dispersion induced power fading for radio frequency signals and its application for fast online PMD and CD monitoring

We derive the expressions for the power fading including first-order polarization mode dispersion (PMD), chromatic dispersion, chirp parameter as well as polarization-dependent chromatic dispersion (PCD), which is dependent on the angle of precession of output state of polarization around the PMD vector. From the expression for radio frequency (RF) signals power fading, we get the average power fading for chromatic dispersion, chirp parameter, first-order PMD and PCD for both double sideband (DSB) modulation and single sideband (SSB) modulation. We also demonstrate a fast PMD and chromatic dispersion monitoring technology with reduced polarization-dependent gain. The measured results agree well with theoretical analysis. PACS 42.81.-i; 42.81.Gs; 42.30.Lr     

Polarization dependent guiding in liquid crystal filled photonic crystal fibers

A theoretical study of nematic liquid crystal filled photonic crystal fibers (LCPCFs) is presented. Detailed investigations including the polarization dependent bandgap formation and the modal properties are given for LCPCFs, in which alignment of the molecules could be controlled by external static electric field. The polarization dependent bandgap splitting caused by the high index difference between the ordinary and the extraordinary dielectric index of nematic liquid crystals provides the possibility of single-mode single-polarization guiding. A polarization operation diagram is proposed to describe the guiding behavior of LCPCFs. The influence of rotation angle ? of the director of liquid crystals on the modal properties is investigated. It is shown that the polarization axis of the guided mode is determined by the rotation angle ?, which could be controlled by external electric field.     

Corner sharing tetrahedral network in Co(3)(HAT)[N(CN)(2)](6)(OH(2))(2) (HAT = 1,4,5,8,9,12-hexaazatriphenylene)

We report a trinuclear Co(II) complex containing bridging dicyanamides and a tris-chelated HAT, which possesses approximately 37% void space. The magnetic exchange pathways appear in the structure as a corner sharing tetrahedral network. The compound crystallizes in the monoclinic space group P2(1)/c [a = 13.655(3) A, b = 15.189(3) A, c = 22.367(4) A, beta = 114.100(2) degrees, V = 4234.5(14) A(3), Z = 4, R(F(o)) = 0.0823]. The magnetic data were fit to an S = 3/2 model for systems dominated by zero-field splitting effects with g = 2.01 and D = 38.9 cm(-1).     

Retract extensions of ordered sets

The concept of retract extension of an ordered set is introduced and studied. We give an example of a retract extension and an example that is not a retract extension. Bibliography: 12 titles. Published in Zapiski Nauchnykh Seminarov POMI, Vol. 321, 2005, pp. 205–212.     

G-Covering Systems of Subgroups for Classes of p-Supersoluble and p-Nilpotent Finite Groups

Let be a class of groups. Given a group G, assign to G some set of its subgroups =(G). We say that is a G-covering system of subgroups for (or, in other words, an -covering system of subgroups in G) if G whenever either =Ø or Ø and every subgroup in belongs to . We find the systems of subgroups in the class of finite soluble groups G which are simultaneously the G-covering systems of subgroups for the classes of p-supersoluble and p-nilpotent groups.     

Wide-passband, temperature-insensitive, and compact pi-phase-shifted long-period gratings in endlessly single-mode photonic crystal fiber

We demonstrate what is believed to be the first fabrication of a wide-passband, temperature-insensitive, and compact spectral filter based on a pi-phase-shifted long-period grating in an endless single-mode photonic crystal fiber. By introducing a pi-phase shift in the middle of a 12-period long-period grating, two symmetrical rejection bands at wavelengths of 1252.65 and 1418.7 nm are obtained with isolation higher than 18 dB and a passband bandwidth of 84.15 nm. The pi-phase-shifted long-period gratings are inscribed by the relaxation of mechanical stress with the focused pulses of a CO2 laser and a point-by-point technique without geometric deformation. The length of the spectral filter is approximately 6.6 mm with a sensitivity of 8 pm/ degrees C at a medium temperature range of 23-190 degrees C.     

Strain-insensitive and high-temperature long-period gratings inscribed in photonic crystal fiber

We fabricate and demonstrate strain-insensitive and high-temperature long-period gratings in endlessly single-mode photonic crystal fiber by use of focused pulses of a CO2 laser and a periodic stress relaxation technique without geometrical deformation and elongation of the fiber. The thermal dependence of mode coupling at 1299.59 nm is 10.9 pm/degrees C from 24 to 992 degrees C, whereas the coefficient of strain sensitivity is -0.192 pm/muepsilon up to the maximum strain of 2.74%epsilon. It is found for what is believed to be the first time that, in contrast with the traditional fiber case, the coupling resonance shifts toward shorter wavelengths under applied strain, indicating that the refractive index of the core is decreased as a result of the rebuilding of tension attributed to the stress-elastic effect, and the cladding modes is highly dispersive because of airholes arranged in the fiber cladding.     

The pyrolysis of dimethyl sulfide,kinetics and mechanism

The kinetics of the gas phase pyrolysis of dimethyl sulfide (DMS) was studied in a static system at 681–723 K by monitoring total pressure-time behavior. Analysis showed the pressure increase to follow DMS loss. The reaction follows two concurrent paths: with a slow, minor, secondary reaction: In a seasoned reactor the reaction follows a 3/2 order rate law with rate coefficient given by with θ = 2.303 RT in kcal/mol. A free radical mechanism is proposed to account for the data and a theoretical rate coefficient is derived from independent data: which agrees well with the experimental one over the range studied. The reaction is initiated by Me₂S → Me + MeS? and propagated by metathetical radical attack on Me₂S. C₂H₄ is formed by an isomerization reaction which may in part be due to a hot radical: Thermochemical data are listed, many from estimations, for both molecular and radical species of interest in the present system.     

The oxidation of HI at low temperatures and the heat of formation of HO2

The kinetics of the oxidation of hydrogen iodide (HI + O₂) at low temperature (414–499 K) in the gas phase by the method of iodination kinetics is complicated by a heterogeneous reaction between hydrogen iodide and oxygen. Present work leads to an upper limit for the bimolecular rate constant k₁ for the first and rate-determining step (1) These data are combined with an estimated A factor A₁ = 10^9.3±0.2 L/mol·s (assuming a tight linear I···H···O— transition state), to calculate the lower limit of the activation energy for the forward reaction E₁. This leads to a minimum value for the heat of formation of the HO₂ radical, ΔH_f298^°(HO₂) < 3.0 kcal/mol.     

Morita equivalence for infinite matrix rings

In this paper, weak distinguished subcategory and distinguished subcategory of modules are introduced. Left(right) local unital rings are particularly considered. Also, representable equivalent functors between categories. By using the replacement techniques of modules, a general theory of Morita equivalence for infinite matrix rings is established. This theory not only extends the classical Morita theory of equivalence from finite matrix rings to infinite matrix rings and also contains some new results which are useful in studying the algebraic structures for infinite matrix rings. Some results of classical Morita theory are included as its special cases.