Nonexistence results for higher order pseudo‐parabolic equations in the Heisenberg group

Sufficient conditions are obtained for the nonexistence of solutions to the nonlinear higher order pseudo‐parabolic equation where is the Kohn‐Laplace operator on the (2N + 1)‐dimensional Heisenberg group , m≥1,p > 1. Then, this result is extended to the case of a 2 × 2‐system of the same type. Our technique of proof is based on judicious choices of the test functions in the weak formulation of the sought solutions. Copyright © 2016 John Wiley & Sons, Ltd.     

The type problem for random walks on trees

We consider the question of whether the simple random walk (SRW) on an infinite tree is transient or recurrent. For random-trees (all vertices of distancen from the root of the tree have degreed _n , where {d _n } are independent random variables), we prove that the SRW is a.s. transient if lim inf _n n E(log(d _n-1))>1 and a.s. recurrent if lim sup _n n E(log(d _n-1))<1. For random trees in which the degrees of the vertices are independently 2 or 3, with distribution depending on the distance from the root, a partial classification of type is obtained.Research supported in part by NSF DMS 8710027.     

Distributed high-temperature pressure sensing using air-hole microstructural fibers

We present spatially resolved Rayleigh scattering measurements in different polarization-maintaining (PM) fibers for high-temperature pressure sensing. The pressure-induced birefringence in the fiber cores is interrogated using polarization-resolved frequency-swept interferometry. The pressure responses of a PM photonic crystal fiber and a twin-air-hole PM fiber are investigated for a pressure range of 0 to 13.8 MPa (0-2000 psi) at room temperature and at temperatures as high as 800 °C. The proposed sensing system provides, for the first time to our knowledge, a truly distributed pressure-sensing solution for high-temperature applications.     

Folding model description of reactions with exotic nuclei

Microscopic folding calculations based upon the effective M3Y nucleon-nucleon interaction and the nuclearmatter densities of the interacting nuclei have been carried out to explain recently measured experimental data of the ⁶He+¹²⁰Sn elastic scattering cross section at four different laboratory energies near the Coulomb barrier. The extracted reaction cross sections are also considered.     

Improving the performance of three level code division multiplexing using the optimization of signal level spacing

In order to optimize the performance of three level code division multiplexing (3LCDM) at 2×20 Gb/s data rate, signal level spacing technique is investigated in this paper. The 3LCDM performance is improved considerably using both electrical and optical level spacing optimization configurations. The results demonstrate that by optimization, in conditions of the optical signal-to-noise ratio, an improvement of around 4.5 dB can be achieved in both approaches as well as 3.3 dB in the electrical configuration and 3.5 dB in the optical configuration can be accomplished for the 3LCDM in terms of the receiver sensitivity.     

Utilization of stimulated Raman Scattering as secondary pump on hybrid remotely-pump l-band Raman/erbium-doped fiber amplifier

An L-band remotely-pumped erbium-doped fiber amplifier incorporating a secondary pumping scheme utilizing stimulated Raman Scattering (SRS) was demonstrated. 1423 nm Raman laser was employed to generate SRS which became the secondary pump source. The amplifier displayed excellent gain of up to 27.3 dB at 1570 nm for −30 dBm input. Noise figures were also kept to a minimum, with the highest figure measured at 11 dB which was influenced by imperfection of the C/L coupler utilized in this architecture. Overall transmission performance was measured as well and demonstrated an encouraging outcome with gain as high as 24 dB while the noise figure was maintained at about 11 dB. The L-band signal amplification was also contributed by the stimulated Raman scattering along the transmission fiber. The outcome of this study emphasized the feasibility of secondary pumping scheme using SRS in L-band gain enhancement.     

The Topkis-Veinott algorithm for solving nonlinear programs with lower and upper bounded variables

In this paper we consider a nonlinear programming problem of the form to minimize f(x) subject to a x b, where f is a differentiable function on E_n and a and b are fixed vectors in E_n. We develop a variation of the feasible direction algorithm of Topkis and Veinott for solving the above problem and provide explicit expressions of the optimal directions for a family of direction-finding problems using different normalization constraints. We show that the algorithm converges to a Kuhn-Tucker point. The reported computational results indicate efficiency of the algorithm. It also indicates the strong effect of the form of the normalization constraint on convergence properties.     

Micro Determination of Ammonia by a Kinetic Spectrophotometric Method

 A simple and sensitive kinetic spectrophotometric method is described for the determination of micro amounts of ammonia. The method is based on the inhibiting effect of ammonia on the oxidation rate of aqua ethylenediamine-tetraacetate chromium(III) [Cr(HEDTA)(H₂O)] with N-bromo succinimide (NBS) to yield chromium(VI). The reaction was followed spectrophotometrically by measuring the rate of change in absorbance with time at 365 nm, which is the maximum absorption wavelength of chromium(VI). Using the recommended procedure, ammonia can be determined up to 153 μg ml⁻¹ with a linear calibration graph and a detection limit of 0.09 μg ml⁻¹. The method was successfully applied to the determination of ammonia in waste water samples. Recovery experiments for the analyzed samples were 97–100% with relative standard deviation, Sr (%) of ≤ 2.9% indicating high accuracy and precision of the proposed method. The interference of various cations and anions in the determination of ammonia was investigated. Received March 30, 2001 Revision September 3, 2001     

Synthesis and spectra of new 3-carbethoxypyrazole sulfonylurea derivatives

The reaction of 1-benzenesulfonyl-3-ethoxycarbonyl-5-[α-substituted-styryl]pyrazoles (1) with isocyanate and thioisocyanate derivatives yield the corresponding benzenesulfonylurea derivatives ( 2 and 3 ). Bromination of 1 afforded the 4-bromopyrazoles 4 which react with isocyanate derivatives giving 5 that were also obtained by bromination of 2 . Alkaline hydrolysis of the benzensulfonylurea derivatives 2 yield the corresponding pyrazole-3-carboxylic acids 7 .