Frequency dependent beating patterns and amplitude increase during the approach of an internal wave packet

A frequency-dependent beating pattern in the spectrogram of broadband signals transmitted during the approach of an internal wave packet to an acoustic propagating path is reported. An analytical expression relating the acoustic signal measurements and environmental parameters under certain conditions is obtained. Three-dimensional parabolic equation modeling results compare well with Shallow Water 2006 experiment data.     

Numerical investigation of relativistic self-focusing of intense laser beam with LG01 mode in plasmas

In this paper, we numerically investigate the relativistic self-focusing of laser beam with LG₀₁ mode in plasmas. An effective potential is introduced to identify the critical power. Numerical methods are employed to solve the governing equations. To verify the numerical procedures, we compare the known analytical solution of the relativistic critical power for TEM₀₀ mode with our numerical method. It is shown that there is a good agreement between our numerical results and the analytical solution. The critical power for relativistic self-focusing of a LG₀₁ laser beam is about 6 times of that for a TEM₀₀ laser beam.     

Classification of skew‐Hadamard matrices of order 32 and association schemes of order 31

Using a backtracking algorithm along with an essential change to the rows of representatives of known 13 710 027 equivalence classes of Hadamard matrices of order 32, we make an exhaustive computer search feasible and show that there are exactly 6662 inequivalent skew‐Hadamard matrices of order 32. Two skew‐Hadamard matrices are considered SH ‐equivalent if they are similar by a signed permutation matrix. We determine that there are precisely 7227 skew‐Hadamard matrices of order 32 up to SH ‐equivalence. This partly settles a problem posed by Kim and Solé. As a consequence, we provide the classification of association schemes of order 31.     

Modelling methane migration in soil

Based on Bear-Bachmat porous medium model, the governing equations for the migration of gases through soil from a buried source are presented. A finite element solution system for the equations is developed. The resulting model is capable of incorporating medium anistropy and inhomogeneity in an axisymmetric configuration. The model has facilities for including time-varying fluid properties and boundary conditions. Convergence of the solution is examined. Potential applications for the modelling of gas migration from waste burial sites and the evaluation of control mechanisms are discussed.     

Fabrication of an ion-selective electrode for determination of propylhexedrine

Electrodes of both conventional and micro-sizes were based on the use of propylhexedrine-reineckate as the ion-exchanger in a plastic membrane. The electrodes exhibited Nernstian response towards propylhexedrine (PX) over the concentration range 10^–6–10^–2 M and had life spans of up to 2 days continuous work. The working pH range was 2.3–8. Investigation of diverseions reveals good selectivity for propylhexedrine over several inorganic cations, amines, aminoacids, sugars and some pharmaceutical compounds. The electrode was applied for determination of the drug in urine with 99.1% recovery and 0.15–0.31% relative standard deviation.     

Electromagnetic field representation in the source region

Representation of electromagnetic fields in the source region in inhomogeneous anisotropic media is developed in terms of Hertz vectors. Differential equations satisfied by these vectors as functions of stream potentials of the sources are obtained. Conditions for representation in terms of uncoupled transverse electric and magnetic modes satisfying second-order differential equations are derived.     

Synthesis of a carbon-14 analogue of aryl N-alkoxycarbamates and its application for synthesis of unsymmetrical N,N′-urea derivatives

Aryl N-alkoxycarbamates labeled with carbon-14 have been synthesized from aryl nitrile-[cyano-¹⁴C] as part of a 2-step sequence. The resulted carbamates were treated with amines, generating [carbonyl-¹⁴C]-Ureas in high yield and purity.     

Catalytic Kinetic Determination of Trace Amounts of Palladium with Photometric Detection

 A new, simple photometric method for the determination of palladium was described. Palladium was determined photometrically at 600 nm and pH = 5.4 based on its heterogeneous catalytic effect on the reduction of thionine (TN) with hypophosphite (HP) using a probe-type photometer system (variable time method). The influence of reaction variables was discussed. The calibration curve was found linear in the range 0.11–5.55 μg/ml (at 30 °C) and the detection limit was 0.06 μg/ml. The relative standard deviation of the developed method was 1.6% (for 10 replicate determinations of 2.22 μg/ml Pd(II)). The effect of interference from other metal ions and anions was studied. The proposed method was successfully applied to catalysts, Pd–C, Al–Si–Pd (new and used). Received March 1, 2001 Revision August 10, 2001     

Convenient and Regiospecific Method for Synthesis of 4,5-Diaryl-1-methyl-2-(methylthio)-1H-imidazole

A convenient, high-yielding, regiospecific synthesis of 1H-imidazole-2-thiones ring has been developed. In addition, a series of 4,5-diaryl-1-methyl-2-(methylthio)-1H-imidazoles 8 were synthesized and characterized. The structure of regioisomers was confirmed through nuclear Overhauser effect spectroscopy and NMR spectroscopy.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communications® to view the free supplemental file.     

A matricial extension of the Helson-Szegö theorem and its application in multivariate prediction

It is shown that the positivity of the angle between the past and future of a multivariate stationary process is sufficient for the existence of a mean-convergent autoregressive series representation of its linear predictor. A large class of multivariate processes whose past and future are at positive angle is characterized, thus providing a matricial extension of the Helson-Szegö theorem.