Real Paley-Wiener theorems associated with the weinstein operator

In this paper we use real analysis techniques to establish a new real Paley-Wiener theorems for the Fourier-Bessel transform associated with the Weinstein operator. More precisely we characterize the C ^∞-functions whose image under the Fourier-Bessel transform are functions with compact support through an L ^p growth condition, p ∈ [1, +∞] and we give another version of the real Paley-Wiener theorem for L ²-functions.     

Dynamic response of permalloy/Cu/Co magnetoresistive sandwiches

The dynamic response of trilayer magnetoresistive permalloy/Cu/Co films was studied by high-frequency permeability spectra measurements. The resonance frequency is shown to depend on the interlayer copper thickness. This dependence is related to exchange coupling between permalloy and cobalt and the interaction field is estimated using the Landau–Lifschitz–Gilbert model.     

A Joint Integral Test for the Locations of Extrema for Brownian Motion

Let μ⁺(t) and μ⁻(t) be the locations of the maximum and minimum, respectively, of a standard Brownian motion in the interval [0,t]. We establish a joint integral test for the lower functions of μ⁺(t) and μ⁻(t), in the sense of Paul Lévy. In particular, it yields the law of the iterated logarithm for max(μ⁺(t),μ⁻(t)) as a straightforward consequence. Our result is in agreement with well-known theorems of Chung and Erdős [(1952) Trans. Amer. Math. Soc. 72, 179–186.], and Csáki, F?ldes and Révész [(1987) Prob. Theory Relat. Fields 76, 477–497].      

Combinatorial Optimization by Dynamic Contraction

A heuristic optimization methodology, Dynamic Contraction (DC), is introduced as an approach for solving a wide variety of hard combinatorial problems. Contraction is an operation that maps an instance of a problem to a smaller instance of the same problem. DC is an iterative improvement strategy that relies on contraction as a mechanism for escaping local minima. As a byproduct of contraction, efficiency is improved due to a reduction of problem size. Effectiveness of DC is shown through simple applications to two classical combinatorial problems: The graph bisection problem and the traveling salesman problem.     

The (1+1) Dimensional Dirac Equation With Pseudoscalar Potentials: Path Integral Treatment

The supersymetric path integrals in solving the problem of relativistic spinning particle interacting with pseudoscalar potentials is examined. The relative propagator is presented by means of path integral, where the spin degrees of freedom are described by odd Grassmannian variables and the gauge invariant part of the effective action has a form similar to the standard pseudoclassical action given by Berezin and Marinov. After integrating over fermionic variables (Grassmannian variables), the problem is reduced to a nonrelativistic one with an effective supersymetric potential. Some explicit examples are considered, where we have extracted the energy spectrum of the electron and the wave functions. PACS numbers: 03.65. Ca-Formalism, 03.65. Db-Functional analytical methods, 03.65. Pm-Relativistic wave equations.     

Effects of Added Surfactant on the Dynamic Interfacial Tension Behavior of Acidic Oil/Alkaline Systems

The effects of a ready-made surfactant (sodium dodecyl sulfate) on the dynamic interfacial tension between a model acidic oil (linoleic acid dissolved in paraffin oil) and various aqueous alkaline (NaOH) systems have been studied using pendant drop tensiometry at surfactant concentrations both below and above the critical micelle concentration (CMC). Below the CMC the added surfactant contributes significantly to a further reduction of interfacial tension of the reacting acid/alkaline system, whereas above the CMC the added surfactant plays an important role in damping the dynamic trends observed for the reactive system alone. Copyright 2001 Academic Press.     

The kinetics of the crystallization of barium chromate in presence of polyphosphate and phosphonates

Summary The inhibiting effect of polyphosphate and phosphonates on the crystallization of barium chromate for both seeded and unseeded systems has been investigated using the changes in ionic conductivity of the lattice ions in supersaturated solutions containing stoichiometric concentrations of barium and chromate at 298 K. The inhibitors studied are sodium tripolyphosphate (STP), ethylenediaminetetramethylenephosphonic acid (ENTMP), and 1-hydroxyethylidene-1,1-diphosphonic acid (HEDP). The effect of these inhibitors on the growth of crystals has been studied at several inhibitor concentrations. The influence of these additives on barium chromate crystallization could be interpreted in terms of aLangmuir type adsorption isotherm. The crystallization retarding effect due to inhibitors is in the orderHEDP>STP>ENTMP. The inhibitors studied can be used as effective compounds for scale formation control.Deceased     

Synthesis of 1H-pyrazolo[3,4-e]-s-triazolo[3,4-c]-as-triazines, 8H-pyrazolo[3,4-e]tetrazolo[5,1-c]-as-triazine and 1,7-dihydro-8H-pyrazolo[3,4-e]-as-triazine derivatives

3-Hydrazino-7-methyl-5-phenyl-5H-pyrazolo[3,4-c]-as-triazine 1 underwent ring closure and/or condensation reaction with formic acid, acetic acid, acetic anhydride and benzoyl chloride to afford 1H-pyrazolo-[3,4-d]-s-triazolo[3,4-c]-as-triazines 2, 5 and 7a and/or N-acyl derivatives 3, 4 and 6 . N-Acyl derivatives 3 and 6 underwent cyclisation reaction on treatment with phosphoryl chloride to give 5 and 7a . 3-Methyl-1-phenyl-8-aryl-1H-pyrazolo[3,4-e]-s-triazolo[34,-c]-as-triazines 7 were also prepared by the reaction of the hydrazono derivatives 8 wit thionyl chloride. On treatment of 1 with nitrous acid gave the 8H-pyrazolo[3,4-e]tetrazolo-[5,1-c]-as-triazine 9 . Compound 1 underwent ring closure with carbon disulphide or ethyl chloroformate to 1,7-dihydro-8H-pyrazolo[3,4-e]-s-triazolo[3,4-c]-as-triazine derivatives 10 and 12 . Reaction of 1 with ethyl acetoacetate or acetylacetone gave 3-pyrazolo derivatives 13 and 14 .     

Studies and microdetermination of some organic sulfur functions by reduction with titanium(III) sulfate solution

Micromethods are described for the determination of organic sulfoxides and disulfides based on reduction with titanium (III) sulfate solution, the excess of which is titrated with standard ferric alum as usual. The procedures developed depended on the nature of the compound whether aromatic or aliphatic. Quantitative reduction of sulfoxides was achieved in presence of ammonium thiocyanate and sodium acetate but whereas aryl sulfoxides required heating at 70 °C for 30 minutes, the alkyl members demanded heating at 90 °C for one hour. Complete reduction of disulfides was possible in presence of acetate buffer and heating at 50 °C for 15 minutes for aromatic disulfides and at 80 °C for 30 minutes in case of the aliphatic ones. a Calculated by dividing the total titer in a ratio of 2:12. b Calculated using the total titer consumed. Sulfonyl halides, thiocyanates, and isothiocyanates do not react with the titanium(III) solution. The effect of the various sulfur functions on the determination of the nitro group with titanium(III) was also studied and various nitro-substituted sulfur compounds were successfully analyzed.