A nonlinear problem having a continuous locus of singular points and no multiple solutions

The boundary-value problem ?z″ = (z² ? t²)z′, ? > 0, z(? 1) = α, z(0) = β, t? [?1, 0], has been shown to have a solution, and moreover, depending on the choice of α and β, multiple solutions to it exist. We consider the more general equation f(z, t)z″ = (z^r ? t^s)z′ for a particular non-negative function f(z, t), and integrate the equation exactly. Depending on α and β, we find that either there are no solutions, or that only unique solutions exist. The conclusion is that the presence of a continuous locus of singular points, given by z^r = t^s, does not necessarily produce multiple solutions.     

NMR studies in the heterocyclic series. XVIII—Carbon-13 NMR study of azolium salts. Attempted correlation of chemical shifts with calculated charge densities

The carbon-13 chemical shifts and the ¹J(CH) coupling constants for 18 azolium salts (di-N-methyl-pyrazolium, -indazolium, -benzimidazolium and -benzotriazolium iodides) have been determined and assigned. The chemical shifts are discussed as a function of substituent effects, positive charge introduction and total electronic density (calculated by the CNDO/2 method). The general problem of correlations between chemical shifts and total charge densities in azoles is discussed. A statistical approach shows that these correlations are of poor quality.     

Studies on 5-aminoisoxazole derivatives: Synthesis of some new fused isoxazoles

Several new fused isoxazole derivatives could be obtained utilising 5-amino-4-ethoxycarbonyl-3-ethoxycarbonylmethyl and 5-amino-4-cyano-3-trichloromethyl-isoxazoles as starting components.

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Untersuchungen an 5-Aminoisoxazol-Derivaten: Synthese einiger neuer kondensierter Isoxazole

Zusammenfassung Es konnten einigen neue Isoxazolderivate über 5-Amino-4-ethoxycarbonyl-3-ethoxycarbonylmethyl-und 5-Amino-4-cyano-3-trichlormethyl-isoxazol als Ausgangsverbindungen erhalten werden.

     

Steady state creep during transformation in Cd-Zn alloys

Apparent steady-state creep of Cd-2 wt. % Zn and Cd-17·4 wt. %Zn alloys has been studied under different constant stresses ranging from 6·4 MPa to 12·7 MPa, near the transformation temperature of 483 K. The strain rate of the steady-state creep for both compositions has shown two temperature regions of deformation, the low-temperature region (below 483 K) and the high-temperature region above this temperature. The stress exponent m' was found to change from 4·7 to 2 for Cd-2 wt. % Zn and from 3·1 to 2·4 for Cd-17·4 wt. % Zn alloys. The activation energies in the temperature region below the transformation temperature have been found to be 84 kJ/mole for Cd-2 wt. % Zn and 70 kJ/mole for Cd-17·4 wt. % Zn alloys characterizing the mechanism of volume self-diffusion in Cd.     

A facile synthesis of substituted benzyl selenocyanates

Benzyl selenocyanates can be made from the corresponding benzylic bromides or chlorides in 30-60 minutes using acetonitrile as a solvent. The products may be obtained pure in satisfactory yields without recourse to chromatography.     

Reactions of ethyl 2-benzoyl-3-phenylcyclopropanecarboxylate with hydrazines and hydroxylamine

While the reaction of the cyclopropane ester 1 with hydrazine hydrate or phenylhydrazine led to the formation of diazabicycloheptenones, its reaction with several para-substituted phenyl-hydrazines gave the corresponding hydrazones. With hydroxylamine, either oxime or 1,2-oxazinone is formed.     

Porous lanthanide-organic framework with zeolite-like topology

Two novel isomorphous porous frameworks of Ln(III), {[Ln2(imidc)2(H2O)3](H2O)}n, [Ln = Gd(III) (1) and Er(III) (2)] have been synthesized hydrothermally using multifunctional 4,5-imidazoledicarboxylic acid (imidc) as a connector; they have a zeolite-like network topology which can provide another form upon dehydration, and exhibit selective adsorption properties for H2O over N2, CO2 and MeOH.     

Laser thermal response of a finite slab as a function of the laser pulse parameters

This paper deals with the problem of heating a finite slab using laser radiation in relation to the parameters characterizing the laser pulse, namely: q_max(W/m²), the maximum laser power density, t₀ the time interval required to reach q_max and t_d, the pulse time duration. The pulse shape q(t) is suggested in the form: q(t)=βq_max(t/t_d)(1-(t/t_d))exp-B(t-t₀/t_d), where β and B are parameters. Fitting with published experimental pulse [Ready JF. Effects due to absorption of laser radiation. J Appl Phys 1965;36:462–68] is made. Fourier series expansion technique is considered to solve the problem. The critical time required to initiate melting t_m is estimated for four metallic elements and five semiconductors, namely: Al, Cu, Ag, Au (aluminum, copper, silver, and gold), cadmium sulfide, germanium, silicon, alpha beryllium oxide, and silicon carbide. Five pulses with different characteristic parameters are considered.Computations revealed that the thermal response of the targets is highly affected by q_max and t_o, while the pulse time duration is less effective in determining the value of t_m. Moreover, it is revealed that the relation between t_m and the melting temperature for the same laser pulse is nonlinear for the considered targets under the indicated conditions.