A General Method for Obtaining Degenerate Solutions to the Dirac and Weyl Equations and a Discussion on the Experimental Detection of Degenerate States

In this work, a general method is described for obtaining degenerate solutions of the Dirac equation, corresponding to an infinite number of electromagnetic 4-potentials and fields, which are explicitly calculated. More specifically, using four arbitrary real functions, one can automatically construct a spinor that satisfies the Dirac equation for an infinite number of electromagnetic 4-potentials, defined by those functions. An interesting characteristic of these solutions is that, in the case of Dirac particles with nonzero mass, the degenerate spinors should be localized, both in space and time. The method is also extended to the cases of massless Dirac and Weyl particles, where the localization of the spinors is no longer required. Finally, two experimental methods are proposed for detecting the presence of degenerate states.     

Synthesis and Properties of Pyrrones Containing p-Benzoquinone Units

Novel pyrrones were synthesized by one-stage polycondensation in polyphosphoric acid of 2,3,5,6-tetraamino-l,4-benzoquinone with pyromellitic anhydride, 3,3′,4,4′-benzophenonetetracarboxylic dianhydride, 1,4,5,8-naphthalenetetracarboxylic dianhydride, or 3,4,9,10-perylenetetracarboxylic dianhydride. The prepared polymers showed a considerable percentage of imide linkages, so they were heated at 350°C under high vacuum to increase the ring closure to the pyrrone structure. The polymers were insoluble in all common polar aprotic solvents, even in dimethylacetamide-water mixture, after reduction with sodium dithionite, but were slightly soluble in concentrated sulfuric and methanesulfonic acid. The thermal decomposition of the polymers (weight loss 5%) started above 400°C both under nitrogen and in air.     

The relation between relaxed enthalpy and volume during physical aging

Several papers have recently presented results of measurements of physical aging by studying the behavior of glassy materials quenched from temperatures above their glass transition temperature T_g. The evolution of the aging process is usually followed by plotting the relaxed enthalpy versus the accompanying decrease in volume. Here, we focus on the slope of such plots, which are found to be similar to the inverse value of the isothermal compressibility close to T_g. An explanation of this empirical result is attempted in the frame of a model that interconnects the defect Gibbs energy with properties of the bulk material.     

Numerical simulations of cessation flows of a Bingham plastic with the augmented Lagrangian method

The augmented Lagrangian/Uzawa method has been used to study benchmark one-dimensional cessation flow problems of a Bingham fluid, such as the plane Couette flow, and the plane, round, and annular Poiseuille flows. The calculated stopping times agree well with available theoretical upper bounds for the whole range of Bingham numbers and with previous numerical results. The applied method allows for easy determination of the yielded and unyielded regions. The evolution of the rigid zones in these unsteady flows is presented. It is demonstrated that the appearance of an unyielded zone near the wall occurs for any non-zero Bingham number not only in the case of a round tube but also in the case of an annular tube of small radii ratio. The advantages of using the present method instead of regularizing the constitutive equation are also discussed.     

Synthesis of a novel pyrrolo[1,2-c][1.3]benzodiazepine analogue of VPA-985

The seven-step synthesis of a novel structural isomer of VPA-985, N-[3-chloro-4-(5H-pyrrolo[1,2-c][1.3]benzodiazepin-6(11H)-ylcarbonyl)phenyl]-5-fluoro-2-methylbenzamide, is described. (2-Aminophenyl)(1H-pyrrol-2-yl)methanone was converted with thiophosgene into (2-isothiocyanatophenyl)(1H-pyrrol-2-yl)methanone which was cyclised in the presence of base to 5-thioxo-5,6-dihydro-11H-pyrrolo[1,2-c][1.3]benzodiazepin-11-one. The latter underwent desulfurisation with Raney nickel followed by reduction with lithium aluminium hydride in the presence of aluminium trichloride and the resulting 6,11-dihydro-5H-pyrrolo[1,2-c][1.3]-benzodiazepine acylated with 2-chloro-4-nitrobenzoyl chloride to afford 6-(2-chloro-4-nitrobenzoyl)-6,11-dihydro-5H-pyrrolo[1,2-c][1.3]benzodiazepine. The nitro group in the latter compound was reduced with zinc and ammonium chloride to give the corresponding aniline derivative which was then acylated with 2-methyl-5-fluorobenzoyl chloride to provide the final product.     

Analyticity and causality of the three-parameter rheological models

In this paper, the basic frequency and time response functions of the three-parameter Poynting–Thomson solid and Jeffreys fluid are revisited. The two rheological models find application in several areas of rheology, structural mechanics, and geophysics. The relation between the analyticity of a frequency response function and the causality of the corresponding time response function is established by identifying all singularities at ω = 0 after applying a partial fraction expansion to the frequency response functions. The strong singularity at ω = 0 in the imaginary part of a frequency response function in association with the causality requirement imposes the addition of a Dirac delta function in the real part in order to make the frequency response function well defined in the complex plane. This external intervention, which was first discovered by PAM Dirac, has not received the attention it deserves in the literature of viscoelasticity and rheology. The addition of the Dirac delta function makes possible the application of time domain techniques that do not suffer from violating the premise of causality.     

Implicit-explicit multistep methods for quasilinear parabolic equations

Summary. Efficient combinations of implicit and explicit multistep methods for nonlinear parabolic equations were recently studied in [1]. In this note we present a refined analysis to allow more general nonlinearities. The abstract theory is applied to a quasilinear parabolic equation. Received March 10, 1997 / Revised version received March 2, 1998     

Use of poly(N,N-dimethylacrylamide-co-sodium acrylate) hydrogel to extract cationic dyes and metals from water

Poly(N,N-dimethylacrylamide-co-sodium acrylate) hydrogel, which bears negatively charged –COO⁻ groups was used to extract organic or inorganic solutes from water. Some model dyes and metal ions have been studied. Cationic dyes are strongly adsorbed and retained by the polymer while adsorbance of hydrophobic dyes was very low and that of anionic dyes was negligible. Both maximum adsorption and equilibrium binding constant varied from one cationic species to the other depending on the chemical structure of the dye, the presence of functional chemical groups and the hydrophobic–hydrophilic balance. In the case of metal cations, adsorption depended on valence. The hydrogel can be regenerated in an aqueous phase of low pH and thus be reused in several adsorption procedures.