Stability of Semiconductor States with Insulating and Contact Boundary Conditions

We prove the existence of global smooth solutions near a given steady state of the hydrodynamic model of the semiconductors in a bounded domain with physical boundary conditions. The steady state and the doping profile are permitted to be of large variation but the initial velocity must be small. Two cases are considered. In the first one the problem is three-dimensional, the boundary conditions are insulating and the steady state velocity vanishes. In the second one, the problem is one-dimensional, the boundary is of contact type and the steady state velocity does not vanish.     

Absence of shocks in an initially dilute collisionless plasma

The Cauchy Problem for the relativistic Vlasov-Maxwell equations is studied in three space dimensions. It is assumed that the initial data satisfy the required constraints and have compact support. If in addition the data have sufficiently smallC ² norm, then a uniqueC ¹ solution to this system is shown to exist on all of spacetime.Research supported in part by NSF DMS 85-20662 and NSF DMS 84-20957     

On a Definitizable Analog of the Trigonometric Moment Problem Generating an Indefinite Toeplitz Form

We prove the existence of an integro-polynomial representation for a sequence of numbers such that there exists a difference operator mapping this sequence to a sequence that generates the solvable trigonometric moment problem. A similar result related to the power moment problem was given in [12].     

Broadening the scope of 1,2,4-triazine synthesis by the application of microwave technology

By the application of microwave technology, a general protocol has been developed for the rapid synthesis of diverse 3,5,6-trisubstituted 1,2,4-triazines in excellent yield and purity, including many previously unknown 3-heterocyclic-1,2,4-triazines.     

Photopolymerization of methyl methacrylate in the presence of tertiary amines

The sensitization effect of tertiary amines on the photopolymerization of methyl methacrylate was studied. N,N-Dimethylbenzylamine, triethylamine, and N,N-dimethylaniline increased the rate of polymerization in this order, but pyridine did not show any effect. A free-radical mechanism was confirmed by the tacticity of polymer, the retarding effect of hydroquinone, and the copolymer composition with styrene. On the basis of the detailed kinetics of the sensitized polymerization and the ultraviolet spectra of the reaction mixtures, a sensitization mechanism is proposed, in which the excited monomer and the amine form a complex and generate an initiating radical.     

Relative Lewis basicities of six AI(ORF)4- superweak anions and the structures of LiA

The relative Lewis basicities of six Al(ORF)4- ions, Al[OC(CH3)(CF3)2]4-, Al(OC(CF3)3]4-, Al(OCPh(CF3)2]4-, Al[OC[4-C6H4(tBu)](CF3)2]4-, Al(OC(Cy)(CF3)2]4-, and Al(OCPh2(CF3)]4-, have been determined by measuring their relative coordinating abilities towards Li+ in dichloromethane. The relative Li- Lewis basicities of the Al(ORF)4- ions are linearly related to the aqueous pKa values of the corresponding parent HORF fluoroalcohols. The Lewis basicity of Al[OCH(CF3)2]4- could not be measured because two of these anions can coordinate to one Li+ cation. The structures of LiAl[OCH(CF3)2]4 and [1-Et-3-Me-1,3-C3H3N2][Li[Al[OCH(CF3)2)4]2] were determined.     

α,ω-Diisocyanatocarbodiimides, -Polycarbodiimides,and Their Derivatives

Research in the field of low-molecular weight, oligomeric and polymeric α,ω-diisocyanatocarbodiimides and -polycarbodiimides has been fruitful, not only in connection with these compounds themselves, but also—as so often happens in chemistry—with quite different problems. Novel synthetic methods, discoveries concerning the properties of low-molecular weight carbodiimides and phosphane imide derivatives, as well as results on the fragmentation reactions of four-membered heterocyclic compounds containing oxygen, phosphorus, and nitrogen, and a better understanding of the diisocyanate polyaddition process are among the many by-products of this research. The “high- and low-temperature formation” of polycarbodiimides and the homogeneous and heterogeneous catalysis of this process are described, and the fundamental importance of four-membered ring fragmentation mechanisms resulting in the formation of phosphane imide derivatives is outlined. Interesting building blocks for the diisocyanate polyaddition and polycondensation processes can be synthesized by many derivatization reactions of oligomeric and high-molecular weight polycarbodiimides and polyuretonimines. The in situ production of polycarbodiimides via matrix reactions in flexible polyurethane foams leads to a cellular arrangement of the material due to the pronounced symmetrical growth processes. Combination-foams with increased carbonation tendencies are formed in this way. Attention is drawn to several industrial applications of α,ω-diisocyanatopolycarbodiimides, of high-molecular weight cross-linked polyuretonimines, and of polycarbodiimide foams.     

The dynamics of rotational isomerism in crystals as studied by vibrational spectroscopy

Vibrational spectroscopy is uniquely capable of determining the structure and dynamics arising from the rotational degrees of freedom in molecular solids. Vibrational spectroscopy is sensitive to phenomena occurring on a time scale between the slow scale of magnetic, resonance methods and fast scale of diffraction methods; a time scale appropriate for both internal and overall rotation. Rotational motion of molecules in crystals provide examples of very simple reactions. Our understanding of the spectra of reacting molecules can thus be tested on these systems, and we conclude that Redfield equations can describe such spectra.A rich variety of motional effects are described: (1) The libration of the water of hydration in sodium perchlorate which illustrates a simple reacting system. (2) The libration of the adamantane molecule in both its ordered and disordered crystal phases which illustrates intermolecular interactions in organic crystals and the consequences of disorder. (3) The libration of the ammonium ion in crystals of ammonium salts which illustrated both change of orientational position by tunneling and the subtle orientating effects of isotopic substitution. (4) The internal rotation in n-alkane crystals which illustrates the ability to determine conformers and the relationship between the occurrence of disordered conformers and the occurrence of phase transitions.