Acylaminoacetyl derivatives of active methylene compounds. 3 . C-Acylation Reactions via the Hippuric Acid Azlactone

The C-acylation reactions of the active methylene compounds, methyl cyanoacetate and Meldrum's acid, with hippuric acid, using the DCC activation and the mixed anhydride conditions, are shown to proceed through initial formation of 2-phenyl-5(4H)-oxazolone, the hippuric acid azlactone. The conditions of these reactions using the azlactone as the acylating agent were investigated and discussed.     

Reactions of furoxano[3,4-b]quinoxaline with alkynes and alkenes. Synthesis of pyrazino[2,3-b]quinoxaline 1,4-dioxides

Pyrazino[2,3-b]quinoxaline 1,4-dioxides 3a-e were prepared by reacting Furoxano[3,4-b]quinoxaline with alkynes and alkenes.     

Reactions of 2,3-bishydroxyimino-1,2,3,4-tetrahydro-quinoxalines and 2,3-bishydroxyimino-2,3-dihydro-4H-1,4-benzoxazines with ethyl chloroformate

Bishydroxyiminoquinoxalines 3a-b react with ethyl chloroformate 4 to afford the furazano[3,4-b]quinoxalines 5a-b . Bishydroxyiminobenzoxazines 6a-c on treatment with 4 are converted into the fused oxadiazolones 7a-c and 8a-c along with the bisethoxycarbonyloxyimino-derivatives 9a-c . From the reactions of 4 with the oxanilide dioximes 12a-c compounds 13a-c and 14a-b are obtained.     

Consumer heterogeneity and the shape of purchase rate functions

This study suggests that non-monotonic purchase rates, frequently observed in empirical studies of consumer purchase timing, can be an artifact of consumer heterogeneity. We use a theoretical purchase timing model with consumer heterogeneity to develop market scenarios under which non-monotonic rates may obtain. The results suggest that non-monotonic rates are more likely to observe in product markets that are either highly concentrated or where the heavy buyer segment is large. In such markets, therefore, one should not rely on non-monotonic rate curves to predict household purchase incidence. © 1998 John Wiley & Sons, Ltd.     

Die Cartesischen Produkte und die Multiplikation von Maßfunktionen in Booleschen Algebren

Ohne ZusammenfassungSeinem verehrten Lehrer Prof.C. Carathéodory zum 70. Geburtstag am 13. September 1943 gewidmet.     

Magnetohydrodynamics and Plasma Cosmology

We study the linear magnetohydrodynamic (MHD) equations, both in the Newtonian and the general-relativistic limit, as regards a viscous magnetized fluid of finite conductivity and discuss instability criteria. In addition, we explore the excitation of cosmological perturbations in anisotropic spacetimes, in the presence of an ambient magnetic field. Acoustic, electromagnetic (e/m) and fast-magnetosonic modes, propagating normal to the magnetic field, can be excited, resulting in several implications of cosmological significance.     

Photoluminescence of hexagonal boron nitride: Effect of surface oxidation under UV-laser irradiation

We report on the UV laser-induced fluorescence of hexagonal boron nitride (h-BN) following nanosecond laser irradiation under vacuum and in different environments of nitrogen gas and ambient air. The observed fluorescence bands are tentatively ascribed to impurity and mono (V_N) or multiple (m-V_N with m=2 or 3) nitrogen vacancies. A structured fluorescence band between 300 and 350 nm is assigned to impurity-band transition and its complex lineshape is attributed to phonon replicas. An additional band at 340 nm, assigned to V_N vacancies on surface, is observed under vacuum and quenched by adsorbed molecular oxygen. UV-irradiation of h-BN under vacuum results in a broad asymmetric fluorescence at ∼400 nm assigned to m-V_N vacancies; further irradiation breaks more B-N bonds enriching the surface with elemental boron. However, no boron deposit appears under irradiation of samples in ambient atmosphere. This effect is explained by oxygen healing of radiation-induced surface defects. Formation of the oxide layer prevents B-N dissociation and preserves the bulk sample stoichiometry.     

Bessel X waves in two- and three-dimensional bidispersive optical systems

We show that new families of two- and three-dimensional nondiffracting Bessel X waves are possible in linear bidispersive optical systems. These X waves can be observed in both bulk and waveguide configurations as well as in photonic crystal lattices that simultaneously exhibit normal and anomalous dispersive-diffractive properties in different spatial or spatiotemporal coordinates.