Errors in approximate solutions of Cauchy's problem for a first-order quasilinear equation

The proximity is investigated of the solution of Cauchy's problem for the equation u _t +((u))_x= u _xx ((u) > 0) to the solution of Cauchy's problem for the equation u_t+ ((u))_x= 0, when the solution of the latter problem has a finite number of lines of discontinuity in the strip 0 t T. It is proved that, everywhere outside a fixed neighborhood of the lines of discontinuity, we have |u–u| C, where the constant C is independent of. Similar inequalities are derived for the first derivatives of u–u.Translated from Matematicheskie Zametki, Vol. 8, No. 3, pp. 309–320, September, 1970.In conclusion we express our gratitude to L. A. Chudov for his valuable advice concerning this work.     

Unexpected interconversion reaction of 1,4-diaminofullerenes

A facile substitution of amine groups attached to the fullerene cage occurs when 1,4-diaminofullerenes C60[NR2]2 are allowed to react with excess of another amine R'2NH; this reaction proceeds rapidly at room temperature without any additional initiators.     

Instability,intermixing and electronic structure at the epitaxial LaAlO3/SrTiO3(001) heterojunction

The question of stability against diffusional mixing at the prototypical LaAlO₃/SrTiO₃(001) interface is explored using a multi-faceted experimental and theoretical approach. We combine analytical methods with a range of sensitivities to elemental concentrations and spatial separations to investigate interfaces grown using on-axis pulsed laser deposition. We also employ computational modeling based on the density function theory as well as classical force fields to explore the energetic stability of a wide variety of intermixed atomic configurations relative to the idealized, atomically abrupt model. Statistical analysis of the calculated energies for the various configurations is used to elucidate the relative thermodynamic stability of intermixed and abrupt configurations. We find that on both experimental and theoretical fronts, the tendency toward intermixing is very strong. We have also measured and calculated key electronic properties such as potential energy gradients and valence band discontinuity at the interface. We find no measurable electric field in either the LaAlO₃ or SrTiO₃, and that the valence band offset is near zero, partitioning the band discontinuity almost entirely to the conduction band edge. Significantly, we find it is not possible to account for these electronic properties theoretically without including extensive intermixing in our physical model of the interface. The atomic configurations which give the greatest electrostatic stability are those that eliminate the interface dipole by intermixing, calling into question the conventional explanation for conductivity at this interface—electronic reconstruction. Rather, evidence is presented for La indiffusion and doping of the SrTiO₃ below the interface as being the cause of the observed conductivity.     

Probing electron transfer dynamics at MgO surfaces by Mg-atom desorption

Ultraviolet excitation of high surface area MgO films using 4.7 eV femtosecond pulses results in neutral Mg-atom desorption with hyperthermal kinetic energies in the range 0.1-0.4 eV. The Mg-atom hyperthermal energies and power dependences are similar to those previously observed using nanosecond pulsed excitation. Femtosecond two-pulse correlation measurements reveal the existence of different dynamical paths for Mg-atom desorption. One mechanism displays a sub-150 fs time scale and involves the simultaneous or near-simultaneous transition of two electrons to a 3-coordinated Mg(2+) site. Other paths display picosecond time scales that we associate with dynamics following electron trapping at 3-coordinated Mg(2+) surface sites.     

Flavone glucosides from Artemisia juncea

A new flavone glucoside, 4′,5-dihydroxy-3′,5′,6-trimethoxyflavone-7-O-β-D-glucoside was obtained from aerial parts of Artemisia juncea, together with the known flavone eupatilin (5,7-dihydroxy-3′,4′,6-trimethoxyflavone). The compounds were comprehensively analytically characterized by IR, UV, NMR and HR-MS, and their chemical structures ascertained. The EtOAc fraction of A. juncea showed the strongest DPPH radical scavenging ability as well as reducing power (in CUPRAC and FRAP assays) and phosphomolybdenum activity. This fraction also exhibited the strongest inhibitory effects on tyrosinase. Additionally, the best antidiabetic effects were observed for eupatilin and the CHCl₃ fraction.     

Effect of molecular and lattice structure on hydrogen transfer in molecular crystals of diamino-dinitroethylene and triamino-trinitrobenzene

We have studied the intra- and intermolecular hydrogen transfer in a crystalline 1,1-diamino-2,2-dinitroethylene (DADNE) and 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) by means of an embedded cluster method and density functional theory (DFT). We found that, even though both of these materials have similar amino- and nitro- functional groups and layered crystalline structures, there are important differences in the mechanisms of hydrogen transfer. In particular, our calculations suggest that the proton migration from an amino-group to a nitro-group of the same molecule is a feasible process in TATB but not in DADNE. At the same time, we have found that no intermolecular hydrogen transfer occurs in either molecular crystal. These results imply that the activation of the decomposition reactions proceeds via different paths in these two materials.     

Self-assembly and high anisotropy thermal expansion of compounds consisting of <Emphasis Type="Italic">T</Emphasis>O<Subscript>3</Subscript> triangular radicals

Thermal motion is the inherent driving force of crystal substances formation. In borates, carbonates and nitrates such an organizing force are the strong anisotropy of thermal vibrations of atoms in the TO₃ triangles (T = B, C, N), flat triborate and other B–O rigid groups containing TO₃ triangles. These triangles and rigid groups, due to the sharp anisotropy of thermal vibrations, tend to be arranged in the parallel (or preferable) orientation. In this case, chemical compound has usually the least energy. The examples of the self-organization of atoms, TO₃ triangles and rigid groups during crystallization process are given.