Lauricella hypergeometric series $$F_A^{(n)}$$ F A ( n ) over finite fields

The Ramanujan Journal - In this paper, we develop a finite field analogue for one of the Lauricella series, $$F^{(n)}_A$$ . Extending results of Greene, a finite field analogue for the multinomial...     

Control over Kinetic and Thermodynamically Driven Pathways of Crystallization to Yield Cofacial and Slipped-Stack Dimers in Single Crystals

Control over the molecular packing in the solid state is of utmost importance in regulating the bulk optical properties of organic semiconductors. The electronic coupling between the molecules makes it possible to improve the properties of the bulk materials. This work reports an example of control over the selective formation of polymorphic single crystals of donor–acceptor-type small-molecule compound 25TR by 1) kinetic or 2) thermodynamic course of crystallisation to yield slipped stack (S) and cofacial (C) dimers in the single crystals. The distinct optical characteristics of the C-dimer and S-dimer are summarised. Both forms show significant excitonic interactions in the solid state, and the S-dimeric form has strong yellowish orange fluorescence, whereas the C-dimeric form is non-fluorescent in the crystalline state. DFT calculations and differential scanning calorimetric experiments revealed that the C-dimer polymorph is the thermodynamically stable form with a free energy offset of 0.43 eV in comparison with the S-dimer. Interestingly, the thermodynamically driven non-fluorescent single crystal was found to be convertible to its fluorescent form irreversibly by thermal trigger. The charge-carrier-transport characteristics of these two polymorphs were computed by using the Marcus–Hush formalism. The computations of the charge-carrier-transport behaviour revealed that the S-dimer ( 25TR_(R) ) is ambipolar, whereas the C-dimer ( 25TR_(Y) ) is predominantly n-type.     

Possibility of weakly charged nonlinear solitary dust clouds near the continuum threshold of dust population in a quasi-neutral dusty plasma

Considering the Boltzmann response of the plasma ions and electrons and inertial dynamics of the charged dust grains, the possibility of very weak compressive soliton near the continuum limit of the dust population has been inferred. It is concluded that the behaviour of such coherent structures could be well described by the numerical analysis of the derived nonlinear classical energy integral equation for bounded solutions. These seem to be higher order dispersive structures within acoustic limit of the nonlinear turbulence. It is observed that the dust density enhancement beyond the continuum threshold causes regular increment in width and amplitude of the soliton structures. It is found that the soliton amplitude sensitively depends on the massive impurity’s population. These coherent structures could be visualized as weakly charged solitary dust clouds of finite extension (∼ plasma Debye length) within Boltzmann environment of plasma particles in their local surroundings. The seeding mechanism of such clouds may be attributed to some plasma instabilities driven by either internal or external free energy sources. Numerical analysis of the problem concludes that the experimental observations of such clouds could be possible in low density plasma regime. It is deduced that for plasma density ∼ 10⁶ cm^-3 at temperatures of a few electron volts and for micron to l0nm sized dust grains, the observation of such structures could be possible within wide range variability of the dust population density.     

Exactness of the cordes condition of the Hölder property for the gradient of nondivergent elliptic systems

We give an example of a nondivergent elliptic system showing that the classical Cordes condition of the Hölder property for the gradient of solution of a nondivergent elliptic equation is exact if properly extended onto systems.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 2, pp. 292–294, February, 1995.     

Partial applicability of Moser's method to nonlinear elliptic systems

We consider nonlinear elliptic systems of divergent-type second-order partial differential equations with solutionsu W _p ¹ . It is proved thatDu L _q with someq (p; +) and it is explicitly shown howq depends on the ellipticity modulus of the system. Some conditions on the ellipticity modulus are obtained under which the solutions satisfy the Hölder conditions and the Liouville theorem holds.Translated fromMatematicheskie Zametki, Vol. 58, No. 4, pp. 547–557, October, 1995.     

Synthesis of novel pyrano[2,3-b]quinolines from simple acetanilides via intramolecular 1,3-dipolar cycloaddition

Some novel isoxazole and pyrazole fused pyrano[2,3-b]quinolines were synthesized from simple acetanilides via intramolecular 1,3-dipolar cycloaddition reactions involving nitrones, nitrile oxides and nitrile imines as 1,3-dipoles, in a regioselective manner.     

Radiation‐Grafted Polymerization from a Gas Phase to Form Polymeric Layers on Metal Surfaces

Summary: Experimentally it is shown that, under irradiation in an atmosphere of non‐saturated vinylidene chloride vapors, a polymeric layer is formed on the surface of oxidized titanium samples. The thickness of this layer increases with the increase of thickness of the oxide film. Such a dependence corresponds to the current understanding of the mechanism of formation and migration of the active excited centers that initiate grafted polymerization.

Wide range XPS spectra of oxidized titanium samples after PVDC grafting from a gas phase.