On Three-Dimensional Non-linear Buoyant Convection in Ternary Solidification

We consider the problem of three-dimensional non-linear buoyant convection in ternary solidification. Under the limit of large far-field temperature, the convective flow is modeled to be in a rectangular cube composing of a horizontal liquid layer above a primary mushy layer, which itself is over a secondary mushy layer. We first apply linear stability analysis to calculate the conditions at the onset of motion. Next, we carry out weakly non-linear analyses to determine solutions in the form of hexagons and their possible stability and to obtain information about tendency for chimney formation. We find that if the flow is driven either from both mushy layers with equal critical conditions at the onset of motion or only by the primary mushy layer, then the flow can be in the form of a double-cell structure vertically with down-hexagons below or above up-hexagons. There is tendency for vertically oriented chimney formation at different horizontal locations in each mushy layer. For the cases where only the critical conditions at the onset of motion are equal in both mushy layers and depending on the values of the mush Rayleigh numbers, the flow can be subcritical (or supercritical) in both mushy layers or mixed subcritical in one layer and supercritical in another layer.     

Wells–Dawson tungsten heteropolyacid-catalyzed reactions of benzylic alcohols, influence of the structure of the substrate

Heterolytic cleavage of the C–OH bond of various benzylic alcohols has been catalyzed with H₆P₂W₁₈O₆₂. Alkenes or symmetric ethers are produced, depending on the structure of the substrate.     

On spatial instability of electrically forced axisymmetric jets with variable applied field

This paper considers the problem of instability of electrically forced axisymmetric jets with respect to spatially growing disturbances and in the presence of a variable applied electric field. A mathematical model, which is developed for the dependent variables of such disturbances, is based on the relevant approximated versions of the equations of the electrohydrodynamics for an electrically forced jet flow. The approximations include the assumptions that the length scale along the axial direction of the jet is much larger than that in the radial direction of the jet and the disturbances are axisymmetric and infinitesimal in amplitude. For neutral temporal stability boundary, we find, in particular, two new spatial modes of instabilities under certain conditions. Both modes are found to be enhanced with increasing the strength of the field. The more dominant instability mode is found to exist for a wider range of values of the wave number in the axial direction. The effect of variable applied electric field is found to increase the growth rates of the disturbances but operate over a more restricted domain in the axial wave number.     

Invariant G2V algorithm for computing SAGBI-Gröbner bases

Faugère and Rahmany have presented the invariant F5 algorithm to compute SAGBI-Grbner bases of ideals of invariant rings. This algorithm has an incremental structure, and it is based on the matrix version of F5 algorithm to use F5 criterion to remove a part of useless reductions. Although this algorithm is more efficient than the Buchberger-like algorithm, however it does not use all the existing criteria (for an incremental structure) to detect superfluous reductions. In this paper, we consider a new algorithm, namely, invariant G2V algorithm, to compute SAGBI-Grbner bases of ideals of invariant rings using more criteria. This algorithm has a new structure and it is based on the G2V algorithm; a variant of the F5 algorithm to compute Grbner bases. We have implemented our new algorithm in Maple , and we give experimental comparison, via some examples, of performance of this algorithm with the invariant F5 algorithm.     

On the finite Mellin transform in quantum calculus and application

The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-convolution product. The application of this transform is also earlier proposed in solving procedure for a new equation with a new fractional differential operator of a variational type.     

The 3G-inequality for general Schrödinger operators on Lipschitz domains

In this paper we prove a new 3G-inequality for the Laplacian Green function on a bounded Lipschitz domain in ⁿ, n3. We exploit this inequality to prove the existence and comparison of perturbed continuous Green functions associated with – where is in a general class of signed Radon measures covering the well known Kato class.Mathematics Subject Classification (2000): 31B05, 35J10     

Calculation of radiative transition probabilities and radiative recombination rate coefficients for H2, OH, H 2+ and OH+ molecules

A method is presented to calculate the radiative transition probabilities and the radiative recombination rate coefficients between electronic molecular states. Total transition probabilities are determined from vibrational transition probabilities without considering the detailed rotational structure of the molecular electronic states. Radiative recombination rate coefficients are obtained from the computation of vibrational photo-ionisation cross sections. Concerning spontaneous emission, Lyman (B → X) and Werner (C → X) band systems of H₂ and Meinel (A → X), (B → A) and (B → X) band systems of OH are investigated. For radiative recombination, transitions between H₂⁺ (X) and H₂(X), and between OH⁺(X, a, A, b, and c) and OH(X) are considered. Transition probabilities and recombination rate coefficients are calculated as a function of temperature in the range 1500–15 000 K.     

Strict directional solutions in vectorial problems: necessary optimality conditions

Journal of Global Optimization - We study directional strict efficiency in vector optimization and equilibrium problems with set-valued map objectives. We devise several possibilities to define a...     

Carleman estimate for Biot consolidation system in poro‐elasticity and application to inverse problems

In this paper, we consider a coupled system of mixed hyperbolic–parabolic type, which describes the Biot consolidation model in poro‐elasticity. We establish a local Carleman estimate for Biot consolidation system. Using this estimate, we prove the uniqueness and a Hölder stability in determining on the one hand a physical parameter arising in connection with secondary consolidation effects λ^? and on the other hand the two spatially varying densities by a single measurement of solution over ω × (0,T), where T > 0 is a sufficiently large time and a suitable subdomain ω satisfying ?ω??Ω. Copyright © 2016 John Wiley & Sons, Ltd.