Polarization Spin-Tensors in Two-Spinor Formalism and Behrends–Fronsdal Spin Projection Operator for D-Dimensional Case

This work evaluates the quality of exchange coupling constant and spin crossover gap calculations using density functional theory corrected by the Approximate Projection model. Results show that improvements using the Approximate Projection model range from modest to significant. This study demonstrates that, at least for the class of systems examined here, spin-projection generally improves the quality of density functional theory calculations of J-coupling constants and spin crossover gaps. Furthermore, it is shown that spin-projection can be important for both geometry optimization and energy evaluations. The Approximate Project model provides an affordable and practical approach for effectively correcting spin-contamination errors in molecular exchange coupling constant and spin crossover gap calculations.

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The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2010.1.007 ◽

2010 ◽

Vol 7 ◽

pp. 90-97

Author(s):

M.N. Galimzianov ◽

I.A. Chiglintsev ◽

U.O. Agisheva ◽

V.A. Buzina

Keyword(s):

Shock Wave ◽

Gas Hydrates ◽

Hydrate Formation ◽

Dimensional Case ◽

Two Dimensional ◽

Wave Impact ◽

Bubble Liquid ◽

One Dimensional ◽

Bubble Media ◽

Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

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New generalized 2D Ostrowski type inequalities on time scales with k2 points using a parameter

Filomat ◽

10.2298/fil1809155k ◽

2018 ◽

Vol 32 (9) ◽

pp. 3155-3169 ◽

Cited By ~ 1

Author(s):

Seth Kermausuor ◽

Eze Nwaeze

Keyword(s):

Numerical Analysis ◽

Time Scales ◽

Type Inequality ◽

Dimensional Case ◽

Multiple Points ◽

Quantum Calculus ◽

Independent Variables ◽

Ostrowski Type Inequality ◽

Two Independent Variables

Recently, a new Ostrowski type inequality on time scales for k points was proved in [G. Xu, Z. B. Fang: A Generalization of Ostrowski type inequality on time scales with k points. Journal of Mathematical Inequalities (2017), 11(1):41-48]. In this article, we extend this result to the 2-dimensional case. Besides extension, our results also generalize the three main results of Meng and Feng in the paper [Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables. Journal of Inequalities and Applications (2012), 2012:74]. In addition, we apply some of our theorems to the continuous, discrete, and quantum calculus to obtain more interesting results in this direction. We hope that results obtained in this paper would find their place in approximation and numerical analysis.

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Regions-based Two-dimensional Continua: The Euclidean Case

10.1093/oso/9780198712749.003.0005 ◽

2018 ◽

Author(s):

Geoffrey Hellman ◽

Stewart Shapiro

Keyword(s):

Mathematical Induction ◽

Dimensional Case ◽

Two Dimensional ◽

Entire Space ◽

Euclidean Case ◽

Free Basis ◽

One Dimensional ◽

Archimedean Property ◽

The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

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