Metric-Affine Vector-Tensor correspondence and implications in F(R, T, Q, T, D) gravity

We extend the results of antecedent literature on quadratic Metric-Affine Gravity by studying a new quadratic gravity action in vacuum which, besides the usual (non-Riemannian) Einstein-Hilbert contri-bution, involves all the parity even quadratic terms in torsion and non-metricity plus a Lagrangian that is quadratic in the field-strengths of the torsion and non-metricity vector traces. The theory results to be equivalent, on-shell, to a Vector-Tensor theory. We also discuss the sub-cases in which the contribution to the Lagrangian quadratic in the field-strengths of the torsion and non-metricity vectors just exhibits one of the aforementioned quadratic terms. We then report on cosmological aspects of the general quadratic theory in the presence of a perfect cosmological hyperfluid and on implications of our findings in the context of F(R, T, Q, T, D) gravity.(c) 2022 Elsevier B.V. All rights reserved

Integrable Zhaidary equations: reductions and gauge equivalence

The present work addresses the study and characterization of the integrability of some generalized spin systems (ISS) in 1+1 dimensions. Lax representations for these ISS are successfully obtained. The gauge equivalent counterparts of these integrable ISS are presented. Finally, we consider Zhanbota transcendents and some integrable Zhanbota equations. In particular, the gauge equivalence between some Zhanbota equations and the six Painleve equations is established.Comment: 17 page

Improvement of methods for semi-finished carbon product tapping from the basic oxygen furnace (BOF)

The article considers the experience of optimizing the slag adjustment mode in the Basic Oxygen Furnace (BOF) and reducing the proportion of oxide non-metallic impurities in steel. The article presents the results of a research on the separation of slag from metal during the starting period of carbon semi-product tapping, on the elimination of an emergency situation when the hole is shut up at any degree of slag viscosity, the use of the device at any tap hole diameter after the heat, the simplicity of the design. The use of the device makes it possible to increase the durability of the taphole lining, reduce repair costs, and improve the quality of steel by reducing non-metallic impurities. The innovative devices proposed by the author can be useful for metallurgical enterprises

Growth factor in f(T) gravity

We derive the evolution equation of growth factor for the matter over-dense perturbation in $f(T)$ gravity. For instance, we investigate its behavior in power law model at small redshift and compare it to the prediction of $\Lambda$CDM and dark energy with the same equation of state in the framework of Einstein general relativity. We find that the perturbation in $f(T)$ gravity grows slower than that in Einstein general relativity if \p f/\p T>0 due to the effectively weakened gravity.Comment: 15 pages,1 figure; v2,typos corrected; v3, discussions added, accepted by JCA

Conformal transformation in f(T)f(T) theories

It is well-known that $f(R)$ theories are dynamically equivalent to a particular class of scalar-tensor theories. In analogy to the $f(R)$ extension of the Einstein-Hilbert action of general relativity, $f(T)$ theories are generalizations of the action of teleparallel gravity. The field equations are always second order, remarkably simpler than $f(R)$ theories. It is interesting to investigate whether $f(T)$ theories have the similar conformal features possessed in $f(R)$ theories. It is shown, however, that $f(T)$ theories are not dynamically equivalent to teleparallel action plus a scalar field via conformal transformation, there appears an additional scalar-torsion coupling term. We discuss briefly what constraint of this coupling term may be put on $f(T)$ theories from observations of the solar system.Comment: 4 pages, Revision to be publishe

Oxidative Carbonylation of Dipropargylarylamines

The catalytic oxidative methoxycarbonylation reaction of N,N-dipropargylarylamines has been investigated. PdCl2-CuCl2 has been studied as a catalytic system. Consecutive reactions of substitutive and additive methoxycarbonylation have been going in this process, which has been complicated by dimerisation, polymerization and cyclization processes. Apparently the results of process are determined by stability of intermediate reactionary complexes with participation of catalytic system PdCl2-CuCl2. The structures of synthesized cyclic amino triesters are established by analysis of experimental spectra NMR 1H and 13C, comparison with calculated spectra of possible hypothetic structures and estimation of thermodynamics properties by Joback fragmentation and MOPAC Semi-empirical PM3 methods