Algebra versus analysis in the theory of flexible polyhedra

Two basic theorems of the theory of flexible polyhedra were proven by completely different methods: R. Alexander used analysis, namely, the Stokes theorem, to prove that the total mean curvature remains constant during the flex, while I.Kh. Sabitov used algebra, namely, the theory of resultants, to prove that the oriented volume remains constant during the flex. We show that none of these methods can be used to prove the both theorems. As a by-product, we prove that the total mean curvature of any polyhedron in the Euclidean 3-space is not an algebraic function of its edge lengths.Comment: 5 pages, 5 figures; condition (iii) in Theorem 5 is correcte

Influence of structural-group composition of sulphur-organic compounds on water solubility in model mixtures

© Published under licence by IOP Publishing Ltd. On model mixtures it is studied the solubility of water in transformer oil in the presence of suphur-organic compounds of the general formulas CnH 2n-11 S, CnH 2n-7 S, CnH 2n-5 S, from 0,6 to 3,0% concentrations. It is established that the greatest dissolving ability of water in model mixtures have suphur-organic compounds s of the general formula CnH 2n-11 S due to the greatest recurrence they have

Influence of the additives of natural sulphur-organic compounds on thermal stability of oil fractions of arlan petroleum

© Published under licence by IOP Publishing Ltd. The influence of additives of natural sulfur-organic compounds on the thermal stability of the oil fraction of Arlan petroleum in an electric field is studied. It has been established that the introduction of additives of natural sulfur-organic compounds into the petroleum fraction leads to a decrease in the formed solid sediment and acid number, which indicates an increase in the dielectric characteristics of the oil and an increase in its thermal stability in the electric field. The optimum amount of addition of natural sulfur-organic compounds in an amount of 0.5% reduces the amount of water-soluble acids formed, and, consequently, also the aging of the oil

Assessment methods of the efficiency and performance of energy use in the public sphere

© 2015, Asian Social Science. All rights reserved. The paper develops a methodical approach to assessment of the efficiency and performance of energy use in the public sector on the basis of the analysis of normative - legal acts of the Russian Federation and the works of Western and Russian scientists in the field of energy saving and energy efficiency. The paper classifies the indicators characterizing the energy saving and energy efficiency, and identifies those that are most fully and accurately reflect the process of energy saving and energy efficiency, and meet such requirements as objectivity, validity and reliability

Deflected mode of junction of pipes of different diameters in the constructions of contact-line supports of electrical transport

© Research India Publications 2015. Rapid pace of development of energy, communications, telecommunications and other industries of economy stimulate fabrication of structural steel with application of tubular rods (round pipe, polyhedral bent studding, profile of closed section and so on), processing a number of constructional qualities which provide decline in demand for steel, decrease intensity of wind loading, increase corrosion resistance [1-3]. Such constructions can be referred to the transmission towers, supports for wind-generated installations, towers of cellular communications, supports of urban illumination, supports of contact-line networks of electrical transport, supports for advertizing structures, supports for lighting (traffic signal installations) and the others. In designing constructions from the pipes one of the most important tasks is support of bearing capacity of node points of junction. It is substantiated by experimental data indicating that in many cases a carrying capacity of the whole construction is determined by the strength of junction bond of its elements. The designs from pipes are performed from separate shafts or in the form of flat, or space grid systems. Urge towards decline in demand for steel in these constructions leads naturally to the use of tubular rods of different diameter. On the whole, the effectiveness of tubular constructions is determined to large extent by constructive design of node points of connection of tubular rods. In practical building it is applied different types junction of tube bars, including assemblies from pipes of various diameter. It has been first developed numerical methods of analysis of determination of deflected mode of the pipes of different diameters by push fit of one into the other. For ECM, using the language FORTRAN it had been coded «AutoRSS. 01», which allows to DM components of telescopic joint of pipes being different in diameter. It has been carried out comparative assessment of the results of calculation of DM joint units according to the suggested program «AutoRSS. 01» the known programs, realizing the method of finite-elements method (FEM). It has been performed the analysis of the results of calculation according to the suggested program «AutoRSS. 01» and determined an optimal push of one pipe into the other, which is within the limits of 2÷2. 3d, where d-diameter of smaller pipe

Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

Seismic resistance estimation of multi-story steel frames under ductility level earthquake impact by nonlinear static method

The article proposes a technique for taking into account the higher vibration modes under seismic resistance estimation of multi-story steel frames by nonlinear static method. The characteristic point search has also been improved. As part of the study, the proposed method was verified by time history analysis. Proposed technique allows one to significantly reduce the calculation time, while excluding the deficit of seismic resistance. © The Authors, published by EDP Sciences, 2021

Application of the theory of compound cores for the assessment of stress pattern in the cross section of a strengthened beam column

© Published under licence by IOP Publishing Ltd. The article considers the results of theoretical studies of the stress-strain state of an eccentrically compressed element reinforced with a reinforced concrete cage. The theory of composite rods is used as a theoretical basis. As a result of the solution of the theoretical problem, analytical expressions are obtained for determining the normal stresses in the cross-section of the reinforced element and tangential stresses along the contact seam. The results of the calculations for the proposed approach are compared with the previously performed research results

Empirical heat transfer correlations of tube bundles under pulsating flows

© Published under licence by IOP Publishing Ltd. In this paper, the influence of the parameters of pulsations on the heat transfer in tube bundles was considered. An analysis of the influence of the parameters of pulsations on heat transfer was carried out by empirical correlation. A new empirical correlation is proposed for calculation of external heat transfer in under of pulsating flow in tube bundles with different configurations. The maximum deviation of the empirical correlation with the data of the numerical experiment was 16.9%

Current state and prospects of development of diagrammatic methods for the calculation of reinforced concrete structures

© Published under licence by IOP Publishing Ltd. The article presents the current state and prospects of development of diagramm methods for the calculation of reinforced concrete construction. A brief review obtained by the authors results in this area, where great attention is paid to the improvement of curvilinear diagrams of concrete for different types of static loading of structures. Topical application of the considered methods for the analysis of structures in the zone of joint action of bending moments and shearing force that is not yet reflected in domestic and foreign regulations. In conclusion, the publication identifies ways for further research in the chosen area