On the total mean curvature of non-rigid surfaces

Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the total mean curvature of a closed smooth surface in the Euclidean 3-space is stationary under an infinitesimal flex.Comment: 4 page

An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevsky 3-space

We give an example of an infinitesimally nonrigid polyhedron in the Lobachevsky 3-space and construct an infinitesimal flex of that polyhedron such that the volume of the polyhedron isn't stationary under the flex.Comment: 10 pages, 2 Postscript figure

Многочлены объема для некоторых многогранников в пространствах постоянной кривизны

It is known that for each simplicial polyhedron P in 3-space there exists a monic polynomial Q depending on the combinatorial structure of P and the lengths of its edges only such that the volume of the polyhedron P as well as one of any polyhedron isometric to P and with the same combinatorial structure are roots of the polynomial Q. But this polynomial contains many millions of terms and it cannot be presented in an explicit form. In this work we indicate some special classes of polyhedra for which these polynomials can be found by a sufficiently effective algorithm which also works in spaces of constsnt curvature of any dimension.Известно, что для каждого симплициального многогранника P в 3-пространстве существует многочлен Q, зависящий только от комбинаторного строения многогранника и длин его ребер, такой, что объемы многогранника P и любого другого изометричного P многогранника с таким же комбинаторным строением являются корнями многочлена Q. Но этот многочлен содержит много миллионов слагаемых, и его нельзя выписать в явном виде. В работе мы указываем один класс многогранников, для которых эти многочлены можно выписать в компактной форме, верной также в пространствах постоянной кривизны любой размерности

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

Evaluation of the applicability of pre-evaporative cooling of air in front of the cooling tower in the conditions of the third climatic zone of the Russian Federation

© Published under licence by IOP Publishing Ltd. This article provides an evaluation of the applicability of the evaporative cooling system of air supplied to the cooling tower in order to reduce the temperature of the cooled water at the outlet from the cooling tower in the conditions of the third climatic zone of the Russian Federation

Increase of efficiency of heat sources work due to application of condensation economizers on an example of a boiler PTVM-180

© Published under licence by IOP Publishing Ltd. In this article, a method is considered to increase the efficiency of boiler room operation with PTVM-180 boilers by the use of a flue gas flue in a condensing economizer. The efficiency evaluation of the utilization of the heat exchanger in accordance with the operating mode of the boiler house was evaluated, and the technical and economic parameters of the project were assessed, depending on the unplanned changes in such key factors as capital costs, operating time, operating mode

Development and investigation of the stressed-deformed state of the demountable foundation for support

© Published under licence by IOP Publishing Ltd. The development is demountable foundation for support, including separate reinforced concrete blocks in the form of prisms mounted on the surface of the base and pulled together by horizontal strands, and anchor devices for fixing the supports. The reinforced concrete blocks are made in the form of hollow prisms consisting of walls and square bottoms, and the strands are made in the form of bolts that tighten the walls along the top and bottom, while the anchoring devices for fixing the supports are made in the form of anchors on the bottom of the central prism and horizontal spacers between the support and the walls of the prism in its upper part. Numerical studies of the foundation have been carried out and its optimal sizes have been found in the PK Lira SAPR

Study of composite coal-water fuel rheological properties

© Published under licence by IOP Publishing Ltd. The rheological characteristics of composite water-coal fuel, as well as the possibility of reducing the viscosity of composite water-coal fuel due to the use of nanomaterials, are studied. Improved rheological properties of composite fuel containing small additions of these substances: carbon nanomaterial at a concentration of 0.005 wt. % or 0.3 wt. % of the dehydrated carbonate slurry. Possible mechanisms for changing the viscosity properties of fuel are considered