We obtain lacunary recurrent relations with gaps of length four for the Bernoulli and Euler polynomials and, as a consequence, known and new lacunary relations for the Bernoulli and Euler numbers.
Abstract
The possibility of obtaining mixed air binder of high strength and water resistance by using active mineral additives has been considered. In this work, the gypsum binder has been replaced ...by a combination of hydrated lime with active additives - metakaolin and granulated slag. The ratio effect of the silica component to the binder on the compressive strength of the stone was studied. According to the results of X-ray phase analysis, the presence of tobermorite-like calcium hydrosilicates and the absence of hydrate lime phase were diagnosed in the stone. The influence of electrolyte additives - salts with three-charged cations - on stone hardening kinetics is shown. Increase in the compressive strength of 28-day-old stone from the modified mixed air binder by 5% with the introduction of 1% of the binder mass aluminum sulfate in the mixing water was established. The use of
FeCl
3
solution for mixing the modified mixed air binder leads to a decrease in the compressive strength of the 28-day-old stone. The mixing of the modified mixed air binder with
Al
2
(SO
4
)
3
solution reduces the time of setting.
Let
be any polynomial of degree
with real coefficients such that
for
. In the paper, in particular, the sum of a series of the form
is expressed as the value at
of the Green function of the ...self-adjoint problem generated by the differential expression
and the boundary conditions
(
). Thus, such a sum is explicitly expressed in terms of the value of an easy-to-construct elementary function. These formulas, obviously, also apply to sums of the form
, while it is well known that similar general formulas for the sum
do not exist.
Against the background of the sanctions pressure of the coalition of G7 countries, the European Union and Australia (hereinafter referred to as the coalition) on the Russian energy sector, the ...introduction of a “ceiling” of prices for the sea transportation of Russian oil, starting from December 5, 2022, it is necessary to transform the traditional flows of oil cargo from Russia to the countries of the Asia-Pacific region.In this regard, in order to identify the potential for the growth of supplies to friendly countries, it is important to assess the existing capacity of pipeline capacities and Russian sea terminals for oil transshipment. In the article, the author analyzes the cargo flows of oil from Russia in the direction of the countries that are part of the coalition, formed proposals for changing the markets for Russian energy resources, taking into account the sanctions pressure, and drew conclusions about the possibilities of diversifying the existing cargo flows of Russian oil.According to the author, Russia could build a dialogue, without violating the sanctions regime, with friendly countries, in order to actually take the share of OPEC countries in the Asia-Pacific market, while OPEC countries will reimburse the supplies of fallen Russian resources to the EU countries at market, not “ceiling” prices.
PDF
