Representations of Menger (2,n)(2,n)-semigroups by multiplace functions

Investigation of partial multiplace functions by algebraic methods plays an important role in modern mathematics were we consider various operations on sets of functions, which are naturally defined. The basic operation for $n$-place functions is an $(n+1)$-ary superposition $[ ]$, but there are some other naturally defined operations, which are also worth of consideration. In this paper we consider binary Mann's compositions \op{1},...,\op{n} for partial $n$-place functions, which have many important applications for the study of binary and $n$-ary operations. We present methods of representations of such algebras by $n$-place functions and find an abstract characterization of the set of $n$-place functions closed with respect to the set-theoretic inclusion

Representations of (2,n)(2,n)-semigroups by multiplace functions

We describe the representations of $(2,n)$-semigroups, i.e. groupoids with $n$ binary associative operations, by partial $n$-place functions and prove that any such representation is a union of some family of representations induced by Schein's determining pairs.Comment: 17 page

Efficacy decametoxin in vitro for quick inactivation of respiratory coronavirus

Despite the fact that specific prophylaxis agents have already been widely introduced into medical practice in all countries of the world, and antiviral drugs are being developed and are undergoing the first stages of clinical trials, SARS-CoV-2 continues to spread in the human population. In this regard, an urgent medical problem today is the expansion of the arsenal of effective disinfectants and antiseptics, the action of which would be aimed at the rapid and complete inactivation of extracellular coronavirus, which is a very important element in controlling the spread of COVID-19. The aim of the study was to evaluate the ability of decamethoxin to have a virucidal effect against SARS-COV-2 and other human coronaviruses on the model of respiratory coronavirus IBV (infectious bronchitis virus) with an exposure time of 30, 60 and 120 seconds. Classical and modern virological research methods were used in the work: determination of the cytotoxic effect of decamethoxin in cell culture by the effect on their viability, cultivation, accumulation and determination of the infectious titer of IBV by cytopathic action in cell culture; assessment of the virucidal effect of decamethoxin by the suspension method to determine the residual infectious titer of the virus in cell culture by the method of limiting dilutions. The effectiveness of the antiseptic decamethoxin from the group of quaternary ammonium compounds was studied in relation to the prototype strain of the IBV (infection bronchitis virus) coronavirus family in vitro. It has been established that an isotonic solution of decamethoxin at a concentration of 100 μg/ml completely inactivates 3.0 lg(TCD50/0.1 ml) of the prototype respiratory coronavirus strain with a clinically significant contact time of 30–120 seconds at room temperature(18–24 оС). Decamethoxine has been shown to be an effective, fast-acting antiseptic capable of completely inactivating a prototype coronavirus strain. The revealed virucidal properties of decamethoxine in pharmacopoeially significant concentrations in relation to coronavirus allow to recommend it as an antiseptic in the development of methods for non-specific prevention of coronavirus infection in humans

D-semigroups and constellations

In a result generalising the Ehresmann–Schein–Nambooripad Theorem relating inverse semigroups to inductive groupoids, Lawson has shown that Ehresmann semigroups correspond to certain types of ordered (small) categories he calls Ehresmann categories. An important special case of this is the correspondence between two-sided restriction semigroups and what Lawson calls inductive categories. Gould and Hollings obtained a one-sided version of this last result, by establishing a similar correspondence between left restriction semigroups and certain ordered partial algebras they call inductive constellations (a general constellation is a one-sided generalisation of a category). We put this one-sided correspondence into a rather broader setting, at its most general involving left congruence D-semigroups (which need not satisfy any semiadequacy condition) and what we call co-restriction constellations, a finitely axiomatized class of partial algebras. There are ordered and unordered versions of our results. Two special cases have particular interest. One is that the class of left Ehresmann semigroups (the natural one-sided versions of Lawson’s Ehresmann semigroups) corresponds to the class of co-restriction constellations satisfying a suitable semiadequacy condition. The other is that the class of ordered left Ehresmann semigroups (which generalise left restriction semigroups and for which semigroups of binary relations equipped with domain operation and the inclusion order are important examples) corresponds to a class of ordered constellations defined by a straightforward weakening of the inductive constellation axioms

Gender Bonds, Gender Binds : Women, Men, and Family in Middle High German Literature

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