Author: A. Berzins

0000000000230605

AUTHOR

A. Berzins

AUTOMORPHISMS OF THE ENDOMORPHISM SEMIGROUP OF A FREE ASSOCIATIVE ALGEBRA

Let [Formula: see text] be the variety of associative algebras over a field K and A = K 〈x1,…, xn〉 be a free associative algebra in the variety [Formula: see text] freely generated by a set X = {x1,…, xn}, End A the semigroup of endomorphisms of A, and Aut End A the group of automorphisms of the semigroup End A. We prove that the group Aut End A is generated by semi-inner and mirror automorphisms of End A. A similar result is obtained for the automorphism group Aut [Formula: see text], where [Formula: see text] is the subcategory of finitely generated free algebras of the variety [Formula: see text]. The later result solves Problem 3.9 formulated in [17].

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Automorphisms of the semigroup of endomorphisms of free associative algebras

Let $A=A(x_{1},...,x_{n})$ be a free associative algebra in $\mathcal{A}$ freely generated over $K$ by a set $X=\{x_{1},...,x_{n}\}$, $End A$ be the semigroup of endomorphisms of $A$, and $Aut End A$ be the group of automorphisms of the semigroup $End A$. We investigate the structure of the groups $Aut End A$ and $Aut \mathcal{A}^{\circ}$, where $\mathcal{A}^{\circ}$ is the category of finitely generated free algebras from $\mathcal{A}$. We prove that the group $Aut End A$ is generated by semi-inner and mirror automorphisms of $End F$ and the group $Aut \mathcal{A}^{\circ}$ is generated by semi-inner and mirror automorphisms of the category $\mathcal{A}^{\circ}$. This result solves an open …

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Cultivation ofZymomonas mobilis 113 S at Different Mixing Regimes and their Influence on the Levan Formation

The Zymomonas mobilis I 13 S strain was cultivated in a bioreactor with a working volume of 1.4 I at different stirring regimes in a 15% initial sucrose medium The levan obtained in the fermentation process was analyzed by gel filtration. Because the sucrose/biomass ratio in the fermentation broth decreased to below 300 g/g, the insufficient concentration of sucrose might have decreased the concentration of levan. Besides the growth characteristics of the population, the mixing intensity and flow structure were also found to influence the molecular mass of levan. At 600 rpm, the microorganisms produced levan with a molecular mass lower than at 300 rpm. The stirring of a fermentation broth w…

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The effect of mixing on glucose fermentation by Zymomonas mobilis continuous culture

Abstract The influence of mixing (in the range from 300 to 1100 rpm) on the performance of Zymomonas mobilis anaerobic continuous culture was studied. Biomass yield and ethanol productivity were improved at higher stirring intensities, in parallel with a decrease in byproduct synthesis. A mixing-dependent formation of minor amounts of fructose was first demonstrated in Z. mobilis anaerobic culture on glucose. The rate of fructose synthesis and the specific activity of the key enzyme in the pathway to fructose, phosphoglucose isomerase (EC 5.3.1.9), had a maximum at 700 rpm.

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THE GROUP OF AUTOMORPHISMS OF THE SEMIGROUP OF ENDOMORPHISMS OF FREE COMMUTATIVE AND FREE ASSOCIATIVE ALGEBRAS

Let W(X) be a free commutative or a free associative algebra. The group of automorphisms of the semigroup End (W(X)) is studied.

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GEOMETRIC EQUIVALENCE OF ALGEBRAS

In this paper, we study the geometric equivalence of algebras in several varieties of algebras. We solve some of the problems formulated in [2], in particular, that of geometric equivalence for real-closed fields and finitely generated commutative groups.

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Influence of Micromixing on Microorganisms and Products

The influence of mixing intensity as well as physical and chemical parameters on the cells of different microorganisms and the biosynthesis process is examined in this paper. Some reactions of cells effecting mixing intensity are described, such as retarded biomass growth, changes in aggregation and mutual arrangement of cells, morphological changes of cells and decreasing of biological activity, caused by an increased intensity of turbulence (turbohypobiosis). Several methods for investigating the local energy in reactors are compared. It is concluded that conventional methods of hydrodynamic analysis do not always allow valid results for the optimization of the mixing regime to be obtaine…

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