Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms

We prove that every mapping torus of any free group endomorphism is residually finite. We show how to use a not yet published result of E. Hrushovski to extend our result to arbitrary linear groups. The proof uses algebraic self-maps of affine spaces over finite fields. In particular, we prove that when such a map is dominant, the set of its fixed closed scheme points is Zariski dense in the affine space.Comment: 18 page

Controlled embeddings into groups that have no non-trivial finite quotients

If a class of finitely generated groups Curly(G) is closed under isometric amalgamations along free subgroups, then every G in Curly(G) can be quasi-isometrically embedded in a group Hat(G) in Curly(G) that has no proper subgroups of finite index. Every compact, connected, non-positively curved space X admits an isometric embedding into a compact, connected, non-positively curved space Overline(X) such that Overline(X) has no non-trivial finite-sheeted coverings.Comment: 18 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon1/paper4.abs.htm

An exceptional geometry for d=11 supergravity?

We analyze the algebraic constraints of the generalized vielbein in SO(1,2) x SO(16) invariant d=11 supergravity, and show that the bosonic degrees of freedom of d=11 supergravity, which become the physical ones upon reduction to d=3, can be assembled into an E_8-valued vielbein already in eleven dimensions. A crucial role in the construction is played by the maximal nilpotent commuting subalgebra of E_8, of dimension 36, suggesting a partial unification of general coordinate and tensor gauge transformations.Comment: 16 pages, LaTeX2

Free Malcev algebra of rank three

We find a basis of the free Malcev algebra on three free generators over a field of characteristic zero. The specialty and semiprimity of this algebra are proved. In addition, we prove the decomposability of this algebra into subdirect sum of the free Lie algebra rank three and the free algebra of rank three of variety of Malcev algebras generated by a simple seven-dimensional Malcev algebra

Entwicklung und Synthese allosterischer Hemmstoffe des Apicomplexa Bewegungs- und Invasionsapparates

Die WHO-Agenda zur Malariaeradikation erfordert hohe Investitionen und das Anpassungspotential der Plasmodium-Parasiten betont den Bedarf an kontinuierlicher Entwicklung von neuen effektiven Ansätzen. Der unter allen Apicomplexa- Parasiten konservierte Fortbewegungs- und Invasionsapparat, das Glideosom, gemeinsam mit seinem zentralen Motorprotein Myosin A, stellt ein attraktives Ziel zur erfolgreichen Hemmung der parasitären Aktivität dar. In dieser Studie wurde die Erhöhung des Effektes eines potentiellen Myosin A-Inhibitors mit biarylischer Grundstruktur durch die Funktionalisierung der ortho-Position geprüft. Eine Reihe von ortho-substituierten Biarylen wurde aus den in silico durchgeführten Strukturmodifizierungen abgeleitet und synthetisiert. Die one-pot SUZUKI-MIYAURA-Kreuzkupplung mit angeschlossener Benzylierung lieferte einen effizienten Zugang zu den potentiellen Inhibitormolekülen. Titrierungsexperimente unter Quantifizierung des Effektes der Biaryle auf die ATPase-Aktivität des Myosin A-Modells über die mittlere inhibitorische Konzentration ergaben inhibitorische Aktivitäten der Substanzen im unteren mikrooder nanomolaren Bereich. Die Proliferation von nicht resistenten und multiresistenten Plasmodium falciparum Stämmen 3D7 und 7G8 wurde durch die Biaryle in vergleichbaren Konzentrationsbereichen effektiv gehemmt, wobei die Glideosomgesteuerten Prozesse der Erythrozyteninvasion und des Egress deutlich inhibiert wurden. In den in vitro Flashphotolyse-Experimenten wurden Biaryl-bedingte Veränderungen der Akto-Myosin-Kinetik und der ATP-Umsetzungsgeschwindigkeit, sowie eine starke Herabsetzung der Bindeaffinität des Myosin A-Modells zum ATP festgestellt. MD-Simulationen ergaben Interaktionen des veränderten Grundgerüstes im allosterischen Bereich der Aktininteraktion um das LYS274, die mit den in vitro Ergebnissen korrelieren und auf eine aktive Veränderung der allosterischen Kommunikation zwischen der Aktin- und Nukleotidbindestelle durch die Biaryle deuten. Der strukturbasierte Ansatz ermöglichte ebenfalls eine potentielle Erklärung für die selektive Aktivität des Carbazols DBC gegenüber Myosin-9b, während mehrere Isoformen von Myosinen der Klassen 1, 2 und 5 nicht beeinflusst wurden. Ensemblebasierten Dockings und beschleunigte MD-Simulationen deuten auf eine stabile Interaktion des DBC in einer spezifischen Bindestelle im Myosin-9b in der Nähe des Bindebereiches von Blebbistatin hin, die zur Störung der Motoraktivität führen kann. Die entsprechenden Bereiche der Myosine 1, 2 und 5 weisen eine niedrige Homologie zum Myosin-9b auf und sind durch DBC weniger populiert

Minsky machines and algorithmic problems

This is a survey of using Minsky machines to study algorithmic problems in semigroups, groups and other algebraic systems.Comment: 19 page

ДИВЕРСИФІКАЦІЯ ПРОМИСЛОВИХ ПІДПРИЄМСТВ ЯК НАПРЯМОК СТРАТЕГІЧНОГО РОЗВИТКУ

The article reviews the problems of diversification of industrial enterprises as a direction of strategic development. The article analyzes the types of diversification of enterprises.  An analysis of development strategies of foreign companies makes it clear that world leaders at the present stage of development use diversification strategies, the main direction of which is to integrate forward by uniting with final consumers of products.  In the classification of strategies for diversification, strategists have been singled out, which are divided into two groups: synergistic and conglomerant.  The directions of diversification processes depend on the stage of the enterprise's life cycle.  To determine the stages of the life cycle, a methodology based on certain seven performance indicators is proposed. The proposed indicators also allow the company's management to assess the diversification by the main criteria: attractiveness in terms of invested funds; "Input costs" to the new industry and additional benefits.  From the above calculations, we can conclude that most of the enterprises are at the stage of the life cycle "Stabilization". We recommend the application of the strategy of viability (long-term development strategy), which is aimed at realizing the goals of sustainable development and operation of the enterprise. To implement the strategy, it is necessary that diversification measures be implemented in all relevant areas and aspects of the activity of the enterprise.  On one front it concerns the personnel and measures on its motivation, management styles, corporate culture, financial and resource support, management competencies. В статті зроблено огляд проблем диверсифікації промислових підприємств як напрямоку стратегічного розвитку. У статті проведено аналіз видів диверсифікації підприємств. Аналіз стратегій розвитку зарубіжних компаній доводить, що світові лідери на сучасному етапі розвитку використовують стратегії диверсифікації, основним напрямком яких є інтеграція вперед шляхом об'єднання з кінцевими споживачами продукції. У класифікації стратегій диверсифікації виділені стратеги, які розділені на дві групи: синергетичні і конгломерантні. Напрямки диверсифікаційних процесів залежать від стадії життєвого циклу підприємства. Для визначення етапів життєвого циклу запропонована методика, заснована на певні семи показників діяльності. Запропоновані показники також дозволяють керівництву компанії оцінити диверсифікацію за основними критеріями: привабливість з точки зору вкладених коштів; «Витрати на вступ» до нової галузі і додаткові вигоди. З наведених розрахунків можна зробити висновок, що більшість підприємств знаходиться на стадії життєвого циклу «Стабілізація». Рекомендується застосування стратегії життєздатності (стратегія довгострокового розвитку), яка спрямована на реалізацію цілей забезпечення стійких темпів розвитку і функціонування підприємства. Для реалізації стратегії необхідно, щоб заходи диверсифікації були здійснені у всіх відповідних областях і аспектах діяльності даного підприємства. На один перед це стосується персоналу і заходи по його мотивації, стилів управління, корпоративної культури, фінансового та ресурсного забезпечення, компетенцій керівництва

Morphological typology of small watershed in river basins of cultivation area

The article proposed the technique of small watershed typification according to four morphometric characteristics, determining the energy of relief: average height, vertical segmentation, the density of ravine network and an average slope. An elementary catchment area is used as an operating-territorial unit. Ward's method was used to perform the typification. The zoning of catchment area allows to determine the ratio of different agricultural lands, to reduce the rate of soil erosion and the amount of sediments entering the channel of permanent and temporary streams through the slopes. The testing of technique was performed within the upper reaches of the r. Medveditsa basin and made it possible to distinguish 6 types of elementary catchments differing by relief energy, as well as to perform their ranking according to relief energy. The zoning map established as the result of the developed method use concerning elementary catchment types may be used for the improvement of land use structure based on the optimization of lands with different erosion hazard, and the inclusion in crop rotation, depending on their soil protection efficiency

Revisiting the Equivalence Problem for Finite Multitape Automata

The decidability of determining equivalence of deterministic multitape automata (or transducers) was a longstanding open problem until it was resolved by Harju and Karhum\"{a}ki in the early 1990s. Their proof of decidability yields a co_NP upper bound, but apparently not much more is known about the complexity of the problem. In this paper we give an alternative proof of decidability, which follows the basic strategy of Harju and Karhumaki but replaces their use of group theory with results on matrix algebras. From our proof we obtain a simple randomised algorithm for deciding language equivalence of deterministic multitape automata and, more generally, multiplicity equivalence of nondeterministic multitape automata. The algorithm involves only matrix exponentiation and runs in polynomial time for each fixed number of tapes. If the two input automata are inequivalent then the algorithm outputs a word on which they differ

Markov semigroups, monoids, and groups

A group is Markov if it admits a prefix-closed regular language of unique representatives with respect to some generating set, and strongly Markov if it admits such a language of unique minimal-length representatives over every generating set. This paper considers the natural generalizations of these concepts to semigroups and monoids. Two distinct potential generalizations to monoids are shown to be equivalent. Various interesting examples are presented, including an example of a non-Markov monoid that nevertheless admits a regular language of unique representatives over any generating set. It is shown that all finitely generated commutative semigroups are strongly Markov, but that finitely generated subsemigroups of virtually abelian or polycyclic groups need not be. Potential connections with word-hyperbolic semigroups are investigated. A study is made of the interaction of the classes of Markov and strongly Markov semigroups with direct products, free products, and finite-index subsemigroups and extensions. Several questions are posed.Comment: 40 pages; 3 figure