673 research outputs found

    Matrix iterations and Cichon's diagram

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    Using matrix iterations of ccc posets, we prove the consistency with ZFC of some cases where the cardinals on the right hand side of Cichon's diagram take two or three arbitrary values (two regular values, the third one with uncountable cofinality). Also, mixing this with the techniques in J Symb Log 56(3):795-810, 1991, we can prove that it is consistent with ZFC to assign, at the same time, several arbitrary regular values on the left hand side of Cichon's diagram.Comment: 14 pages, 2 figures, article in press for the journal Archive for Mathematical Logi

    Physical paradigm of Life as a generalization of biochemical conception. A Physical law governing life origin and development

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    The present view of biological phenomena is based on a biomolecular paradigm that development of living organisms is entirely defined by information stored in a molecular form as some genetic code. However, new facts and discoveries indicate that biological phenomena cannot be reduced to a biomolecular realm alone, but are also governed by mechanisms of other nature. These mechanisms, acting in tight cooperation with biochemical mechanisms, define life cycles of individual organisms, and, through this, the origin and evolution of the living world. Here, we present such a physical mechanism (General growth law), which represents a new physical law of nature acting at cellular, organ, system and whole organism levels, directing growth and reproduction together with biomolecular mechanisms. It imposes uniquely defined constraints on distribution of nutrients between biomass production and maintenance, thus defining the composition of biochemical reactions, their change and irreversibility during the organismal life cycle. Mathematically, this law is represented by the growth equation. Using this equation, we introduce growth models and explain division mechanisms for unicellular organisms. High adequacy of obtained results to experiments proves validity of the General growth law and of the new physical paradigm of Life based on this law.Comment: 38 pages, 8 figures, 1 table. Analysis of general principles of Life organization was added, as well as new material and two figures. In particular, analysis of views of E. Schrodinger, whose famous lectures contributed to origin of a biochemical paradigm, exposes what assumptions led him to make inaccurate conclusions. A new, more general physical paradigm of Life was propose

    Propulsion and control of deformable bodies in an ideal fluid

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    Motivated by considerations of shape changing propulsion of underwater robotic vehicles, this paper analyses the mechanics of deformable bodies operating in an ideal fluid. The application of methods from geometric mechanics results in a compact and insightful formulation of the problem. We develop an explicit formula for the fluid mechanical connection, in terms of the fluid potential function, for this class of systems. The connection can be used to analyze many issues in motion planning and control. The theory is illustrated by application to an amoeba-like device
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