scholarly journals The Minimal System of Defining Relations of the Free Modular Lattice of Rank 3 and Lattices Close to Modular One

2014 ◽  
Vol 2 (1) ◽  
pp. 27-31
Author(s):  
Alexander G. Gein ◽  
Mikhail P. Shushpanov
Keyword(s):  
Modular Lattice ◽  
Minimal System ◽  
Defining Relations ◽  
Free Modular Lattice

scholarly journals Defining relations of a free modular lattice of rank 3

2013 ◽  
Vol 57 (10) ◽  
pp. 59-61 ◽  
Author(s):  
A. G. Gein ◽  
M. P. Shushpanov
Keyword(s):  
Modular Lattice ◽  
Defining Relations ◽  
Free Modular Lattice

The free modular lattice on four generators is not finitely presentable

1972 ◽  
Vol 2 (1) ◽  
pp. 284-285 ◽  
Author(s):  
T. Evans ◽  
D. Y. Hong
Keyword(s):  
Modular Lattice ◽  
Free Modular Lattice

On the Word Problem for Orthocomplemented Modular Lattices

1989 ◽  
Vol 41 (6) ◽  
pp. 961-1004 ◽  
Author(s):  
Michael S. Roddy
Keyword(s):  
Word Problem ◽  
Division Ring ◽  
Modular Lattice ◽  
Modular Lattices ◽  
Commutative Field ◽  
Free Modular Lattice ◽  
Finitely Presented ◽  
Unsolvable Word Problem

In [16] Freese showed that the word problem for the free modular lattice on 5 generators is unsolvable. His proof makes essential use of Mclntyre's construction of a finitely presented field with unsolvable word problem [30]. (We follow Cohn [7] in calling what is commonly called a division ring a field, and what is commonly called a field a commutative field.) In this paper we will use similar ideas to obtain unsolvability results for varieties of modular ortholattices. The material in this paper is fairly wide ranging, the following are recommended as reference texts.

Toward living nanomachines

2018 ◽  
Author(s):  
Christof Mast ◽  
Friederike Möller ◽  
Moritz Kreysing ◽  
Severin Schink ◽  
Benedikt Obermayer ◽  
...  
Keyword(s):  
Molecular Evolution ◽  
Thermal Gradient ◽  
Molecular Level ◽  
Minimal System ◽  
Thermal Gradients ◽  
Temperature Oscillations ◽  
Fluid Convection ◽  
Inanimate Matter ◽  
High Concentrations ◽  
Periodic Temperature

How does inanimate matter become transformed into animate matter? Living systems evolve by replication and selection at the molecular level and this chapter considers how to establish a synthetic, minimal system that can support molecular evolution and thus life. Molecular evolution cannot be explained by starting with high concentrations of activated chemicals that react toward their chemical equilibrium; persistent non-equilibria are required to maintain continuous reactivity and we especially consider thermal gradients as an early driving force for Darwinian molecular evolution. The temperature difference across water-filled compartments implements a laminar fluid convection with periodic temperature oscillations that allow for the melting and replication of DNA. Simultaneously, dissolved molecules are moved along the thermal gradient by an effect called thermophoresis. The combined result is an efficient molecule trap that exponentially favors long over short DNA and thus maintains complexity. Future experiments will reveal how thermal gradients could actively drive the Darwinian process of replication and selection.

scholarly journals Multidimensional Multiplicative Combinatorial Properties of Dynamical Syndetic Sets

2021 ◽  
Author(s):  
Jiahao Qiu ◽  
Jianjie Zhao
Keyword(s):  
Normal Subgroup ◽  
Finite Index ◽  
Minimal System ◽  
Combinatorial Properties ◽  
Return Times ◽  
Residual Set ◽  
Closed Sets ◽  
Open Set ◽  
Geometric Progressions ◽  
Set Of Points

AbstractIn this paper, it is shown that for a minimal system (X, G), if H is a normal subgroup of G with finite index n, then X can be decomposed into n components of closed sets such that each component is minimal under H-action. Meanwhile, we prove that for a residual set of points in a minimal system with finitely many commuting homeomorphisms, the set of return times to any non-empty open set contains arbitrarily long geometric progressions in multidimension, extending a previous result by Glasscock, Koutsogiannis and Richter.

Archaeal DNA uracil repair via direct strand incision: A minimal system reconstituted from purified components

DNA Repair ◽  
2010 ◽  
Vol 9 (4) ◽  
pp. 438-447 ◽  
Author(s):  
Lars Schomacher ◽  
K. Anke Schürer ◽  
Elena Ciirdaeva ◽  
Paul McDermott ◽  
James P.J. Chong ◽  
...  
Keyword(s):  
Minimal System ◽  
Uracil Repair

LORENTZ COVARIANCE FOR THE QUANTUM ALGEBRA OF OBSERVABLES: NAMBU–GOTO STRINGS IN 3 + 1 DIMENSIONS

2002 ◽  
Vol 17 (17) ◽  
pp. 2331-2349 ◽  
Author(s):  
GERRIT HANDRICH
Keyword(s):  
Rest Frame ◽  
Poisson Algebra ◽  
Quantum Algebra ◽  
Substantial Part ◽  
Quantum Case ◽  
Generators And Relations ◽  
Defining Relations ◽  
Algebra Of Observables ◽  
The One ◽  
The Relationship

To postulate correspondence for the observables only is a promising approach to a fully satisfying quantization of the Nambu–Goto string. The relationship between the Poisson algebra of observables and the corresponding quantum algebra is established in the language of generators and relations. A very valuable tool is the transformation to the string's rest frame, since a substantial part of the relations are solved. It is the aim of this paper to clarify the relationship between the fully covariant and the rest frame description. Both in the classical and in the quantum case, an efficient method for recovering the covariant algebra from the one in the rest frame is described. Restrictions on the quantum defining relations are obtained, which are not taken into account when one postulates correspondence for the rest frame algebra. For the part of the algebra studied up to now in explicit computations, these further restrictions alone determine the quantum algebra uniquely — in full consistency with the further restrictions found in the rest frame.

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