The Structure of the Polytope of Hereditary Information

2019 ◽  
Vol 8 (2) ◽  
pp. 7-22
Author(s):  
Gennadiy Vladimirovich Zhizhin
Keyword(s):  
Nucleic Acid ◽  
Hydrogen Bonds ◽  
Phosphoric Acid ◽  
High Intensity ◽  
Information Exchange ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Nitrogen Bases ◽  
Higher Dimensional ◽  
Low Dimensional

The representations of the sugar molecule and the residue of phosphoric acid in the form of polytopes of higher dimension are used. Based on these ideas and their simplified three-dimensional images, a three-dimensional image of nucleic acids is constructed. The geometry of the neighborhood of the compound of two nucleic acid helices with nitrogen bases has been investigated in detail. It is proved that this neighborhood is a cross-polytope of dimension 13 (polytope of hereditary information), in the coordinate planes of which there are complementary hydrogen bonds of nitrogenous bases. The structure of this polytope is defined, and its image is given. The total incident flows from the low-dimensional elements to the higher-dimensional elements and vice versa of the hereditary information polytope are calculated equal to each other. High values of these flows indicate a high intensity of information exchange in the polytope of hereditary information that ensures the transfer of this information.

scholarly journals The Polytope of Hereditary Information the Structure, Location, Signification

2019 ◽  
pp. 56-62 ◽  
Author(s):  
Gennadiy Vladimirovich Zhizhin
Keyword(s):  
Nucleic Acid ◽  
Hydrogen Bonds ◽  
High Intensity ◽  
Information Exchange ◽  
Nitrogen Bases ◽  
Higher Dimensional ◽  
Low Dimensional

The geometry of the neighborhood of the compound of two nucleic acid helices with nitrogen bases was investigated. It is proved that this neighborhood is a cross-polytope of dimension 13 (polytope of hereditary information), in the coordinate planes of which there are complementary hydrogen bonds of nitrogenous bases. The structure of this polytope is defined, its image is given. The total incident flows from the low-dimensional elements to the higher-dimensional elements and vice versa of the hereditary information polytope are calculated equal to each other. High values of these flows indicate a high intensity of information exchange in the polytope of hereditary information that ensures the transfer of this information

The Geometry of the Structure of Nucleic Acids With Regard to the Higher Dimension of the Components

2019 ◽  
pp. 203-218
Keyword(s):  
Protein Synthesis ◽  
Nucleic Acid ◽  
Phosphoric Acid ◽  
Nucleic Acids ◽  
Three Dimensional ◽  
Acid Form ◽  
Higher Dimension

Using three-dimensional visualization of nucleic acid molecules, obtained in the previous chapter, an analysis of the geometry of nucleic acid molecules in the space of higher dimension is carried out. It is shown that phosphoric acid residues and five-carbon sugar molecules in a double-stranded nucleic acid form polytopes of higher dimension with anti-parallel edges. These polytopes are of type n-cross-polytope (n = 5 for phosphoric acid residues, n = 13 for sugar molecules). It was found that these n-cross-polytopes located in right- and left-twisted spirals are enantiomorphic. It has been found that in cross-polytopes constructed of two sugar molecules there are 12 coordinate planes, each of which may contain a bond of nitrogenous bases (one of the 12 known ones). The formation of codons (triplets) corresponds to the separation in space of the highest dimension of nucleic acids of three-dimensional regions. This also occurs in the ribosomes upon contact with transport and adapter RNA during protein synthesis.

TIME LOWER BOUNDS FOR PERMUTATION ROUTING ON MULTI-DIMENSIONAL BUSED MESHES

1993 ◽  
Vol 03 (02) ◽  
pp. 129-138
Author(s):  
STEVEN CHEUNG ◽  
FRANCIS C.M. LAU
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Routing Problem ◽  
Higher Dimensional ◽  
Low Dimensional ◽  
Permutation Routing

We present time lower bounds for the permutation routing problem on three- and higher-dimensional n x…x n meshes with buses. We prove an (r–1)n/r lower bound for the general case of an r-dimensional bused mesh, r≥2, which is not as strong for low-dimensional as for higher-dimensional cases. We then use a different approach to construct a 0.705n lower bound for the three-dimensional case.

Di- bis Pentahydrate von fünf Alkylendiaminen. Eine Fallstudie zu ein- und zweidimensionalen Wasserpolymeren in Festkörpern/Di- to Pentahydrates of Five Alkylenediamines. A Case Study of One- and Two-Dimensional Water Polymers in Solids

1999 ◽  
Vol 54 (1) ◽  
pp. 103-108 ◽  
Author(s):  
Stephanie Janeda ◽  
Dietrich Mootz
Keyword(s):  
Hydrogen Bonding ◽  
Hydrogen Bonds ◽  
Crystal Structures ◽  
Three Dimensional ◽  
Unit Cell ◽  
Water Molecules ◽  
Two Dimensional ◽  
Group I ◽  
Low Dimensional

The crystal structures of five low-melting hydrates of n-alkane-α,ω-diamines, H2N(CH2)nNH2 · x H2O, for short Cn · x W, have been determined. As a common feature, the water molecules are mutually linked by hydrogen bonds O-H· · ·O to form low-dimensional polymers. These are a meandering chain in C2 · 2 W (space group I 2/a, Z = 4 formula units per unit cell), a zig zag chain in C6 · 2 W (P 21/c, Z = 2), a ribbon of consecutively condensed five-membered rings in C3 · 3 W (P 21/c, Z = 4) and a layer of condensed and spiro-linked rings of varying size each in C7 · 3 W (P 1̄, Z = 4) and C4 · 5 W (C 2/c, Z = 4). Further hydrogen bonding, between the water polymers and the bifunctional amine molecules, leads to overall connectivities which are three-dimensional in each structure.

Quadratate Und Hydrogenquadratate Cyclischer Stickstoffbasen Mit Schicht-, Ketten- und Leiterstrukturen / Squarates and Hydrogensquarates of Cyclic Nitrogen Bases with Layer-, Chainand Ladder-Structures

2003 ◽  
Vol 58 (1) ◽  
pp. 27-35 ◽  
Author(s):  
Rainer Mattes ◽  
Jörg Ebbing ◽  
Annette Grüss ◽  
Jens Köppe ◽  
Krystyna Majcher
Keyword(s):  
Hydrogen Bonds ◽  
Layer Structure ◽  
Three Dimensional ◽  
Squaric Acid ◽  
Ladder Structure ◽  
X Ray ◽  
Nitrogen Bases ◽  
Π Interactions ◽  
Order Form ◽  
Cyclic Nitrogen

Abstract The synthesis and single crystal X-ray structures of four adducts of squaric acid with cyclic nitrogen bases are reported. Extensive hydrogen bonding, ionic interactions and (in one case) π-π-interactions lead to layered, and to two- and three-dimensional assemblies. [Pyrimidinium][ hydrogenquadratate] (1) has a layer structure, consisting of head-to-tail infinite chains of pyrimidinium and [HC4O4]− ions, which are cross-linked by short N-H···O and C-H···O hydrogen bonds. [C9H11N2][HC4O4] ・0.5H2C4O4 (2), the adduct of a benzodiazepin and squaric acid, has a ladder-structure. Chains of [HC4O4]− ions and H2C4O4 molecules in alternating order form the ladder-beam. Layers of cations and anions in the ratio 2:1 build the crosspieces at an angle of 49° to the beam. The layers contain dimers of [HC4O4]− ions. [H2L2][HC4O4]2 (3) with L2 = 5,6,7,8,9,14,15,16,17,18-decahydrodibenzo[e,l]-1,4,8,11-tetraaza-cyclotetradecine shows zigzag chains made of [HC4O4]− ions. Between the [H2L2]2+ and the [HC4O4]− ions π-π interactions exist besides up to four N-H···O hydrogen bonds. The [H2L2]2+ ions possess two different conformations. [H2cyclam][C2O4] ·4H2O (4) contains strongly undulated layers of the composition [C4O4 ·4H2O]2−. The cations, which show two intramolecular N-H···N hydrogen bonds with N···N distances of 2.870 (3) Å , are interlinked at an angle of 41.5°.

scholarly journals Linked Weyl surfaces and Weyl arcs in photonic metamaterials

Science ◽  
2021 ◽  
Vol 373 (6554) ◽  
pp. 572-576
Author(s):  
Shaojie Ma ◽  
Yangang Bi ◽  
Qinghua Guo ◽  
Biao Yang ◽  
Oubo You ◽  
...  
Keyword(s):  
Electromagnetic Waves ◽  
Three Dimensional ◽  
Electromagnetic Properties ◽  
Higher Dimension ◽  
Surface Phenomena ◽  
Physical Systems ◽  
Higher Dimensional ◽  
Topological Singularities ◽  
Lower Dimensional

Generalization of the concept of band topology from lower-dimensional to higher-dimensional (n > 3) physical systems is expected to introduce new bulk and boundary topological effects. However, theoretically predicted topological singularities in five-dimensional systems—Weyl surfaces and Yang monopoles—have either not been demonstrated in realistic physical systems or are limited to purely synthetic dimensions. We constructed a system possessing Yang monopoles and Weyl surfaces based on metamaterials with engineered electromagnetic properties, leading to the observation of several intriguing bulk and surface phenomena, such as linking of Weyl surfaces and surface Weyl arcs, via selected three-dimensional subspaces. The demonstrated photonic Weyl surfaces and Weyl arcs leverage the concept of higher-dimension topology to control the propagation of electromagnetic waves in artificially engineered photonic media.

Higher Dimensions in the Theory of Heredity

2021 ◽  
pp. 84-110
Keyword(s):  
Mathematical Model ◽  
Nucleic Acid ◽  
Hydrogen Bonds ◽  
Plant Development ◽  
Equilibrium Position ◽  
Higher Dimensions ◽  
Multidimensional Space ◽  
Nitrogen Bases ◽  
Wide Range ◽  
The Mathematical Model

On the basis Mendel's experiments, a mathematical model is constructed that describes the results of these experiments in a wide range of parameters. There is shown that in the mathematical model of Mendel's experiments, based on real patterns of plant development, there are equilibrium positions between the dominant and recessive forms. This equilibrium position is stable and located in the multidimensional space of system phenotypes. This newly discovered behavior of the dominant and recessive forms in the vicinity of the equilibrium position (true) differs significantly from the logistic equilibrium position in the Hardy-Weinberg principle, built without taking into account the real patterns in the plant population. The geometry of the neighborhood of the compound of two nucleic acid helices with nitrogen bases was investigated. It is proved that this neighborhood is a cross-polytope of dimension 13 (polytope of hereditary information), in the coordinate planes of which there are complementary hydrogen bonds of nitrogenous bases.

On the Conditions for the Existence of Higher-Dimensional Polytopes

2021 ◽  
pp. 1-26
Keyword(s):  
High Dimensional ◽  
Necessary Condition ◽  
Higher Dimension ◽  
Main Condition ◽  
Higher Dimensional ◽  
Analytic Expressions ◽  
Different Dimensions ◽  
Number Of Faces ◽  
Low Dimensional ◽  
Analytical Expressions

For irregular n-simplex, n-cross-polytope, n-cube (n-prismahedron) analytic expressions are obtained for calculating the number of faces of different dimensions included in these polytopes. It is shown that the expressions obtained for each of these types of polytopes lead to the Euler-Poincaré equation, regardless of its general topological conclusion. The fulfillment of the Euler-Poincaré equation is the main condition for the existence of polytopes of higher dimension. It is proved that from the obtained analytical expressions for the numbers of faces of different dimensions, the necessary condition for the existence of polytopes follows, which determines the incidence coefficients of low-dimensional faces with respect to high-dimensional faces. It was found that a cross-polytope of any dimension is the result of the rotation of a simplex around the helicoid axis.

Van der Waals Epitaxy of GaSe on GaAs(111)

1994 ◽  
Vol 340 ◽  
Author(s):  
L. E. Rumaner ◽  
F.S. Ohuchi
Keyword(s):  
Lattice Mismatch ◽  
Van Der Waals ◽  
Three Dimensional ◽  
Structured Materials ◽  
Lattice Matching ◽  
Molecular Beam Deposition ◽  
Crystal Films ◽  
Low Dimensional ◽  
Matching Constraints ◽  
Lattice Matched

ABSTRACTAlthough heteroepitaxy of lattice-matched and lattice-mismatched materials leading to artificially structured materials has resulted in impressive performance in various electronics devices, material combinations are usually limited by lattice matching constraints. A new concept for fabricating material systems using the atomically abrupt and low dimensional nature of layered materials, called van der Waals epitaxy (VDWE), has been developed. GaSe (Eg = 2.1 eV) has been deposited on the three dimensional surface of GaAs (111) using a molecular beam deposition system. GaSe was evaporated from a single Knudsen source, impinging on a heated substrate. Even with a lattice mismatch of 6% between the substrate and the growing film, good quality single crystal films were grown as determined by RHEED. The films have further been analyzed using a complementary combination of XPS and X-ray reflectivity.

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

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