scholarly journals Quantum Field of Functional Density

2020 ◽  
Author(s):  
Eugene Machusky ◽  
Olexander Goncharov
Keyword(s):  
Quantum Physics ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Weighted Average ◽  
Discrete Mathematics ◽  
Engineering Practice ◽  
Clock Frequency ◽  
Mesh Topology ◽  
Functional Density ◽  
Frequency Calculation

For the first time in scientific and engineering practice, it is logically and mathematically substantiated, computationally verified and metrologically confirmed that classic and quantum physics, analytical and quantum chemistry, as well as continuous symbolic and discrete digital mathematical analysis, all have computational limits of information entropy, upper 1/10^16 and lower 1/10^64. Mutual displacement of these limits relatively center of Euclidean three-dimensional and of Cartesian two-dimensional space generate sets of quantum dots of mesh topology and weighted average harmonic units of quantum metrics of internal atomic and outer cosmic space, as well as determines limits of communication speed, clock frequency, calculation power and accuracy for any computing machine with subatomic elements of memory. The matrices of functional density and entropy of energy and information fields reconciles classic and quantum physics with continuous and discrete mathematics of special and general relativity.

Weighted average geodesic distance of Vicsek network in three-dimensional space

2021 ◽  
pp. 2150077
Author(s):  
Yan Liu ◽  
Meifeng Dai ◽  
Yuanyuan Guo
Keyword(s):  
Dimensional Space ◽  
Geodesic Distance ◽  
Three Dimensional ◽  
Weighted Average ◽  
Weight Vector ◽  
Natural Generalization ◽  
The Self ◽  
Self Similarity ◽  
Similar Measure ◽  
Three Dimensional Space

Fractal generally has self-similarity. Using the self-similarity of fractal, we can obtain some important theories about complex networks. In this paper, we concern the Vicsek fractal in three-dimensional space, which provides a natural generalization of Vicsek fractal. Concretely, the Vicsek fractal in three-dimensional space is obtained by repeatedly removing equilateral cubes from an initial equilateral cube of unit side length, at each stage each remaining cube is divided into [Formula: see text] smaller cubes of which [Formula: see text] are kept and the rest discarded, where [Formula: see text] is odd. In addition, we obtain the skeleton network of the Vicsek fractal in three-dimensional space. Then we focus on weighted average geodesic distance of the Vicsek fractal in three-dimensional space. Take [Formula: see text] as an example, we define a similar measure on the Vicsek fractal in three-dimensional space by weight vector and calculate the weighted average geodesic distance. At the same time, asymptotic formula of weighted average geodesic distance on the skeleton network is also obtained. Finally, the general formula of weighted average geodesic distance should be applicable to the models when [Formula: see text], the base of a power, is odd.

Installing Technology of Spherical Welding Lattice Shell in Three-Dimensional Space

2013 ◽  
Vol 838-841 ◽  
pp. 273-279
Author(s):  
Xiao Bo Xu ◽  
Qian Zhao ◽  
Hui Ying Li
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Shell Structures ◽  
Engineering Practice ◽  
High Quality ◽  
Good Efficiency ◽  
The Common ◽  
Lattice Shell ◽  
Technical Measures ◽  
Three Dimensional Space

Spherical welding lattice shell structures are usually used in stadiums and public buildings. The main difficult problems in construction are positioning of welding members and controlling welding deformations in three-dimensional space. The common positioning methods are poor in operability and accuracy, which cannot meet the demands of precise construction. In this paper, a three-dimensional positioner was developed according to the spherical latitude and longitude lines intersect positioning principle based on the Kitwitt monolayer welding lattice shell in Guangzhou Conghua Liuxi Square project. In addition, the welding deformations were controlled effectively by innovative technical measures. Good efficiency has been achieved in engineering practice with this technology and the installation is of high quality.

scholarly journals Generalized 2N Color Theorem

2020 ◽  
pp. 1-4
Author(s):  
Joseph Edward Brierly ◽  
Keyword(s):  
Quantum Physics ◽  
Dimensional Space ◽  
Bubble Chamber ◽  
Space Station ◽  
Three Dimensional ◽  
Physical Reality ◽  
Four Dimensions ◽  
Color Problem ◽  
Four Color Theorem ◽  
The Universe

2N-Color Theorem This article gives a standard proof of the famous Four-Color theorem and generalizes it be the 2N-Color problem. The article gives a number of possible applications of the 2N-Color problem that is the essence of orientation. Orientation is fundamental to many fields of scientific knowledge. The Fourcolor theorem applies to map making by the knowledge that only four colors are necessary to color a planar map. The Six-color theorem applies to three dimensional space implying that a space station could be ideally designed to have six compartments adjacent to one another allowing a door from any one of the compartments to the other five. The 2N-color generalization applies to the physical reality of quantum physics. Bubble chamber investigations suggest that the universe is four or more dimensions. Thus the 2N-color theorem applies to the N dimensional universe. At this time string theorists have suggested that the universe could be greater than four dimensions. Physics has not as of yet proven the exact dimension of the universe that could even be infinite as a possibility

scholarly journals Geometry of real objects in shipbuilding and ship repair

2020 ◽  
Vol 2020 (1) ◽  
pp. 31-44
Author(s):  
Vladimir Egorovich Lelyukhin ◽  
Olga Valeryevna Kolesnikova
Keyword(s):  
Dimensional Space ◽  
Space Structure ◽  
Geometric Configuration ◽  
Discrete Mathematics ◽  
Engineering Practice ◽  
Real Plane ◽  
Geometric Configurations ◽  
Geometric Objects ◽  
Real Objects ◽  
Ship Repair

The article considers the modern engineering practice of designing and manufacturing that uses various analytical and graphic forms representing geometric objects. Both of these forms are characterized by the presence of two problems in terms of production practice: 1 - tools of modern geometry cannot operate with non-ideal forms and configurations of material objects; 2 - lack of methods and tools for describing patterns of generating geometric objects, from production lines to the structure that characterizes the relative location of surfaces. The generalized provisions of the geometry of non-ideal objects theoretically justified for formal synthesis and their elements have been presented, which avoids problems of geometric configuration in the practice of designing and developing manufacturing technologies in shipbuilding and ship repair. A special toolkit based on discrete mathematics is proposed for the formal description of the geometric configuration of non-ideal objects. The principles of geometry of real objects describe the structural-parametric representation of objects in a six-dimensional space that is defined by linear and angular vectors. The concepts of linear and angular vectors are analyzed. It has been stated that the presence of an angular vector simplifies the perception and makes easier calculating the processes of geometric transformations. A geometrical object refers to a closed subspace bounded by a single surface, a set of mating or intersecting surfaces. The examples of the real plane deviations from its reference, location of the planes for creating the ideal geometric configuration, variants of real images, forming the basis for six-dimensional space, structure of geometric configurations have been illustrated. It has been found that any specific part acting as a geometric object can be represented by a set of surfaces and the structure of their relationships, which contributes to the correctness of its manufacture. The use of six-dimensional space allows to describe the spatial geometric configurations of parts of various mechanisms with mathematical accuracy.

Three Dimensional structure and organization of diploid chromosomes by optical section microscopy

1987 ◽  
Vol 45 ◽  
pp. 633-635
Author(s):  
David A. Agard ◽  
Yasushi Hiraoka ◽  
John W. Sedat
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Developmental State ◽  
Mitotic Cell ◽  
Biological Properties ◽  
Dimensional Structure ◽  
Specific Gene ◽  
Three Dimensional Structure ◽  
Complementary Techniques ◽  
Dynamic Structures

In an effort to understand the complex relationship between structure and biological function within the nucleus, we have embarked on a program to examine the three-dimensional structure and organization of Drosophila melanogaster embryonic chromosomes. Our overall goal is to determine how DNA and proteins are organized into complex and highly dynamic structures (chromosomes) and how these chromosomes are arranged in three dimensional space within the cell nucleus. Futher, we hope to be able to correlate structual data with such fundamental biological properties as stage in the mitotic cell cycle, developmental state and transcription at specific gene loci.Towards this end, we have been developing methodologies for the three-dimensional analysis of non-crystalline biological specimens using optical and electron microscopy. We feel that the combination of these two complementary techniques allows an unprecedented look at the structural organization of cellular components ranging in size from 100A to 100 microns.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

Flavin radicals, conformational sampling and robust design principles in interprotein electron transfer: the trimethylamine dehydrogenase-electron-transferring flavoprotein complex

2004 ◽  
Vol 71 ◽  
pp. 1-14
Author(s):  
David Leys ◽  
Jaswir Basran ◽  
François Talfournier ◽  
Kamaldeep K. Chohan ◽  
Andrew W. Munro ◽  
...  
Keyword(s):  
Electron Transfer ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Kinetic Studies ◽  
Molecular Assembly ◽  
Conformational Sampling ◽  
Trimethylamine Dehydrogenase ◽  
Key Residues ◽  
Electron Transferring Flavoprotein ◽  
Electron Transfer Complex

TMADH (trimethylamine dehydrogenase) is a complex iron-sulphur flavoprotein that forms a soluble electron-transfer complex with ETF (electron-transferring flavoprotein). The mechanism of electron transfer between TMADH and ETF has been studied using stopped-flow kinetic and mutagenesis methods, and more recently by X-ray crystallography. Potentiometric methods have also been used to identify key residues involved in the stabilization of the flavin radical semiquinone species in ETF. These studies have demonstrated a key role for 'conformational sampling' in the electron-transfer complex, facilitated by two-site contact of ETF with TMADH. Exploration of three-dimensional space in the complex allows the FAD of ETF to find conformations compatible with enhanced electronic coupling with the 4Fe-4S centre of TMADH. This mechanism of electron transfer provides for a more robust and accessible design principle for interprotein electron transfer compared with simpler models that invoke the collision of redox partners followed by electron transfer. The structure of the TMADH-ETF complex confirms the role of key residues in electron transfer and molecular assembly, originally suggested from detailed kinetic studies in wild-type and mutant complexes, and from molecular modelling.

Topics in Quaternion Linear Algebra

2014 ◽  
Author(s):  
Leiba Rodman
Keyword(s):  
Linear Algebra ◽  
Complex Analysis ◽  
Dimensional Space ◽  
Applied Mathematics ◽  
Three Dimensional ◽  
Number System ◽  
Graduate Course ◽  
Open Problems ◽  
Unpublished Research ◽  
Reference Tool

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

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