scholarly journals Neutrosophic Extended Triplet Group Based on Neutrosophic Quadruple Numbers

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 696 ◽  
Author(s):  
Qiaoyan Li ◽  
Yingcang Ma ◽  
Xiaohong Zhang ◽  
Juanjuan Zhang
Keyword(s):  
Dimensional Space ◽  
Multiplication Operator ◽  
Neutral Element ◽  
Algebra Structure ◽  
Multiplication Operation ◽  
Group 2

In this paper, we explore the algebra structure based on neutrosophic quadruple numbers. Moreover, two kinds of degradation algebra systems of neutrosophic quadruple numbers are introduced. In particular, the following results are strictly proved: (1) the set of neutrosophic quadruple numbers with a multiplication operation is a neutrosophic extended triplet group; (2) the neutral element of each neutrosophic quadruple number is unique and there are only sixteen different neutral elements in all of neutrosophic quadruple numbers; (3) the set which has same neutral element is closed with respect to the multiplication operator; (4) the union of the set which has same neutral element is a partition of four-dimensional space.

scholarly journals Study on the Algebraic Structure of Refined Neutrosophic Numbers

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 954
Author(s):  
Qiaoyan Li ◽  
Yingcang Ma ◽  
Xiaohong Zhang ◽  
Juanjuan Zhang
Keyword(s):  
Abelian Group ◽  
Algebraic Structure ◽  
Multiplication Operator ◽  
Neutral Element ◽  
Algebra Structure ◽  
Multiplication Operation ◽  
General Field ◽  
Neutrosophic Number

This paper aims to explore the algebra structure of refined neutrosophic numbers. Firstly, the algebra structure of neutrosophic quadruple numbers on a general field is studied. Secondly, The addition operator ⊕ and multiplication operator ⊗ on refined neutrosophic numbers are proposed and the algebra structure is discussed. We reveal that the set of neutrosophic refined numbers with an additive operation is an abelian group and the set of neutrosophic refined numbers with a multiplication operation is a neutrosophic extended triplet group. Moreover, algorithms for solving the neutral element and opposite elements of each refined neutrosophic number are given.

Quaternions and Vector Mapping in Three-Dimensional Space

2012 ◽  
Vol 235 ◽  
pp. 101-106
Author(s):  
Gui San Li
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Unit Vector ◽  
Geometric Representation ◽  
Space Vector ◽  
Vector Operation ◽  
Spatial Mechanism ◽  
Multiplication Operation ◽  
Vector Mapping ◽  
Three Dimensional Space

On the basis of analyzing the relations between vector operation and properties of multiplication operation of quaternions, the geometric representation and mapping of quaternions and vectors defined in three-dimensional space are established. The mathmatic operation of space vector, in addition to any space unit vector, rotating around three coordinate axises is carried based on the utilization of quaternions.The main purpose of this paper is to solve the issues of mathmatic tools introduced in spatial mechanism analysises and integrations by making use of quatnions.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Morphological Changes in the Rat Granulosa Cell Surface During Differentiation Induced by Estradiol and Gonadotropins

1977 ◽  
Vol 35 ◽  
pp. 484-485
Author(s):  
P. Bagavandoss ◽  
JoAnne S. Richards ◽  
A. Rees Midgley
Keyword(s):  
Cell Surface ◽  
Granulosa Cell ◽  
Morphological Changes ◽  
Follicular Development ◽  
Female Rats ◽  
Functional Changes ◽  
Group 4 ◽  
Group 3 ◽  
Group 5 ◽  
Group 2

During follicular development in the mammalian ovary, several functional changes occur in the granulosa cells in response to steroid hormones and gonadotropins (1,2). In particular, marked changes in the content of membrane-associated receptors for the gonadotropins have been observed (1).We report here scanning electron microscope observations of morphological changes that occur on the granulosa cell surface in response to the administration of estradiol, human follicle stimulating hormone (hFSH), and human chorionic gonadotropin (hCG).Immature female rats that were hypophysectcmized on day 24 of age were treated in the following manner. Group 1: control groups were injected once a day with 0.1 ml phosphate buffered saline (PBS) for 3 days; group 2: estradiol (1.5 mg/0.2 ml propylene glycol) once a day for 3 days; group 3: estradiol for 3 days followed by 2 days of hFSH (1 μg/0.1 ml) twice daily, group 4: same as in group 3; group 5: same as in group 3 with a final injection of hCG (5 IU/0.1 ml) on the fifth day.

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.

Correlation of γ-radioactivity and Scanning Electron Microscopy in measurement of retention of 111Indium-labeled canine endothelial cells on synthetic vascular grafts

1989 ◽  
Vol 47 ◽  
pp. 886-887
Author(s):  
E.J. Prendiville ◽  
S. Laliberté Verdon ◽  
K. E. Gould ◽  
K. Ramberg ◽  
R. J. Connolly ◽  
...  
Keyword(s):  
Blood Flow ◽  
Ex Vivo ◽  
Vascular Grafts ◽  
Retention Data ◽  
Vascular Prostheses ◽  
Group 4 ◽  
Human Fibronectin ◽  
Insufficient Time ◽  
Group 3 ◽  
Group 2

Endothelial cell (EC) seeding is postulated as a mechanism of improving patency in small caliber vascular grafts. However the majority of seeded EC are lost within 24 hours of restoration of blood flow in previous canine studies . We postulate that the cells have insufficient time to fully develop their attachment to the graft surface prior to exposure to hemodynamic stress. We allowed EC to incubate on fibronectin-coated ePTFE grafts for four different time periods after seeding and measured EC retention after perfusion in a canine ex vivo shunt circuit.Autologous canine EC, were enzymatically harvested, grown to confluence, and labeled with 30 μCi 111 Indium-oxine/80 cm 2 flask. Four groups of 5 cm x 4 mm ID ePTFE vascular prostheses were coated with 1.5 μg/cm.2 human fibronectin, and seeded with 1.5 x 105 EC/ cm.2. After seeding grafts in Group 1 were incubated in complete growth medium for 90 minutes, Group 2 were incubated for 24 hours, Group 3 for 72 hours and Group 4 for 6 days. Grafts were then placed in the canine ex vivo circuit, constructed between femoral artery and vein, and subjected to blood flow of 75 ml per minute for 6 hours. Continuous counting of γ-activity was made possible by placing the seeded graft inside the γ-counter detection crystal for the duration of perfusion. EC retention data after 30 minutes, 2 hours and 6 hours of flow are shown in the table.

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.

Ultrastructural Immunocytochemistry of Five Rat Pituitary Adenomas

1980 ◽  
Vol 38 ◽  
pp. 724-725
Author(s):  
D. J. McComb ◽  
N. Ryan ◽  
E. Horvath ◽  
K. Kovacs ◽  
E. Nagy ◽  
...  
Keyword(s):  
Pituitary Adenomas ◽  
Pituitary Tumors ◽  
Electron Microscopic ◽  
Electron Microscopic Immunocytochemistry ◽  
Transmission Electron ◽  
Rat Pituitary ◽  
Radiation Induced ◽  
Group 5 ◽  
Group 2 ◽  
Microscopic Techniques

Conventional light and electron microscopic techniques failed to clarify the cellular composition and derivation of spontaneous and induced, intrasellar and transplanted pituitary adenomas in rats (1). In the present work, electron microscopic immunocytochemistry was applied to evaluate five adenohypo-physial tumors using a technique described by Moriarty and Garner (2). Spontaneously occurring pituitary adenomas (group 1) were harvested from aging female Long-Evans rats. R-Amsterdam rats were treated with 2 x 1.0 mg estrone acetate (HogivaI) s.c. weekly for 6 months. Pituitary adenomas in excess of 30 mg were removed from these animals to make up the tumors of group 2. Groups 3 and 4 consisted of estrogen-induced autonomous transplan¬ted pituitary tumors MtT.WlO and MtT.F4. Group 5 was a radiation-induced transplanted autonomous pituitary tumor MtT.W5. The tumors of groups 3,4 and 5 were allowed to proliferate in host rats 6-8 weeks prior to removal for processing. Tissue was processed for transmission electron microscopy (glutaraldehyde fixation, OsO4 postfixation and epoxy resin embedding), and electron microscopic immunocytochemistry (3% paraformaldehyde fixation and Araldite embedding).

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