scholarly journals A Kind of Variation Symmetry: Tarski Associative Groupoids (TA-Groupoids) and Tarski Associative Neutrosophic Extended Triplet Groupoids (TA-NET-Groupoids)

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 714
Author(s):  
Xiaohong Zhang ◽  
Wangtao Yuan ◽  
Mingming Chen ◽  
Florentin Smarandache
Keyword(s):  
Associative Ring ◽  
Disjoint Union ◽  
Structural Characteristics ◽  
Basic Properties ◽  
Generalized Symmetries ◽  
Associative Law

The associative law reflects symmetry of operation, and other various variation associative laws reflect some generalized symmetries. In this paper, based on numerous literature and related topics such as function equation, non-associative groupoid and non-associative ring, we have introduced a new concept of Tarski associative groupoid (or transposition associative groupoid (TA-groupoid)), presented extensive examples, obtained basic properties and structural characteristics, and discussed the relationships among few non-associative groupoids. Moreover, we proposed a new concept of Tarski associative neutrosophic extended triplet groupoid (TA-NET-groupoid) and analyzed related properties. Finally, the following important result is proved: every TA-NET-groupoid is a disjoint union of some groups which are its subgroups.

scholarly journals Study of Two Kinds of Quasi AG-Neutrosophic Extended Triplet Loops

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xiaogang An ◽  
Mingming Chen
Keyword(s):  
Structural Characteristics ◽  
Algebraic Structures ◽  
Basic Properties ◽  
Generalized Symmetries

Abel-Grassmann’s groupoid and neutrosophic extended triplet loop are two important algebraic structures that describe two kinds of generalized symmetries. In this paper, we investigate quasi AG-neutrosophic extended triplet loop, which is a fusion structure of the two kinds of algebraic structures mentioned above. We propose new notions of AG-(l,r)-Loop and AG-(r,l)-Loop, deeply study their basic properties and structural characteristics, and prove strictly the following statements: (1) each strong AG-(l,r)-Loop can be represented as the union of its disjoint sub-AG-groups, (2) the concepts of strong AG-(l,r)-Loop, strong AG-(l,l)-Loop, and AG-(l,lr)-Loop are equivalent, and (3) the concepts of strong AG-(r,l)-Loop and strong AG-(r,r)-Loop are equivalent.

scholarly journals Symmetry in Hyperstructure: Neutrosophic Extended Triplet Semihypergroups and Regular Hypergroups

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1217 ◽  
Author(s):  
Xiaohong Zhang ◽  
Florentin Smarandache ◽  
Yingcang Ma
Keyword(s):  
Disjoint Union ◽  
Basic Properties ◽  
New Concepts

The symmetry of hyperoperation is expressed by hypergroup, more extensive hyperalgebraic structures than hypergroups are studied in this paper. The new concepts of neutrosophic extended triplet semihypergroup (NET- semihypergroup) and neutrosophic extended triplet hypergroup (NET-hypergroup) are firstly introduced, some basic properties are obtained, and the relationships among NET- semihypergroups, regular semihypergroups, NET-hypergroups and regular hypergroups are systematically are investigated. Moreover, pure NET-semihypergroup and pure NET-hypergroup are investigated, and a strucuture theorem of commutative pure NET-semihypergroup is established. Finally, a new notion of weak commutative NET-semihypergroup is proposed, some important examples are obtained by software MATLAB, and the following important result is proved: every pure and weak commutative NET-semihypergroup is a disjoint union of some regular hypergroups which are its subhypergroups.

scholarly journals The Polypermutation Group of an Associative Ring

2021 ◽  
Author(s):  
Jason K. C. Polak
Keyword(s):  
Associative Ring ◽  
Permutation Polynomials ◽  
Basic Properties

We study permutation polynomials through the device of the polypermutation group of an associative ring R, denoted by Pgr(R). We derive some basic properties and compute the cardinality of Pgr(Z/pk ) when p ≥ k. We use this computation to determine the structure of Pgr(Z/p2 ).

F-µ-Semiregular Modules

2021 ◽  
pp. 1271-1275
Author(s):  
Eman Mohammed ◽  
Wasan Khalid
Keyword(s):  
Associative Ring ◽  
Basic Properties

Let  R be an associative ring with identity and let M be a left R-module . As a generalization of µ-semiregular modules, we introduce an F-µ-semiregular module. Let F be a submodule of M and x∊M. x is called F-µ-semiregular element in M , if there exists a decomposition M=A⨁B, such that A is a projective submodule of  and . M is called  F-µ-semiregular if x is F-µ-semiregular element for each x∊M. A condition under which the module µ-semiregular is F-µ-semiregular module was given. The basic properties and some characterizations of the F-µ-semiregular module were provided.

scholarly journals On Semiannahilator Supplement Submodules

2020 ◽  
pp. 16-20
Author(s):  
Layla H. Helal ◽  
Sahira M. Yaseen
Keyword(s):  
Associative Ring ◽  
Basic Properties ◽  
Supplement Submodule

Let R be associative; ring; with an identity and let D be unitary left R- module; . In this work we present semiannihilator; supplement submodule as a generalization of R-a- supplement submodule, Let U and V be submodules of an R-module D if D=U+V and whenever Y≤ V and D=U+Y, then annY≪R;. We also introduce the the concept of semiannihilator -supplemented ;modules and semiannihilator weak; supplemented modules, and we give some basic properties of this conseptes.

A High Resolution Study of G.P. Zones in Aluminum - 4.2 at % Silver

1982 ◽  
Vol 40 ◽  
pp. 722-723 ◽  
Author(s):  
R. Gronsky
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
High Resolution ◽  
Computer Simulations ◽  
Structural Characteristics ◽  
X Ray Diffraction ◽  
X Ray ◽  
Transmission Electron ◽  
Resolution Study

The phenomenon of clustering in Al-Ag alloys has been extensively studied since the early work of Guinierl, wherein the pre-precipitation state was characterized as an assembly of spherical, ordered, silver-rich G.P. zones. Subsequent x-ray and TEM investigations yielded results in general agreement with this model. However, serious discrepancies were later revealed by the detailed x-ray diffraction - based computer simulations of Gragg and Cohen, i.e., the silver-rich clusters were instead octahedral in shape and fully disordered, atleast below 170°C. The object of the present investigation is to examine directly the structural characteristics of G.P. zones in Al-Ag by high resolution transmission electron microscopy.

SEM analysis of the change in the reaction rates with deposit structures in the copper-iron cementation system

1978 ◽  
Vol 36 (1) ◽  
pp. 456-457
Author(s):  
V. Annamalai ◽  
L.E. Murr
Keyword(s):  
Structural Characteristics ◽  
Secondary Electron Emission ◽  
Copper Deposit ◽  
Reaction Rates ◽  
Sem Analysis ◽  
Experimental Conditions ◽  
Major Drawback ◽  
Emission Mode ◽  
Scrap Iron ◽  
Image Position

Economical recovery of copper metal from leach liquors has been carried out by the simple process of cementing copper onto a suitable substrate metal, such as scrap-iron, since the 16th century. The process has, however, a major drawback of consuming more iron than stoichiometrically needed by the reaction.Therefore, many research groups started looking into the process more closely. Though it is accepted that the structural characteristics of the resultant copper deposit cause changes in reaction rates for various experimental conditions, not many systems have been systematically investigated. This paper examines the deposit structures and the kinetic data, and explains the correlations between them.A simple cementation cell along with rotating discs of pure iron (99.9%) were employed in this study to obtain the kinetic results The resultant copper deposits were studied in a Hitachi Perkin-Elmer HHS-2R scanning electron microscope operated at 25kV in the secondary electron emission mode.

Use of 2½ D imaging in analysis of NiTi martensite

1978 ◽  
Vol 36 (1) ◽  
pp. 610-611
Author(s):  
G. M. Michal
Keyword(s):  
Memory Effect ◽  
Monoclinic Phase ◽  
Reaction Path ◽  
Structural Characteristics ◽  
Salient Feature ◽  
Martensite Phase ◽  
Orientation Relationships ◽  
Low Symmetry ◽  
Hydride Phases ◽  
Unusual Shape

Several TEM investigations have attempted to correlate the structural characteristics to the unusual shape memory effect in NiTi, the consensus being the essence of the memory effect is ostensible manifest in the structure of NiTi transforming martensitic- ally from a B2 ordered lattice to a low temperature monoclinic phase. Commensurate with the low symmetry of the martensite phase, many variants may form from the B2 lattice explaining the very complex transformed microstructure. The microstructure may also be complicated by the enhanced formation of oxide or hydride phases and precipitation of intermetallic compounds by electron beam exposure. Variants are typically found in selfaccommodation groups with members of a group internally twinned and the twins themselves are often observed to be internally twinned. Often the most salient feature of a group of variants is their close clustering around a given orientation. Analysis of such orientation relationships may be a key to determining the nature of the reaction path that gives the transformation its apparently perfect reversibility.

Use of light microscopy in the qualitative and quantitative study of liquid crystalline order

1992 ◽  
Vol 50 (1) ◽  
pp. 264-265
Author(s):  
Christopher Viney
Keyword(s):  
Light Microscopy ◽  
Liquid Crystalline ◽  
Structural Characteristics ◽  
Molecular Order ◽  
Liquid Crystalline Phases ◽  
Convenient Technique ◽  
Liquid Crystalline Materials ◽  
Transparent Windows

Light microscopy is a convenient technique for characterizing molecular order in fluid liquid crystalline materials. Microstructures can usually be observed under the actual conditions that promote the formation of liquid crystalline phases, whether or not a solvent is required, and at temperatures that can range from the boiling point of nitrogen to 600°C. It is relatively easy to produce specimens that are sufficiently thin and flat, simply by confining a droplet between glass cover slides. Specimens do not need to be conducting, and they do not have to be maintained in a vacuum. Drybox or other controlled environmental conditions can be maintained in a sealed chamber equipped with transparent windows; some heating/ freezing stages can be used for this purpose. It is relatively easy to construct a modified stage so that the generation and relaxation of global molecular order can be observed while specimens are being sheared, simulating flow conditions that exist during processing. Also, light only rarely affects the chemical composition or molecular weight distribution of the sample. Because little or no processing is required after collecting the sample, one can be confident that biologically derived materials will reveal many of their in vivo structural characteristics, even though microscopy is performed in vitro.

Ascidian Mitochondrial tRNAMet Possessing Unique Structural Characteristics

1998 ◽  
Vol 17 (1) ◽  
pp. 531-539 ◽  
Author(s):  
Akiko Kondow ◽  
Shin-ichi Yokobori ◽  
Takuya Ueda ◽  
Kimitsuna Watanabe
Keyword(s):  
Structural Characteristics
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