scholarly journals Hybrid Structures Applied to Ideals in BCI-Algebras

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
G. Muhiuddin ◽  
D. Al-Kadi ◽  
A. Mahboob
Keyword(s):  
Hybrid Structure ◽  
Ideal Theory ◽  
Hybrid Structures ◽  
The Ideal

In this paper, the notion of hybrid structure is applied to the ideal theory in BCI-algebras. In fact, we introduce the notions of hybrid p -ideal, hybrid h-ideal, and hybrid a-ideal in BCI-algebras and investigate their related properties. Furthermore, we show that every hybrid p -ideal (or h-ideal or a-ideal) is a hybrid ideal in a BCI-algebra but converse need not be true in general and in support, and we exhibit counter examples for each case. Moreover, we consider characterizations of hybrid p -ideal, hybrid h-ideal, and hybrid a-ideal in BCI-algebras.

scholarly journals Hybrid structures applied to ideals in near-rings

2021 ◽  
Author(s):  
B. Elavarasan ◽  
G. Muhiuddin ◽  
K. Porselvi ◽  
Y. B. Jun
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Real World ◽  
Rough Set Theory ◽  
Wide Spectrum ◽  
Hybrid Structure ◽  
Soft Set ◽  
Hybrid Structures ◽  
Classical Mathematics ◽  
Classical Means

AbstractHuman endeavours span a wide spectrum of activities which includes solving fascinating problems in the realms of engineering, arts, sciences, medical sciences, social sciences, economics and environment. To solve these problems, classical mathematics methods are insufficient. The real-world problems involve many uncertainties making them difficult to solve by classical means. The researchers world over have established new mathematical theories such as fuzzy set theory and rough set theory in order to model the uncertainties that appear in various fields mentioned above. In the recent days, soft set theory has been developed which offers a novel way of solving real world issues as the issue of setting the membership function does not arise. This comes handy in solving numerous problems and many advancements are being made now-a-days. Jun introduced hybrid structure utilizing the ideas of a fuzzy set and a soft set. It is to be noted that hybrid structures are a speculation of soft set and fuzzy set. In the present work, the notion of hybrid ideals of a near-ring is introduced. Significant work has been carried out to investigate a portion of their significant properties. These notions are characterized and their relations are established furthermore. For a hybrid left (resp., right) ideal, different left (resp., right) ideal structures of near-rings are constructed. Efforts have been undertaken to display the relations between the hybrid product and hybrid intersection. Finally, results based on homomorphic hybrid preimage of a hybrid left (resp., right) ideals are proved.

scholarly journals Topological Atomic Chains on 2D Hybrid Structure

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3289
Author(s):  
Tomasz Kwapiński ◽  
Marcin Kurzyna
Keyword(s):  
Tight Binding ◽  
Wide Band ◽  
Hybrid Structure ◽  
Spectral Density Function ◽  
Hybrid Structures ◽  
Function Technique ◽  
Edge States ◽  
Surface Singularities ◽  
Atomic Chains ◽  
Topological States

Mid-gap 1D topological states and their electronic properties on different 2D hybrid structures are investigated using the tight binding Hamiltonian and the Green’s function technique. There are considered straight armchair-edge and zig-zag Su–Schrieffer–Heeger (SSH) chains coupled with real 2D electrodes which density of states (DOS) are characterized by the van Hove singularities. In this work, it is shown that such 2D substrates substantially influence topological states end evoke strong asymmetry in their on-site energetic structures, as well as essential modifications of the spectral density function (local DOS) along the chain. In the presence of the surface singularities the SSH topological state is split, or it is strongly localized and becomes dispersionless (tends to the atomic limit). Additionally, in the vicinity of the surface DOS edges this state is asymmetrical and consists of a wide bulk part together with a sharp localized peak in its local DOS structure. Different zig-zag and armachair-edge configurations of the chain show the spatial asymmetry in the chain local DOS; thus, topological edge states at both chain ends can appear for different energies. These new effects cannot be observed for ideal wide band limit electrodes but they concern 1D topological states coupled with real 2D hybrid structures.

A Hesitant Intuitionistic Fuzzy Set Approach to Study Ideals of Semirings

2021 ◽  
Vol 10 (3) ◽  
pp. 1-17
Author(s):  
Debabrata Mandal
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Set ◽  
Ideal Theory ◽  
Hesitant Fuzzy Set ◽  
Neutrosophic Set ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
The Ideal

The classical set theory was extended by the theory of fuzzy set and its several generalizations, for example, intuitionistic fuzzy set, interval valued fuzzy set, cubic set, hesitant fuzzy set, soft set, neutrosophic set, etc. In this paper, the author has combined the concepts of intuitionistic fuzzy set and hesitant fuzzy set to study the ideal theory of semirings. After the introduction and the priliminary of the paper, in Section 3, the author has defined hesitant intuitionistic fuzzy ideals and studied several properities of it using the basic operations intersection, homomorphism and cartesian product. In Section 4, the author has also defined hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals of a semiring and used these to find some characterizations of regular semiring. In that section, the author also has discussed some inter-relations between hesitant intuitionistic fuzzy ideals, hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals, and obtained some of their related properties.

The Foundations of the Ideal Theory of Zolotarev

1930 ◽  
Vol 37 (3) ◽  
pp. 117 ◽  
Author(s):  
N. Tchebotarev
Keyword(s):  
Ideal Theory ◽  
The Ideal

scholarly journals Bivariate Lagrange interpolation at the Padua points: the ideal theory approach

2007 ◽  
Vol 108 (1) ◽  
pp. 43-57 ◽  
Author(s):  
Len Bos ◽  
Stefano De Marchi ◽  
Marco Vianello ◽  
Yuan Xu
Keyword(s):  
Lagrange Interpolation ◽  
Ideal Theory ◽  
Theory Approach ◽  
Padua Points ◽  
The Ideal

Bridging Ideal and Non-Ideal Theory

2017 ◽  
Vol 66 (4) ◽  
pp. 887-902 ◽  
Author(s):  
Alexandru Volacu
Keyword(s):  
Political Theory ◽  
Ideal Theory ◽  
Two Dimensional ◽  
Current State ◽  
The World ◽  
Normative Models ◽  
The Ideal

Many of the recent methodological debates within political theory have focused on the ideal/non-ideal theory distinction. While ideal theorists recognise the need to develop an account of the transition between the two levels of theorising, no general proposal has been advanced thus far. In this article, I aim to bridge this conceptual gap. Towards this end, I first reconstruct the ideal/non-ideal theory distinction within a simplified two-dimensional framework, which captures the primary meanings usually attributed to it. Subsequently, I use this framework to provide an algorithm for the bidirectional transition between ideal and non-ideal theory, based on the incremental derivation of normative models. The approach outlined illuminates the various ways in which principles derived under highly idealised assumptions might be distorted by the circumstances of our current world and illustrates the various paths which we can pursue in moving from our current state of the world to an ideal one.

The Foundations of the Ideal Theory of Zolotarev

1930 ◽  
Vol 37 (3) ◽  
pp. 117-128
Author(s):  
N. Tchebotarev
Keyword(s):  
Ideal Theory ◽  
The Ideal

scholarly journals Degenerations of the generic square matrix, the polar map and the determinantal structure

2018 ◽  
Vol 28 (07) ◽  
pp. 1255-1297 ◽  
Author(s):  
Rainelly Cunha ◽  
Zaqueu Ramos ◽  
Aron Simis
Keyword(s):  
Hessian Matrix ◽  
Main Tool ◽  
Affirmative Answer ◽  
Ideal Theory ◽  
Geometric Means ◽  
The Matrix ◽  
Hessian Determinant ◽  
The Ideal ◽  
Polar Map ◽  
Square Matrix

One studies certain degenerations of the generic square matrix over a field [Formula: see text] along with its main related structures, such as the determinant of the matrix, the ideal generated by its partial derivatives, the polar map defined by these derivatives, the Hessian matrix and the ideal of the submaximal minors of the matrix. The main tool comes from commutative algebra, with emphasis on ideal theory and syzygy theory. The structure of the polar map is completely identified and the main properties of the ideal of submaximal minors are determined. Cases where the degenerated determinant has non-vanishing Hessian determinant show that the former is a factor of the latter with the (Segre) expected multiplicity, a problem envisaged by Landsberg–Manivel–Ressayre by geometric means. Another byproduct is an affirmative answer to a question of F. Russo concerning the codimension in the polar image of the dual variety to a hypersurface.

Optimization Design of Core Thickness of Exterior Frame and Core Hybrid Structures in High-Rise Buildings

2012 ◽  
Vol 166-169 ◽  
pp. 14-18
Author(s):  
Shu Yun Zhang ◽  
Wen Wei Zhao ◽  
Hai Hua Wang
Keyword(s):  
Seismic Response ◽  
Optimization Design ◽  
Dynamic Properties ◽  
Response Spectrum ◽  
Optimization Method ◽  
Hybrid Structure ◽  
Hybrid Structures ◽  
Response Analysis ◽  
High Rise ◽  
Core Thickness

Considering core thickness is important issue to performance of exterior frame and core hybrid structure in high-rise buildings, seismic response analysis is conducted by response spectrum method for finite element models with different core thickness. The optimization design of core thickness of hybrid Structures on the basis of the seismic response is studied, the core thicknesses are chosen as design variables, the objective function about core volume is adopted, some specification requirements such as deformation, the ratio of lateral stiffness to gravity, storey shear to gravity, storey shear of exterior frame, axial compression ratio of column and wall limb, bearing capacity of structural member and core construction are regarded as restricting conditions, the optimal mathematical model is established for reflecting integrity dynamic properties of hybrid structure. The ANSYS software is used for optimizing tool, the hybrid structures optimization design are made through different initial values for verifying convergence of optimization method, the optimal result show that the performances of hybrid structure are improved, the internal forces are reduced and the ratios of inner force born by exterior frames are increased in the optimal scheme.

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