scholarly journals The Lattice Structure of L-Contact Relations

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Xueyou Chen
Keyword(s):  
Algebraic Structure ◽  
Lattice Structure ◽  
Point Of View ◽  
Symmetric Relations ◽  
Contact Relation

From the point of view of graded truth approach, we define the notion of a contact relation on the collection of allL-sets, discuss the connection to the set of all close, reflexive, and symmetric relations on allL-ultrafilters onX, and investigate the algebraic structure of allL-contact relations.

scholarly journals Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 417 ◽  
Author(s):  
Hu Zhao ◽  
Hong-Ying Zhang
Keyword(s):  
Algebraic Structure ◽  
Rough Sets ◽  
Lattice Structure ◽  
Single Domain ◽  
One Dimensional ◽  
Basic Properties ◽  
Approximation Operators ◽  
Rough Approximation ◽  
The One ◽  
Comprehensive Study

As a generalization of single value neutrosophic rough sets, the concept of multi-granulation neutrosophic rough sets was proposed by Bo et al., and some basic properties of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators were studied. However, they did not do a comprehensive study on the algebraic structure of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators. In the present paper, we will provide the lattice structure of the pessimistic multigranulation neutrosophic rough approximation operators. In particular, in the one-dimensional case, for special neutrosophic relations, the completely lattice isomorphic relationship between upper neutrosophic rough approximation operators and lower neutrosophic rough approximation operators is proved.

Finite Element Analysis to Predict the Mechanical Behavior of Lattice Structures Made by Selective Laser Melting Technology

2014 ◽  
Vol 657 ◽  
pp. 231-235 ◽  
Author(s):  
Răzvan Păcurar ◽  
Ancuţa Păcurar ◽  
Anna Petrilak ◽  
Nicolae Bâlc
Keyword(s):  
Finite Element ◽  
Mechanical Behavior ◽  
Selective Laser Melting ◽  
Lattice Structure ◽  
Point Of View ◽  
Mechanical Resistance ◽  
Lattice Structures ◽  
Laser Melting ◽  
Element Analysis ◽  
Medical Implant

Within this article, there are presented a series of researches that are related to the field of customized medical implants made by Additive Manufacturing techniques, such as Selective Laser Melting (SLM) technology. Lattice structures are required in this case for a better osteointegration of the medical implant in the contact area of the bone. But the consequence of using such structures is important also by the mechanical resistance point of view. The shape and size of the cells that are connected within the lattice structure to be manufactured by SLM is critical in this case. There are also few limitations related to the possibilities and performances of the SLM equipment, as well. This is the reason why, several types of lattice structures were designed as having different geometric features, with the aim of analyzing by using finite element method, how the admissible stress and strain will be varied in these cases and what would be the optimum size and shape of the cells that confers the optimum mechanical behavior of lattice structures used within the SLM process of the customized medical implant manufactured from titanium-alloyed materials.

scholarly journals Lattice Structure of Some Closed Classes for Three-Valued Logic and Its Applications

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 94
Author(s):  
Elmira Yu. Kalimulina
Keyword(s):  
Heterogeneous Computing ◽  
Closure Operator ◽  
Lattice Structure ◽  
Point Of View ◽  
Theoretical Problem ◽  
Computing Systems ◽  
Dummy Variables ◽  
Finite Set ◽  
Heterogeneous Computing Systems ◽  
Class Of Functions

This paper provides a brief overview of modern applications of nonbinary logic models, where the design of heterogeneous computing systems with small computing units based on three-valued logic produces a mathematically better and more effective solution compared to binary models. For application, it is necessary to implement circuits composed of chipsets, the operation of which is based on three-valued logic. To be able to implement such schemes, a fundamentally important theoretical problem must be solved: the problem of completeness of classes of functions of three-valued logic. From a practical point of view, the completeness of the class of such functions ensures that circuits with the desired operations can be produced from an arbitrary (finite) set of chipsets. In this paper, the closure operator on the set of functions of three-valued logic that strengthens the usual substitution operator is considered. It is shown that it is possible to recover the sublattice of closed classes in the general case of closure of functions with respect to the classical superposition operator. The problem of the lattice of closed classes for the class of functions T2 preserving two is considered. The closure operators R1 for the functions that differ only by dummy variables are considered equivalent. This operator is withiin the scope of interest of this paper. A lattice is constructed for closed subclasses in T2={f|f(2,…,2)=2}, a class of functions preserving two.

SLIT-WAVE MODEL FOR BAND STRUCTURES IN SOLID STATE PHYSICS

2011 ◽  
Vol 25 (03) ◽  
pp. 151-161
Author(s):  
I. B. TAHIRBEGI ◽  
M. MIR
Keyword(s):  
State Physics ◽  
Solid State ◽  
Band Structure ◽  
Lattice Structure ◽  
Wave Model ◽  
Point Of View ◽  
Solid State Physics ◽  
Atomic Diameter ◽  
Diffraction Patterns ◽  
Wave Properties

The reason behind the entire development in silicon technology was band models in solid state physics. However, the theories postulated in order to give response to this phenomenon do not explain all kinds of materials. In a bid to overcome this limitation, we approach the problem from another point of view. In this work, the wave properties of the electrons from the external orbitals of the atoms and its diffraction patterns through the lattice structure of the material have been used to explain the band structure of metals, semiconductor and insulators. In order to probe this hypothesis, a simulation has been used and according to the relation between the lattice constant and the atomic diameter, the splitting of the bands have been observed for different kind of materials, showing a strong correlation between the simulation and the experimental results.

Unique decomposition of homogeneous languages and application to isothetic regions

2018 ◽  
Vol 29 (5) ◽  
pp. 681-730
Author(s):  
EMMANUEL HAUCOURT ◽  
NICOLAS NININ
Keyword(s):  
Algebraic Structure ◽  
Geometric Model ◽  
Geometric Realization ◽  
Point Of View ◽  
Boolean Algebras ◽  
Theoretical Point ◽  
Prime Decomposition ◽  
Unique Decomposition ◽  
Algebraic Properties ◽  
Factoring Algorithm

A language is said to be homogeneous when all its words have the same length. Homogeneous languages thus form a monoid under concatenation. It becomes freely commutative under the simultaneous actions of every permutation group on the collection of homogeneous languages of length n ∈ ℕ. One recovers the isothetic regions from (Haucourt 2017, to appear (online since October 2017)) by considering the alphabet of connected subsets of the space |G|, viz the geometric realization of a finite graph G. Factoring the geometric model of a conservative program amounts to parallelize it, and there exists an efficient factoring algorithm for isothetic regions. Yet, from the theoretical point of view, one wishes to go beyond the class of conservative programs, which implies relaxing the finiteness hypothesis on the graph G. Provided that the collections of n-dimensional isothetic regions over G (denoted by |G|) are co-unital distributive lattices, the prime decomposition of isothetic regions is given by an algorithm which is, unfortunately, very inefficient. Nevertheless, if the collections |G| satisfy the stronger property of being Boolean algebras, then the efficient factoring algorithm is available again. We relate the algebraic properties of the collections |G| to the geometric properties of the space |G|. On the way, the algebraic structure |G| is proven to be the universal tensor product, in the category of semilattices with zero, of n copies of the algebraic structure |G|.

Scalar Actions

1983 ◽  
Vol 35 (4) ◽  
pp. 750-768
Author(s):  
A. Lebow ◽  
M. Schreiber
Keyword(s):  
Abelian Group ◽  
Algebraic Structure ◽  
Ring Homomorphism ◽  
Space Structure ◽  
Point Of View ◽  
Identity Operator ◽  
Representation Space ◽  
New Space ◽  
The Subject ◽  
Scalar Action

The subject of this paper arises from the familiar process whereby an automorphism of a field generates new representations from old. One may think of that process spatially, as a change of vector space structure in the representation space by means of the automorphism. The operators of the representation acting in the “new“ space then constitute the new representation. This point of view makes visible an algebraic structure we call a scalar action. A scalar action f of a ring R (with unity) in an abelian group Kis a ring homomorphism f:R → End(V) taking the unity element of R to the identity operator in End(V). If f is a scalar action of a field F and ϕ is an automorphism of F then f ∘ ϕ is another scalar action of F, and it is this construction which is used to define the “new” representation space mentioned above. But the variety of scalar actions goes rather beyond that construction.

scholarly journals Quasisymmetric functions from a topological point of view

2008 ◽  
Vol 103 (2) ◽  
pp. 208 ◽  
Author(s):  
Andrew Baker ◽  
Birgit Richter
Keyword(s):  
Algebraic Structure ◽  
Symmetric Functions ◽  
Point Of View ◽  
Classifying Space ◽  
Quasisymmetric Functions ◽  
Witt Vector ◽  
Algebraic Properties ◽  
Vector Structure ◽  
Topological Hochschild Homology ◽  
Shed Light

It is well-known that the homology of the classifying space of the unitary group is isomorphic to the ring of symmetric functions $\mathsf {Symm}$. We offer the cohomology of the space $\Omega \Sigma {\mathsf C} P^{\infty}$ as a topological model for the ring of quasisymmetric functions $\mathsf {QSymm}$. We exploit standard results from topology to shed light on some of the algebraic properties of $\mathsf {QSymm}$. In particular, we reprove the Ditters conjecture. We investigate a product on $\Omega \Sigma {\mathsf C} P^{\infty}$ that gives rise to an algebraic structure which generalizes the Witt vector structure in the cohomology of $BU$. The canonical Thom spectrum over $\Omega \Sigma {\mathsf C} P^{\infty}$ is highly non-commutative and we study some of its features, including the homology of its topological Hochschild homology spectrum.

THE LATTICE STRUCTURE OF PRERADICALS II: PARTITIONS

2002 ◽  
Vol 01 (02) ◽  
pp. 201-214 ◽  
Author(s):  
FRANCISCO RAGGI ◽  
JOSÉ RÍOS ◽  
HUGO RINCÓN ◽  
ROGELIO FERNÁNDEZ-ALONSO ◽  
CARLOS SIGNORET
Keyword(s):  
Lattice Point ◽  
Lattice Structure ◽  
Point Of View

We continue the study of the preradicals of a ring in the lattice point of view. We introduce several interesting preradicals associated to a given preradical and some partitions of the whole lattice in terms of preradicals. As an application, we also give some classification theorems.

The Geosciences Applied to Lunar Exploration

1962 ◽  
Vol 14 ◽  
pp. 169-257 ◽  
Author(s):  
J. Green
Keyword(s):  
Lunar Surface ◽  
Probable Mechanism ◽  
Point Of View ◽  
Lunar Exploration ◽  
Geological Model ◽  
Apply Geophysics ◽  
Surface Features ◽  
The Impact

The term geo-sciences has been used here to include the disciplines geology, geophysics and geochemistry. However, in order to apply geophysics and geochemistry effectively one must begin with a geological model. Therefore, the science of geology should be used as the basis for lunar exploration. From an astronomical point of view, a lunar terrain heavily impacted with meteors appears the more reasonable; although from a geological standpoint, volcanism seems the more probable mechanism. A surface liberally marked with volcanic features has been advocated by such geologists as Bülow, Dana, Suess, von Wolff, Shaler, Spurr, and Kuno. In this paper, both the impact and volcanic hypotheses are considered in the application of the geo-sciences to manned lunar exploration. However, more emphasis is placed on the volcanic, or more correctly the defluidization, hypothesis to account for lunar surface features.

How a sheperd guides a sheep herd?

1984 ◽  
Vol 75 ◽  
pp. 331-337
Author(s):  
Richard Greenberg
Keyword(s):  
Point Of View ◽  
Single Ring ◽  
Damping Effects ◽  
Ring Particle

ABSTRACTThe mechanism by which a shepherd satellite exerts a confining torque on a ring is considered from the point of view of a single ring particle. It is still not clear how one might most meaningfully include damping effects and other collisional processes into this type of approach to the problem.

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