scholarly journals Some fundamental properties of fuzzy linear relations between vector spaces

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 41-53 ◽  
Author(s):  
Sorin Nădăbana
Keyword(s):  
Linear Relation ◽  
Scalar Multiplication ◽  
Vector Spaces ◽  
Fuzzy Relations ◽  
Linear Relations ◽  
Fundamental Properties ◽  
The Family ◽  
Natural Way

This paper aims at studying the fundamental properties of fuzzy linear relations between vector spaces. The sum of two fuzzy relations and the scalar multiplication are defined, in a natural way, and some properties of this operations are established. Fuzzy linear relations are investigated and among the results obtained, there should be underlined a characterization of fuzzy linear relations and the fact that the inverse of a fuzzy linear relation is also a fuzzy linear relation. Moreover, the paper shows that the composition of two fuzzy linear relations is a fuzzy linear relation as well. Finally, the article highlights that the family of all fuzzy linear relations is closed under addition and it is closed under scalar multiplication.

Left-right fredholm and left-right browder linear relations

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 255-271 ◽  
Author(s):  
T. Álvarez ◽  
Fatma Fakhfakh ◽  
Maher Mnif
Keyword(s):  
Banach Space ◽  
Finite Rank ◽  
Linear Relation ◽  
Finite Rank Operator ◽  
Linear Relations ◽  
Rank Operator ◽  
Type Decomposition ◽  
Converse Results

In this paper we introduce the notions of left (resp. right) Fredholm and left (resp. right) Browder linear relations. We construct a Kato-type decomposition of such linear relations. The results are then applied to give another decomposition of a left (resp. right) Browder linear relation T in a Banach space as an operator-like sum T = A + B, where A is an injective left (resp. a surjective right) Fredholm linear relation and B is a bounded finite rank operator with certain properties of commutativity. The converse results remain valid with certain conditions of commutativity. As a consequence, we infer the characterization of left (resp. right) Browder spectrum under finite rank operator.

scholarly journals The Local spectral theory and surjective spectrum of linear relations

2021 ◽  
Vol 73 (2) ◽  
pp. 222-237
Author(s):  
M. Mnif ◽  
A.-A. Ouled-Hmed
Keyword(s):  
Banach Space ◽  
Spectral Theory ◽  
Linear Relation ◽  
Local Spectrum ◽  
Linear Relations ◽  
Analytic Core ◽  
Local Spectral Theory

UDC 517.98 This paper initiates a study of local spectral theory for linear relations. At the beginning, we define the local spectrum and study its properties. Then we obtain results related to the correlation analytic core and quasinilpotent part of a linear relation in a Banach space . As an application, we give a characterization of the surjective spectrum in terms of the local spectrum and show that if , then does not cluster at .

Prothrombin Metz : Purification and Characterization of a Variant of Human Prothrombin

1979 ◽  
Author(s):  
M Ribieto ◽  
J Elion ◽  
D Labie ◽  
F Josso
Keyword(s):  
Molecular Weight ◽  
Gel Electrophoresis ◽  
Polyacrylamide Gel Electrophoresis ◽  
Factor Xa ◽  
Polyacrylamide Gel ◽  
Cleavage Pattern ◽  
Purification And Characterization ◽  
Double Immunodiffusion ◽  
The Family

For the purification of the abnormal prothrombin (Pt Metz), advantage has been taken of the existence in the family of three siblings who, being double heterozygotes for Pt Metz and a hypoprothrombinemia, have no normal Pt. Purification procedures included barium citrate adsorption and chromatography on DEAE Sephadex as for normal Pt. As opposed to some other variants (Pt Barcelona and Madrid), Pt Metz elutes as a single symetrical peak. By SDS polyacrylamide gel electrophoresis, this material is homogeneous and appears to have the same molecular weight as normal Pt. Comigration of normal and abnormal Pt in the absence of SDS, shows a double band suggesting an abnormal charge for the variant. Pt Metz exhibits an identity reaction with the control by double immunodiffusion. Upon activation by factor Xa, Pt Metz can generate amydolytic activity on Bz-Phe-Val-Arg-pNa (S2160), but only a very low clotting activity. Clear abnormalities are observed in the cleavage pattern of Pt Metz when monitored by SDS gel electrophoresis. The main feature are the accumulation of prethrombin l (Pl) and the appearance of abnormal intermediates migrating faster than Pl.

Induced L-bornological vector spaces and L-Mackey convergence1

2021 ◽  
Vol 40 (1) ◽  
pp. 1277-1285
Author(s):  
Zhen-yu Jin ◽  
Cong-hua Yan
Keyword(s):  
Complete Lattice ◽  
Vector Spaces ◽  
Specific Description ◽  
Equivalent Characterization ◽  
Fuzzy Setting

Motivated by the concept of lattice-bornological vector spaces of J. Paseka, S. Solovyov and M. Stehlík, which extends bornological vector spaces to the fuzzy setting over a complete lattice, this paper continues to study the theory of L-bornological vector spaces. The specific description of L-bornological vector spaces is presented, some properties of Lowen functors between the category of bornological vector spaces and the category of L-bornological vector spaces are discussed. In addition, the notions and some properties of L-Mackey convergence and separation in L-bornological vector spaces are showed. The equivalent characterization of separation in L-bornological vector spaces in terms of L-Mackey convergence is obtained in particular.

scholarly journals M-Hazy Vector Spaces over M-Hazy Field

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1118
Author(s):  
Faisal Mehmood ◽  
Fu-Gui Shi
Keyword(s):  
Vector Space ◽  
Linear Transformation ◽  
Binary Operation ◽  
Vector Spaces ◽  
Fundamental Properties ◽  
Classical Algebra ◽  
Important Development ◽  
Fuzzy Algebra ◽  
Convex Spaces

The generalization of binary operation in the classical algebra to fuzzy binary operation is an important development in the field of fuzzy algebra. The paper proposes a new generalization of vector spaces over field, which is called M-hazy vector spaces over M-hazy field. Some fundamental properties of M-hazy field, M-hazy vector spaces, and M-hazy subspaces are studied, and some important results are also proved. Furthermore, the linear transformation of M-hazy vector spaces is studied and their important results are also proved. Finally, it is shown that M-fuzzifying convex spaces are induced by an M-hazy subspace of M-hazy vector space.

Genetic characterization of novel polymorphic microsatellite markers for Epilobium nankotaizanense (Onagraceae), an endemic and threatened herb in Taiwan

2021 ◽  
pp. 1-4
Author(s):  
Yu-Wei Tseng ◽  
Chi-Chun Huang ◽  
Chih-Chiang Wang ◽  
Chiuan-Yu Li ◽  
Kuo-Hsiang Hung
Keyword(s):  
Microsatellite Markers ◽  
Natural Populations ◽  
Conservation Strategy ◽  
Sequencing Data ◽  
Germplasm Collections ◽  
The Family ◽  
Conservation Genetic ◽  
Population Sizes ◽  
Polymorphic Microsatellite

Abstract Epilobium belongs to the family Onagraceae, which consists of approximately 200 species distributed worldwide, and some species have been used as medicinal plants. Epilobium nankotaizanense is an endemic and endangered herb that grows in the high mountains in Taiwan at an elevation of more than 3300 m. Alpine herbs are severely threatened by climate change, which leads to a reduction in their habitats and population sizes. However, only a few studies have addressed genetic diversity and population genetics. In the present study, we developed a new set of microsatellite markers for E. nankotaizanense using high-throughput genome sequencing data. Twenty polymorphic microsatellite markers were developed and tested on 30 individuals collected from three natural populations. These loci were successfully amplified, and polymorphisms were observed in E. nankotaizanense. The number of alleles per locus (A) ranged from 2.000 to 3.000, and the observed (Ho) and expected (He) heterozygosities ranged from 0.000 to 0.929 and from 0.034 to 0.631, respectively. The developed polymorphic microsatellite markers will be useful in future conservation genetic studies of E. nankotaizanense as well as for developing an effective conservation strategy for this species and facilitating germplasm collections and sustainable utilization of other Epilobium species.

scholarly journals Color-Metallographic Characterization of Alloyed White Cast Irons Ni-Hard Type

Metals ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 728
Author(s):  
Milagrosa González Fernández de Castro ◽  
Yolanda Martín Álvarez ◽  
Juan José Moreno-Labella ◽  
Miguel Panizo-Laiz ◽  
Benito del Río
Keyword(s):  
Impact Resistance ◽  
Solidification Structure ◽  
Hard Alloys ◽  
Metallic Materials ◽  
Low Carbon ◽  
Cast Irons ◽  
The Family ◽  
Color Metallography ◽  
Hard Type

The Ni-hard alloys white-cast irons are generally used for high wear work. Among them, those with better impact resistance because of its low carbon content compared to the rest of the family, are studied in this paper. One experimental technique of characterizing the metallic materials is the microstructural study. Several metallographic attacks intended to reveal qualitatively each microconstituent that forms the alloy, as well as the segregation and solidification structure of casting, are studied in this article. The use of color metallography is fundamental in this case to distinguish clearly the microconstituents. The main objective of this paper is to propose a series of attacks that identify each one of the microconstituents present in the alloy that has not been reported up to date.

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