The Primitive Idempotents of the Clifford Algebras and the Amorphic Spinor Fiber Bundles

1990 ◽  
pp. 276-298
Author(s):  
Albert Crumeyrolle
Keyword(s):  
Clifford Algebras ◽  
Fiber Bundles ◽  
Primitive Idempotents

scholarly journals Structures of spinors fiber bundles with special relativity of Dirac operator using the Clifford algebra

2021 ◽  
Vol 54 (1) ◽  
pp. 410-424
Author(s):  
Yousif Atyeib Ibrahim Hassan
Keyword(s):  
Dirac Operator ◽  
Clifford Algebra ◽  
Special Relativity ◽  
Riemannian Manifolds ◽  
Clifford Algebras ◽  
Cohomology Theory ◽  
Fiber Bundles

Abstract The purpose of this article is to demonstrate how to use the mathematics of spinor bundles and their category. We have used the methods of principle fiber bundles obey thorough solid harmonic treatment of pseudo-Riemannian manifolds and spinor structures with Clifford algebras, which couple with Dirac operator to study important applications in cohomology theory.

scholarly journals ALGEBRA AND STRUCTURES OF SPINORS FIBER BUNDLES

2015 ◽  
Vol 11 (1) ◽  
pp. 376-401
Author(s):  
Adam Abdallah ◽  
Yousif Eltaeeb
Keyword(s):  
Dirac Operator ◽  
Riemannian Manifolds ◽  
Clifford Algebras ◽  
Cohomology Theory ◽  
Fiber Bundles ◽  
Principal Fiber Bundles

The aim of this paper is to investigate the mathematics of spinor bundles and their classification.  We devote the methods of principal fiber bundles allows through a coherent treatment of Pseudo-Riemannian manifolds and spinor structures with Clifford algebras which couple to Dirac operator to study important applications in cohomology theory.

Dupuytren's Contracture and Microvessels

1981 ◽  
Vol 39 ◽  
pp. 470-471
Author(s):  
C. W. Klscher ◽  
D. Speer
Keyword(s):  
Hypertrophic Scar ◽  
Active Form ◽  
Scar Tissue ◽  
Vascular Supply ◽  
Fiber Bundles ◽  
Dupuytren’S Contracture ◽  
Palmar Fascia ◽  
Immune Disease ◽  
Dupuytren's Contracture ◽  
Longitudinal Fiber

Dupuytren's Contracture is a nodular proliferation of the longitudinal fiber bundles of palmar fascia with its attendant contraction. The factors attributed to its etiology have included trauma, diabetes, alcoholism, arthritis, and auto-immune disease. The tissue has been observed by electron microscopy and found to contain myofibroblasts.Dupuytren's Contracture constitutes a scar, and as such, excessive collagen can be observed, along with an active form of fibroblast.Previous studies of the hypertrophic scar have led us to propose that integral in the initiation and sustenance of scar tissue is a profusion of microvascular regeneration, much of which becomes and remains occluded producing a hypoxia which stimulates fibroblast synthesis. Thus, when considering a study of Dupuytren's Contracture, we predicted finding occluded microvessels at or near the fascial scarring focus.Three cases of Dupuytren's Contracture yielded similar specimens, which were fixed in Karnovskys fluid for 2 to 20 days. Upon removal of the contracture bands care was taken to include the contiguous fatty and areolar tissue which contain the vascular supply and to identify the junctional area between old and new fascia.

Ultrastructural Features of the Oral Apparatus of Stentor

1976 ◽  
Vol 34 ◽  
pp. 142-143
Author(s):  
Elizabeth F. Howell
Keyword(s):  
Plasma Membrane ◽  
Osmium Tetroxide ◽  
Buccal Cavity ◽  
Fiber Bundles ◽  
Microtubular Root ◽  
Stentor Coeruleus ◽  
Root Fiber

The ultrastructure of the normal oral apparatus of Stentor has not been extensively studied. I report here on the ultrastructure of the buccal cavity of Stentor coeruleus.Stentor coeruleus was fixed in either a buffered mixture of osmium tetroxide and glutaraldehyde, or in buffered glutaraldehyde alone. Cells were then dehydrated and embedded in a mixture of Epon and Araldite.An extensive adoral zone of membranelles surrounds the anterior of the cell, and each membranelle consists of 2 parallel rows of cilia. These extend down into the buccal cavity. Two microtubular root fibers, or nemadesmata (Figs. 2 and 5), extend deeply into the cytoplasm from the base of each ciliary kinetosome. Mitochondria are usually closely associated with the root fiber bundles, and small vesicles are present between the nemadesmata of adjacent kinetosomes (Fig. 5). In the cytopharyngeal, non-ciliated areas of the buccal cavity, microtubular ribbons which extend into the cytoplasm are aligned perpendicular to the plasma membrane of the buccal cavity (Figs. 1 and 2).

Microstructures of SiC and Si3N4 with fibrous inclusions

1986 ◽  
Vol 44 ◽  
pp. 492-493
Author(s):  
N. J. Tighe ◽  
J. Sun ◽  
R.-M. Hu
Keyword(s):  
Vapor Deposition ◽  
Chemical Vapor ◽  
Crack Deflection ◽  
Fiber Bundles ◽  
High Temperature Strength ◽  
Graphite Fiber ◽  
Triple Junctions ◽  
Transmission Electron ◽  
Compact Graphite ◽  
Deposition Techniques

Particles of BN,and C are added in amounts of 1 to 40% to SiC and Si3N4 ceramics in order to improve their mechanical properties. The ceramics are then processed by sintering, hot-pressing and chemical vapor deposition techniques to produce dense products. Crack deflection at the particles can increase toughness. However the high temperature strength and toughness are determined byphase interactions in the environmental conditions used for testing. Examination of the ceramics by transmission electron microscopy has shown that the carbon and boron nitride particles have a fibrous texture. In the sintered aSiC ceramic the carbon appears as graphite fiber bundles in the triple junctions and as compact graphite particles within some grains. Examples of these inclusions are shown in Fig. 1A and B.

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

Isomorphisms of graded skew Clifford algebras

2020 ◽  
Vol 13 (5) ◽  
pp. 871-878
Author(s):  
Richard G. Chandler ◽  
Nicholas Engel
Keyword(s):  
Clifford Algebras
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