The Position Vectors of Space Curves with constant Curvatures According to Type-1 Bishop Frame in Euclidean 3- Space E^3

2016 ◽  
Vol 5 (5) ◽  
pp. 6700-6703
Author(s):  
Dr. Fathi El-Zaki
Keyword(s):  
Space Curves ◽  
Bishop Frame

New models of normal motions of the inextensible curves according to type-1 Bishop frame in ℝ3

2020 ◽  
Vol 18 (01) ◽  
pp. 2150009
Author(s):  
Samah Gaber Mohamed
Keyword(s):  
Time Evolution ◽  
Evolution Equations ◽  
Sufficient Condition ◽  
Frenet Frame ◽  
Comparison Study ◽  
Necessary And Sufficient Condition ◽  
Bishop Frame ◽  
New Models ◽  
Necessary And Sufficient

In this work, we compute the time evolution equations (TEEs) of the type-1 Bishop frame of the curve. Also, we study the time evolution equations for type-1 Bishop curvatures (TEEBCs) as a system of partial differential equations (PDEs). Through this study, we give a necessary and sufficient condition for the normal and binormal Bishop velocities. Also, we construct new models of normal motions of inextensible curves in [Formula: see text]. These models are constructed for curves that move according to the type-1 Bishop frame. Also, we make a comparison study between surfaces obtained by the motions of inextensible curves according to the two frames, the type-1 Bishop frame and the Frenet frame.

scholarly journals Some New Characterizations of The Harmonic and Harmonic 1-Type Curves in Euclidean 3-Space

2021 ◽  
Vol 46 (3) ◽  
pp. 235-254
Author(s):  
Hatice Kuşak Samanci ◽  
Sedat Ayaz ◽  
Huseyin Kocayiğit
Keyword(s):  
Differential Equation ◽  
Wave Propagation ◽  
Quantum Mechanics ◽  
Fluid Flow ◽  
Engineering Science ◽  
Type Curves ◽  
Space Curves ◽  
Bishop Frame ◽  
New Space ◽  
Heat And Fluid Flow

Abstract A Laplace operator and harmonic curve have very important uses in various engineering science such as quantum mechanics, wave propagation, diffusion equation for heat, and fluid flow. Additionally, the differential equation characterizations of the harmonic curves play an important role in estimating the geometric properties of these curves. Hence, this paper proposes to compute some new differential equation characterizations of the harmonic curves in Euclidean 3-space by using an alternative frame named the N-Bishop frame. Firstly, we investigated some new differential equation characterizations of the space curves due to the N-Bishop frame. Secondly, we firstly introduced some new space curves which have the harmonic and harmonic 1-type vectors due to alternative frame N-Bishop frame. Finally, we compute new differential equation characterizations using the N-Bishop Darboux and normal Darboux vectors. Thus, using these differential equation characterizations we have proved in which conditions the curve indicates a helix.

Crystalloid Inclusions in Hepatocyte Mitochondria and Their Similarity to Cytoplasmic Crystalloids

1974 ◽  
Vol 32 ◽  
pp. 198-199
Author(s):  
Odell T. Minick ◽  
Hidejiro Yokoo
Keyword(s):  
Liver Disease ◽  
Alcoholic Liver Disease ◽  
Special Interest ◽  
Structural Variations ◽  
Mitochondrial Alterations ◽  
The Matrix ◽  
Crystalloid Inclusions ◽  
Liver Biopsies

Mitochondrial alterations were studied in 25 liver biopsies from patients with alcoholic liver disease. Of special interest were the morphologic resemblance of certain fine structural variations in mitochondria and crystalloid inclusions. Four types of alterations within mitochondria were found that seemed to relate to cytoplasmic crystalloids.Type 1 alteration consisted of localized groups of cristae, usually oriented in the long direction of the organelle (Fig. 1A). In this plane they appeared serrated at the periphery with blind endings in the matrix. Other sections revealed a system of equally-spaced diagonal lines lengthwise in the mitochondrion with cristae protruding from both ends (Fig. 1B). Profiles of this inclusion were not unlike tangential cuts of a crystalloid structure frequently seen in enlarged mitochondria described below.

Evidence for a shear mechanism for the precipitation of γ-zirconium hydride in zirconium

1978 ◽  
Vol 36 (1) ◽  
pp. 658-659
Author(s):  
G.J.C. Carpenter
Keyword(s):  
Elevated Temperature ◽  
Strain Field ◽  
Zirconium Hydride ◽  
Zirconium Atom ◽  
Atom Diffusion ◽  
Solvus Temperature ◽  
Hexagonal Close Packed ◽  
Partial Dislocations ◽  
The Face

In zirconium-hydrogen alloys, rapid cooling from an elevated temperature causes precipitation of the face-centred tetragonal (fct) phase, γZrH, in the form of needles, parallel to the close-packed <1120>zr directions (1). With low hydrogen concentrations, the hydride solvus is sufficiently low that zirconium atom diffusion cannot occur. For example, with 6 μg/g hydrogen, the solvus temperature is approximately 370 K (2), at which only the hydrogen diffuses readily. Shears are therefore necessary to produce the crystallographic transformation from hexagonal close-packed (hep) zirconium to fct hydride.The simplest mechanism for the transformation is the passage of Shockley partial dislocations having Burgers vectors (b) of the type 1/3<0110> on every second (0001)Zr plane. If the partial dislocations are in the form of loops with the same b, the crosssection of a hydride precipitate will be as shown in fig.1. A consequence of this type of transformation is that a cumulative shear, S, is produced that leads to a strain field in the surrounding zirconium matrix, as illustrated in fig.2a.

Direct structure images of 30° partial dislocation cores in silicon

1987 ◽  
Vol 45 ◽  
pp. 242-243
Author(s):  
J. C. Barry ◽  
H. Alexander
Keyword(s):  
Dislocation Core ◽  
Preparation Technique ◽  
Burgers Vector ◽  
Vector Type ◽  
Sample Preparation Technique ◽  
Lattice Images ◽  
Dislocation Core Structure ◽  
Type Lattice ◽  
Direct Inspection

Dislocations in silicon produced by plastic deformation are generally dissociated into partials. 60° dislocations (Burgers vector type 1/2[101]) are dissociated into 30°(Burgers vector type 1/6[211]) and 90°(Burgers vector type 1/6[112]) dislocations. The 30° partials may be either of “glide” or “shuffle” type. Lattice images of the 30° dislocation have been obtained with a JEM 100B, and with a JEM 200Cx. In the aforementioned experiments a reasonable but imperfect match was obtained with calculated images for the “glide” model. In the present experiment direct structure images of 30° dislocation cores have been obtained with a JEOL 4000EX. It is possible to deduce the 30° dislocation core structure by direct inspection of the images. Dislocations were produced by compression of single crystal Si (sample preparation technique described in Alexander et al.).

Electron Microscopic investigation of crooke’s change in the pituitaries of patients with hypercorticism

1989 ◽  
Vol 47 ◽  
pp. 848-849
Author(s):  
E. Horvath ◽  
K. Kovacs ◽  
L. Stefaneanu ◽  
N. Losinski
Keyword(s):  
Nucleolar Organizer ◽  
Microscopic Investigation ◽  
Electron Microscopic Investigation ◽  
Ectopic Acth Syndrome ◽  
Nucleolar Organizer Regions ◽  
Electron Microscopic ◽  
Human Pituitary ◽  
Ectopic Acth ◽  
Crooke’S Hyalinization

Human pituitary corticotropins have unique morphologic markers: bundles of type-1 filaments, measuring approximately 70 A in width and representing cytokeratin. The extreme ring-like accumulation of type-1 filaments, known as Crooke's hyalinization, signals functional suppression of the corticotropins and occurs in endogenous and exogenous glucocorticoid excess, caused by ACTH-secreting pituitary adenoma, glucocorticoid secreting adrenocortical tumor, ectopic ACTH-syndrome and administration of pharmacologic doses of glucocorticoids. Cells of autonomous corticotroph adenomas usually do not show Crooke's hyalin change. A minority of these tumors, however, retains sensitivity to the negative feed-back effect of elevated blood glucocorticoid levels and display typical Crooke’s change.In the present study pituitary corticotropins in various phases of Crooke's hyalinization were investigated in patients with glucocorticoid excess of various origin, applying histology, immunocytochemistry, count of argyrophilic nucleolar organizer regions (AgNOR), and transmission electron microscopy.

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