On the splitting type of holomorphic vector bundles induced from regular systems of differential equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Grigori Giorgadze ◽  
Gega Gulagashvili
Keyword(s):  
Vector Bundles ◽  
Riemann Sphere ◽  
Complete Characterization ◽  
Fuchsian System ◽  
Hölder Continuous ◽  
Holomorphic Vector Bundles ◽  
Splitting Type ◽  
Second Order Systems ◽  
The Relationship

Abstract We calculate the splitting type of holomorphic vector bundles on the Riemann sphere induced by a Fuchsian system of differential equations. Using this technique, we indicate the relationship between Hölder continuous matrix functions and a moduli space of vector bundles on the Riemann sphere. For second order systems with three singular points we give a complete characterization of the corresponding vector bundles by the invariants of Fuchsian system.

Characterization and Coordination of Point-line Trajectories

2004 ◽  
Vol 127 (3) ◽  
pp. 502-505 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Yi Zhang ◽  
Ruj Bunduwongse
Keyword(s):  
Orientation Relationship ◽  
Complete Characterization ◽  
Free Form ◽  
Directed Line ◽  
Free Form Surface ◽  
Point Line ◽  
Line Trajectory ◽  
The Relationship ◽  
Line Direction

A point-line refers to a rigid combination of a directed line and an endpoint along the line. To trace a point-line trajectory, one must control not only the trajectory of the endpoint (the directrix) but also the direction of the point-line (the indicatrix). This paper addresses three issues on point-line trajectories. First of all, by considering the relationship between the point trajectory and the corresponding point-line direction, it offers the complete characterization of point-line trajectories. It presents the coordination of the point-line axis with a free point trajectory and also with a point trajectory constrained on a free form surface. The issue of maintaining an invariant orientation relationship between the point-line axis and the point trajectory is also addressed.

scholarly journals If the skull fits: magnetic resonance imaging and microcomputed tomography for combined analysis of brain and skull phenotypes in the mouse

2012 ◽  
Vol 44 (20) ◽  
pp. 992-1002 ◽  
Author(s):  
Brian J. Nieman ◽  
Marissa C. Blank ◽  
Brian B. Roman ◽  
R. Mark Henkelman ◽  
Kathleen J. Millen
Keyword(s):  
Magnetic Resonance Imaging ◽  
Magnetic Resonance ◽  
Prognostic Significance ◽  
Microcomputed Tomography ◽  
Complete Characterization ◽  
Mammalian Brain ◽  
Resonance Imaging ◽  
The Relationship ◽  
The Brain

The mammalian brain and skull develop concurrently in a coordinated manner, consistently producing a brain and skull that fit tightly together. It is common that abnormalities in one are associated with related abnormalities in the other. However, this is not always the case. A complete characterization of the relationship between brain and skull phenotypes is necessary to understand the mechanisms that cause them to be coordinated or divergent and to provide perspective on the potential diagnostic or prognostic significance of brain and skull phenotypes. We demonstrate the combined use of magnetic resonance imaging and microcomputed tomography for analysis of brain and skull phenotypes in the mouse. Co-registration of brain and skull images allows comparison of the relationship between phenotypes in the brain and those in the skull. We observe a close fit between the brain and skull of two genetic mouse models that both show abnormal brain and skull phenotypes. Application of these three-dimensional image analyses in a broader range of mouse mutants will provide a map of the relationships between brain and skull phenotypes generally and allow characterization of patterns of similarities and differences.

scholarly journals A geometrical characterization of a class of holomorphic vector bundles over a complex torus

1976 ◽  
Vol 61 ◽  
pp. 197-202 ◽  
Author(s):  
Jun-Ichi Hano
Keyword(s):  
Vector Bundle ◽  
Heisenberg Group ◽  
Vector Bundles ◽  
Holomorphic Vector Bundle ◽  
Projective Bundle ◽  
Geometrical Characterization ◽  
Complex Torus ◽  
Holomorphic Vector Bundles ◽  
Holomorphic Representation

This note is to be a supplement of the preceeding paper in the journal by Matsushima, settling a question raised by him. In his paper he associates a holomorphic vector bundle over a complex torus to a holomorphic representation of what he calls Heisenberg group. We shall show that a simple holomorphic vector bundle is determined in this manner if and only if the associated projective bundle admits an integrable holomorphic connection. A theorem by Morikawa ([3], Theorem 1) is the motivation of this problem and is somewhat strengthened by our result.

Sulphite Electrooxidation in Alkaline Media on Skeletal Nickel Based 6 Layers Platinum Nanoparticles Electrode

2018 ◽  
Vol 27 ◽  
pp. 176-187 ◽  
Author(s):  
Andreea Floriana Enache ◽  
Mircea Laurentiu Dan ◽  
Nicolae Vaszilcsin
Keyword(s):  
Kinetic Parameters ◽  
Platinum Nanoparticles ◽  
Electrochemical Impedance ◽  
Oxidation Mechanism ◽  
Complete Characterization ◽  
Alkaline Media ◽  
Skeletal Nickel ◽  
Spectroscopy Studies ◽  
The Relationship

In this paper, anodic oxidation of sulphite ions on skeletal nickel based platinum nanoparticles electrode (6 layers) in aqueous alkaline solution was investigated in order to find the relationship between kinetic parameters and sulphite concentration. The purpose of this research is both to understand the oxidation mechanism and determine optimal parameters for oxidation process. Electrochemical behavior of sulphite ions has been studied by cyclic voltammetry and linear polarization. Tafel method was used in order to determine kinetic parameters and electrochemical impedance spectroscopy studies were performed to confirm the oxidation mechanism. For a complete characterization of sulphite electrooxidation process chrono-electrochemical methods (chronoamperometry, chronopotentiometry, chronocoulometry) were used.

scholarly journals The ray transference of a reversed optical system

2008 ◽  
Vol 67 (2) ◽  
Author(s):  
W. F. Harris
Keyword(s):  
Optical Properties ◽  
Optical System ◽  
Complete Characterization ◽  
Reverse Direction ◽  
First Order ◽  
Optical Character ◽  
Relationship Of ◽  
The Relationship ◽  
Explicit Expressions

The optical character of an optical system is changed if the system is reversed.  This is as true of eyes as it is of telescopes.  In vision light traverses the eye from cornea to retina; in ophthalmoscopy the practitioner views the retina via light traversing the eye in the reverse direction.  The purpose of this paper is to determine the relationship of the optical character of the reversed system to that of the system itself. The result is in terms of the ray transference of the system.  Since the ray transference gives a complete characterization of the first-order optics of a system the analysis is complete in this sense as well.  Explicit expressions are also presented for the effect of reversal on the six fundamental first-order optical properties of the system.

Skeletal elements of crinoid echinoderms: High-resolution structural and microanalytical results

1983 ◽  
Vol 41 ◽  
pp. 194-195
Author(s):  
D. F. Blake ◽  
L. F. Allard ◽  
D. R. Peacor
Keyword(s):  
High Resolution ◽  
Marine Invertebrates ◽  
Sea Urchins ◽  
Structural Features ◽  
Sea Stars ◽  
High Resolution Tem ◽  
Relationship Of ◽  
The Relationship ◽  
Insight Into

Echinodermata is a phylum of marine invertebrates which has been extant since Cambrian time (c.a. 500 m.y. before the present). Modern examples of echinoderms include sea urchins, sea stars, and sea lilies (crinoids). The endoskeletons of echinoderms are composed of plates or ossicles (Fig. 1) which are with few exceptions, porous, single crystals of high-magnesian calcite. Despite their single crystal nature, fracture surfaces do not exhibit the near-perfect {10.4} cleavage characteristic of inorganic calcite. This paradoxical mix of biogenic and inorganic features has prompted much recent work on echinoderm skeletal crystallography. Furthermore, fossil echinoderm hard parts comprise a volumetrically significant portion of some marine limestones sequences. The ultrastructural and microchemical characterization of modern skeletal material should lend insight into: 1). The nature of the biogenic processes involved, for example, the relationship of Mg heterogeneity to morphological and structural features in modern echinoderm material, and 2). The nature of the diagenetic changes undergone by their ancient, fossilized counterparts. In this study, high resolution TEM (HRTEM), high voltage TEM (HVTEM), and STEM microanalysis are used to characterize tha ultrastructural and microchemical composition of skeletal elements of the modern crinoid Neocrinus blakei.

Microstructural Characterization of Au-Ge-Ni based ohmic contacts to GaAs/AlGaAs modfet device

1987 ◽  
Vol 45 ◽  
pp. 326-327
Author(s):  
A.K. Rai ◽  
A.K. Petford-Long ◽  
A. Ezis ◽  
D.W. Langer
Keyword(s):  
Contact Resistance ◽  
Ohmic Contact ◽  
Ohmic Contacts ◽  
Microstructural Characterization ◽  
Almost Everywhere ◽  
Spacer Layer ◽  
Good Contact ◽  
The Relationship ◽  
Lower Contact

Considerable amount of work has been done in studying the relationship between the contact resistance and the microstructure of the Au-Ge-Ni based ohmic contacts to n-GaAs. It has been found that the lower contact resistivity is due to the presence of Ge rich and Au free regions (good contact area) in contact with GaAs. Thus in order to obtain an ohmic contact with lower contact resistance one should obtain a uniformly alloyed region of good contact areas almost everywhere. This can possibly be accomplished by utilizing various alloying schemes. In this work microstructural characterization, employing TEM techniques, of the sequentially deposited Au-Ge-Ni based ohmic contact to the MODFET device is presented.The substrate used in the present work consists of 1 μm thick buffer layer of GaAs grown on a semi-insulating GaAs substrate followed by a 25 Å spacer layer of undoped AlGaAs.

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