scholarly journals Lie algebras of infinitesimal CR automorphisms of weighted homogeneous and homogeneous CR-generic submanifolds of CN

Filomat ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1387-1411 ◽  
Author(s):  
Masoud Sabzevari ◽  
Amir Hashemi ◽  
Benyamin Alizadeh ◽  
Joël Merker
Keyword(s):  
Lie Algebras ◽  
Divide And Conquer ◽  
Homogeneous Polynomials ◽  
Generic Submanifolds ◽  
Pde Systems ◽  
Set Up ◽  
Infinitesimal Cr Automorphisms ◽  
Significant Class ◽  
Homogeneous Cr Manifolds ◽  
Natural Gradation

We consider the significant class of homogeneous CR manifolds represented by some weighted homogeneous polynomials and we derive some plain and useful features which enable us to set up a fast effective algorithm to compute homogeneous components of their Lie algebras of infinitesimal CR automorphisms. This algorithm mainly relies upon a natural gradation of the sought Lie algebras, and it also consists in treating separately the related graded components. While classical methods are based on constructing and solving some associated PDE systems which become time consuming as soon as the number of variables increases, the new method presented here is based on plain techniques of linear algebra. Furthermore, it benefits from a divide-and-conquer strategy to break down the computations into some simpler subcomputations. Also, we consider the new and effective concept of comprehensive Gr?bner systems which provides us some powerful tools to treat the computations in the much complicated parametric case. The designed algorithm is also implemented in the Maple software, what required also implementing a recently designed algorithm of Kapur et al.

Isolation and characterization of oleochemical compounds from watermelon seed

2020 ◽  
Vol 10 (4) ◽  
pp. 79-82
Author(s):  
Madhubhushan M ◽  
Seshaiah S ◽  
Chandrudu J ◽  
Sagar R ◽  
Akila CR
Keyword(s):  
Cutting Tool ◽  
Citrullus Lanatus ◽  
Fatty Esters ◽  
Mineral Oils ◽  
Light Yellow ◽  
Isolation And Characterization ◽  
The Common ◽  
Set Up ◽  
Natural Gradation

The common watermelon item (Citrullus lanatus) seeds were gained from castoffs verdant nourishments for use by decorating, sun ventilation and pulverizing. Light yellow-toned oil was gotten by dissolvable withdrawal using oil atmosphere and the going with traits were gotten using oil ether: pH, refractive rundown, thickness, dissolvable miscibility, coagulating temperature, fire nature, express gravity, streak point and warmth of consuming. With a shallow level of unsaturation, stepped level of smoothness, and proximity of raised degree of the sensible proportion of free unsaturated fats. The low assessment of the solidifying temperature of the oil offered a hint that the oil can be managed in various areas paying little heed to the qualification in temperature. The following level of linoleic destructive of the oil offers a hint of natural gradation of solidarity. Fatty esters are increasing expanding significance as a biodegradable swap for mineral oils. In some request regions, for example, cutting tool oil, gearbox, pressure-driven oils, and greases for raw petroleum creation, the oleochemical items are set up. Nonetheless, certain particular wellsprings of fatty esters are hitherto to be abused for this comparative reason. This exploration subsequently tests into one of the less used wellsprings of fatty esters in watermelon. The oil from the kernels demonstrations a top-notch yield presents significant utilitarian gatherings for change and thus was utilized to set up an assortment of oleochemicals which demonstrated excellence materials in contrast with the routinely utilized oils feed frameworks for oleochemicals after portrayal. The photopolymers acquired indicated piercing vinyl protons for consistent polymerize.

scholarly journals Applications of differential algebra for computing Lie algebras of infinitesimal CR-automorphisms

2014 ◽  
Vol 57 (9) ◽  
pp. 1811-1834 ◽  
Author(s):  
Masoud Sabzevari ◽  
Amir Hashemi ◽  
Benyamin M.-Alizadeh ◽  
Joël Merker
Keyword(s):  
Lie Algebras ◽  
Differential Algebra ◽  
Infinitesimal Cr Automorphisms

NEW SOLUTIONS OF YANG-BAXTER EQUATION AND NEW LINK POLYNOMIALS

1992 ◽  
Vol 01 (01) ◽  
pp. 31-46 ◽  
Author(s):  
YI CHENG ◽  
MO-LIN GE ◽  
G. C. LIU ◽  
KANG XUE
Keyword(s):  
Lie Algebras ◽  
Braid Group ◽  
Baxter Equation ◽  
Group Representations ◽  
Rational Solutions ◽  
New Family ◽  
Set Up

A new family of braid group representations associated with Lie algebras An, Bn, Cn and Dn is proved to be Birman-Wenzl algebra, then Yang-Baxterize them to trigonometric and rational solutions of YBE. New link polynomials are set up.

scholarly journals Triality for Homogeneous Polynomials

2021 ◽  
Author(s):  
Laura P. Schaposnik ◽  
◽  
Sebastian Schulz ◽  
Keyword(s):  
Lie Algebras ◽  
Homogeneous Polynomials ◽  
Invariant Polynomials ◽  
Homogeneous Basis

Through the triality of SO(8,C), we study three interrelated homogeneous basis of the ring of invariant polynomials of Lie algebras, which give the basis of three Hitchin fibrations, and identify the explicit automorphisms that relate them.

The Violence of the Normative

2017 ◽  
Author(s):  
Amy L. Brandzel
Keyword(s):  
United States ◽  
Hate Crime ◽  
The United States ◽  
Divide And Conquer ◽  
Complex Nature ◽  
Hate Crime Legislation ◽  
Crime Legislation ◽  
Set Up ◽  
Biopolitical Power

This introductory chapter provides an overview of the book's main themes. This book argues that citizenship is not only the central structure for reifying the norms of whiteness, heterosexuality, consumerism, and settler colonialism within the United States, but that these norms are brutally enforced against nonnormative bodies, practices, behaviors, and forms of affiliation through oppositional, divide-and-conquer logics that set up nonnormative subjects to compete against each other in order to gain the privileged access to citizenship. The book examines the complex nature of the violence of normative citizenship by offering a comparative analysis of three case studies, namely same-sex marriage law, hate crime legislation, and Native Hawaiian sovereignty. The remainder of the chapter discusses the notion of citizenship as a form of disciplinary and biopolitical power, and the anti-intersectionality of citizenship discourses in the United States.

The Effects of Drying Techniques on Clay-Rich Soil Texture

1974 ◽  
Vol 32 ◽  
pp. 466-467
Author(s):  
T. G. Naymik
Keyword(s):  
Critical Point ◽  
Liquid Nitrogen ◽  
Liquid Nitrogen Temperature ◽  
Drying Methods ◽  
Air Drying ◽  
Freeze Dried ◽  
Critical Point Drying ◽  
Set Up ◽  
The Relationship ◽  
Quartz Grains

Three techniques were incorporated for drying clay-rich specimens: air-drying, freeze-drying and critical point drying. In air-drying, the specimens were set out for several days to dry or were placed in an oven (80°F) for several hours. The freeze-dried specimens were frozen by immersion in liquid nitrogen or in isopentane at near liquid nitrogen temperature and then were immediately placed in the freeze-dry vacuum chamber. The critical point specimens were molded in agar immediately after sampling. When the agar had set up the dehydration series, water-alcohol-amyl acetate-CO2 was carried out. The objectives were to compare the fabric plasmas (clays and precipitates), fabricskeletons (quartz grains) and the relationship between them for each drying technique. The three drying methods are not only applicable to the study of treated soils, but can be incorporated into all SEM clay soil studies.

Evaluation of Freezing Methods by Low Temperature X-Ray Diffraction

1977 ◽  
Vol 35 ◽  
pp. 330-333
Author(s):  
T. Gulik-Krzywicki ◽  
M.J. Costello
Keyword(s):  
Biological Materials ◽  
Molecular Organization ◽  
X Ray Diffraction ◽  
Glass Capillary ◽  
X Ray ◽  
Rate Dependent ◽  
Before And After ◽  
Freeze Etching ◽  
Diffraction Patterns ◽  
Set Up

Freeze-etching electron microscopy is currently one of the best methods for studying molecular organization of biological materials. Its application, however, is still limited by our imprecise knowledge about the perturbations of the original organization which may occur during quenching and fracturing of the samples and during the replication of fractured surfaces. Although it is well known that the preservation of the molecular organization of biological materials is critically dependent on the rate of freezing of the samples, little information is presently available concerning the nature and the extent of freezing-rate dependent perturbations of the original organizations. In order to obtain this information, we have developed a method based on the comparison of x-ray diffraction patterns of samples before and after freezing, prior to fracturing and replication.Our experimental set-up is shown in Fig. 1. The sample to be quenched is placed on its holder which is then mounted on a small metal holder (O) fixed on a glass capillary (p), whose position is controlled by a micromanipulator.

Eels Under Standing Wave Conditions

1982 ◽  
Vol 40 ◽  
pp. 492-495
Author(s):  
O.L. Krivanek ◽  
J. TaftØ
Keyword(s):  
Standing Wave ◽  
Wave Conditions ◽  
Set Up ◽  
A Site ◽  
Complex Crystal

It is well known that a standing electron wavefield can be set up in a crystal such that its intensity peaks at the atomic sites or between the sites or in the case of more complex crystal, at one or another type of a site. The effect is usually referred to as channelling but this term is not entirely appropriate; by analogy with the more established particle channelling, electrons would have to be described as channelling either through the channels or through the channel walls, depending on the diffraction conditions.

Low-Loss Images in a Stem/Tem Microscope

1976 ◽  
Vol 34 ◽  
pp. 496-497 ◽  
Author(s):  
David C. Joy ◽  
Dennis M. Maher
Keyword(s):  
High Resolution ◽  
Surface Topography ◽  
Beam Direction ◽  
Low Loss ◽  
Specimen Holder ◽  
Glancing Angle ◽  
High Resolution Images ◽  
Set Up ◽  
Conventional Manner ◽  
Objective Type

High-resolution images of the surface topography of solid specimens can be obtained using the low-loss technique of Wells. If the specimen is placed inside a lens of the condenser/objective type, then it has been shown that the lens itself can be used to collect and filter the low-loss electrons. Since the probeforming lenses in TEM instruments fitted with scanning attachments are of this type, low-loss imaging should be possible.High-resolution, low-loss images have been obtained in a JEOL JEM 100B fitted with a scanning attachment and a thermal, fieldemission gun. No modifications were made to the instrument, but a wedge-shaped, specimen holder was made to fit the side-entry, goniometer stage. Thus the specimen is oriented initially at a glancing angle of about 30° to the beam direction. The instrument is set up in the conventional manner for STEM operation with all the lenses, including the projector, excited.

UHV-TEM studies of laser-induced damage

1991 ◽  
Vol 49 ◽  
pp. 632-633
Author(s):  
T.S. Savage ◽  
R. Ai ◽  
D. Dunn ◽  
L.D. Marks
Keyword(s):  
Surface Science ◽  
Rapid Heating ◽  
Local Heating ◽  
Routine Practice ◽  
Transmission Electron ◽  
Northwestern University ◽  
Laser Induced Damage ◽  
Set Up ◽  
Focusing Lens ◽  
Diffusion Of Impurities

The use of lasers for surface annealing, heating and/or damage has become a routine practice in the study of materials. Lasers have been closely looked at as an annealing technique for silicon and other semiconductors. They allow for local heating from a beam which can be focused and tuned to different wavelengths for specific tasks. Pulsed dye lasers allow for short, quick bursts which can allow the sample to be rapidly heated and quenched. This short, rapid heating period may be important for cases where diffusion of impurities or dopants may not be desirable.At Northwestern University, a Candela SLL - 250 pulsed dye laser, with a maximum power of 1 Joule/pulse over 350 - 400 nanoseconds, has been set up in conjunction with a Hitachi UHV-H9000 transmission electron microscope. The laser beam is introduced into the surface science chamber through a series of mirrors, a focusing lens and a six inch quartz window.

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