scholarly journals A new approach to the Fraser-Li conjecture with the Weierstrass representation formula

2021 ◽  
pp. 1
Author(s):  
Jaehoon Lee ◽  
Eungbeom Yeon
Keyword(s):  
Representation Formula ◽  
Weierstrass Representation ◽  
New Approach

scholarly journals The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1

2008 ◽  
Vol 80 (1) ◽  
pp. 3-19
Author(s):  
Shuguo Shi
Keyword(s):  
Nonlinear Equation ◽  
Representation Formula ◽  
Gauss Map ◽  
Weierstrass Representation ◽  
Fully Nonlinear ◽  
Duality Property ◽  
Fully Nonlinear Equation ◽  
Monge Ampere

In this paper, we introduce the fourth fundamental forms for hypersurfaces in Hn+1 and space-like hypersurfaces in S1n+1, and discuss the conformality of the normal Gauss map of the hypersurfaces in Hn+1 and S1n+1. Particularly, we discuss the surfaces with conformal normal Gauss map in H³ and S³1, and prove a duality property. We give a Weierstrass representation formula for space-like surfaces in S³1 with conformal normal Gauss map. We also state the similar results for time-like surfaces in S³1. Some examples of surfaces in S³1 with conformal normal Gauss map are given and a fully nonlinear equation of Monge-Ampère type for the graphs in S³1 with conformal normal Gauss map is derived.

scholarly journals A New Approach to Slice Analysis Via Slice Topology

2021 ◽  
Vol 31 (5) ◽  
Author(s):  
Xinyuan Dou ◽  
Ming Jin ◽  
Guangbin Ren ◽  
Irene Sabadini
Keyword(s):  
Taylor Expansion ◽  
Regular Function ◽  
Alternative Algebra ◽  
Representation Formula ◽  
Monogenic Functions ◽  
Slice Regular Functions ◽  
New Approach ◽  
Regular Functions ◽  
Several Variables ◽  
Slice Monogenic Functions

AbstractIn this paper we summarize some known facts on slice topology in the quaternionic case, and we deepen some of them by proving new results and discussing some examples. We then show, following Dou et al. (A representation formula for slice regular functions over slice-cones in several variables, arXiv:2011.13770, 2020), how this setting allows us to generalize slice analysis to the general case of functions with values in a real left alternative algebra, which includes the case of slice monogenic functions with values in Clifford algebra. Moreover, we further extend slice analysis, in one and several variables, to functions with values in a Euclidean space of even dimension. In this framework, we study the domains of slice regularity, we prove some extension properties and the validity of a Taylor expansion for a slice regular function.

scholarly journals A generalized Weierstrass representation of Lorentzian surfaces in ℝ2,2 and applications

2016 ◽  
Vol 13 (06) ◽  
pp. 1650074 ◽  
Author(s):  
Victor Patty
Keyword(s):  
Dimensional Space ◽  
Representation Formula ◽  
De Sitter Space ◽  
Weierstrass Representation ◽  
Spinor Representation ◽  
De Sitter ◽  
Lorentzian Surface ◽  
Lorentz Surface

We give a generalized Weierstrass formula for a Lorentz surface conformally immersed in the four-dimensional space [Formula: see text] using spinors and Lorentz numbers. We also study the immersions of a Lorentzian surface in the Anti-de Sitter space (a pseudo-sphere in [Formula: see text]): we give a new spinor representation formula and deduce the conformal description of a flat Lorentzian surface in that space.

Flat Lorentz surfaces in anti-de Sitter 3-space and Gravitational Instantons

2016 ◽  
Vol 13 (02) ◽  
pp. 1650012
Author(s):  
Jun-Ichi Inoguchi ◽  
Marianty Ionel ◽  
Sungwook Lee
Keyword(s):  
Representation Formula ◽  
Gauss Map ◽  
Conformal Structure ◽  
Weierstrass Representation ◽  
De Sitter ◽  
Gravitational Instantons ◽  
Hyperbolic Gauss Map ◽  
Monge Ampere ◽  
The Relationship ◽  
Lorentz Surface

In this paper, we study flat Lorentz surfaces in anti-de Sitter 3-space [Formula: see text] in terms of the second conformal structure. Those flat Lorentz surfaces can be represented in terms of a Lorentz holomorphic and a Lorentz anti-holomorphic data similarly to Weierstraß representation formula. An analogue of hyperbolic Gauß map is considered for timelike surfaces in [Formula: see text] and the relationship between the conformality (or the holomorphicity) of hyperbolic Gauß map and the flatness of a Lorentz surface is discussed. It is shown that flat Lorentz surfaces in [Formula: see text] are associated with a hyperbolic Monge–Ampère equation. It is also known that Monge–Ampére equation may be regarded as a 2-dimensional reduction of the Einstein’s field equation. Using this connection, we construct a class of anti-self-dual gravitational instantons from flat Lorentz surfaces in [Formula: see text].

The O–C diagrams of minor planets − a new approach to modelling the rotation

1999 ◽  
Vol 173 ◽  
pp. 185-188
Author(s):  
Gy. Szabó ◽  
K. Sárneczky ◽  
L.L. Kiss
Keyword(s):  
Error Analysis ◽  
Time Dependence ◽  
Theoretical Work ◽  
Minor Planet ◽  
Minor Planets ◽  
New Approach ◽  
Preliminary Results ◽  
Ccd Observations

AbstractA widely used tool in studying quasi-monoperiodic processes is the O–C diagram. This paper deals with the application of this diagram in minor planet studies. The main difference between our approach and the classical O–C diagram is that we transform the epoch (=time) dependence into the geocentric longitude domain. We outline a rotation modelling using this modified O–C and illustrate the abilities with detailed error analysis. The primary assumption, that the monotonity and the shape of this diagram is (almost) independent of the geometry of the asteroids is discussed and tested. The monotonity enables an unambiguous distinction between the prograde and retrograde rotation, thus the four-fold (or in some cases the two-fold) ambiguities can be avoided. This turned out to be the main advantage of the O–C examination. As an extension to the theoretical work, we present some preliminary results on 1727 Mette based on new CCD observations.

A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

1973 ◽  
Vol 31 ◽  
pp. 698-699
Author(s):  
V. Mizuhira ◽  
Y. Futaesaku
Keyword(s):  
Cross Section ◽  
Tannic Acid ◽  
Elastic Fiber ◽  
The Other ◽  
New Approach ◽  
Tissue Block ◽  
Active Reaction ◽  
The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

Processing Immunoperoxidase Labeled Cell Monolayers and Cryostat Sesctions For Electron Microscopy

1985 ◽  
Vol 43 ◽  
pp. 714-715
Author(s):  
K. Chien ◽  
R. Van de Velde ◽  
I.P. Shintaku ◽  
A.F. Sassoon
Keyword(s):  
Cell Monolayer ◽  
Cell Types ◽  
Surface Antigens ◽  
Immunoperoxidase Method ◽  
Reaction Step ◽  
Hot Plate ◽  
Air Drying ◽  
New Approach ◽  
Cell Monolayers ◽  
Glass Slides

Immunoelectron microscopy of neoplastic lymphoma cells is valuable for precise localization of surface antigens and identification of cell types. We have developed a new approach in which the immunohistochemical staining can be evaluated prior to embedding for EM and desired area subsequently selected for ultrathin sectioning.A freshly prepared lymphoma cell suspension is spun onto polylysine hydrobromide- coated glass slides by cytocentrifugation and immediately fixed without air drying in polylysine paraformaldehyde (PLP) fixative. After rinsing in PBS, slides are stained by a 3-step immunoperoxidase method. Cell monolayer is then fixed in buffered 3% glutaraldehyde prior to DAB reaction. After the DAB reaction step, wet monolayers can be examined under LM for presence of brown reaction product and selected monolayers then processed by routine methods for EM and embedded with the Chien Re-embedding Mold. After the polymerization, the epoxy blocks are easily separated from the glass slides by heatingon a 100°C hot plate for 20 seconds.

TEM study of a biofilm on copper corrosion

1996 ◽  
Vol 54 ◽  
pp. 220-221
Author(s):  
W. A. Chiou ◽  
N. Kohyama ◽  
B. Little ◽  
P. Wagner ◽  
M. Meshii
Keyword(s):  
Marine Bacterium ◽  
Culture Medium ◽  
Copper Alloys ◽  
Pure Copper ◽  
Localized Corrosion ◽  
Natural Seawater ◽  
Copper Corrosion ◽  
New Approach ◽  
The Past ◽  
Copper Tolerant

The corrosion of copper and copper alloys in a marine environment is of great concern because of their widespread use in heat exchangers and steam condensers in which natural seawater is the coolant. It has become increasingly evident that microorganisms play an important role in the corrosion of a number of metals and alloys under a variety of environments. For the past 15 years the use of SEM has proven to be useful in studying biofilms and spatial relationships between bacteria and localized corrosion of metals. Little information, however, has been obtained using TEM capitalizing on its higher spacial resolution and the transmission observation of interfaces. The research presented herein is the first step of this new approach in studying the corrosion with biological influence in pure copper.Commercially produced copper (Cu, 99%) foils of approximately 120 μm thick exposed to a copper-tolerant marine bacterium, Oceanospirillum, and an abiotic culture medium were subsampled (1 cm × 1 cm) for this study along with unexposed control samples.

High resolution at low voltage: A new approach

1989 ◽  
Vol 47 ◽  
pp. 76-77
Author(s):  
Arthur V. Jones
Keyword(s):  
Low Voltage ◽  
Emission Sources ◽  
New Approach ◽  
Design Concepts ◽  
Probe Diameter ◽  
Low Voltage Operation ◽  
Sufficient Intensity ◽  
Electron Microscopes ◽  
Scanning Electron Microscopes ◽  
Immersion Type

With the introduction of field-emission sources and “immersion-type” objective lenses, the resolution obtainable with modern scanning electron microscopes is approaching that obtainable in STEM and TEM-but only with specific types of specimens. Bulk specimens still suffer from the restrictions imposed by internal scattering and the need to be conducting. Advances in coating techniques have largely overcome these problems but for a sizeable body of specimens, the restrictions imposed by coating are unacceptable.For such specimens, low voltage operation, with its low beam penetration and freedom from charging artifacts, is the method of choice.Unfortunately the technical dificulties in producing an electron beam sufficiently small and of sufficient intensity are considerably greater at low beam energies — so much so that a radical reevaluation of convential design concepts is needed.The probe diameter is usually given by

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