scholarly journals ASSOCIATED LAMÉ EQUATION, PERIODIC POTENTIALS AND sl(2, ℝ)

2000 ◽  
Vol 15 (31) ◽  
pp. 1923-1930 ◽  
Author(s):  
ASISH GANGULY
Keyword(s):  
Band Edge ◽  
Energy Spectra ◽  
New Approach ◽  
Lamé Equation ◽  
Half Integer ◽  
Periodic Potentials ◽  
Explicit Expressions

We propose a new approach based on the algebraization of the associated Lamé equation [Formula: see text] within sl(2, ℝ) to derive the corresponding periodic potentials. The band edge eigenfunctions and energy spectra are explicitly obtained for integers m, l. We also obtain the explicit expressions of the solutions for half-integer m and integer or half-integer l.

scholarly journals BAND EDGE EIGENFUNCTIONS AND EIGENVALUES FOR PERIODIC POTENTIALS THROUGH THE QUANTUM HAMILTON–JACOBI FORMALISM

2004 ◽  
Vol 19 (27) ◽  
pp. 2047-2058 ◽  
Author(s):  
S. SREE RANJANI ◽  
A. K. KAPOOR ◽  
P. K. PANIGRAHI
Keyword(s):  
Type Equation ◽  
Band Edge ◽  
Conformal Transformations ◽  
Edge States ◽  
Straightforward Manner ◽  
Singularity Structure ◽  
Periodic Potentials ◽  
Jacobi Formalism ◽  
Momentum Function

We demonstrate the procedure of finding the band edge eigenfunctions and eigenvalues of periodic potentials, through the quantum Hamilton–Jacobi formalism. The potentials studied here are the Lamé and associated Lamé, which belong to the class of elliptic potentials. The formalism requires an assumption about the singularity structure of the quantum momentum function p, obeying a Riccati type equation in the complex x-plane. Essential use is made of suitable conformal transformations, which lead to the eigenvalues and the eigenfunctions corresponding to the band edges, in a straightforward manner. Our study reveals interesting features about the singularity structure of p, underlying the band edge states.

scholarly journals Subdiffractive band-edge solitons in Bose-Einstein condensates in periodic potentials

2006 ◽  
Vol 73 (6) ◽  
Author(s):  
Kestutis Staliunas ◽  
Ramon Herrero ◽  
Germán J. de Valcárcel
Keyword(s):  
Band Edge ◽  
Periodic Potentials ◽  
Bose Einstein

scholarly journals A new approach to Bell and poly-Bell numbers and polynomials

2021 ◽  
Vol 7 (3) ◽  
pp. 4004-4016
Author(s):  
Taekyun Kim ◽  
◽  
Dae San Kim ◽  
Dmitry V. Dolgy ◽  
Hye Kyung Kim ◽  
...  
Keyword(s):  
Recurrence Relations ◽  
Bell Polynomials ◽  
Bell Numbers ◽  
New Approach ◽  
Special Polynomials ◽  
Explicit Expressions

<abstract><p>Bell polynomials are widely applied in many problems arising from physics and engineering. The aim of this paper is to introduce new types of special polynomials and numbers, namely Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving those polynomials and numbers. We also consider degenerate versions of those polynomials and numbers, namely degenerate Bell polynomials and numbers of the second kind and degenerate poly-Bell polynomials and numbers of the second kind, and deduce their similar results.</p></abstract>

scholarly journals A New Approach to the Non Relativistic Schrödinger Equation for an Energy-Depended Potential V(r,En,l)=V0(1+ηEn,l)r2 in both Noncommutative Three Dimensional Spaces and Phases

2015 ◽  
Vol 60 ◽  
pp. 11-19 ◽  
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Bound States ◽  
Zeeman Effect ◽  
Three Dimensional ◽  
Energy Spectra ◽  
Noncommutative Space ◽  
New Approach ◽  
3 Dimensional ◽  
New States ◽  
Space Phase ◽  
Ordinary Quantum

In present work we study the 3-dimensional non relativistic and noncommutative space-phase Schrödinger equation for modified potential (see formula in paper) depends on energy and quadratic on the relative distance, we have obtained the exact modified bound-states solutions. It has been observed that, the energy spectra in ordinary quantum mechanics was changed, and replaced by degenerate new states, depending on new discreet quantum numbers:n, l, j and s=±1/2 . We show the noncommutative new anisotropic Hamiltonian containing two new important terms, the first new term describe the spin-orbit interaction while the second describes the modified Zeeman effect.

The photonic band edge laser: A new approach to gain enhancement

1994 ◽  
Vol 75 (4) ◽  
pp. 1896-1899 ◽  
Author(s):  
Jonathan P. Dowling ◽  
Michael Scalora ◽  
Mark J. Bloemer ◽  
Charles M. Bowden
Keyword(s):  
Band Edge ◽  
New Approach ◽  
Gain Enhancement ◽  
Photonic Band

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.

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