Translation partitions of unity, symmetry properties, and Gabor frames

2021 ◽  
Vol 47 (4) ◽  
Author(s):  
Ole Christensen ◽  
Say Song Goh ◽  
Hong Oh Kim ◽  
Rae Young Kim
Keyword(s):  
Gabor Frames ◽  
Symmetry Properties

Semi-automated methods for 3-D reconstruction of macromolecular complexes

1995 ◽  
Vol 53 ◽  
pp. 42-43
Author(s):  
B. Carragher ◽  
M. Whittaker
Keyword(s):  
Three Dimensional ◽  
Time Saving ◽  
Macromolecular Complexes ◽  
Symmetry Properties ◽  
Dimensional Reconstruction ◽  
Experienced Operator ◽  
Projection Images ◽  
The Individual ◽  
Natural Symmetry

Techniques for three-dimensional reconstruction of macromolecular complexes from electron micrographs have been successfully used for many years. These include methods which take advantage of the natural symmetry properties of the structure (for example helical or icosahedral) as well as those that use single axis or other tilting geometries to reconstruct from a set of projection images. These techniques have traditionally relied on a very experienced operator to manually perform the often numerous and time consuming steps required to obtain the final reconstruction. While the guidance and oversight of an experienced and critical operator will always be an essential component of these techniques, recent advances in computer technology, microprocessor controlled microscopes and the availability of high quality CCD cameras have provided the means to automate many of the individual steps.During the acquisition of data automation provides benefits not only in terms of convenience and time saving but also in circumstances where manual procedures limit the quality of the final reconstruction.

Symmetry properties of a universal interaction

Physica ◽  
1952 ◽  
Vol 18 (2) ◽  
pp. 1017-1019 ◽  
Author(s):  
D PURSEY
Keyword(s):  
Symmetry Properties ◽  
Universal Interaction

On the symmetry properties of the incommensurate phase of thiourea

1987 ◽  
Vol 48 (11) ◽  
pp. 2023-2026 ◽  
Author(s):  
T. Simonson ◽  
F. Ddnoyer ◽  
R. Currat
Keyword(s):  
Incommensurate Phase ◽  
Symmetry Properties

Symmetry properties of the transitional sphere wake

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 579-582 ◽  
Author(s):  
R. Mittal ◽  
J. Wilson ◽  
F. M. Najjar
Keyword(s):  
Symmetry Properties

Symmetry properties of fractional order transport equations

2012 ◽  
Vol 9 (1) ◽  
pp. 59-64
Author(s):  
R.K. Gazizov ◽  
A.A. Kasatkin ◽  
S.Yu. Lukashchuk
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lie Group ◽  
Initial Conditions ◽  
Group Analysis ◽  
Equivalence Transformation ◽  
Point Change ◽  
Infinitesimal Operator ◽  
Symmetry Properties ◽  
Fractional Differential

In the paper some features of applying Lie group analysis methods to fractional differential equations are considered. The problem related to point change of variables in the fractional differentiation operator is discussed and some general form of transformation that conserves the form of Riemann-Liouville fractional operator is obtained. The prolongation formula for extending an infinitesimal operator of a group to fractional derivative with respect to arbitrary function is presented. Provided simple example illustrates the necessity of considering both local and non-local symmetries for fractional differential equations in particular cases including the initial conditions. The equivalence transformation forms for some fractional differential equations are discussed and results of group classification of the wave-diffusion equation are presented. Some examples of constructing particular exact solutions of fractional transport equation are given, based on the Lie group methods and the method of invariant subspaces.

Axially Chiral Bis(α-amino Acid)s and Their Deamino Analogues. Synthesis and Configurational Assignment

1998 ◽  
Vol 63 (2) ◽  
pp. 211-221 ◽  
Author(s):  
Miloš Tichý ◽  
Luděk Ridvan ◽  
Miloš Buděšínský ◽  
Jiří Závada ◽  
Jaroslav Podlaha ◽  
...  
Keyword(s):  
Amino Acid ◽  
Nmr Spectra ◽  
Building Blocks ◽  
X Ray Diffraction ◽  
Amino Groups ◽  
X Ray ◽  
Configurational Assignment ◽  
Symmetry Properties ◽  
Axially Chiral ◽  
Polymeric Structures

The axially chiral bis(α-amino acid)s cis-2 and trans-2 as possible building blocks for polymeric structures of novel type of helicity were prepared. Their configuration has been determined by NMR spectroscopy and, in the case of the trans-isomer, confirmed by single-crystal X-ray diffraction. Analogous pair of stereoisomeric diacids cis-3 and trans-3, devoid of the amino groups, was also prepared and their configuration assigned. The observed differences in the NMR spectra of cis- and trans-isomers of 2 and 3 are discussed from the viewpoint of their different symmetry properties.

Quantum Boxes, Stringed Instruments

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Energy Level ◽  
Schrödinger Equation ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Probability Distributions ◽  
Wave Functions ◽  
Energy Level Diagram ◽  
One Dimensional ◽  
Stringed Instruments ◽  
Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

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