The solution of the one-dimensional sign problem for Fourier transforms

1984 ◽  
Vol 40 (2) ◽  
pp. 137-142 ◽  
Author(s):  
D. I. Svergun ◽  
L. A. Feigin ◽  
B. M. Schedrin
Keyword(s):  
Fourier Transforms ◽  
One Dimensional ◽  
Sign Problem ◽  
The One

The shift lattice: an interpretation of some infinitely adaptive structures

1993 ◽  
Vol 440 (1908) ◽  
pp. 23-36 ◽  
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Periodic Systems ◽  
Adaptive Structures ◽  
One Dimensional ◽  
Modulated Structures ◽  
Simple Generalization ◽  
The One

The structures of various ordered, but non-periodic, systems have been investigated and exhibit features which can be directly described by means of a construction which the authors call the shift lattice , which is a simple generalization of the concept of the lattice. This paper is devoted to a description of the properties of the one-dimensional shift lattice and its Fourier transform. Its applications to the phases related to L–Ta 2 O 5 and some Bi 2 TeO 5 -related systems are outlined and its relation to the theory of modulated structures and their Fourier transforms is briefly discussed.

FAST DHT ALGORITHMS FOR COMPOSITE SEQUENCE LENGTHS

1998 ◽  
Vol 08 (03) ◽  
pp. 421-434
Author(s):  
GUOAN BI ◽  
YANQIU CHEN
Keyword(s):  
Fourier Transforms ◽  
Fast Algorithms ◽  
Sequence Length ◽  
Discrete Fourier Transforms ◽  
One Dimensional ◽  
Discrete Hartley Transform ◽  
Hartley Transform ◽  
Computational Structure ◽  
The One

This paper presents fast algorithms for the computation of discrete Hartley transform (DHT). When the sequence length N = p*q, where p and q are integers and relatively prime, the one dimensional DHT can be decomposed into p length-q DHT's and q length-p discrete Fourier transforms (DFT). Compared to other reported algorithms, the proposed one has a regular computational structure, provides flexibility for composite sequence lengths and achieves substantial savings on the required number of operations.

X-ray diffraction of helices with arbitrary periodic ligand binding

1999 ◽  
Vol 55 (12) ◽  
pp. 2022-2027 ◽  
Author(s):  
Jin Gu ◽  
Leepo C. Yu
Keyword(s):  
Ligand Binding ◽  
Fourier Transforms ◽  
Muscle Actin ◽  
X Ray Diffraction ◽  
Helical Structures ◽  
One Dimensional ◽  
X Ray ◽  
Classical Formalism ◽  
Diffraction Patterns ◽  
The One

The classical formalism for studying diffraction from helical structures extended to include ligand binding is presented. The diffraction from such a binding pattern is the convolution of the Fourier transforms of the helix and the one-dimensional binding distribution. It is shown in the present analysis that it is not necessary to assume that the binding distribution is strictly periodic, as long as its Fourier transform can be determined. Analysis of the convolution gives a general expression for the diffracted intensities and the selection rule for the layer-lines. It shows two groups of layer-lines: one group is the familiar layer-line set from the original helix, while the other group shows reciprocal spacings shifted by 1/a from the original helix layer-lines, where a is the average repeat of the binding distribution. This group of layer-lines is contributed by the ligand only. By way of examples, calculated diffraction patterns from muscle actin filaments with bound myosin heads in three different binding patterns are presented. This approach provides a method for determining the ligand-binding distribution along helices by an analysis of their X-ray diffraction patterns.

On the SU(2)×SU(2) symmetry in the Hubbard model

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Dorota Jakubczyk ◽  
Paweł Jakubczyk
Keyword(s):  
Hubbard Model ◽  
Spin Chain ◽  
Fourier Transforms ◽  
Exact Diagonalization ◽  
Unitary Groups ◽  
Conserved Quantities ◽  
One Dimensional ◽  
Hubbard Hamiltonian ◽  
Quantum Numbers ◽  
The One

AbstractWe discuss the one-dimensional Hubbard model, on finite sites spin chain, in context of the action of the direct product of two unitary groups SU(2)×SU(2). The symmetry revealed by this group is applicable in the procedure of exact diagonalization of the Hubbard Hamiltonian. This result combined with the translational symmetry, given as the basis of wavelets of the appropriate Fourier transforms, provides, besides the energy, additional conserved quantities, which are presented in the case of a half-filled, four sites spin chain. Since we are dealing with four elementary excitations, two quasiparticles called “spinons”, which carry spin, and two other called “holon” and “antyholon”, which carry charge, the usual spin-SU(2) algebra for spinons and the so called pseudospin-SU(2) algebra for holons and antiholons, provide four additional quantum numbers.

scholarly journals OPTIMIZED AND QUASI-OPTIMAL SCHWARZ WAVEFORM RELAXATION FOR THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2010 ◽  
Vol 20 (12) ◽  
pp. 2167-2199 ◽  
Author(s):  
LAURENCE HALPERN ◽  
JÉRÉMIE SZEFTEL
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fourier Transforms ◽  
Optimal Algorithm ◽  
Waveform Relaxation ◽  
One Dimensional ◽  
Schwarz Waveform Relaxation ◽  
Discrete Algorithms ◽  
Relaxation Algorithms ◽  
The One

Schwarz waveform relaxation algorithms are designed for the linear Schrödinger equation with potential. Two classes of algorithms are introduced: the quasi-optimal algorithm, based on the transparent continuous or discrete boundary condition, and the optimized complex Robin algorithm. We analyze their properties in one dimension. First, well-posedness and convergence are studied, in the overlapping and the non-overlapping case, for constant or non-constant potentials. Then discrete algorithms are established, for which convergence is proved through discrete energies or Fourier transforms, as in the continuous case. Numerical results illustrate the efficiency of the methods, for various types of potentials and any number of subdomains.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Adiabatic large polarons in anisotropic molecular crystals

2011 ◽  
Vol 35 (1) ◽  
pp. 15-27
Author(s):  
Zoran Ivić ◽  
Željko Pržulj
Keyword(s):  
Energy Transfer ◽  
Effective Mass ◽  
Molecular Crystals ◽  
Single Chain ◽  
Proper Understanding ◽  
One Dimensional ◽  
Interchain Coupling ◽  
Large Polaron ◽  
The One

Adiabatic large polarons in anisotropic molecular crystals We study the large polaron whose motion is confined to a single chain in a system composed of the collection of parallel molecular chains embedded in threedimensional lattice. It is found that the interchain coupling has a significant impact on the large polaron characteristics. In particular, its radius is quite larger while its effective mass is considerably lighter than that estimated within the one-dimensional models. We believe that our findings should be taken into account for the proper understanding of the possible role of large polarons in the charge and energy transfer in quasi-one-dimensional substances.

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