The q-deformed mKP hierarchy with two parameters

2018 ◽  
Vol 32 (16) ◽  
pp. 1850170
Author(s):  
Kelei Tian ◽  
Yanyan Ge ◽  
Xiaoming Zhu
Keyword(s):  
Additional Symmetry ◽  
Lax Equation ◽  
Quantum Calculus ◽  
Two Parameters ◽  
Sato Theory

In this paper, with the help of the biparametric quantum calculus we construct the Sato theory on the q-deformation modified Kadomtsev–Petviashvili hierarchy with two parameters (qp-mKP), which is a new deformation of classical mKP hierarchy. The Lax equation and dressing operator of qp-mKP hierarchy are derived. By considering the M operator and [Formula: see text] operator, the additional symmetry of qp-mKP hierarchy is obtained.

Symmetries of the multi-component Boussinesq hierarchy

2021 ◽  
pp. 2150111
Author(s):  
Meiyan Hu ◽  
Chuanzhong Li
Keyword(s):  
Wave Function ◽  
Generating Function ◽  
String Equation ◽  
Additional Symmetry ◽  
Infinite Dimensional ◽  
Lax Operator ◽  
Sato Theory ◽  
The Way

In this paper, we construct the Lax operator of the multi-component Boussinesq hierarchy. Based on the Sato theory and the dressing structure of the multi-component Boussinesq hierarchy, the adjoint wave function and the Orlov–Schulman’s operator are introduced, which are useful for constructing the additional symmetry of the multi-component Boussinesq hierarchy. Besides, the additional flows can commute with the original flows, and these flows form an infinite dimensional [Formula: see text] algebra. Taking the above discussion into account, we mainly study the additional symmetry flows and the generating function for both strongly and weakly multi-component of the Boussinesq hierarchies. By the way, using the [Formula: see text] constraint of the multi-component Boussinesq hierarchy, the string equation can be derived.

scholarly journals DISPERSIONLESS BIGRADED TODA HIERARCHY AND ITS ADDITIONAL SYMMETRY

2012 ◽  
Vol 24 (07) ◽  
pp. 1230003 ◽  
Author(s):  
CHUANZHONG LI ◽  
JINGSONG HE
Keyword(s):  
Additional Symmetry ◽  
Tau Function ◽  
Toda Hierarchy ◽  
Definition Of ◽  
Sato Theory ◽  
Bilinear Equations

In this paper, we firstly give the definition of dispersionless bigraded Toda hierarchy (dBTH) and introduce some Sato theory on dBTH. Then we define Orlov–Schulman's [Formula: see text], [Formula: see text] operator and give the additional Block symmetry of dBTH. Meanwhile we give tau function of dBTH and some related dispersionless bilinear equations.

scholarly journals Certain Inequalities Involving the Fractionalq-Integral Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Dumitru Baleanu ◽  
Praveen Agarwal
Keyword(s):  
Integral Operator ◽  
Integral Operators ◽  
Quantum Calculus ◽  
Special Cases ◽  
Two Parameters

We establish some inequalities involving Saigo fractionalq-integral operator in the theory of quantum calculus by using the two parameters of deformation,q1andq2, whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville and Kober fractionalq-integral operators, respectively. Furthermore, we also consider their relevance with other related known results.

scholarly journals Generalized Weighted Ostrowski, Trapezoid and Grüss Type Inequalities on Time Scales

2018 ◽  
Vol 60 (1) ◽  
pp. 123-144 ◽  
Author(s):  
A. A. El-Deeb ◽  
H. A. Elsennary ◽  
Eze R. Nwaeze
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Type Inequality ◽  
Quantum Calculus ◽  
Arbitrary Time ◽  
Ostrowski Type Inequality ◽  
Grüss Type Inequalities ◽  
Two Parameters ◽  
Delta Derivatives

Abstract In this article, using two parameters, we obtain generalizations of a weighted Ostrowski type inequality and its companion inequalities on an arbitrary time scale for functions whose first delta derivatives are bounded. Our work unifies the continuous and discrete versions and can also be applied to the quantum calculus case.

Photo-electric Hβ and uvby photometry

1966 ◽  
Vol 24 ◽  
pp. 170-180
Author(s):  
D. L. Crawford
Keyword(s):  
Narrow Band ◽  
Line Strength ◽  
Interference Filter ◽  
B Stars ◽  
Relative Line ◽  
The Mean ◽  
F Stars ◽  
Two Parameters ◽  
Filter Photometry ◽  
The Continuum

Early in the 1950's Strömgren (1, 2, 3, 4, 5) introduced medium to narrow-band interference filter photometry at the McDonald Observatory. He used six interference filters to obtain two parameters of astrophysical interest. These parameters he calledlandc, for line and continuum hydrogen absorption. The first measured empirically the absorption line strength of Hβby means of a filter of half width 35Å centered on Hβand compared to the mean of two filters situated in the continuum near Hβ. The second index measured empirically the Balmer discontinuity by means of a filter situated below the Balmer discontinuity and two above it. He showed that these two indices could accurately predict the spectral type and luminosity of both B stars and A and F stars. He later derived (6) an indexmfrom the same filters. This index was a measure of the relative line blanketing near 4100Å compared to two filters above 4500Å. These three indices confirmed earlier work by many people, including Lindblad and Becker. References to this earlier work and to the systems discussed today can be found in Strömgren's article inBasic Astronomical Data(7).

Radiation Damage of Support Films

1981 ◽  
Vol 39 ◽  
pp. 28-29
Author(s):  
H.A. Cohen ◽  
W. Chiu
Keyword(s):  
Transfer Function ◽  
Low Temperatures ◽  
Carbon Support ◽  
Contrast Transfer Function ◽  
Electron Dose ◽  
Imaging Parameters ◽  
Negative Stain ◽  
Phase Corrections ◽  
Two Parameters ◽  
Medium Dose

The goal of imaging the finest detail possible in biological specimens leads to contradictory requirements for the choice of an electron dose. The dose should be as low as possible to minimize object damage, yet as high as possible to optimize image statistics. For specimens that are protected by low temperatures or for which the low resolution associated with negative stain is acceptable, the first condition may be partially relaxed, allowing the use of (for example) 6 to 10 e/Å2. However, this medium dose is marginal for obtaining the contrast transfer function (CTF) of the microscope, which is necessary to allow phase corrections to the image. We have explored two parameters that affect the CTF under medium dose conditions.Figure 1 displays the CTF for carbon (C, row 1) and triafol plus carbon (T+C, row 2). For any column, the images to which the CTF correspond were from a carbon covered hole (C) and the adjacent triafol plus carbon support film (T+C), both recorded on the same micrograph; therefore the imaging parameters of defocus, illumination angle, and electron statistics were identical.

Applications of Scanning Microscopy in Biomedical Research

1968 ◽  
Vol 26 ◽  
pp. 354-355
Author(s):  
T. L. Hayes
Keyword(s):  
Information Content ◽  
Biomedical Research ◽  
Biomedical Applications ◽  
Three Dimensional ◽  
Dental Enamel ◽  
Resolving Power ◽  
Whole Mount ◽  
Two Parameters ◽  
Content Information ◽  
Sectioned Tissue

Biomedical applications of the scanning electron microscope (SEM) have increased in number quite rapidly over the last several years. Studies have been made of cells, whole mount tissue, sectioned tissue, particles, human chromosomes, microorganisms, dental enamel and skeletal material. Many of the advantages of using this instrument for such investigations come from its ability to produce images that are high in information content. Information about the chemical make-up of the specimen, its electrical properties and its three dimensional architecture all may be represented in such images. Since the biological system is distinctive in its chemistry and often spatially scaled to the resolving power of the SEM, these images are particularly useful in biomedical research.In any form of microscopy there are two parameters that together determine the usefulness of the image. One parameter is the size of the volume being studied or resolving power of the instrument and the other is the amount of information about this volume that is displayed in the image. Both parameters are important in describing the performance of a microscope. The light microscope image, for example, is rich in information content (chemical, spatial, living specimen, etc.) but is very limited in resolving power.

Transcription factor/DNA interactions visualized by electron spectroscopic imaging

1992 ◽  
Vol 50 (1) ◽  
pp. 450-451
Author(s):  
David P. Bazett-Jones ◽  
Mark L. Brown
Keyword(s):  
Transcription Factor ◽  
Dna Sequences ◽  
Transcription Initiation ◽  
Molecular Mechanisms ◽  
Phosphorus Content ◽  
Spectroscopic Imaging ◽  
Electron Spectroscopic Imaging ◽  
Dna Backbone ◽  
Two Parameters ◽  
High Level

A multisubunit RNA polymerase enzyme is ultimately responsible for transcription initiation and elongation of RNA, but recognition of the proper start site by the enzyme is regulated by general, temporal and gene-specific trans-factors interacting at promoter and enhancer DNA sequences. To understand the molecular mechanisms which precisely regulate the transcription initiation event, it is crucial to elucidate the structure of the transcription factor/DNA complexes involved. Electron spectroscopic imaging (ESI) provides the opportunity to visualize individual DNA molecules. Enhancement of DNA contrast with ESI is accomplished by imaging with electrons that have interacted with inner shell electrons of phosphorus in the DNA backbone. Phosphorus detection at this intermediately high level of resolution (≈lnm) permits selective imaging of the DNA, to determine whether the protein factors compact, bend or wrap the DNA. Simultaneously, mass analysis and phosphorus content can be measured quantitatively, using adjacent DNA or tobacco mosaic virus (TMV) as mass and phosphorus standards. These two parameters provide stoichiometric information relating the ratios of protein:DNA content.

Practical Importance of Spatial Resolution and Analytical Sensitivity in AEM X-ray Microanalysis

1990 ◽  
Vol 48 (2) ◽  
pp. 432-433
Author(s):  
J. Zhang ◽  
D.B. Williams ◽  
J.I. Goldstein
Keyword(s):  
Spatial Resolution ◽  
Practical Importance ◽  
Beam Current ◽  
Specimen Thickness ◽  
Analytical Sensitivity ◽  
Related Factors ◽  
X Ray ◽  
Probe Size ◽  
Excitation Volume ◽  
Two Parameters

Analytical sensitivity and spatial resolution are important and closely related factors in x-ray microanalysis using the AEM. Analytical sensitivity is the ability to distinguish, for a given element under given conditions, between two concentrations that are nearly equal. The analytical sensitivity is directly related to the number of x-ray counts collected and, therefore, to the probe current, specimen thickness and counting time. The spatial resolution in AEM analysis is determined by the probe size and beam broadening in the specimen. A finer probe and a thinner specimen give a higher spatial resolution. However, the resulting lower beam current and smaller X-ray excitation volume degrade analytical sensitivity. A compromise must be made between high spatial resolution and an acceptable analytical sensitivity. In this paper, we show the necessity of evaluating these two parameters in order to determine the low temperature Fe-Ni phase diagram.A Phillips EM400T AEM with an EDAX/TN2000 EDS/MCA system and a VG HB501 FEG STEM with a LINK AN10 EDS/MCA system were used.

On the influence of specimen thickness in TEM images of super-conducting vortices

1996 ◽  
Vol 54 ◽  
pp. 724-725
Author(s):  
J. Bonevich ◽  
D. Capacci ◽  
G. Pozzi ◽  
K. Harada ◽  
H. Kasai ◽  
...  
Keyword(s):  
Flux Line ◽  
Analytical Form ◽  
Realistic Model ◽  
Electron Holography ◽  
Specimen Thickness ◽  
Flux Tubes ◽  
Analytical Expression ◽  
Flux Lines ◽  
Normal Core ◽  
Two Parameters

The successful observation of superconducting flux lines (fluxons) in thin specimens both in conventional and high Tc superconductors by means of Lorentz and electron holography methods has presented several problems concerning the interpretation of the experimental results. The first approach has been to model the fluxon as a bundle of flux tubes perpendicular to the specimen surface (for which the electron optical phase shift has been found in analytical form) with a magnetic flux distribution given by the London model, which corresponds to a flux line having an infinitely small normal core. In addition to being described by an analytical expression, this model has the advantage that a single parameter, the London penetration depth, completely characterizes the superconducting fluxon. The obtained results have shown that the most relevant features of the experimental data are well interpreted by this model. However, Clem has proposed another more realistic model for the fluxon core that removes the unphysical limitation of the infinitely small normal core and has the advantage of being described by an analytical expression depending on two parameters (the coherence length and the London depth).

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