scholarly journals Spectral curves are transcendental

2021 ◽  
Vol 111 (1) ◽  
Author(s):  
H. W. Braden
Keyword(s):  
Spectral Curve ◽  
Spectral Curves ◽  
Arithmetic Properties ◽  
A Charge

AbstractSome arithmetic properties of spectral curves are discussed: the spectral curve, for example, of a charge $$n\ge 2$$ n ≥ 2 Euclidean BPS monopole is not defined over $$\overline{\mathbb {Q}}$$ Q ¯ if smooth.

NEGATIVE NUMBERS AND ANTIMATTER PARTICLES

2012 ◽  
Vol 21 (01) ◽  
pp. 1250005 ◽  
Author(s):  
UNG CHAN TSAN
Keyword(s):  
Complete Agreement ◽  
Negative Numbers ◽  
Arithmetic Properties ◽  
A Value ◽  
Great Hope ◽  
Baryonic Number ◽  
The Standard Model ◽  
The Difference ◽  
A Charge ◽  
Precise Testing

Dirac's equation states that an electron implies the existence of an antielectron with the same mass (more generally same arithmetic properties) and opposite charge (more generally opposite algebraic properties). Subsequent observation of antielectron validated this concept. This statement can be extended to all matter particles; observation of antiproton, antineutron, antideuton … is in complete agreement with this view. Recently antihypertriton was observed and 38 atoms of antihydrogen were trapped. This opens the path for use in precise testing of nature's fundamental symmetries. The symmetric properties of a matter particle and its mirror antimatter particle seem to be well established. Interactions operate on matter particles and antimatter particles as well. Conservation of matter parallels addition operating on positive and negative numbers. Without antimatter particles, interactions of the Standard Model (electromagnetism, strong interaction and weak interaction) cannot have the structure of group. Antimatter particles are characterized by negative baryonic number A or/and negative leptonic number L. Materialization and annihilation obey conservation of A and L (associated to all known interactions), explaining why from pure energy (A = 0, L = 0) one can only obtain a pair of matter particle antimatter particle — electron antielectron, proton and antiproton — via materialization where the mass of a pair of particle antiparticle gives back to pure energy with annihilation. These two mechanisms cannot change the difference in the number of matter particles and antimatter particles. Thus from pure energy only a perfectly symmetric (in number) universe could be generated as proposed by Dirac but observation showed that our universe is not symmetric, it is a matter universe which is nevertheless neutral. Fall of reflection symmetries shattered the prejudice that there is no way to define in an absolute way right and left or matter and antimatter. Experimental observation of CP violation aroused a great hope for explaining why our universe is not exactly matter antimatter symmetric. Sakharov stated that without the violation of baryonic number, it is not possible to obtain from pure energy a universe made of only matter. The fact that our universe is asymmetric (in number) but perfectly neutral, points toward the existence of a hypothetic interaction violating A and L but conserving all charges. This Matter Creation (MC) interaction creating either a pair of matter particles or antimatter particles (instead of a pair of particle antiparticle) would have a charge BAL = (A-L) and a neutral messenger Z*. Even if CP is conserved, MC would allow the creation of a number of matter particles not exactly equal to the number of antimatter particles. Our universe would then correspond to the remaining excess when all matter antimatter pairs have disappeared. Observation of matter nonconservation processes would be of great interest to falsify this speculation. In a plan with A and L as axes, pure energy is represented by the origin (A = 0, L = 0). A symmetric universe is also represented by (A = 0, L = 0) meaning that there are exactly the same number of baryons and antibaryons, and the same number of leptons and antileptons. Our present matter universe is instead represented by a point of the diagonal with A = L = present A value. This value is tiny relative to the number of gammas resulting from the annihilation of matter–antimatter particles.

JNR monopoles

2020 ◽  
Author(s):  
Michael K Murray ◽  
Paul Norbury
Keyword(s):  
Energy Density ◽  
Simple Form ◽  
Spectral Curve ◽  
Rational Maps ◽  
Rational Map ◽  
Spectral Curves

Abstract We review the theory of JNR, mass $\frac{1}{2}$ hyperbolic monopoles in particular their spectral curves and rational maps. These are used to establish conditions for a spectral curve to be the spectral curve of a JNR monopole and to show that the rational map of a JNR monopole arises by scattering using results of Atiyah. We show that for JNR monopoles the holomorphic sphere has a remarkably simple form and show that this can be used to give a formula for the energy density at infinity. In conclusion, we illustrate some examples of the energy density at infinity of JNR monopoles.

A New Method for Spectral Matching Pretreatment

2014 ◽  
Vol 556-562 ◽  
pp. 527-530
Author(s):  
Yun Ting Zhou ◽  
Xiao Ping Du ◽  
Ming Zhe Li
Keyword(s):  
Numerical Simulations ◽  
Spectral Curve ◽  
Initial Period ◽  
New Method ◽  
Spectral Absorption ◽  
Spectral Matching ◽  
Spectral Curves ◽  
Peak Point ◽  
The Times ◽  
Spectral Match

Since spectral curves were obtained by experiment, on the basis of the fully use of the waveform characters, a new method for spectral matching pretreatment has been proposed in this paper. Corresponding to the spectral curve, we can accurately get the spectral absorption curve of the number of bands, it can effectively suppress the effects of the noise according to the times of fitting the points. Besides, it can also prominent the peak point of the material. This method can have an effective influence on the initial period of spectral match and detailed resolution; some numerical simulations have been made to test the validity and capability of the proposed method.

Full Automation of Infrared Qualitative Analysis of Binary Mixtures by Use of a Spectral Curve Compilation

1984 ◽  
Vol 38 (5) ◽  
pp. 693-697 ◽  
Author(s):  
Shinnosuke Saëki ◽  
Kazutoshi Tanabe
Keyword(s):  
Qualitative Analysis ◽  
Binary Mixtures ◽  
Spectral Curve ◽  
National Chemical Laboratory ◽  
Chemical Laboratory ◽  
Spectral Curves ◽  
Cpu Time ◽  
Infrared Spectral ◽  
Full Automation ◽  
Coefficient Method

A project for the compilation of infrared spectral curves is now in progress at the National Chemical Laboratory for Industry, Japan On the basis of this compilation, a computer program has been developed for the full automation of infrared qualitative analysis of binary mixtures by means of the correlation coefficient method The program has been applied to six binary mixtures Four of them had resolutions as high as that in file spectra, and the other two, which were prepared from the former by convolution, had lower resolution The correct answers have been obtained automatically in all cases The CPU time necessary for the running of this program was from 60 to 90 seconds with the use of a FACOM M200 computer system

scholarly journals Identification of Typical Solid Hazardous Chemicals Based on Hyperspectral Imaging

2021 ◽  
Vol 13 (13) ◽  
pp. 2608
Author(s):  
Yanlong Sun ◽  
Xinming Qian ◽  
Yangyang Liu ◽  
Jianwei Wang ◽  
Qunbo Lv ◽  
...  
Keyword(s):  
Hyperspectral Imaging ◽  
Corn Starch ◽  
Spectral Curve ◽  
Spectral Characteristics ◽  
Wheat Starch ◽  
Carbon Powder ◽  
Strontium Nitrate ◽  
Hazardous Chemicals ◽  
Spectral Curves ◽  
Matching Degree

The identification of hazardous chemicals based on hyperspectral imaging is an important emergent means for the prevention of explosion accidents and the early warning of secondary hazards. In this study, we used a combination of spectral curve matching based on full-waveform characteristics and spectral matching based on spectral characteristics to identify the hazardous chemicals, and proposed a method to quantitatively characterize the matching degree of the spectral curves of hazardous chemicals. The results showed that the four hazardous chemicals, sulfur, red phosphorus, potassium permanganate, and corn starch had bright colors, distinct spectral curve characteristics, and obvious changes in reflectivity, which were easy to identify. Moreover, the matching degree of their spectral curves was positively correlated with their reflectivity. However, the spectral characteristics of carbon powder, strontium nitrate, wheat starch, and magnesium–aluminum alloy powder were not obvious, with no obvious characteristic peaks or trends of change in reflectivity. Except for the reflectivity and the matching degree of the carbon powder being maintained at a low level, the reflectivity of the remaining three samples was relatively close, so that it was difficult to identify with the spectral curves alone, and color information should be considered for further identification.

scholarly journals Compressed Sensing Technology for Spectral Reconstruction Based on Maximum Entropy Criterion

2021 ◽  
Author(s):  
Shoubo Zhao ◽  
Mengyu Yang ◽  
Yang Wang ◽  
Jianying Fan
Keyword(s):  
Compressed Sensing ◽  
Maximum Entropy ◽  
Spectral Reflectance ◽  
Spectral Curve ◽  
Hyperspectral Data ◽  
Threshold Method ◽  
Data Set ◽  
Spectral Curves ◽  
Sensing Technology ◽  
Entropy Criterion

Abstract In order to choose the related sampling ratio in the information-poor and information-rich spectral fragments, this paper attempts to recover the spectral reflectance by compressed sensing technology based on maximum entropy criterion. The maximum entropy threshold method is the criterion that the optimal threshold is determined to segment the information content of spectral curves. The spectral reflectance in each sub-spectral fragment is reconstructed by compressed sensing. The wavelet orthogonal matrix performs a sparse representation of each segmented spectral curve. Undersampling spectral curve be collected by random gaussian measurement matrix. The orthogonal matching pursuit algorithm recovers sparse original signals from undersampling observed signals. In this paper, the four standard color blocks of Munsell and the spectral curves of five types of ground objects in the hyperspectral data set are used as the exper-imental objects. The reconstructed results are evaluated by spectral curve reconstruction, root mean square error and information entropy difference. The experimental results show that our approach improves the reconstruction accuracy of spectral reflectance effectively, compared with the traditional method.

scholarly journals Topological recursion with hard edges

2019 ◽  
Vol 30 (03) ◽  
pp. 1950014
Author(s):  
Leonid Chekhov ◽  
Paul Norbury
Keyword(s):  
Matrix Model ◽  
Spectral Curve ◽  
Partition Functions ◽  
Tau Function ◽  
Spectral Curves ◽  
Topological Recursion ◽  
The Matrix ◽  
Type Decomposition

We prove a Givental type decomposition for partition functions that arise out of topological recursion applied to spectral curves. Copies of the Konstevich–Witten KdV tau function arise out of regular spectral curves and copies of the Brezin–Gross–Witten KdV tau function arise out of irregular spectral curves. We present the example of this decomposition for the matrix model with two hard edges and spectral curve [Formula: see text].

scholarly journals Spectral Curves for the Derivative Nonlinear Schrödinger Equations

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1203
Author(s):  
Aleksandr O. Smirnov
Keyword(s):  
Nonlinear Optics ◽  
Spectral Data ◽  
Nonlinear Waves ◽  
Fourier Transforms ◽  
Spectral Curve ◽  
Evolutionary Equations ◽  
Nonlinear Schrödinger ◽  
Spectral Curves ◽  
The Third ◽  
Nonlinear Signal

Currently, in nonlinear optics, models associated with various types of the nonlinear Schrödinger equation (scalar (NLS), vector (VNLS), derivative (DNLS)), as well as with higher and mixed equations from the corresponding hierarchies are usually studied. Typical tools for solving the problem of propagation of optical nonlinear waves are the forward and inverse nonlinear Fourier transforms. One of the methods for reconstructing a periodic nonlinear signal is based on the use of spectral data in the form of spectral curves. In this paper, we study the properties of the spectral curves for all the derivatives NLS equations simultaneously. For all the main DNLS equations (DNLSI, DNLSII, DNLSIII), we have obtained unified Lax pairs, unified hierarchies of evolutionary and stationary equations, as well as unified equations of spectral curves of multiphase solutions. It is shown that stationary and evolutionary equations have symmetries, the presence of which leads to the existence of holomorphic involutions on spectral curves. Because of this symmetry, spectral curves of genus g are covers over other curves of genus M and N=g−M, where M is a number of phase of solutions. We also showed that the number of the genus g of the spectral curve is related to the number of phases M of the solution of one of the two formulas: g=2M or g=2M+1. The third section provides examples of the simplest solutions.

Electron Holographic Nano-Characterization of Gold Catalyst at Interface

2002 ◽  
Vol 727 ◽  
Author(s):  
S. Ichikawa ◽  
T. Akita ◽  
M. Okumura ◽  
M. Haruta ◽  
K. Tanaka
Keyword(s):  
Contact Angle ◽  
Titanium Oxide ◽  
Gold Catalyst ◽  
Three Dimensional ◽  
High Resolution Electron Microscopy ◽  
Electron Holography ◽  
Gold Particles ◽  
Oxide Support ◽  
The Mean ◽  
A Charge

AbstractThe catalytic properties of nanostructured gold catalyst are known to depend on the size of the gold particles and to be activated when the size decreases to a few nanometers. We investigated the size dependence of the three-dimensional nanostructure on the mean inner potential of gold catalysts supported on titanium oxide using electron holography and high-resolution electron microscopy (HREM). The contact angle of the gold particles on the titanium oxide tended to be over 90° for gold particles with a size of over 5 nm, and below 90° for a size of below 2 nm. This decreasing change in the contact angle (morphology) acts to increase the perimeter and hence the area of the interface between the gold and titanium oxide support, which is considered to be an active site for CO oxidation. The mean inner potential of the gold particles also changed as their size decreased. The value of the inner potential of gold, which is approximately 25 V in bulk state, rose to over 40 V when the size of the gold particles was less than 2 nm. This phenomenon indicates the existence of a charge transfer at the interface between gold and titanium oxide. The 3-D structure change and the inner potential change should be attributed to the specific electronic structure at the interface, owing to both the “nano size effect” and the “hetero-interface effect.”

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