Idea Of Quantization Research Articles

Helton-Howe trace, Connes-Chern characters and Toeplitz quantization of Bergman spaces

We study the Helton-Howe trace and the Connes-Chern character for Toeplitz operators on weighted Bergman spaces via the idea of quantization. We prove a local formula for the large t-limit of the Connes-Chern character as the weight goes to infinity. And we show that the Helton-Howe trace of Toeplitz operators is independent of the weight t and obtain a local formula for the Helton-Howe trace for all weighted Bergman spaces using harmonic analysis and quantization.

A blind color image watermarking algorithm using the energy concentration principle of Hadamard matrix

The convenience of the network has brought the copyright crisis of some multimedia works. Therefore, a secure digital watermarking algorithm is urgently needed to realize the copyright maintenance of digital works. A blind digital watermarking algorithm using approximate Hadamard transform is presented in this paper. Since Hadamard transform has a certain energy aggregation effect, in this paper, the principle of energy concentration of Hadamard transform is explored, and the Hadamard transform is slightly treated, so that the multiple increase of large energy coefficient is realized. This modified approximate Hadamard transform is applied to the process of changing from spatial domain to transform domain in the embedding and extraction stage of our proposed watermarking algorithm. In this algorithm, the color image digital watermark is hided in the maximum energy coefficient of color host image in transform domain by using the idea of quantization. In the extraction stage, the watermark image can be extracted completely without the participation of any original information. In order to check on the feasibility of the algorithm, a large number of simulation experiments have been done. The results of simulation experiments show that the proposed algorithm has excellent effect in various performance index.

Angular Spectral Density and Information Entropy for Eddy Current Distribution

Here, a new method is proposed to quantitatively evaluate the eddy current distribution induced by different exciting coils of an eddy current probe. Probability of energy allocation of a vector field is modeled via conservation of energy and imitating the wave function in quantum mechanics. The idea of quantization and the principle of circuit sampling is utilized to discretize the space of the vector field. Then, a method to calculate angular spectral density and Shannon information entropy is proposed. Eddy current induced by three different exciting coils is evaluated with this method, and the specific nature of eddy current testing is discussed.

Структурно-топологический анализ взаимодействия акторов мирохозяйственной системы: на примере исследования интеграции стран ЕС и ЕАЭС

More than 100 years ago, the concept of quantization began to go beyond natural and physical sciences. For instance, quantum numbers are used to determine the electron configuration of an atom, the probable location of the atom’s electronsand other characteristics of atoms. The main idea of quantization is the application of “double nature” logic to observed processes and phenomena, as well as to their driving forces and structure. Based on this logic, the principle of wave -particle duality was developed in physics and mathematics and provides the basis for quantum mechanics and relativistic theory. This principle applied to analysis and calculations helps to formulate fundamental theories to explain processes and structure using relativistic velocity and, in turn, describe operations of the material world at the macro and micro levels. This article applies the concepts of quantization and representation duality (which is the analysis of the dual nature of facts and events observed at the macro and micro levels) to social, economic and political data to describe the dynamics of actors and processes of the multiple connections of the global system. The analysis of the current state of world’s multiple connections in a macroeconomic context is conducted with inapproved parameters that characterize the dynamics of various changes that explain events in a two-dimensional manner.Often criticized by experts, these parameters have been supplemented by new ones, which have not yet resolved the flaw sin such a study of changes in economic processes. This article describes a theoretical concept of a structural-topological approach based on presenting global multiple connections in the form of two aggregated spaces - the space of events and the space of states - that complement each other to create a single system. The study demonstrates the representation method of the global economy illustrated through a practical analysis of integrational processes in the European Union and the Eurasian Economic Union. The method presented in this article can be used along with existing research methods to understand global fluctuations.

Quantization Strategies of RFID Routing in Internet of Things

This paper researches wireless RFID routings in Internet of Things based on the idea of quantization. The researches include the obtaining of routing contexts, the measurement of contexts in evaluating the performance of routing, methods for controlling the quantification of contexts, the realization of a perceptive computational model, the mergence of the security policies. Its goal is to construct a precise lightweight and perceptive model of wireless RFID routing protocols in Internet of Things, and to lay a foundation for accelerating the developments in Internet of Things.

The correspondence principle in Abelian Lagrangian geometry

We present a new idea of quantization of classical mechanical systems, which uses the constructions of [2], [7] and [1]. As a first step, we verify the correspondence between the Poisson brackets on the initial symplectic manifold and on the moduli space of half-weighted Bohr-Sommerfeld Lagrangian cycles of a fixed volume.

Modern Physics, 3rd edn

The number of broadly based physics texts written at a level corresponding to second year and above of UK physics degrees is limited. This is such a book thoroughly updated in a third edition, the first edition having been published 20 years ago. The book is unusual in that the reader is referred to the Freeman website www.whfreeman.com/physics for some additional sections. It will be interesting to see whether this proves to be an attractive feature. The coverage reflects the US emphasis on topics and contains both theoretical and experimental details. It should not be regarded as an introductory text although it is clearly written. Thus the first two chapters take the reader straight into relativity, concentrating mainly on special relativity but going on to general relativity. From here the reader is led to ideas of quantization of charge, light and energy, followed by an exploration of the nuclear atom, wavelike properties of particles and Schr�dinger's equation. Solution of this equation for the hydrogen atom introduces a section on spectroscopy. The next chapter on statistical physics includes Fermi-Dirac and Bose-Einstein statistics and brings to a close Part 1, which concentrates on the theoretical groundwork. Consistent with its title, the book does not cover traditional aspects of thermodynamics and electromagnetic theory. Part 2 is entitled `Applications' and begins with a chapter on molecular structure and spectra. Lasers and masers are included here but geometrical, physical and nonlinear optics get limited or no coverage. Solid state physics follows but, despite the title of the book, there is little on modern devices, although the section on superconductivity mentions high temperature materials. The chapters on nuclear physics, fission, fusion reactors and medical applications and a chapter on particle physics are comprehensive. Finally a chapter on astrophysics and cosmology is referred to, but the reader must find this at the website. As this is an attractive chapter it is a pity that it is not printed within the book. Although viewing the chapter on the Web gives the benefit of full colour, it is not easy to read the textual information off the screen. Within the printed material, there are good diagrams with the addition of a single colour, burgundy, a colour that is wasted on those of us who are red-green colour-blind! Each chapter is provided with an impressive number of graded problems (it is not easy to provide such a comprehensive range of problems at this level) and numerical answers are given in the back for every third problem. There is a student solution manual available for these problems and a complete instructor's solution manual has also been produced. It is therefore a useful book for both students and lecturers.