Deformed Bosons: Combinatorics of Normal Ordering

We solve the normal ordering problem for (A A) ⁿ where A and A are one mode deformed ([A,A ] = [N+1] – [N]) bosonic ladder operators. The solution generalizes results known for canonical bosons. It involves combinatorial polynomials in the number operator N for which the generating function and explicit expressions are found. Simple deformations provide examples of the method.     

Combinatorial Coherent States via Normal Ordering of Bosons

We construct and analyze a family of coherent states built on sequences of integers originating from the solution of the boson normal ordering problem. These sequences generalize the conventional combinatorial Bell numbers and are shown to be moments of positive functions. Consequently, the resulting coherent states automatically satisfy the resolution of unity condition. In addition they display such non-classical fluctuation properties as super-Poissonian statistics and squeezing.     

Generalized Dirichlet Normal Ordering in Open Bosonic Strings

Generally, open string boundary conditions play a nontrivial role in string theory. For example, in the presence of an antisymmetric tensor background field, they will lead the spacetime coordinates noncommutative. In this paper, we mainly discuss how to build up a generalized Dirichlet normal ordered product of open bosonic string embedding operators that satisfies both the equations of motion and the generalized Dirichlet boundary conditions at the quantum level in the presence of an antisymmetric background field, as the generalized Neumann case has already been discussed in the literature. Further, we also give a brief check of the consistency of the theory under the newly introduced normal ordering.     

Normal Ordering Solution to Quantum Dissipation and Its Induced Decoherence

We implement the normal ordering technique to study the quantum dissipation of a single mode harmonic oscillator system. The dynamic evolution of the system is investigated for a reasonable initial state by solving the Schrödinger equation directly through the normal ordering technique. The decoherence process of the system for the cases T=0 K and T≠0 K is investigated as an application.     

Normal Ordering the Squeeze Operator by Generalized Wick Theorem

The recently proposed generalized Wick theorem offers a simple way to normal ordering the squeeze operator, shown by the present notes dedicated to the memory of J. Janszky.     

正规排列和反正规排列相互展开的计算

文章给出了产生算符和湮灭算例的正规排列与反正规排列相互展开的二个计算公式为（^a)^n(^a^ )^m=p/∑／k=0m!n!/(m-k)!(n-k)!k!(^a^ )^m-k(^a)^n-k和（^a^ )^n(^a)^m)=p/∑k=0(-1)^km!n!/(m-k)!(n-k)!k!(^a)^m-k(^a^ )^n-k，式中求和的上项p取m和n中较小的一个正整数。并用数学归纳法进行了证明，本文给出的这二次公式可广泛应用于各类激发态光场量子统计性质的研究。     

Normal and Abnormal Grain Growth as Transient Phenomena

For the case of uniform grain boundaries the basic equations of the statistical theory of grain growth (GG) of the present authors are shortly reviewed and compared to the classical Hillert model. On the basis of this present theory normal and abnormal 3-D GG is simulated and particularly the effect of the initial grain size distribution function (SDF) on the GG behaviour which may lead to normal or abnormal GG is demonstrated. Finally results of simulations of normal 2-D GG by the statistical method and by a direct model (curvature driven grain boundaries (GBs)) are presented which exhibit good agreement with one another. It is shown by this comparison that the possibility of finding by such direct methods a self similar SDF as long time asymptote can be excluded because, in contrast to the simulations based on the statistical theory, for the direct models the very large computational capacities required for the long simulation times are not available yet. The conclusion repeatedly claimed in literature that the true self similar SDF deviates from the Hillert distribution can thus be shown not to be justified.     

正常和异常血清的共振散射光谱

用日本岛津RF-5301荧光分光光度计研究了高甘油三脂、高胆同醇、高血糖血清和正常血清的散射光谱及同一生化指标不同浓度血清散射光谱的规律.实验结果表明,正常血清散射光谱与高血脂和高血糖血清散射光谱的特征峰差异明显,可以据此区分正常和高血糖、高血脂血清;同一生化指标不同浓度血清散射光谱的峰值强度随血脂、血糖浓度的增大而增...     

Normal Ordering Expansion of Hermite Polynomials of Radial Coordinate Operator in Three-Dimensional Coordinate Space

For Hermite polynomials of radial coordinate operator in three-dimensional coordinate space we derive its normal ordering expansion, which are new operator identities. This is done by virtue of the technique of integration within an ordered product of operators. Application of the new formulas is briefly discussed.     

Operator Formulas Involving Generalized Stirling Number Derived by Virtue of Normal Ordering of Vacuum Projector

By virtue of the normal ordering of vacuum projector we directly derive some new complicated operator identities, regarding to the generalized Stirling number.     

CNN-FWS: A Model for the Diagnosis of Normal and Abnormal ECG with Feature Adaptive

(1) Background and objective: Cardiovascular disease is one of the most common causes of death in today’s world. ECG is crucial in the early detection and prevention of cardiovascular disease. In this study, an improved deep learning method is proposed to diagnose abnormal and normal ECG accurately. (2) Methods: This paper proposes a CNN-FWS that combines three convolutional neural networks (CNN) and recursive feature elimination based on feature weights (FW-RFE), which diagnoses abnormal and normal ECG. F1 score and Recall are used to evaluate the performance. (3) Results: A total of 17,259 records were used in this study, which validated the diagnostic performance of CNN-FWS for normal and abnormal ECG signals in 12 leads. The experimental results show that the F1 score of CNN-FWS is 0.902, and the Recall of CNN-FWS is 0.889. (4) Conclusion: CNN-FWS absorbs the advantages of convolutional neural networks (CNN) to obtain three parts of different spatial information and enrich the learned features. CNN-FWS can select the most relevant features while eliminating unrelated and redundant features by FW-RFE, making the residual features more representative and effective. The method is an end-to-end modeling approach that enables an adaptive feature selection process without human intervention.     

Time Ordering and Counting Statistics

The basic quantum mechanical relation between fluctuations of transported charge and current correlators is discussed. It is found that, as a rule, the correlators are to be time-ordered in an unusual way. Instances where the difference with the conventional ordering matters are illustrated by means of a simple scattering model. We apply the results to resolve a discrepancy concerning the third cumulant of charge transport across a tunnel junction.     

Ordering in alloys

Abstract

The continuous ordering process can be viewed as a development and a gradual amplification of concentration modulations with wave lengths of the order of a few lattice spacings. How the development of different concentration modulaltions leads to different superlattice structures in cubic systems is explained with the help of some illustrative examples. The importance of concentration modulations with special point wave vectors in the stability of the various coherent superlattice structures is discussed. Experimental evidences for such continuous ordering is cited from recent results on ordering in Ni-Mo alloys.

The evolution of ordering in some systems can also be viewed as progressively tiling the disordered lattice by superlattice tiles. When more than one type of coherent superlattice tiles compete, juxtaposition of different types of tiles can occur during the course of ordering. The transitional states between the short range and the long range ordered Ni-Mo alloys indeed exhibit such structures where different types of superlattice tiles decorate the fcc lattice. The role of special point concentration waves in the development of such structures will be discussed in relation to the secondary ordering processes involving two perpendicular ?1 ½ 0? waves and a combination of an ?1 ½ 0? and an appropriate ?100? wave.     

Ordering and conformational transitions in cholesteryl benzoate

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 49, No. 5, pp. 833–839, November, 1988.     

Ordering energy and stability of perfect superlattices

The rigorous solution to the problem of stability of stochiometric ordered phases is considered. Conditions of stability are found relative to phases with maximal degree of order for given stochiometry. The treatment is given for all known superlattices that arise from an fcc solid solution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 22–26, September, 1980.     

Ordering and phase transitions in liquid crystals

Structures and properties of different types of liquid crystals are discussed from a uniform point of view. Apart from the traditional mesophases (nematics, cholesterics, smectics), some new examples, including polymeric, metalloorganic and ferromagnetic liquid crystals, are also investigated. Systems with several macroscopic scales on which the type of ordering may differ, are described and analysed. Phase transitions and certain types of critical behaviour in different liquid crystals are studied.     

Generalized Weyl Ordering and Nonlinear Coherent States

In the context of the nonlinear coherent state (NLCS) theory we introduce the generalized Weyl orderingoperator formulation. The corresponding generalized Wigner operator turns out to be the Weyl ordered Dirac δ-operatorfunctions. The completeness relation of NLCS is recast into generalized Weyl ordering form. The relationship betweennormal ordering, antinormal ordering and the generalized Weyl ordering is established which constitute a self-consistenttheory for NLCS.     

Generalized Weyl Ordering and Nonlinear Coherent States

In the context of the nonlinear coherent state(NLCS)theory we introduce the generalized weyl ordering operator formulation.The corresponding generalzied wigner operator turns out to be the Weyl ordered diracδ-operator functions.The completeness relation of NLCS is recast into generalized Weyl ordering form,The relationship between normal ordering,antinormal ordering and the generalized Weyl ordering is established which constitute a self-consistent theory for NLCS.