Energy—Momentum Pseudo—tensor of Cylindrical Gravitational Waves of Both the Polarized States

According to the Einstein-Tolman expression of the energy-momentum pseudo-tensor(EMPT),we calculate the EMPT of cylindrical gravitational waves (CGW) of both the polarized states (BPS) in cylindrical polar coordinates and Cartesian coordinates.We find that Cartesian coordinates are the more suitable coordinates to describe the CGW of BPS.     

T-duality as permutation of coordinates in double space

We introduce the 2D dimensional double space with the coordinates Z~M=(x~μ,y_μ),whose components are the coordinates of initial space x~μ and its T-dual y_μ.We shall show that in this extended space the T-duality transformations can be realized simply by exchanging the places of some coordinates x~a,along which we want to perform T-duality,and the corresponding dual coordinates y_a.In such an approach it is evident that T-duality leads to the physically equivalent theory and that a complete set of T-duality transformations forms a subgroup of the 2D permutation group.So,in double space we are able to represent the backgrounds of all T-dual theories in a unified manner.     

Hawking Temperature of a Static Black Hole in Harmonic Coordinates

Hawking radiation is usually studied in standard coordinates. In this paper,we calculate the Hawking temperature of a Schwarzschild black hole in harmonic coordinates,as well as that of a Reissner–Nordstr?m black hole.The action of a scalar field near the event horizon can be formulated exactly without omitting some high-order terms.We show dimensional reduction for Hawking temperature is also valid for harmonic coordinates,and verify further that the results are independent on concrete coordinates. With the help of Lorentz transformation,our work might also serve as a basis to investigate the thermal radiation from a moving black hole.     

Pose measurement method based on geometrical constraints

The pose estimation method based on geometric constraints is studied.The coordinates of the five feature points in the camera coordinate system are calculated to obtain the pose of an object on the basis of the geometric constraints formed by the connective lines of the feature points and the coordinates of the feature points on the CCD image plane;during the solution process,the scaling and orthography projection model is used to approximate the perspective projection model.The initial values of the coordinates of the five feature points in the camera coordinate system are obtained to ensure the accuracy and convergence rate of the non-linear algorithm.In accordance with the perspective projection characteristics of the circular feature landmarks,we propose an approach that enables the iterative acquisition of accurate target poses through the correction of the perspective projection coordinates of the circular feature landmark centers.Experimental results show that the translation positioning accuracy reaches ±0.05 mm in the measurement range of 0-40 mm,and the rotation positioning accuracy reaches ±0.06° in the measurement range of 4°-60°.     

Quantum Hamilton--Jacobi Approach to Two Dimensional Singular Oscillator

We obtain the solutions of two-dimensional singular oscillator which is known as the quantum Calogero-Sutherland model both in cartesian and parabolic coordinates within the framework of quantum Hamilton Jacobi formalism. Solvability conditions and eigenfunctions are obtained by using the singularity structures of quantum momentum functions under some conditions. New potentials are generated by using the first two states of singular oscillator for parabolic coordinates.     

Chaos game representation （CGR）-walk model for DNA sequences

Chaos game representation (CGR) is an iterative mapping technique that processes sequences of units, such as nucleotides in a DNA sequence or amino acids in a protein, in order to determine the coordinates of their positions in a continuous space. This distribution of positions has two features: one is unique, and the other is source sequence that can be recovered from the coordinates so that the distance between positions may serve as a measure of similarity between the corresponding sequences. A CGR-walk model is proposed based on CGR coordinates for the DNA sequences. The CGR coordinates are converted into a time series, and a long-memory ARFIMA (p, d, q) model, where ARFIMA stands for autoregressive fractionally integrated moving average, is introduced into the DNA sequence analysis. This model is applied to simulating real CGR-walk sequence data of ten genomic sequences. Remarkably long-range correlations are uncovered in the data, and the results from these models are reasonably fitted with those from the ARFIMA (p, d, q) model.     

Finite entropy of Schwarzschild anti-de sitter black hole in different coordinates

This paper studies the finite statistical-mechanical entropy of the Schwarzschild anti-de Sitter (AdS) spacetime arising from quantum massless scalar field by using the `brick wall' approach in the Painlev\'e and Lemaitre coordinates. At first glance, it seems that the results would be different from that in the Schwarzschild-like coordinate since both the Painlev\'e and the Lemaitre spacetimes do not possess the event horizon obviously. However, this paper proves that the entropies in these coordinates are exactly equivalent to that in the Schwarzschild-like coordinate.     

Approach to a Cauchy Problem in Stability Study of the Schwarzschild Black Hole

Generally, the Schwarzschild black hole is proven to be stable by two different methods： the mode-decomposition method and the integral method. We show that the integral method can only apply to the initial data vanishing at both the horizon and the spatial infinity. It can not treat the initial data only vanishing at the spatial infinity. We give an example to show the misleading information caused by the use of tortoise coordinates in the perturbation equations. Subsequently, the perturbation equations in the Schwarzschild coordinates are shown to be insuftlcient for the stability study.     

Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations with Redundant Coordinates

Structural equations and Mei conserved quantity of Mei symmetry for Appell equations in a holonomic system with redundant coordinates are studied. Some aspects, including the differential equations of motion, the definition and the criterion of Mei symmetry, the form of structural equations and Mei conserved quantity of Mei symmetry of Appell equations for a holonomic system with redundant coordinates, are also investigated. Finally, an example is given to illustrate the application of the results.     

Restudy of the stability problem of the Schwarzschild black hole

The stability of the Schwarzschild black hole is restudied in the Painlevé coordinates. Using the Painlevé time coordinate to define the initial time, we reconsider the odd perturbation and find that the Schwarzschild black hole in the Painlevé coordinates is unstable. The Painlevé metric in this paper corresponds to the white-hole-connected region of the Schwarzschild black hole (r>2m) and the odd perturbation may be regarded as the angular perturbation. Therefore, the white-hole-connected region of the Schwarzschild black hole is unstable with respect to the rotating perturbation.     

Invariant expression for tunneling rate under canonical transformations

The original formula to calculate the tunneling rate through event horizons is apparently dependent on the type of coordinates used.In this paper,we propose an invariant expression under canonical transformations to study the tunneling effect.Moreover,the problem of factor 2 is solved naturally.As an application of this expression,we obtain the same tunneling rate both in the Schwarzschild and the Painleve′coordinates.It is shown that once the suitable formula to calculate tunneling rate is correctly identified,the tunneling method is manifestly covariant.     

Brick Walls for Nonstationary Black Holes

The validity condition of the brick-wall model is analysed in nonstationary space-time.It is shown that the model holds only in thin regions,only by using tortoise coordinates near the event horizon of a slowly varying(quasistationary)black hole.The reason for the use of tortoise cooridnates is that the stationary state solutions of quantum field equations in other coordinates do not exist for any region in nonstationary space-time.Meanwhile,the quantum corrections to the entropy of the Vaidya-Bonner black hole due to the spin fields are calculated in terms of the brick-wall model.     

Covariant Anomaly and Hawking Radiation from Kerr-Newman Black Hole in Dragging Coordinates Frame

in the light of Robinson and Wilczek＇s new idea, and motivated by Banerjee and Kulkarni＇s simplified method of using only the covariant anomaly to derive Hawking radiation from a black hole, we generally extend the work to Kerr-Newman black hole in dragging coordinates frame. It is shown that the flows introduced to cancel the anomaly at the event horizon are equal to the corresponding Hawking radiation in dragging coordinates frame, which supports and extends Robinson and Wilczek＇s opinion.     

Pure RGB Emissions Based on a White OLED Combined with Optical Colour Filters

We report on a white organic light emitting device （OLED） with a single light emitting layer consisting of a greenish-white emitting host bis-（2-（2-hydroxyphenyl） benzothiazole）zinc （Zn（BTZ）2 ） and an orange-red dopant 5,6,11,12-tetraphenylnaphthacene （rubrene）. The Commission Internationale De L＇Eclairage （CIE） coordinates, external quantum efficiency, and brightness of the white OLED are （0.341, 0.334）, 0.63% and 4000 Cd/m^2 at the bias of 20 V, respectively. Pure red-green-blue （RGB） emissions have been successfully achieved from the white OLED combined well with several built-in optical colour filters （CFs）. The CIE coordinates of the white mixture calculated in theory are very close to the coordinates of the white mixture which recorded with spectrophotometer in practice.     

The parametric orbits and the form invariance of three-body in one-dimension

In this paper, the differential equations of motion of a three-body interacting pairwise by inverse cubic forces(“centrifugal potential”) in addition to linear forces (“harmonical potential”) are expressed in Ermakov formalism in two-dimension polar coordinates, and the Ermakov invariant is obtained. By rescaling of the time variable and the space coordinates, the parametric orbits of the three bodies are expressed in terms of relative energy H1 and Ermakov invariant. The form invariance of the transformations of two conserved quantities are also studied.     

New Types of the Lie Symmetries and Conserved Quantities for a Relativistic Hamiltonian System

For a relativistic Hamiltonian system,two new types of the Lie symmetries and conservation laws are given under infinitesimal transformaitons of groups.On the basis of the theory of invariance of the relativistic Hamiltonian equations under infinitesimal transformations and introducing infinitesimal transformations for time t,generalized coordinates qs and generalized monenta ps,we obtain the determinging equations,the structure equations and the conserved quantities of the Lie symmetries.Introducing infinitesimal transformation for generalized coordinates qs and generalized momenta ps,we construct the Lie symmetrical transformations of the system,which only depend on the canonical variables.A set of conserved quantities are directly obtained from the Lie symmetries of the syste.An example is given to illustrante the application of the results.     

Global dynamical analysis of vibrational manifolds of HOCl and HOBr under anharmonicity and Fermi resonance: the dynamical potential approach

The vibrational dynamics of HOCl and HOBr between bending and OCl/OBr stretching coordinates with anharmonicity and Fermi coupling is studied with the classical dynamical potential approach. The quantal vibrational dynamics is mostly mapped out by the classical nonlinear variables such as fixed points, except for the state energies, which are quantized. This approach is global in the sense that the focus is on a set of levels instead of individual ones. The dynamics of HOBr is demonstrated to be less complicated. The localized modes along the OCl/OBr stretching coordinates are also shown to have O--Br bonds more prone to dissociation.     

General Noncommuting Curvilinear Coordinates and Fluid Mechanics

We show that restricting the states of a charged particle to the lowest Landau level introduces noncommutativity between general curvilinear coordinate operators. The Cartesian, circular cylindrical and spherical polar coordinates are three special cases of our quite general method. The connection between U（1） gauge fields defined on a general noncommuting curvilinear coordinates and fluid mechanics is explained. We also recognize the Seiberg-Witten map from general noncommuting to commuting variables as the quantum correspondence of the Lagrange-to-Euler map in fluid mechanics.     

The construction of conserved quantities for linearly coupled oscillators and study of symmetries about the conserved quantities

In this paper, the conserved quantities are constructed using two methods. The first method is by making an ansatz of the conserved quantity and then using the definition of Poisson bracket to obtain the coefficients in the ansatz. The main procedure for the second method is given as follows. Firstly, the coupled terms in Lagrangian are eliminated by changing the coordinate scales and rotating the coordinate axes, secondly, the conserved quantities are obtain in new coordinate directly, and at last, the conserved quantities are expressed in the original coordinates by using the inverse transform of the coordinates. The Noether symmetry and Lie symmetry of the infinitesimal transformations about the conserved quantities are also studied in this paper.     

Ground state energy of He isoelectronic sequence treated variationally via Hylleraas-like wavefunction

In this study, the energy for the ground state of helium and a few helium-like ions (Z=1-6) is computed variationally by using a Hylleraas-like wavefunction. A four-parameters wavefunction, satisfying boundary conditions for coalescence points, is combined with a Hylleraas-like basis set which explicitly incorporates r12 interelectronic distance. The main contribution of this work is the introduction of modified correlation terms leading to the definition of integral transforms which provide the calculation of expectation value of energy to be done analytically over single-particle coordinates instead of Hylleraas coordinates.