Super W_(1+∞) n-Algebra in the Supersymmetric Landau Problem

We analyze the super n-bracket built from associative operator products.Since the super n-bracket with n even satisfies the so-called generalized super Jacobi identity,we deal with the n odd case and give the generalized super Bremner identity.For the infinite conserved operators in the supersymmetric Landau problem,we derive the super W_(1+∞) n-algebra which satisfies the generalized super Jacobi and Bremner identities for the n even and odd cases,respectively.Moreover the super W_(1+∞) sub-2n-algebra is also given.     

Algebraic Treatment of the MIC-Kepler System in Spherical Coordinates

The MIC-Kepler system is studied via the Milshtein Strakhovenko variant of the so（2,1） Lie algebra. Green＇s function is constructed in spherical coordinates, with the help of the Kustaanheimo Stiefel variables and the generators of the S0（2,1） group. The energy spectrum and the normalized wavefunctions of the bound states are obtained.     

A Complex Higher-Dimensional Lie Algebra with Real and Imaginary Structure Constants as Well as Its Decomposition

A new Lie algebra G of the Lie algebra sl（2） is constructed with complex entries whose structure constants are real and imaginary numbers. A loop algebra G corresponding to the Lie algebra G is constructed, for which it is devoted to generating a soliton hierarchy of evolution equations under the framework of generalized zero curvature equation which is derived from the compatibility of the isospectral problems expressed by Hirota operators. Finally, we decompose the Lie algebra G to obtain the subalgebras G1 and G2. Using the G2 and its one type of loop algebra G2, a Liouville integrable soliton hierarchy is obtained, furthermore, we obtain its bi-Hamiltonian structure by employing the quadratic-form identity.     

Hamiltonian analysis of 4-dimensional spacetime in Bondi-like coordinates

We discuss the Hamiltonian formulation of gravity in four-dimensional spacetime under Bondi-like coordinates {v,r,x~a,a=2,3}. In Bondi-like coordinates, the three-dimensional hypersurface is a null hypersurface, and the evolution direction is the advanced time v. The internal symmetry group SO(1,3) of the four-dimensional spacetime is decomposed into SO(1,1), SO(2), and T~±(2), whose Lie algebra so(1,3) is decomposed into so(1,1), so(2), and t~±(2) correspondingly. The SO(1,1) symmetry is very obvious in this type of decomposition, which is very useful in so(1,1) BF theory. General relativity can be reformulated as the four-dimensional coframe(e_μ~I) and connection(ω_μ~(IJ))dynamics of gravity based on this type of decomposition in the Bondi-like coordinate system. The coframe consists of two null 1-forms e~-, e~+and two spacelike 1-forms e~2, e~3. The Palatini action is used. The Hamiltonian analysis is conducted by Dirac's methods. The consistency analysis of constraints has been done completely. Among the constraints, there are two scalar constraints and one two-dimensional vector constraint. The torsion-free conditions are acquired from the consistency conditions of the primary constraints about π_(IJ)~μ. The consistency conditions of the primary constraints π_(IJ)~0=0 can be reformulated as Gauss constraints. The conditions of the Lagrange multipliers have been acquired. The Poisson brackets among the constraints have been calculated. There are 46 constraints including 6 first-class constraints π_(IJ)~0=0 and 40 second-class constraints. The local physical degrees of freedom is 2.The integrability conditions of Lagrange multipliers n_0, l_0, and e_0~A are Ricci identities. The equations of motion of the canonical variables have also been shown.     

A diagrammatic categorification of q-boson and q-fermion algebras

In this paper,we study the diagrammatic categorification of q-boson algebra and also q-fermion algebra.We construct a graphical category corresponding to q-boson algebra.q-Fock states correspond to some kind of 1-morphisms,and the graded dimension of the graded vector space of 2-morphisms is exactly the inner product of the corresponding q-Fock states.We also find that this graphical category can be used to categorify q-fermion algebra.     

su（1,2） Algebraic Structure of XYZ Antiferromagnetic Model in Linear Spin-Wave Frame

The XYZ antiferromagnetic model in linear spin-wave frame is shown explicitly to have an su（1,2） algebraic structure： the Hamiltonian can be written as a linear function of the su（1,2） algebra generators. Based on it, the energy eigenvalues are obta/ned by making use of the similar transformations, and the algebraic diagonalization method is investigated. Some numerical solutions are given, and the results indicate that only one group solution could be accepted in physics.     

Integrable Coupling of （2＋1）-Dimensional Multi-component DLW Integrable Hierarchy and Its Hamiltonian Structure

A new multi-component Lie algebra is constructed, and a type of new loop algebra is presented. A （2＋1）-dimensional multi-component DLW integrable hierarchy is obtained by using a （2＋1）-dimensional zero curvature equation. Furthermore, the loop algebra is expanded into a larger one and a type of integrable coupling system and its corresponding Hamiltonian structure are worked out.     

STATISTICAL ENTROPIES OF THE TAUB－NUT/BOLT AdS SPACES FROM THE HORIZON CONFORMAL FIELD THEORY

The covariant phase technique is used to compute the constraint algebra of the four-dimensional space-times which are asymptotic to anti-de Sitter (AdS), such as the planar Taub－NUT AdS and Taub－bolt AdS spaces, and the hyperbolic Taub－bolt AdS space. The standard Virasoro subalgebrae with corresponding central charges for these objects are constructed and the resulting densities of states yield the expected Bekenstein－Hawking entropies.     

Kac-Moody-Virasoro Symmetry Algebra of （2＋1）-Dimensional Dispersive Long-Wave Equation with Arbitrary Order Invariant

By Lie symmetry method, the Lie point symmetries and its Kac Moody-Virasoro （KMV） symmetry algebra of （2＋1）-dimensional dispersive long-wave equation （DLWE） are obtained, and the finite transformation of DLWE is given by symmetry group direct method, which can recover Lie point symmetries. Then KMV symmetry algebra of DLWE with arbitrary order invariant is also obtained. On basis of this algebra the group invariant solutions and similarity reductions are also derived.     

An integrable Hamiltonian hierarchy, a high-dimensional loop algebra and associated integrable coupling system

A subalgebra of loop algebra ?_2 is established. Therefore, a new isospectral problem is designed. By making use of Tu's scheme, a new integrable system is obtained, which possesses bi-Hamiltonian structure. As its reductions, a formalism similar to the well-known Ablowitz－Kaup－Newell－Segur (AKNS) hierarchy and a generalized standard form of the Schr?dinger equation are presented. In addition, in order for a kind of expanding integrable system to be obtained, a proper algebraic transformation is supplied to change loop algebra ?_2 into loop algebra ?_1. Furthermore, a high-dimensional loop algebra is constructed, which is different from any previous one. An integrable coupling of the system obtained is given. Finally, the Hamiltonian form of a binary symmetric constrained flow of the system obtained is presented.     

Effects of W~(6+) occupying Sc~(3+) on the structure,vibration, and thermal expansion properties of scandium tungstate

We experimentally investigate effects of W~(6+)occupying the sites of Sc~(3+)in the unit cell of Sc_2 W_3 O_(12)(Sc_8 W_(12) O_(48))on the structure, vibration and thermal expansion. The composition and structure of the doped sample(Sc_6 W_2)W_(12) O_(48±δ)(with two W~(6+)occupying two sites of Sc~(3+)in the unit cell of Sc_8 W_(12) O_(48)) are analyzed and identified by combining the x-ray photoelectron spectroscopy and the synchronous x-ray diffraction with first-principles calculations based on density functional theory. Results show that the crystal with even W~(6+)occupying even Sc~(3+)in the unit cell is stable and maintains the orthorhombic structure at room temperature. The structure of the doped sample is similar to that of Sc_2 W_3 O_(12), and with even W occupying even positions of Sc in the unit cell and constituting the WO_6 octahedra. Raman analyses show that the doped sample possesses stronger W–O bonds and wider Raman linewidths than those of Sc_2 W_3 O_(12). The sample doped with W also exhibits intrinsic negative thermal expansion in the measured range of 150 K–650 K.     

Generation of an isolated sub-30 attosecond pulse in a two-color laser field and a static electric field

We theoretically investigate high-order harmonic generation(HHG) from a helium ion model in a two-color laser field,which is synthesized by a fundamental pulse and its second harmonic pulse.It is shown that a supercontinuum spectrum can be generated in the two-color field.However,the spectral intensity is very low,limiting the application of the generated attosecond(as) pulse.By adding a static electric field to the synthesized two-color field,not only is the ionization yield of electrons contributing to the harmonic emission remarkably increased,but also the quantum paths of the HHG can be significantly modulated.As a result,the extension and enhancement of the supercontinuum spectrum are achieved,producing an intense isolated 26-as pulse with a bandwidth of about 170.5 eV.In particular,we also analyse the influence of the laser parameters on the ultrabroad supercontinuum spectrum and isolated sub-30-as pulse generation.     

An Approximate Analytical Solution of Imploding Strong Shocks in a Non-Ideal Gas through Lie Group Analysis

The method of Lie group transformation is used to obtain an approximate analytical solution to the system of first-order quasilinear partial differential equations that govern a one-dimensional unsteady planer, cylindrically symmetric and spherically symmetric motion in a non-ideal gas, involving strong shock waves. Invariance groups admitted by the governing system of partial differential equations, which are indeed continuous group of transformations under which the system of partial differential equations remains invariant, are determined, and the complete Lie algebra of infinitesimal symmetries is established. The infinitesimal generators are used to construct the similarity variables. These similarity variables are used to reduce the governing system of partial differential equations into a system of ordinary differential equations.     

Aspheric surface measurement based on sub-aperture stitching interferometry

In order to test convex aspheric surfaces without the aid of other null optics, a novel method combined sub-aperture stitching and interferometry called SSI （sub-aperture stitching interferometry） is introduced. In this letter, the theory, basic principle, and flow chart of SSI are researched. A synthetical optimization stitching mode and an effective stitching algorithm are established based on homogeneous coordinate＇s transformation and simultaneous least-squares fitting. The software of SSI is devised, and the prototype for testing of large aspheres by SSI is designed and developed. The experiment is carried out with five sub- apertures for a convex silicon carbide （SIC） aspheric mirror with a clear aperture of 130 ram. The peak-to- valley （PV） and root-mean-square （RMS） error are 0.186 λand 0.019 λ, respectively. For the comparison and validation, the TMA system which contained the convex asphere is tested by interferometry. The wavefront error of the central field of the optical system is 0.068 λRMS which approaches to diffraction limitation. The results conclude that this technique is feasible and accurate. It enables the non-null testing of aspheric surfaces especially for convex aspheres.     

Yield estimation of metallic layers in integrated circuits

In the existing models of estimating the yield and critical area, the defect outline is usually assumed to be circular, but the observed real defect outlines are irregular in shape. In this paper, estimation of the yield and critical area is made using the Monte Carlo technique and the relationship between the errors of yield estimated by circular defect and the rectangle degree of the defect is analysed. The rectangular model of a real defect is presented, and the yield model is provided correspondingly. The models take into account an outline similar to that of an original defect, the characteristics of two-dimensional distribution of defects, the feature of a layout routing, and the character of yield estimation. In order to make the models practicable, the critical area computations related to rectangular defect and regular (vertical or horizontal) routing are discussed. The critical areas associated with rectangular defect and non-regular routing are developed also, based on the mathematical morphology. The experimental results show that the new yield model may predict the yield caused by real defects more accurately than the circular model. It is significant that the yield is accurately estimated using the proposed model for IC metals.     

A diagrammatic categorification of the fermion algebra

In this paper, we study the diagrammatic categorification of the fermion algebra. We construct a graphical category corresponding to the one-dimensional （1D） fermion algebra, and we investigate the properties of this category. The categorical analogues of the Fock states are some kind of 1-morphisms in our category, and the dimension of the vector space of 2-morphisms is exactly the inner product of the corresponding Fock states. All the results in our categorical framework coincide exnetlv with those in normal quantum mechanics.     

Cluster Observation of Eelectrostatic Solitary Waves around Magnetic Null Point in Thin Current Sheet

Electrostatic solitary waves （ESWs） are observed in the vicinity of the magnetic null of the widely studied magnetic reconnection taking place at the near-earth tail when current sheet becomes dramatic thinning during substorm time on 1 October 2001. We use the Imada method for the 2-D reconnection model and study the characteristics of ESWs near the X-line region and the magnetic null points. The result shows that the amplitude of the observed ESWs in the vicinity of X-line region ranges from 0.1mV/m to 5mV/m, and the amplitude is larger near the magnetic null points. The generation mechanism and the role of ESWs associated with magnetic reconnection are also discussed.     

Measurement of large aspheric surfaces by annular subaperture stitching interferometry

A new method for testing aspheric surfaces by annular subaperture stitching interferometry is introduced. It can test large-aperture and large-relative-aperture aspheric surfaces at high resolution,low cost,and high efficiency without auxiliary null optics.The basic principle of the method is described,the synthetical optimization stitching model and effective algorithm are established based on simultaneous least-square fitting.A hyperboloid with an aperture of 350 mm is tested by this method.The obtained peak-to-valley (PV) and root-mean-square (RMS) values of the surface error after stitching are 0.433λand 0.052λ(λis 632.8 nm),respectively.The reconstructed surface map is coincide with the entire surface map from null test,and the difference of PV and RMS errors between them are 0.031λand 0.005λ,respectively. This stitching model provides another quantitive method for testing large aspheric surfaces besides null compensation.     

New Matrix Loop Algebra and Its Application

A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly, as its application, the multi-component TC equation hierarchy is obtained, then by use of trace identity the Hamiltonian structure of the above system is presented. Finally, the integrable couplings of the obtained system is worked out by the expanding matrix Loop algebra.     

Therapeutic ultrasound cavitation and its free radical ESR determination

The formation of free radicals (?)OH and (?)H in a naturallyair-saturated aqueous solution exposed to therapeutic CW ultrasound at afrequency of 820 kHz has been confirmed by using spin trapping 5,5-dimethyl-1-pyrroline-1-oxide(DMPO)and electron spin resonance(ESR)technique.It is suggested that these radicals are formed due tothe high temperature and pressure produced by the ultrasonic transientcavitation.The transient cavitation threshold is found at 0.537-0.632W/cm~2 under a sonication time of 3 minutes.With increasing soundintensity the yield of free radicals (?)OH raises rapidly at the intensityranging from 1—2W/cm~2,and no longer increase is observed at above3W/cm~2.The sound intensity (I) dependence of the yield of (?)OH (D)can be approximately described by a regression equation:D=8.1(I~(1/2) -(I_c)~(1/2))~(1/2), where I_c=0.667W/cm~2 .Under a fixing soundintensity the yield of OH increases monotonously with the sonicationtime.