Matrix elements in the SU(1,1)⊗SO(6)limit of the proton-neutron symplectic model

The matrix elements along the reduction chain Sp(12,R)⊃SU(1,1)⊗SO(6)⊃U(1)⊗SUpn(3)⊗SO(2)⊃SO(3)of the proton-neutron symplectic model(PNSM)are considered.Closed analytical expressions are obtained for the matrix elements of the basic building blocks of the PNSM and the Sp(12,R)symplectic generators,allowing the computation of matrix elements of other physical operators as well.The computational technique developed in the present study generally provides us with the required algebraic tool for performing realistic symplectic-based shell-model calculations of nuclear collective excitations.Utilizing two simple examples,we illustrate the application of the theory.

Research on convergence of the nuclear matrix elements for 2νββ decays

In this work,the characteristics of 2νββ decays for six nuclei(36Ar,46Ca,48Ca,50Cr,70Zn,and 136Xe)in a mass range from A=36 to A=136 are studied within the nuclear shell model(NSM)framework.Calculations are presented for the half-lives,nuclear matrix elements(NMEs),phase space factors(G2ν),and convergence of the NMEs.The theoretical results agree well with the experimental data.In addition,we predict the half-lives of 2νββ decays for four nuclei.We focus on the convergence of the NMEs by analyzing the number of contributing intermediate 1+states(NC)for the nuclei of interest.We assume that NC is safely determined when the accumulated NMEs saturate 99.7%of the final calculated magnitude.From the calculations of the involved nuclei,we discover a connection between NC and the total number of intermediate 1+states(NT).According to the least squares fit,we conclude that the correlation is NC=(10.8±1.2)×N(0.29±0.02)T.

THE DYNAMIC STIFFNESS MATRIX OF THE FINITE ANNULAR PLATE ELEMENT

The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.

THE GENERATION OF NON－LINEAR STIFFNESS MATRIX OF TRIANGLE ELEMENT WHENCONSIDERING BOTH THE BENDING AND IN－PLANEME MBRANE FORCES

Using Stricklin Melhod￣[5],we have this paper has derived the formulas for the ge-neration of non-linear element stiffness matrix of a triangle element when considering both the bending and the in-plane membrane forces. A computer programme for the calculation of large deflection and inner forces of shallow shells is designed on theseformulas. The central deflection curve computed by this programme is compared with other pertaining results.

Non Degeneration of Fibonacci Series, Pascal’s Elements and Hex Series

Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I explored the inter relations of Fibonacci series when I was intent on Fibonacci series in my difference parallelogram. In which, I found there is no degeneration on Fibonacci series. In my thought, Pascal triangle seemed like a lower triangular matrix, so I tried to find the inverse for that. In inverse form, there is no change against original form of Pascal elements matrix. One day I played with ring magnets, which forms hexagonal shapes. Number of rings which forms Hexagonal shape gives Hex series. In this paper, I give the general formula for generating various types of Fibonacci series and its non-degeneration, how Pascal elements maintain its identities and which shapes formed by hex numbers by difference and matrices.

Magic wavelengths for 6s_(1/2)→5d_(3/2,5/2)transitions of Yb~+ions

The wave functions,energy levels and matrix elements of Yb+ions are calculated using the relativistic configuration interaction plus core polarization(RCICP)method.The static and dynamic electric dipole polarizabilities of the ground state and low-lying excited states are determined.Then,the magic wavelengths of the magnetic sublevel 6s_(1/2,m=1/2)→5d_(3/2,m=±3/2,±1/2)and 6s_(1/2,m=1/2)→5_(d5/2,m=±5/2,±3/2,±1/2)transitions in the linearly,right-handed,and left-handed polarized light are further determined.The dependence of the magic wavelengths upon the angle between the direction of magnetic field and the direction of laser polarization is analyzed.

Variational Calculations for (ns2) 1Se, (np2) 1De and (nd2) 1Ge Resonance States for He Isoelectronic Sequences below the n = 2, 3 and 4 Hydrogenic Thresholds

This work presents results of the different parameters which characterize the nonrelativistic Hamilton operator for the helium atoms allowing us to solve the Schrödinger equation. The total energy is decomposed into three terms allowing to separate the kinetic energy, the electrons-nucleus interaction energy and the electron-electron interaction energy of the (2s2, 3s2 and 4s2) 1Se, (2p2, 3p2 and 4p2) 1De and (3d2 and 4d2) 1Ge resonance singlet states of the helium isoelectronic sequences. The states have been defined by using special forms of the Hylleraas type wave functions. The calculations have been carried out in the framework of the variational method using configuration interaction basis states with a real Hamiltonian. The agreement of the energy value of other states between the present theoretical values available in the literature is excellent. But as for the comparison of the kinetic energies, the electrons-nucleus energies interaction and the electron-electron interaction energies, we note a slight difference with the theoretical values common in literature.

NORMALIZED ELEMENT NODE TOPOLOGICAL MATRIX OF FINITE ELEMENT MESHES

On the basis of concept of element node topological analysis, the normalized element node topological matrices for finite element meshes are presented in the paper, including 3-node and 6-node triangular element, 4-node and 8-node quadrilateral element, 8-node and 20-node hexahedral element. It is beneficial to further analyzing topological characteristics of finite element models and automatic generation of meshes

Rotation and vibration of diatomic molecule oscillator with hyperbolic potential function

The explicit expressions of energy eigenvalues and eigenfunctions of bound states for a three-dimensional diatomic molecule oscillator with a hyperbolic potential function are obtained approximately by means of the hypergeometric series method. Then for a one-dimensional system, the rigorous solutions of bound states are solved with a similar method. The eigenfunctions of a one-dimensional diatomic molecule oscillator, expressed in terms of the Jacobi polynomial, are employed as an orthonormal basis set, and the analytic expressions of matrix elements for position and momentum operators are given in a closed form.

Energy Positions of the ^1,3D^eRydberg Series of the He-Like Ions Up to the <i>N</i>= 9 Threshold

The doubly excited states of helium-like ions are investigated using a combination of the no-linear parameters of Hylleraas and the β-parameters of screening constant by unit nuclear charge. Calculations are performed for total energies of low-lying doubly excited states (N = 2 - 9) in He-like ions up to Z = 10. The results obtained from the novel method are in good agreement with the available theoretical calculations and experimental observations.

Optimizing the atmospheric sampling sites using fuzzy mathe-matic methods

A new approach applying fuzzy mathematic theorems, including the Primary Matrix Element Theorem and the Fisher Classification Method, was established to solve the optimization problem of atmospheric environmental sampling sites. According to its basis, an application in the optimization of sampling sites in the atmospheric environmental monitoring was discussed. The method was proven to be suitable and effective. The results were admitted and applied by the Environmental Protection Bureau (EPB) of many cities of China. A set of computer software of this approach was also completely compiled and used.

Analysis of the decay B^0→χc1~π~0 with light-cone QCD sum rules

In this article, we calculate the contribution from the nonfactorizable soft hadronic matrix element to the decay B^0→Xc1π^0 with the light-cone quantum chromo-dynamic （QCD） sum rules. The numerical results show that its contribution is rather large and should not be neglected. The total amplitudes lead to a branching fraction which is in agreement with the experimental data marginally.

Application of Viscoelastic Material in Structures Control

The factors influencing mechanical performances of viscoelastic material are studied.The proper finite element model for dynamical calculating the passive control of wind-earthquake resistance is constructed.A combined element stiffness matrix of damper-brace system is deduced.At last,the theoretical deduction is verified by comparing the theoretical results with experimental ones.

Evidence for Non-existence of Oscillations in Photofield Emission Current in Gallium Arsenide

We have shown here the results of PFEC(photofield emission current)calculated for GaAs(gallium arsenide).We have used the initial state wavefunctions derived using the Kronig-Penney potential model for evaluating the PFEC.We have found that PFEC is not oscillatory as obtained by Modinos and Klient,[Solid State Commun.50,651(1984)],but it is an exponential function.

Hypoxia-controlled matrix metalloproteinase-9 hyperexpression promotes behavioral recovery after ischemia

Matrix metalloproteinase-9（MMP-9） plays a beneficial role in the sub-acute phase after ischemic stroke.However,unrestrained MMP-9 may disrupt the blood-brain barrier（BBB）,which has limited its use for the treatment of brain ischemia.In the present study,we constructed lentivirus mediated hypoxiacontrolled MMP-9 expression and explored its role after stroke.Hypoxia response element（HRE）was used to confine MMP-9 expression only to the hypoxic region of mouse brain after 120-min transient middle cerebral artery occlusion.Lentiviruses were injected into the peri-infarct area on day 7 after transient ischemia.We found hyperexpression of exogenous HRE-MMP-9 under the control of hypoxia,and its expression was mainly located in neurons and astrocytes without aggravation of BBB damage compared to the CMV group.Furthermore,mice in the HRE-MMP-9 group showed the best behavioral recovery compared with the normal saline,GFP,and SB-3CT groups.Therefore,hypoxia-controlled MMP-9 hyperexpression during the sub-acute phase of ischemia may provide a novel promising approach of gene therapy for stroke.

Theoretical Study on Electron Transfer Matrix Element in Oxidation of α-Amino Carbon-Centered Radical by O_2

As a successive work of our previous paper, 1 the electron transfer matrix element (V rp) in the oxidation of the simplified model molecule of α-amino carbon-centered radical by O 2 has been investigated with ab initio calculation at the level of UHF/6-31++G**. Based on the optimized geometries of the reactant and the ion-pair complex obtained previously, the reaction heat and the inner reorganization energy have been obtained by constructing the potential energy curves of reactant and product states considering the solvent effect with the conductor-like screening model (COSMO). The solvent reorganization energy has been estimated using Lippert-Mataga relationship. The calculated results show that the value of V rp is several times larger than that of RT, which means that the model reaction is an adiabatic one. Theoretical investigation indicates that the solvent effect on the direct electron transfer (ET) process of oxidation of α-amino carbon-centered radical by oxygen is remarkable.

Stiffness Matrix Derivation of Space Beam Element at Elevated Temperature

<Abstract>Element stiffness equation is very important in structural analysis,and directly influences the accuracy of the results.At present,derivation method of element stiffness equation is relatively mature under ambient temperature,and the elastic phrase of material stress-strain curve is generally adopted as physical equation in derivation.However,the material stress-strain relationship is very complicated at elevated temperature,and its form is not unique,which brings great diffculty to the derivation of element stiffness equation.Referring to the derivation method of element stiffness equation at ambient temperature,by using the continuous function of stress-strain-temperature at elevated temperature,and based on the principle of virtual work,the stiffness equation of space beam element and the formulas of stiffness matrix are derived in this paper,which provide basis for finite element analysis on structures at elevated temperature.

Coupling matrix element of electron self-exchange reactions in solution

On the basis of the common feature among the electron transfer process and the ion hydration process as well as the relevant experimental kinetic data of electron trader reaction, a new accurate hydration potential function scheme for the determination of electron transfer coupling matrix element is presented. The coupling matrix element between two hydrated ions of the reacting system in solution is calculated. The results and the applicability of this scheme are discussed.

First lattice QCD calculation of semileptonic decays of charmed-strange baryonsΞc

While the standard model is the most successful theory to describe all the interactions and constituents of elementary particle physics,it has been constantly scrutinized for over four decades.Weak decays of charm quarks can be used to measure the coupling strength between quarks in different families and serve as an ideal probe for CP violation.As the lowest charm-strange baryons with three different flavors,Ξ;baryons(composed of csu or csd)have been extensively studied in experiments.In this study,we use state-of-the-art lattice QCD techniques to generate 2+1 clover fermion ensembles with two lattice spacings,a=(0.108,0.080 fm).Then,we present the first ab-initio lattice QCD calculation of the Ξ;→Ξ form factors.Our theoretical results for the Ξc→Ξl;v;decay widths are consistent with and approximately two times more precise than the latest measurements by the ALICE and Belle collaborations.Based on the latest experimental measurements,we independently obtain the quark-mixing matrix element |V;|,which is in good agreement with results from other theoretical approaches.

Physics program of open charm and heavy c states at the BES-Ⅲ experiment

We present the physics program of the open charm and heavy cc states above the DD production energy threshold, which will be studied with the BES-Ⅲ detector at the BEPC- Ⅱ collider in the coming years. Based on some full Monte Carlo simulations with the BES-Ⅲ detector, we predict the accuracy levels on measuring some physical quantities related to D^0, D^＋ and Ds^＋ decays as well as some non-charmed decays of the heavy cc states.