Classification of classical and non-local symmetries of fourth-order nonlinear evolution equations

In this paper, we consider group classification of local and quasi-local symmetries for a general fourth-order evolution equations in one spatial variable. Following the approach developed by Zhdanov and Lahno, we construct all inequivalent evolution equations belonging to the class under study which admit either semi-simple Lie groups or solvable Lie groups. The obtained lists of invariant equations (up to a local change of variables) contain both the well-known equations and a variety of new ones possessing rich symmetry. Based on the results on the group classification for local symmetries, the group classification for quasi-local symmetries of the equations is also given.Comment: LaTeX, 60 page

ACTIVATION OF DIFFERENT CEREBRAL FUNCTIONAL REGIONS FOLLOWING ACUPUNCTURE AT BOT H TAIXI AND TAICHONG ACUPOINTS AND TAIXI ACUPOINTALONE: AN FMRI STUDY

Background: To explore the brain function regions characteristics of the acupoint combination, this study observed activity changes in the brain regions of healthy volunteers after acupuncture at both Taixi (KI3) and Taichong (LR3) (KI3 + LR3) and KI3 alone using resting-state functional magnetic resonance imaging (fMRI). Methods and Materials: 30 healthy volunteers were randomly allocated into two groups, one group received acupuncture at KI3 and LR3, the other only acupuncture at KI3, 15 cases in each group. All volunteers underwent resting-state fMRI of the brain 15 minutes before acupuncture, and which the needle was retained in place for 30 minutes; 15 minutes after withdrawing the needle underwent a further session of resting-state fMRI. The amplitude of low-frequency fluctuation (ALFF) and regional homogeneity (ReHo) were used to analyze the changes in brain regions. Results: The KI3+LR3 group compared with the KI3 group, the ALFF analysis indicated that the brain changes relatively concentrated in BA 2, 3, 7, 8, 9, 10, 18, 19, 20, 31, 32, 40, 46 and the cerebellum posterior lobe, the ReHo analysis indicated that the brain changes relatively concentrated in BA 4, 6, 7, 10, 11, 18, 19, 20, 21, 22, 31, 40 and the cerebellum posterior lobe. Conclusion: Based on this study, compared with acupuncture at KI3, acupuncture at KI3 + LR3 which could specifically influence BA 7, 10, 18, 19, 20, 31, 40 and cerebellum posterior lobe, which may be related to synergy mechanism of two acupoints combination treatment

Partial Wave Analysis of J/ψ→γ(K+K−π+π−)J/\psi \to \gamma (K^+K^-\pi^+\pi^-)

BES data on $J/\psi \to \gamma (K^+K^-\pi^+\pi^-)$ are presented. The $K^*\bar K^*$ contribution peaks strongly near threshold. It is fitted with a broad $0^{-+}$ resonance with mass $M = 1800 \pm 100$ MeV, width $\Gamma = 500 \pm 200$ MeV. A broad $2^{++}$ resonance peaking at 2020 MeV is also required with width $\sim 500$ MeV. There is further evidence for a $2^{-+}$ component peaking at 2.55 GeV. The non-$K^*\bar K^*$ contribution is close to phase space; it peaks at 2.6 GeV and is very different from $K^{*}\bar{K^{*}}$.Comment: 15 pages, 6 figures, 1 table, Submitted to PL

Energy levels and multipole transition properties of C

Plasma screening effects on the energy structure and radiative transition properties of helium-like C4+ ions embedded in Debye plasmas are investigated by using the multi-configuration Dirac-Hartree-Fock method incorporating the Debye-Hückel potential for both the electron-nucleus and electron-electron interactions. Seventeen fine-structure energy levels of the low-lying 1s2, 1s2l(l = s,p) and 1s3l′(l′ = s,p,d) configurations, as well as the electric-dipole (E1), magnetic-dipole (M1) and magnetic-quadrupole (M2) transition probabilities and oscillator strengths between these levels have been calculated over a wide range of screening parameters. It is found that the plasma screening leads to a decrease of excitation energies and alters the energy levels remarkably. For Δn ≠ 0 transitions, the spontaneous decay spectra are red-shifted and their oscillator strengths and transition probabilities decrease with increasing the interaction screening, while those for the Δn = 0 transitions exhibit opposite patterns. The influence of electron-nucleus and electron-electron screened interactions on the changes of energy levels and transition properties are analyzed. Comparison is made of present results with other data available in the literature for this ion