Chiral Symmetry and Scalars

The suggestion by Jaffe that if $\sigma$ is a light $q^{2}\bar{q}^{2}$ state $0^{++}$ then even the fundamental chiral transformation properties of the $\sigma$ becomes {\bf unclear}, has stimulated much interest. Adler pointed out that in fact the seminal work on chiral symmetry via PCAC consistency, is really quite consistent with the $\sigma$ being predominantly $q^{2}\bar{q}^{2}$. This interpretation was actually backed by subsequent work on effective Lagrangian methods for linear and non linear realizations. More recent work of Achasov suggests that intermediate four-quark states determine amplitudes involving other scalars $a_{0}(980)$ and $f_{0}(980)$ below 1 GeV, and the report by Ning Wu that study on $\sigma$ meson in $J/\psi \to \omega\pi^{+}\pi^{-}$ continue to support a non $q\bar{q}$ $\sigma$ with mass as low as 390 MeV. It is also noted that more recent re-analysis of $\pi K$ scattering by S. Ishida {\em et al.} together with the work of the E791 Collaboration, support the existence of the scalar $\kappa$ particle with comparatively light mass as well.Comment: 4 pages, aipproc style file. Parallel session talk at Hadron 2001-Protvin

The ρ−π\rho - \pi Puzzle of J/\psi and \psi' Decays

The recent BES Collaboration data on \psi' \ra PV, particularly the isospin violating mode \psi' \ra \pi^0 \omega^0 and finding of a finite number for B(\psi' \ra K^{*0}\bar{K}^0), enable us now to deal more precisely about the challenges to theory concerning this extraordinary and remarkable so called $\rho - \pi$ Puzzle of $J/\psi$ and $\psi'$ Decays. In terms of existing data, and deploying the simplest phenomenology, measurement of \psi' \ra \pi^+\pi^- and whether a finite number for the $K^{*+} K^-$ mode might require a significantly larger accumulation of data, remain interesting questions.Comment: 9pages, added reference, typos, and very slight change in text, LATEX forma

Aspects of Charmonium Physics

I review possible resolution of the $J/\psi (\psi^{\prime}) \to \rho-\pi$ puzzle based on two inputs: the relative phase between the one- photon and the gluonic decay amplitudes, and a possible hadronic excess in the inclusive nonelectromagnetic decay rate of $\psi^{\prime}$. The status of a universal large phase here is examined for its meaning and implications (including those for B-physics). Since the future of tau/charm facility(s) are again under consideration together with a future anti-proton facility at GSI, I propose to extend my review to include a broader discussion of charmonium physics. Outstanding questions like the status of the $^{1}P_{1}$ state of charmonium, measuring $D^{0}-\bar D^{0}$ mixing and relative strong phases, status of molecular P(S) - wave charmonia will also be discussed amongst others.Comment: 7 pages, aipproc style file. Plenary session talk at Hadron 2001-Protvin

Linearized Asymptotic Stability for Fractional Differential Equations

We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector \{\lambda \in \C : |\arg \lambda| > \frac{\alpha \pi}{2}\} where $\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable

A second-generation autologous chondrocyte implantation approach to the treatment of focal articular cartilage defects

Autologous chondrocyte implantation (ACI) is the most widely used cell-based surgical procedure for the repair of articular cartilage defects. Challenges to successful ACI outcomes include limitation in defect size and geometry as well as inefficient cell retention. Second-generation ACI procedures have thus focused on developing three-dimensional constructs using native and synthetic biomaterials. Clinically significant and satisfactory results from applying autologous chondrocytes seeded in fibrin within a biodegradable polymeric material were recently reported. In the future, third-generation cell-based articular cartilage repair should focus on the use of chondroprogenitor cells and biofunctionalized biomaterials for more extensive and permanent repair