Submodels of Nonlinear Grassmann Sigma Models in Any Dimension and Conserved Currents, Exact Solutions

In the preceding paper(hep-th/9806084), we constructed submodels of nonlinear Grassmann sigma models in any dimension and, moreover, an infinite number of conserved currents and a wide class of exact solutions. In this paper, we first construct almost all conserved currents for the submodels and all ones for the one of ${\bf C}P^1$-model. We next review the Smirnov and Sobolev construction for the equations of ${\bf C}P^1$-submodel and extend the equations, the S-S construction and conserved currents to the higher order ones.Comment: 13 pages, AMSLaTex; an new section and an appendix adde

Nonlinear Grassmann Sigma Models in Any Dimension and An Infinite Number of Conserved Currents

We first consider nonlinear Grassmann sigma models in any dimension and next construct their submodels. For these models we construct an infinite number of nontrivial conserved currents. Our result is independent of time-space dimensions and, therfore, is a full generalization of that of authors (Alvarez, Ferreira and Guillen). Our result also suggests that our method may be applied to other nonlinear sigma models such as chiral models, $G/H$ sigma models in any dimension.Comment: 11 pages, AMSLaTe

Original Article

Tetrodotoxin, a toxic substance obtained from the globe fish, has been known to paralise the neuromuscular system as well as the central nervous system and recently, it was found to block production of the action potential through its selective inhibition of the sodium-carrying mechanism, but has no effect on the resting potential. In this paper, the effects of tetrodotoxin on the four kinds of skeletal muscle fibers were compared and analysed. Four muscle fibers are tonic and phasic fibers of the extrafusal muscle, and nuclear-bag and nuclear-chain fibers of the intrafusal muscle fibers. The extrafusal muscle is a dynamic source of posture and locomotion, the intrafusal muscle being the regulating source of them. Paralysis of the extrafusal muscle fibers was determined by measuring the decrease in maximum contraction of the soleus (tonic muscle) and tibialis anterior (phasic) produced stimulation of the distal cut end of the ventral root. Paralysis of the intrafusal muscle fibers wasmeasured by a change in the frequency of Group la discharge led from the functionally isolated single filaments of the distal cut end of the dorsal root. By intravenous administration of 4γ/kg tetrodotoxin, paralysis advaces beginning with the intrafusal muscle fibers, and then on to the tonic muscle and phasic muscle fibers. They recover according to the same order. When the intrafusal muscle fiber recovers during an advance in paralysis of the extrafusal muscle, intrafusal muscle fibers contract by the γ-efferent activated by stimulation of the ventral root, and the Group la discharge increases. Frequency of the Group la discharge increases in proportion to muscle extension, therefore the contraction curve of the intrafusal muscle fiber is measured from augmentation of the discharge frequency. Contraction of the intrafusal muscle fibers lasts for several hundred msec, and the curve has two peaks at about 60 msec, and 110 (Fig. 5).It is clear then that the former corresponds to contraction of the nuclear-bag fiber, and the latter to contraction of the nuclearchain fiber