J Chris Eilbeck

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J. C. Eilbeck,1 V. Z. Enolski,2 S. Matsutani,3 Y. Ônishi4 and E. Previato5 1Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS UK, 2Institute of Magnetism, Vernadski blvd. 36, Kiev-142, Ukraine, 38-21-1 Higashi-Linkan, Sagamihara, 228-0811, Japan, 4Faculty of Humanities and Social(More)
We consider a hierarchy of the natural type Hamiltonian systems of n degrees of freedom with polynomial potentials separable in general ellipsoidal and general paraboloidal coordinates. We give a Lax representation in terms of 2×2 matrices for the whole hierarchy and construct the associated linear r-matrix algebra with the r-matrix dependent on the(More)
Numerical predictions of a simple myelinated nerve fiber model are compared with theoretical results in the continuum and discrete limits, clarifying the nature of the conduction process on an isolated nerve axon. Since myelinated nerve fibers are often arranged in bundles, this model is used to study ephaptic (nonsynaptic) interactions between impulses on(More)
We develop the theory of generalized Weierstrass σ and ℘ functions defined on a trigonal curve of genus three. The specific example of the “purely trigonal”curve y = x +λ3x 3 +λ2x 2 +λ1x+λ0 is discussed in detail, including a list of the associated partial differential equations satisfied by the ℘ functions, and the derivation of two addition formulae.
1. Voltage signals of about 1 mV evoked in photoreceptors of the drone honey bee by shallow modulation of a background illumination of an intensity useful for behaviour are thought to be amplified by voltage-dependent Na+ channels. To elucidate the roles of the various membrane conductances in this amplification we have studied the effects of the Na+(More)
We give an analytical description of the locus of the two-gap elliptic potentials associated with the corresponding flow of the Calogero– Moser system. We start with the description of Treibich–Verdier two– gap elliptic potentials. The explicit formulae for the covers, wave functions and Lamé polynomials are derived, together with a new Lax representation(More)