A genus six cyclic tetragonal reduction of the Benney equations

A reduction of Benney’s equations is constructed corresponding to Schwartz–Christoffel maps associated with a family of genus six cyclic tetragonal curves. The mapping function, a second kind Abelian integral on the associated Riemann surface, is constructed explicitly as a rational expression in derivatives of the Kleinian σ-function of the curve

Using the Regular Chains Library to build cylindrical algebraic decompositions by projecting and lifting

Cylindrical algebraic decomposition (CAD) is an important tool, both for quantifier elimination over the reals and a range of other applications. Traditionally, a CAD is built through a process of projection and lifting to move the problem within Euclidean spaces of changing dimension. Recently, an alternative approach which first decomposes complex space using triangular decomposition before refining to real space has been introduced and implemented within the RegularChains Library of Maple. We here describe a freely available package ProjectionCAD which utilises the routines within the RegularChains Library to build CADs by projection and lifting. We detail how the projection and lifting algorithms were modified to allow this, discuss the motivation and survey the functionality of the package

Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains

A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of the decomposition. Secondly, the computation uses regular chains theory to first build a cylindrical decomposition of complex space (CCD) incrementally by polynomial. Significant modification of the regular chains technology was used to achieve the more sophisticated invariance criteria. Experimental results on an implementation in the RegularChains Library for Maple verify that combining these advances gives an algorithm superior to its individual components and competitive with the state of the art

Information-theoretic bound on the entropy production to maintain a classical nonequilibrium distribution using ancillary control

There are many functional contexts where it is desirable to maintain a mesoscopic system in a nonequilibrium state. However, such control requires an inherent energy dissipation. In this article, we unify and extend a number of works on the minimum energetic cost to maintain a mesoscopic system in a prescribed nonequilibrium distribution using ancillary control. For a variety of control mechanisms, we find that the minimum amount of energy dissipation necessary can be cast as an information-theoretic measure of distinguishability between the target nonequilibrium state and the underlying equilibrium distribution. This work offers quantitative insight into the intuitive idea that more energy is needed to maintain a system farther from equilibrium.Comment: 6 pages, 2 figure

The Effect of Vincristine Sulphate on the Axoplasmic Flow of Proteins in Cultured Sympathetic Neurons

The effect of vincristine sulphate on the axoplasmic flow of labelled proteins in neurites of chick embryo sympathetic neurons growing in tissue culture was studied by autoradiography. In control neurons most of the 3H-proteins synthesized during a 90-min pulse with a 3H-amino acid were localized in cell bodies. There was a diminishing gradient of labelled proteins in the neurites which was highest in portions adjacent to the cell bodies and lowest at the periphery. During a physiological chase there was a gradual increase in the amount of label in the neurites, so that after a 15-h chase even the most peripheral portions were well labelled. This indicates that a portion of the labelled proteins synthesized in the cell bodies are transported peripherally into the neurites. The centrifugal movement of labelled proteins in neurites was markedly decreased when cells were grown in medium containing 10 µg/ml vincristine sulphate. After a 15-h chase in the presence of drug only a small amount of label was in the peripheral portion of the neurites. Treatment with vincristine did not decrease the rate of amino acid incorporation or alter the rate of protein turnover during the course of the experiment. Thus an explanation of the results based on an altered rate of total cell protein synthesis or degradation is unlikely. The capacity of sympathetic neurons to take up and concentrate exogenous [3H]norepinephrine in their neurites was only slightly reduced by vincristine. This indicates that at least some cellular activities requiring metabolic energy are relatively unaffected by the interruption in axoplasmic flow caused by vincristine and that the mechanism by which vincristine interferes with axoplasmic flow does not involve general cellular toxicity. The major morphological differences between control and vincristine-treated neurons were the absence of microtubules and the presence of crystal-like structures within the cells. The relationship between the effect of vincristine on the axoplasmic flow of proteins and the arrangement of the microtubule system is discussed

Study of techniques for the reduction of creep in plated wire memories Final report, 28 Jun. 1967 - 28 Aug. 1968

Magnetization reversal in thin films of plated wire memory element

Morphological heterogeneity of HeLa cell mitochondria visualized by a modified diaminobenzidine staining technique

The diaminobenzidine (DAB) technique for the ultrastructural localization of sites of cytochrome c oxidase activity in animal tissues has been adapted to the visualization of mitochondria in animal cells growing in culture. The modified technique allows the staining of mitochondria in all cells in coverslip preparatins for light microscopy. Electron microscopy of thin sections of material treated by this method has revealed that all mitochondrial profiles within a cell (and only these) are stained and they exhibit a well preserved size and internal structure. Coverslip cultures of synchronized and unsynchronized HeLa (F-315) cells stained with the DAB reaction were examined under oil immersion. In the majority of the cells, mitochondria were recognized as discrete bodies in the thinner peripheral portion of the cytoplasm. This observation indicates that in a large proportion of HeLa F-315 cells, at least under the growth conditions used here, the mitochondrial complement is dividied into distinct organelles. This examination also revealed a considerable morphological heterogeneity of mitochondria, which exhibited an ovoid or short rod-like or, less frequently, long filamentous shape, with some evidence of branching. The variability in mitochondrial morphology appeared to be far more prounced between different cells than within individual cells; this cellular heterogeneity was not related in any obvious way to cell-cycle-dependent changes

Some New Addition Formulae for Weierstrass Elliptic Functions

We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These new results were inspired by new addition formulae found in the case of an equianharmonic curve, which we can now observe as a specialisation of the results here. The new formulae, and the techniques used to find them, also follow the recent work for the generalisation of Weierstrass' functions to curves of higher genus.Comment: 20 page

Generalised Elliptic Functions

We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstras P-function using two different approaches. These functions arise naturally as solutions to some of the important equations of mathematical physics and their differential equations, addition formulae, and applications have all been recent topics of study. The first approach discussed sees the functions defined as logarithmic derivatives of the sigma-function, a modified Riemann theta-function. We can make use of known properties of the sigma function to derive power series expansions and in turn the properties mentioned above. This approach has been extended to a wide range of non hyperelliptic and higher genus curves and an overview of recent results is given. The second approach defines the functions algebraically, after first modifying the curve into its equivariant form. This approach allows the use of representation theory to derive a range of results at lower computational cost. We discuss the development of this theory for hyperelliptic curves and how it may be extended in the future.Comment: 16 page