From number theory to string theory, analyzing algebraic relations in two variables still dominates how we view laws governing relations between quantities. An algebraic relation between two variables defines a nonsingular projective curve. Our understanding starts with moduli of curves. From, however, cryptography to Hamiltonian mechanics, we command complicated data through a key data variabl...

In his 1981 Fundamental Theorem of Algebra paper Steve Smale initiated the complexity theory of finding a solution of polynomial equations of one complex variable by a variant of Newton’s method. In this paper we reconsider his algorithm in the light of work done in the intervening years. Smale’s upper bound estimate was infinite average cost. Our’s is polynomial in the Bézout number and the di...

This talk is based on [2]. We establish, generalizing Di Nola and Lettieri’s categorical equivalence [3], a Morita-equivalence between the theory of lattice-ordered abelian groups and that of perfect MValgebras. Further, after observing that the two theories are not bi-interpretable in the classical sense, we identify, by considering appropriate topos-theoretic invariants on their common classi...

[1] Recent experimental and modeling studies show that large quasi-static electric fields (2–20 kV/m) can be developed in a Martian or terrestrial dust devil as a result of contact electrification and charge separation of dust grains with different sizes and compositions. Electric discharging occurs when the maximum electric field reaches breakdown values ( 20 kV/m on Mars and 3 MV/m on Earth, ...

Kiriakos Kotzabasis and Horst Senger Fachbereich Biologie/Botanik, Philipps-Universität, Lahnberge, D-3550 Marburg, Bundesrepublik Deutschland Z. Naturforsch. 41c, 1001 — 1003 (1986); received July 1, 1986 Scenedesmus obliquus, Protochlorophyllide, Monovinyl Protochlorophyllide, Divinyl Protochlorophyllide Three Protrochlorophyllides (protochlorophyllide) were separated from mutant C-2 A' of th...

Learning over multi-view data is a challenging problem with strong practical applications. Most related studies focus on the classification point of view and assume that all the views are available at any time. We consider an extension of this framework in two directions. First, based on the BiGAN model, the Multi-view BiGAN (MV-BiGAN) is able to perform density estimation from multi-view input...

We demonstrate, for the first time, the large electromechanical response in ne-matic liquid crystalline elastomers filled with a very low (∼ 0.01%) concentration of carbon nanotubes, aligned along the nematic director at preparation. The nan-otubes create a very large effective dielectric anisotropy of the composite. Their local field-induced torque is transmitted to the rubber-elastic network ...

A new design for a true-linear generator suitable for electrochemical measures is presented. The main component of generation system is an MAX038 chip, a high-frequency relaxation-type oscillator. The design is completed with a digital interface for computer control and an output stage to make signal suitable for cyclic voltammetry experiments. A digital circuit is also included to obtain singl...