Search results for "curves"
showing 10 items of 152 documents
Extremal properties of the determinant of the Laplacian in the Bergman metric on the moduli space of genus two Riemann surfaces
2005
We study extremal properties of the determinant of the Laplacian in the Bergman metric on the moduli space of compact genus two Riemann surfaces. By a combination of analytical and numerical methods we identify four non-degenerate critical points of this function and compute the signature of the Hessian at these points. The curve with the maximal number of automorphisms (the Burnside curve) turns out to be the point of the absolute maximum. Our results agree with the mass formula for orbifold Euler characteristics of the moduli space. A similar analysis is performed for the Bolza's strata of symmetric Riemann surfaces of genus two.
Measurement of take-off forces in ski jumping
2007
The force measuring system constructed under the frost rail inrun track element was used for measurement of take-off forces in ski jumping. Several calibrations of the normal forces made on several days showed no significant differences between the calibration sessions. Loading the different places of the track element showed differences less than 5% between the places for the total 10-m distance and less than 3% for the straight take-off table. Two international-level ski jumpers served as subjects during the testing of the system. Further preliminary results from 2 different performances techniques are presented. The force curves of subjects displayed totally different patterns: Two disti…
Optical-Microwave Sensor for Real-Time Measurement of Water Contamination in Oil Derivatives
2023
This paper presents a novel microwave sensor using optical activation for measuring in real-time the water contamination in crude oil or its derivatives. The sensor is constructed from an end-coupled microstrip resonator that is interconnected to two pairs of identical fractal structures based on Moore curves. Electromagnetic (EM) interaction between the fractal curves is mitigated using a T-shaped microstrip-stub to enhance the performance of the sensor. The gap in one pair of fractal curves is loaded with light dependent resistors (LDR) and the other pair with microwave chip capacitors. The chip capacitors were used to increase the EM coupling between the fractal gaps to realize a high Q-…
Algebraic Curves and Riemann Surfaces in Matlab
2010
In the previous chapter, a detailed description of the algorithms for the ‘algcurves’ package in Maple was presented. As discussed there, the package is able to handle general algebraic curves with coefficients given as exact arithmetic expressions, a restriction due to the use of exact integer arithmetic. Coefficients in terms of floating point numbers, i.e., the representation of decimal numbers of finite length on a computer, can in principle be handled, but the floating point numbers have to be converted to rational numbers. This can lead to technical difficulties in practice. One also faces limitations if one wants to study families of Riemann surfaces, where the coefficients in the al…
MR 3215343 Reviewed Pirola G.P., Rizzi C. and Schlesinger E. A new curve algebraically but not rationally uniformized by radicals. Asian J. Math., 18…
2014
A smooth projective complex curve C is called rationally uniformized by radicals if there exists a covering map C \rightarrow P^1 with solvable Galois group. C is called algebraically uniformized by radicals if there exists a finite covering C^{\prime} \rightarrow C with C^{\prime} rationally uniformized by radicals. Abramovich and Harris posed the following problem in [D. Abramovich and J. Harris, Abelian varieties and curves in $W_{d}(C)$, Compositio Math., 78 (1991), pp. 227–-238]. \vspace{1ex} Statement S(d, h, g): \textit{Suppose C^{\prime} \rightarrow C is a nonconstant map of smooth curves with C of genus g. If C^{\prime} admits a map of degree d or less to a curve of genus h or less…
The multi-state CASPT2 method
1998
Abstract An extension of the multiconfigurational second-order perturbation approach CASPT2 is suggested, where several electronic states are coupled at second order via an effective-Hamiltonian approach. The method has been implemented into the MOLCAS-4 program system, where it will replace the single-state CASPT2 program. The accuracy of the method is illustrated through calculations of the ionic-neutral avoided crossing in the potential curves for LiF and of the valence-Rydberg mixing in the V-state of the ethylene molecule.
Single cigar-shaped nanopores functionalized with amphoteric amino acid chains: experimental and theoretical characterization.
2012
We present an experimental and theoretical characterization of single cigar-shaped nanopores with pH-responsive carboxylic acid and lysine chains functionalized on the pore surface. The nanopore characterization includes (i) optical images of the nanostructure obtained by FESEM; (ii) different chemical procedures for the nanopore preparation (etching time and functionalizations; pH and electrolyte concentration of the external solution) allowing externally tunable nanopore responses monitored by the current-voltage (I-V) curves; and (iii) transport simulations obtained with a multilayer nanopore model. We show that a single, approximately symmetric nanopore can be operated as a reconfigurab…
Visual aftereffects and sensory nonlinearities from a single statistical framework
2015
When adapted to a particular scenery our senses may fool us: colors are misinterpreted, certain spatial patterns seem to fade out, and static objects appear to move in reverse. A mere empirical description of the mechanisms tuned to color, texture, and motion may tell us where these visual illusions come from. However, such empirical models of gain control do not explain why these mechanisms work in this apparently dysfunctional manner. Current normative explanations of aftereffects based on scene statistics derive gain changes by (1) invoking decorrelation and linear manifold matching/equalization, or (2) using nonlinear divisive normalization obtained from parametric scene models. These p…
A robust evolutionary algorithm for the recovery of rational Gielis curves
2013
International audience; Gielis curves (GC) can represent a wide range of shapes and patterns ranging from star shapes to symmetric and asymmetric polygons, and even self intersecting curves. Such patterns appear in natural objects or phenomena, such as flowers, crystals, pollen structures, animals, or even wave propagation. Gielis curves and surfaces are an extension of Lamé curves and surfaces (superquadrics) which have benefited in the last two decades of extensive researches to retrieve their parameters from various data types, such as range images, 2D and 3D point clouds, etc. Unfortunately, the most efficient techniques for superquadrics recovery, based on deterministic methods, cannot…