scholarly journals On the birational gonalities of smooth curves

2014 ◽  
Vol 68 (1) ◽  
Author(s):  
E. Ballico
Keyword(s):  
Positive Integer ◽  
Smooth Curve ◽  
Smooth Curves

AbstractLet C be a smooth curve of genus g. For each positive integer r the birational r-gonality s

Quantitation of measurement error with Optimal Segments: basis for adaptive time course smoothing

1993 ◽  
Vol 264 (6) ◽  
pp. E902-E911 ◽  
Author(s):  
D. C. Bradley ◽  
G. M. Steil ◽  
R. N. Bergman
Keyword(s):  
Measurement Error ◽  
Measurement Errors ◽  
Time Course ◽  
Smooth Curve ◽  
Random Group ◽  
Smooth Curves ◽  
Original Curve ◽  
Wide Range ◽  
Data Points ◽  
Time Courses

We introduce a novel technique for estimating measurement error in time courses and other continuous curves. This error estimate is used to reconstruct the original (error-free) curve. The measurement error of the data is initially assumed, and the data are smoothed with "Optimal Segments" such that the smooth curve misses the data points by an average amount consistent with the assumed measurement error. Thus the differences between the smooth curve and the data points (the residuals) are tentatively assumed to represent the measurement error. This assumption is checked by testing the residuals for randomness. If the residuals are nonrandom, it is concluded that they do not resemble measurement error, and a new measurement error is assumed. This process continues reiteratively until a satisfactory (i.e., random) group of residuals is obtained. In this case the corresponding smooth curve is taken to represent the original curve. Monte Carlo simulations of selected typical situations demonstrated that this new method ("OOPSEG") estimates measurement error accurately and consistently in 30- and 15-point time courses (r = 0.91 and 0.78, respectively). Moreover, smooth curves calculated by OOPSEG were shown to accurately recreate (predict) original, error-free curves for a wide range of measurement errors (2-20%). We suggest that the ability to calculate measurement error and reconstruct the error-free shape of data curves has wide applicability in data analysis and experimental design.

scholarly journals Relative geodesics in bi-invariant Lie groups

2017 ◽  
Vol 473 (2201) ◽  
pp. 20160619
Author(s):  
E. Zhang ◽  
L. Noakes
Keyword(s):  
Order Differential Equation ◽  
Homogeneous Spaces ◽  
Lagrange Equation ◽  
Smooth Curve ◽  
Curve Matching ◽  
Matching Problem ◽  
Smooth Curves ◽  
First Order ◽  
Finite Dimensional ◽  
Special Cases

Motivated by registration problems, this paper deals with a curve matching problem in homogeneous spaces. Let G be a connected finite-dimensional bi-invariant Lie group and K a closed subgroup. A smooth curve g in G is said to be admissible if it can transform two smooth curves f 1 and f 2 in G / K from one to the other. An ( f 1 , f 2 )- relative geodesic (Holm et al. 2013 Proc. R. Soc. A 469 , 20130297. ( doi:10.1098/rspa.2013.0297 )) is defined as a critical point of the total energy E ( g ) as g varies in the set of all ( f 1 , f 2 )-admissible curves. We obtain the Euler–Lagrange equation, a first-order differential equation, satisfied by a relative geodesic. Furthermore, the Euler–Lagrange equation is simplified for the case where G / K is globally symmetric. As a concrete example, relative geodesics are found for special cases where G is SO(3) and K is SO(2). As an application of discrepancy for curves in S 2 , we construct and study a new measure of non-congruency for constant speed curves in Euclidean 3-space. Numerical examples are given to illustrate results.

Reordering the Absorption Coefficient Within the Wide Band for Predicting Gaseous Radiant Exchange

1996 ◽  
Vol 118 (2) ◽  
pp. 394-400 ◽  
Author(s):  
P. Y. C. Lee ◽  
K. G. T. Hollands ◽  
G. D. Raithby
Keyword(s):  
Absorption Coefficient ◽  
Smooth Curve ◽  
Wide Band ◽  
Computational Effort ◽  
Complex Nature ◽  
Smooth Curves ◽  
Exact Answer ◽  
Radiant Exchange ◽  
Vibration Rotation ◽  
Isothermal Gas

The “exact” calculation of the radiant transfer in gaseous enclosures has remained impractical for design; the highly complex nature of the absorption spectrum of the gases has meant that an inordinately large computational effort is required to effect an exact answer. In this paper we show how the complex absorption distribution for an isothermal gas can be replaced by a set of smooth curves. This procedure can be visualized as one of actually reordering the full complex absorption distribution within each vibration-rotation band, and then replacing it by a smooth curve. Such a smooth curve can then be readily approximated by a stepwise function, and radiant exchange calculations can be carried out at each step and then summed over all the steps to get the total exchange. This paper explains how the reordered curve can be obtained and gives some sample plots of the reordered absorption coefficient curve. Fitted functions for the rearranged curves have been provided, and some solutions to the radiant exchange problems are given and compared to line-by-line solutions. About 50 to 200 steps in the stepwise curve are found to be adequate in order to obtain an answer within a few percent of the exact answer.

scholarly journals Singular Curves of Low Degree and Multifiltrations from Osculating Spaces

2020 ◽  
Vol 2020 (21) ◽  
pp. 8139-8182 ◽  
Author(s):  
Jarosław Buczyński ◽  
Nathan Ilten ◽  
Emanuele Ventura
Keyword(s):  
Linear System ◽  
Smooth Curve ◽  
Rational Curves ◽  
Arithmetic Genus ◽  
Smooth Curves ◽  
Low Degree ◽  
Complete Linear System ◽  
Osculating Spaces ◽  
Special Case ◽  
Schubert Cycles

Abstract In order to study projections of smooth curves, we introduce multifiltrations obtained by combining flags of osculating spaces. We classify all configurations of singularities occurring for a projection of a smooth curve embedded by a complete linear system away from a projective linear space of dimension at most two. In particular, we determine all configurations of singularities of non-degenerate degree $d$ rational curves in $\mathbb{P}^n$ when $d-n\leq 3$ and $d<2n$. Along the way, we describe the Schubert cycles giving rise to these projections. We also reprove a special case of the Castelnuovo bound using these multifiltrations: under the assumption $d<2n$, the arithmetic genus of any non-degenerate degree $d$ curve in $\mathbb{P}^n$ is at most $d-n$.

ON THE REPRESENTATION AERODROME SURFACEROUTING NETWORK EDGE BY SMOOTH CURVES

2020 ◽  
pp. 3-11
Author(s):  
V. V. Shustov ◽  
K. A. Veresov
Keyword(s):  
Linear Equations ◽  
Smooth Curve ◽  
Interpolation Polynomial ◽  
Actual Problem ◽  
Smooth Curves ◽  
Route Network ◽  
Approximation Estimate ◽  
Hermite Interpolation Polynomial ◽  
Statistical Indicators ◽  
Selection Of

The actual problem of ways to represent aerodrome surface route network is considered. Based on the analysis of various options, an approach is proposed for representing route network sections as smooth curves, which are described by parametric vector functions. Each of the vector function components is represented by a two-point Hermite interpolation polynomial, which uses derivatives up to some order inclusive. Within this approach, the optimization problem related to the coefficients selection of these polynomials based on minimizing the distance between the broken line and smooth curve is solved. The problem is reduced to solving a system of linear equations by the derivatives values at the ends of the route network section. The corresponding finite formulas for approximating broken lines by smooth curves are proposed. Based on the formulas obtained, algorithm and program for approximating route network sections using information about taxi lines, which are stored in aerodrome mapping database (AMDB), were developed. The program also allows you to calculate statistical indicators, what allow to get a quantitative approximation estimate. Numerical experiments based on the Sheremetyevo aerodrome dataset have shown the promise of this approach to presenting aerodrome surface route network, which can significantly (2 – 4 times) reduce the amount of data and increase the realism of the aerodrome model.

scholarly journals MODULI SPACES OF PARABOLIC HIGGS BUNDLES AND PARABOLIC K(D) PAIRS OVER SMOOTH CURVES: I

1996 ◽  
Vol 07 (05) ◽  
pp. 573-598 ◽  
Author(s):  
HANS U. BODEN ◽  
KÔJI YOKOGAWA
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Morse Theory ◽  
Smooth Curve ◽  
Higgs Bundles ◽  
Poincaré Polynomial ◽  
Smooth Curves ◽  
Connected Manifold ◽  
Parabolic Bundles ◽  
Simply Connected

This paper concerns the moduli spaces of rank-two parabolic Higgs bundles and parabolic K(D) pairs over a smooth curve. Precisely which parabolic bundles occur in stable K(D) pairs and stable Higgs bundles is determined. Using Morse theory, the moduli space of parabolic Higgs bundles is shown to be a non-compact, connected, simply connected manifold, and a computation of its Poincaré polynomial is given.

Smooth curve drawing using a Bessel function

2015 ◽  
Author(s):  
Y. Q. Du ◽  
M. J. Pan ◽  
Q. Li ◽  
L. Li
Keyword(s):  
Bessel Function ◽  
Smooth Curve

The Order of Monochromatic Subgraphs with a Given Minimum Degree

10.37236/1725 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Yair Caro ◽  
Raphael Yuster
Keyword(s):  
Positive Integer ◽  
Minimum Degree

Let $G$ be a graph. For a given positive integer $d$, let $f_G(d)$ denote the largest integer $t$ such that in every coloring of the edges of $G$ with two colors there is a monochromatic subgraph with minimum degree at least $d$ and order at least $t$. Let $f_G(d)=0$ in case there is a $2$-coloring of the edges of $G$ with no such monochromatic subgraph. Let $f(n,k,d)$ denote the minimum of $f_G(d)$ where $G$ ranges over all graphs with $n$ vertices and minimum degree at least $k$. In this paper we establish $f(n,k,d)$ whenever $k$ or $n-k$ are fixed, and $n$ is sufficiently large. We also consider the case where more than two colors are allowed.

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