Characterization of algebraic curves by Chebyshev quadrature

1998 ◽  
Vol 75 (1) ◽  
pp. 233-246 ◽  
Author(s):  
J. Korevaar ◽  
L. Bos
Keyword(s):  
Algebraic Curves ◽  
Chebyshev Quadrature

scholarly journals ON THE DIMENSION OF SPACES OF ALGEBRAIC CURVES PASSING THROUGH $ n $-INDEPENDENT NODES

2019 ◽  
Vol 53 (2 (249)) ◽  
pp. 91-100
Author(s):  
H.A. Hakopyan ◽  
H.M. Kloyan
Keyword(s):  
Algebraic Curves ◽  
Important Application ◽  
Maximal Curve ◽  
Linearly Independent ◽  
Special Construction ◽  
Fundamental Polynomial

Let the set of nodes $ \LARGE{x} $ in the plain be $ n $-independent, i.e., each node has a fundamental polynomial of degree $ n $. Suppose also that $ \vert \LARGE{x} \normalsize \vert \mathclose{=} (n \mathclose{+} 1) \mathclose{+} n \mathclose{+} \cdots \mathclose{+} (n \mathclose{-} k \mathclose{+} 4) \mathclose{+} 2 $ and $ 3 \mathclose{\leq} k \mathclose{\leq} n \mathclose{-} 1 $. We prove that there can be at most 4 linearly independent curves of degree less than or equal to $ k $ passing through all the nodes of $ \LARGE{x} $. We provide a characterization of the case when there are exactly 4 such curves. Namely, we prove that then the set $ \LARGE{x} $ has a very special construction: all its nodes but two belong to a (maximal) curve of degree $ k \mathclose{-} 2 $. At the end, an important application to the Gasca-Maeztu conjecture is provided.

scholarly journals Smoothing of Limit Linear Series of Rank One on Saturated Metrized Complexes of Algebraic Curves

2018 ◽  
Vol 70 (3) ◽  
pp. 628-682 ◽  
Author(s):  
Ye Luo ◽  
Madhusudan Manjunath
Keyword(s):  
Algebraic Curves ◽  
Linear Series ◽  
Compact Type ◽  
Nodal Curves ◽  
Dual Graphs ◽  
Rank One ◽  
Limit Linear Series

AbstractWe investigate the smoothing problem of limit linear series of rank one on an enrichment of the notions of nodal curves and metrized complexes called saturated metrized complexes. We give a finitely verifiable full criterion for smoothability of a limit linear series of rank one on saturated metrized complexes, characterize the space of all such smoothings, and extend the criterion to metrized complexes. As applications, we prove that all limit linear series of rank one are smoothable on saturated metrized complexes corresponding to curves of compact-type, and we prove an analogue for saturated metrized complexes of a theorem of Harris and Mumford on the characterization of nodal curves contained in a given gonality stratum. In addition, we give a full combinatorial criterion for smoothable limit linear series of rank one on saturated metrized complexes corresponding to nodal curves whose dual graphs are made of separate loops.

scholarly journals Characterization of smooth, compact algebraic curves in ℝ²

1995 ◽  
Vol 31 (1) ◽  
pp. 125-134
Author(s):  
L. Bos ◽  
N. Levenberg ◽  
B. Taylor
Keyword(s):  
Algebraic Curves

scholarly journals A characterization of dividing real algebraic curves

Topology ◽  
1996 ◽  
Vol 35 (2) ◽  
pp. 451-455 ◽  
Author(s):  
Jacek Bochnak ◽  
Wojciech Kucharz
Keyword(s):  
Algebraic Curves ◽  
Real Algebraic Curves

ALGEBRAICALLY OPTIMAL PARAMETRIZATIONS OF QUASI-POLYNOMIAL ALGEBRAIC CURVES

2002 ◽  
Vol 01 (01) ◽  
pp. 51-74 ◽  
Author(s):  
J. RAFAEL SENDRA ◽  
CARLOS VILLARINO
Keyword(s):  
Algebraic Curves ◽  
Field Extension ◽  
Ground Field ◽  
Polynomial Curves ◽  
Implicit Equations

In this paper we deal with the problem of computing algebraically optimal parametrizations for quasi-polynomial algebraic curves. The algebraic optimality parametrization problem consists in computing rational parametrizations which coefficients are in the smallest possible field extension of the ground field. In [6], and in [30], it is shown that for the class of polynomial curves the optimal parametrization problem is reduced to check whether the corresponding Weil's descente variety of the curve is a line over the ground field. In this paper, we introduce a bigger class of curves, namely the class of quasi-polynomial curves, and we show that this property is still true. Furthermore, we present an algorithm to decide whether the 1-dimensional component of the Weil's descente variety is a line over the ground field that avoids to compute the usually huge implicit equations of Weil's variety. In addition, we analyze main properties of quasi-polynomial curves, we present an algorithmic characterization of the definability, over a field, of curves given parametrically by means of the Weil's descente variety, and we extend Manocha and Canny's criteria, given in [20], for polynomial curves to the case of quasi-polynomial curves.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

AEM analysis of crystallization in Ti-based amorphous alloys

1983 ◽  
Vol 41 ◽  
pp. 270-271
Author(s):  
A.R. Pelton ◽  
A.F. Marshall ◽  
Y.S. Lee
Keyword(s):  
Magnetic Properties ◽  
Amorphous Alloys ◽  
Amorphous Materials ◽  
Isothermal Annealing ◽  
Amorphous Matrix ◽  
Nucleation And Growth ◽  
Current Interest ◽  
Amorphous Films ◽  
Electrical And Magnetic Properties

Amorphous materials are of current interest due to their desirable mechanical, electrical and magnetic properties. Furthermore, crystallizing amorphous alloys provides an avenue for discerning sequential and competitive phases thus allowing access to otherwise inaccessible crystalline structures. Previous studies have shown the benefits of using AEM to determine crystal structures and compositions of partially crystallized alloys. The present paper will discuss the AEM characterization of crystallized Cu-Ti and Ni-Ti amorphous films.Cu60Ti40: The amorphous alloy Cu60Ti40, when continuously heated, forms a simple intermediate, macrocrystalline phase which then transforms to the ordered, equilibrium Cu3Ti2 phase. However, contrary to what one would expect from kinetic considerations, isothermal annealing below the isochronal crystallization temperature results in direct nucleation and growth of Cu3Ti2 from the amorphous matrix.

Characterization of Coherent, Ordered Precipitates in Nickel-Base Alloys

1973 ◽  
Vol 31 ◽  
pp. 144-145
Author(s):  
B. H. Kear ◽  
J. M. Oblak
Keyword(s):  
Stable Phase ◽  
Nickel Base Superalloy ◽  
Alloy 718 ◽  
Commercial Alloy ◽  
Precipitate Morphology ◽  
Continuous Precipitation ◽  
Nickel Base ◽  
Base Superalloy ◽  
Strengthening Precipitate

A nickel-base superalloy is essentially a Ni/Cr solid solution hardened by additions of Al (Ti, Nb, etc.) to precipitate a coherent, ordered phase. In most commercial alloy systems, e.g. B-1900, IN-100 and Mar-M200, the stable precipitate is Ni3 (Al,Ti) γ′, with an LI2structure. In A lloy 901 the normal precipitate is metastable Nis Ti3 γ′ ; the stable phase is a hexagonal Do2 4 structure. In Alloy 718 the strengthening precipitate is metastable γ″, which has a body-centered tetragonal D022 structure.Precipitate MorphologyIn most systems the ordered γ′ phase forms by a continuous precipitation re-action, which gives rise to a uniform intragranular dispersion of precipitate particles. For zero γ/γ′ misfit, the γ′ precipitates assume a spheroidal.

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