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 CONSTRUCTING SIMULTANEOUS HECKE EIGENFORMS

2010 ◽  
Vol 06 (05) ◽  
pp. 1117-1137 ◽  
Author(s):  
T. SHEMANSKE ◽  
S. TRENEER ◽  
L. WALLING
Keyword(s):  
Hecke Operators ◽  
Cusp Forms ◽  
Hecke Eigenforms ◽  
Linearly Independent ◽  
Integral Weight ◽  
Trivial Character ◽  
Free Level ◽  
Fixed Space ◽  
Space Of Cusp Forms

It is well known that newforms of integral weight are simultaneous eigenforms for all the Hecke operators, and that the converse is not true. In this paper, we give a characterization of all simultaneous Hecke eigenforms associated to a given newform, and provide several applications. These include determining the number of linearly independent simultaneous eigenforms in a fixed space which correspond to a given newform, and characterizing several situations in which the full space of cusp forms is spanned by a basis consisting of such eigenforms. Part of our results can be seen as a generalization of results of Choie–Kohnen who considered diagonalization of "bad" Hecke operators on spaces with square-free level and trivial character. Of independent interest, but used herein, is a lower bound for the dimension of the space of newforms with arbitrary character.

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 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.

APPLICATION OF BRAIDING SEQUENCES, I: ON THE CHARACTERIZATION OF VASSILIEV AND POLYNOMIAL LINK INVARIANTS

2010 ◽  
Vol 12 (05) ◽  
pp. 681-726 ◽  
Author(s):  
A. STOIMENOW
Keyword(s):  
Finite Number ◽  
Polynomial Growth ◽  
Embedded Graphs ◽  
Vassiliev Invariants ◽  
Link Invariants ◽  
Polynomial Coefficients ◽  
Linearly Independent

We apply the concept of braiding sequences to extend the polynomial growth result for Vassiliev invariants to links, tangles and embedded graphs. It implies the non-existence of Vassiliev invariants that depend on any finite number of link polynomial coefficients, and allows to define two norms on the space of Vassiliev invariants. Then we show that (apart from well-known relations) the coefficients of the link polynomials are linearly independent.

Quantitative Energy-Filtering Transmission Electron Microscopy (EFTEM) In Materials Science

1998 ◽  
Vol 4 (S2) ◽  
pp. 128-129
Author(s):  
F. Hofer ◽  
W. Grogger ◽  
P. Warbichler
Keyword(s):  
Materials Science ◽  
Important Application ◽  
Elemental Mapping ◽  
Secondary Phases ◽  
Edge Image ◽  
Energy Filtering ◽  
Window Method ◽  
Transmission Electron ◽  
Elemental Maps

Equipping a transmission electron microscope with an energy-filter offers extraordinary advantages for the characterization of both materials science and biological samples. Besides improvements for TEM imaging and electron diffraction like better contrast and resolution, elemental mapping using inner-shell ionizations has become the main application of EFTEM. Elemental maps with resolution down to 1 nm and elemental sensitivities down to a single monolayer have been reported. Using a Philips CM20 equipped with a Gatan Imaging Filter (GIF) for our experimental work, we acquired elemental maps with the three window method (A.E-1r background extrapolation from two pre-edge windows) and jump ratio images (division of post-edge image by a pre-edge image). One important application of EFTEM is the detection of secondary phases in materials e.g. precipitates and grain boundary phases. For example, fig.la shows the TEM-image of a 10%Cr steel with the secondary phases mostly invisible.

scholarly journals On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
J. M. Sepulcre
Keyword(s):  
Important Class ◽  
Exponential Polynomial ◽  
Critical Interval ◽  
Real Numbers ◽  
Positive Real ◽  
Exponential Polynomials ◽  
The Real ◽  
Linearly Independent ◽  
Pointwise Characterization

We provide the proof of a practical pointwise characterization of the setRPdefined by the closure set of the real projections of the zeros of an exponential polynomialP(z)=∑j=1ncjewjzwith real frequencieswjlinearly independent over the rationals. As a consequence, we give a complete description of the setRPand prove its invariance with respect to the moduli of thecj′s, which allows us to determine exactly the gaps ofRPand the extremes of the critical interval ofP(z)by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.

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

Synthesis and Properties of Acrylic Emulsion with Core-Shell Structure in Antifouling Paints

2009 ◽  
Vol 79-82 ◽  
pp. 537-540
Author(s):  
Chao Liu ◽  
Yu Bin Fu ◽  
Ji Yong Zheng
Keyword(s):  
Shell Structure ◽  
Important Application ◽  
Core Shell ◽  
Acrylic Emulsion ◽  
Antifouling Paints ◽  
Comprehensive Properties ◽  
Volatile Organic ◽  
Core Shell Structure ◽  
Seed Emulsion Polymerization

Water based resins have an important application in environmental benign coating to reduce the volatile organic compounds (VOC). This work describes the synthesis and characterization of an acrylic emulsion with core-shell structure by using pre-emulsion and seed emulsion polymerization technology for antifouling paints. The results indicate that when the ratio of soft and hard monomer is in the range of 1:1~2:1 and the amount of cross-linking agent is added, the comprehensive properties of acrylic emulsion are good. Although the coatings were found to develop a whitish aspect (blushing) due to water retrodiffusion, the films did not break and splint, further research are focused to increase their comprehensive properties for marine antifouling application.

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
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