A Remark Concerning the Parametric Representation of an Algebraic Variety

1937 ◽  
Vol 59 (2) ◽  
pp. 363 ◽  
Author(s):  
Oscar Zariski
Keyword(s):  
Algebraic Variety ◽  
Parametric Representation

A Parametric Representation of Wind-Driven Rain in Experimental Setups

2012 ◽  
Author(s):  
Thomas Baheru ◽  
Arindam Gan Chowdhury ◽  
Girma Bitsuamlak ◽  
Ali Tokay
Keyword(s):  
Parametric Representation

Pattern Theory

2006 ◽  
Author(s):  
Ulf Grenander ◽  
Michael I. Miller
Keyword(s):  
Computational Linguistics ◽  
Parametric Representation ◽  
Bayes Estimation ◽  
Geometric Transformation ◽  
Central Component ◽  
Pattern Theory ◽  
Infinite Dimensional ◽  
Engineering Mathematics ◽  
Dimensional Shape ◽  
The Continuum

Pattern Theory provides a comprehensive and accessible overview of the modern challenges in signal, data, and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer science, and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website. The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via condition structure. Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn. Chapters 10 and 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy. Finally, Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.

Error analysis of higher order trace finite element methods for the surface Stokes equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Thomas Jankuhn ◽  
Maxim A. Olshanskii ◽  
Arnold Reusken ◽  
Alexander Zhiliakov
Keyword(s):  
Finite Element ◽  
Stokes System ◽  
Parametric Representation ◽  
Higher Order ◽  
Optimal Order ◽  
Helmholtz Instability ◽  
Surface Stability ◽  
Instability Problem ◽  
Convergence Results ◽  
Optimal Order Convergence

AbstractThe paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in ℝ3. The method employs parametric Pk-Pk−1 finite element pairs on tetrahedral bulk mesh to discretize the Stokes system on embedded surface. Stability and optimal order convergence results are proved. The proofs include a complete quantification of geometric errors stemming from approximate parametric representation of the surface. Numerical experiments include formal convergence studies and an example of the Kelvin--Helmholtz instability problem on the unit sphere.

Proof Without Words: Parametric Representation of Primitive Pythagorean Triples

1996 ◽  
Vol 69 (3) ◽  
pp. 189-189
Author(s):  
Raymond A. Beauregard ◽  
E. R. Suryanarayan
Keyword(s):  
Parametric Representation ◽  
Pythagorean Triples

A Module-theoretic Characterization of Algebraic Hypersurfaces

2018 ◽  
Vol 61 (1) ◽  
pp. 166-173
Author(s):  
Cleto B. Miranda-Neto
Keyword(s):  
Algebraic Variety ◽  
Characteristic Zero ◽  
Vector Fields ◽  
Exterior Power ◽  
Algebraic Hypersurfaces ◽  
Theoretic Characterization

AbstractIn this note we prove the following surprising characterization: if X ⊂ is an (embedded, non-empty, proper) algebraic variety deûned over a field k of characteristic zero, then X is a hypersurface if and only if the module of logarithmic vector fields of X is a reflexive -module. As a consequence of this result, we derive that if is a free -module, which is shown to be equivalent to the freeness of the t-th exterior power of for some (in fact, any) t ≤ n, then necessarily X is a Saito free divisor.

Parametric Description of Vibration Using the Autocorrelation Function

2009 ◽  
Vol 147-149 ◽  
pp. 606-611
Author(s):  
Adam Kotowski
Keyword(s):  
Autocorrelation Function ◽  
Curve Fitting ◽  
Vibration Signal ◽  
Analytic Form ◽  
Parametric Representation ◽  
Rotating Machine ◽  
Fitting Procedure ◽  
Power Spectral ◽  
Parametric Description ◽  
Harmonic Components

The paper presents the use of the autocorrelation function for the description of vibrations and the problems connected with. The proposed method is based on the analysis of vibration signal recorded for machine during its operations using an analytic form of the autocorrelation function. The parameters are obtained using a curve fitting procedure. To keep a quality of parametric representation of considered vibration, only the curve fitting causes a determination coefficient over 0.90 is taken into consideration. Therefore, the autocorrelation functions are submitted for the fast Fourier transform to be helped, in determination of number of the dominant harmonic components. Also, the analytic form and parameters of power spectral density has been also calculated. Finally, the set of parameters has been collected to describe the selected fragment of vibration of the simple rotating machine. The influence of duration of analyzed vibration on the parameters values is also examined in this work.

Some results concerning the local analytic branches of an algebraic variety

1953 ◽  
Vol 49 (3) ◽  
pp. 386-396 ◽  
Author(s):  
D. G. Northcott
Keyword(s):  
Algebraic Geometry ◽  
Power Series ◽  
Algebraic Variety ◽  
Recent Progress ◽  
Rapid Development ◽  
Noetherian Rings ◽  
Local Rings ◽  
Power Series Rings ◽  
Analytic Algebra ◽  
Topological Theories

The recent progress of modern algebra in analysing, from the algebraic standpoint, the foundations of algebraic geometry, has been marked by the rapid development of what may be called ‘analytic algebra’. By this we mean the topological theories of Noetherian rings that arise when one uses ideals to define neighbourhoods; this includes, for instance, the theory of power-series rings and of local rings. In the present paper some applications are made of this kind of algebra to some problems connected with the notion of a branch of a variety at a point.

"CROSSROAD AREA–SPRING AREA" TRANSITION (II) FOLIATED PARAMETRIC REPRESENTATION

1991 ◽  
Vol 01 (02) ◽  
pp. 339-348 ◽  
Author(s):  
C. MIRA ◽  
J. P. CARCASSÈS ◽  
M. BOSCH ◽  
C. SIMÓ ◽  
J. C. TATJER
Keyword(s):  
Complete Information ◽  
Parametric Representation ◽  
Periodic Points ◽  
Parameter Plane ◽  
Flip Bifurcation ◽  
Cusp Point ◽  
Dimensional Representation ◽  
Bifurcation Structure ◽  
Spring Area

The areas considered are related to two different configurations of fold and flip bifurcation curves of maps, centred at a cusp point of a fold curve. This paper is a continuation of an earlier one devoted to parameter plane representation. Now the transition is studied in a thee-dimensional representation by introducing a norm associated with fixed or periodic points. This gives rise to complete information on the map bifurcation structure.

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