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Algebraic curves

Bounding and Estimating the Hausdorff distance between real space algebraic curves

Bounding and Estimating the Hausdorff distance between real space algebraic curves

... In Section 2, we present a situation in which the Hausdorff distance between the real part of two algebraic curves is finite. In such situation, an estimation method for the supremum of the distances ...

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Topological Behavior of Families of Algebraic Curves Continuously Depending on a Parameter Under Certain Conditions

Topological Behavior of Families of Algebraic Curves Continuously Depending on a Parameter Under Certain Conditions

... say that such a family is a family of algebraic curves continuously depending on the parameter t. Once again, by Semialgebraic Hardt’s Triviality Theorem such a family contains finitely many topology types. ...

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Radical parametrization of algebraic curves and surfaces

Radical parametrization of algebraic curves and surfaces

... of algebraic curves and surfaces is a fundamental topic in CAGD (inter- sections; offsets and conchoids; ...elliptic curves can be parametrized with one square ...of curves and surfaces by ...

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On the approximate parametrization problem of algebraic curves

On the approximate parametrization problem of algebraic curves

... approximately algebraic curves and surfaces is an active research field, with many implications in practical ...of algebraic curves (planar or spatial), and we report on some algorithms ...

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An Algebraic Analysis of Conchoids to Algebraic Curves

An Algebraic Analysis of Conchoids to Algebraic Curves

... Note that we get a cardioid; let us denote it as C (see Fig.. Next theorem states the main property of the components of a conchoid.. Remark 5 If C is a line through the focus, then €{C)[r] ...

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Approximate parametrization of plane algebraic curves by linear systems of curves

Approximate parametrization of plane algebraic curves by linear systems of curves

... In this paper, given a tolerance e > 0 and an e -irreducible algebraic affine plane curve C of proper degree d, we introduce the notion of e -rationality, and we provide an algorith[r] ...

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Rational parametrization of conchoids to algebraic curves

Rational parametrization of conchoids to algebraic curves

... the union of C and finitely many lines. So all components of T are rational, and using a parametrization of each component we determine conditions on the parameter to get double ration[r] ...

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Efficient detection of symmetries polynomially parametrized curves

Efficient detection of symmetries polynomially parametrized curves

... an algebraic curve has been previously investigated mainly because of its applications in pose estimation and patter ...of algebraic curves representing different objects, the one that best fits a ...

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On the development of early algebraic thinking

On the development of early algebraic thinking

... M ETHODOLOGY : D ATA C OLLECTION AND A NALYSIS Our data comes from a 3-year longitudinal research program conducted in an ur- ban primary school in which a class of 25 8-year old students was followed as the students ...

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Group representations, algebraic dynamics and torsion theories

Group representations, algebraic dynamics and torsion theories

... More generally, when R is a ring with left Gabriel dimension e.g., a left Noetherian ring, see Chapter 2, we can prove a complete structure theorem for all the length functions of R-Mod,[r] ...

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Detecting Symmetries of Rational Plane Curves

Detecting Symmetries of Rational Plane Curves

... parametric curves (in fact not necessarily rational, but with more general parametrizations) and can be performed exactly, to give a deterministic ...low-degree curves); otherwise, they were conceived to ...

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Detecting Similarity of Plane Rational Curves

Detecting Similarity of Plane Rational Curves

... A novel and deterministic algorithm is presented to detect whether two given planar rational curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it ...

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Sparse differential resultant formulas: between the linear and the nonlinear case

Sparse differential resultant formulas: between the linear and the nonlinear case

... A matrix representation of the sparse differential resultant is the basis for efficient compu- tation algorithms, whose study promises a great contribution to the development and applica- bility of differential elimination ...

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“Open dynamical systems for beginners: algebraic foundations”

“Open dynamical systems for beginners: algebraic foundations”

... Open System Theory provides a rich challenge to mathematicians. As we mentioned, one starts by defining a main system -supporting our observables- and write down the main dynamics. This main system is continuously ...

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Linear Response Theory: An Analytic-Algebraic Approach.

Linear Response Theory: An Analytic-Algebraic Approach.

... • We want a formalism which works simultaneously for random and deterministic systems in the discrete and in the continuum. • The formalism is also suitable to treat interacting systems [r] ...

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On neutrino masses in the MSSM with BRpV

On neutrino masses in the MSSM with BRpV

... Algebraic approximations Here, approximated algebraic expressions for second and third order terms from the top–stop contribution to the solar mass are found, in order to better understa[r] ...

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Characterization of the evolutes of planes curves

Characterization of the evolutes of planes curves

... También se determinará la evoluta de α usando algunos resultados de la teoría de contacto y singularidades [1], es decir se verificará que el conjunto formado por los puntos que son cent[r] ...

5

An algorithm to parametrize approximately space curves

An algorithm to parametrize approximately space curves

... space curves) might have suffered some tiny perturbations, for instance in the coefficients of their equations and, in consequence, their expected properties do not hold anymore (in our case, the genus ...

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Layers of generality and types of generalization in pattern activities

Layers of generality and types of generalization in pattern activities

... of algebraic thinking sketched above and the then-emerging Vygotskian perspective in mathematics education (Bartolini-Bussi, 1995; Lerman, 1996), we formulated our research problem in semiotic ...some ...

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