Conjugate nets in asymptotic parameters ...
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Conjugate nets in asymptotic parameters ... by MacDonald, Janet

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Published in [n.p .
Written in English

Subjects:

  • Projective differential geometry.,
  • Curves on surfaces.

Book details:

Edition Notes

Statementby Janet MacDonald ...
Classifications
LC ClassificationsQA660 .M18
The Physical Object
Pagination1 p.l., 697-709 p.
Number of Pages709
ID Numbers
Open LibraryOL187847M
LC Control Numbera 45002191

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In the book of Sauer one can find also other examples of discrete surfaces, or better Z 2 lattices in R 3; in particular, he defined discrete asymptotic nets and discrete conjugate nets (consult also 2 Quadrilateral lattices and congruences, 5 Discrete asymptotic nets). These definitions, not only have clear geometric meaning, but also provide Cited by: We discretize some notions of the theory of asymptotic nets and of the theory of transformations of asymptotic nets. These are the Lelieuvre formulas, the Moutard equation, the Moutard transformation, the Weingarten congruences and the Jonas formulas. that conjugate nets (see, e.g., i.e. parameters (u,v) imprint asymptotic nets on Cited by: CONJUGATE NETS R AND THEIR TRANSFORMATIONS.* BY LU-THER PFAHLER EISENHART. 1. A rectilinear congruence for which the asymptotic lines on the two focal surfaces correspond is called a TV-congruence. When the tan-gents to the curves of each family of a conjugate system of curves on a surface form WV congruences, the system is called a net R.* . Variational Asymptotic Method (VAM) is a powerful mathematical approach to simplify the process of finding stationary points for a described functional by taking an advantage of small parameters. VAM is the synergy of variational principles and asymptotic approaches, variational principles are applied to the defined functional as well as the asymptotes are applied to the same functional.

CONJUGATE NETS IN PROJECTIVE HYPERSPACE 1. Differential equations and integrability conditions. Let us consider a conjugate net Nx with parameters u, v in a linear space S„ of w (^4) dimen-sions so that the homogeneous projective coordinates XU) x(n+l). 4. Studies in Asymptotic Parameters. For many purposes, when studv-ing conjugate nets on a surface S, it is convenient to take the asymptotic curves on the surface as parametric. In this section we shall mnake use of Fubini's canonical formn of the differential equations of the surface, supposed not ruled and referred to its asymptotic curves. the Conjugate Gradient Method Without the Agonizing Pain Edition 11 4 Jonathan Richard Shewchuk August 4, School of Computer Science Carnegie Mellon University Pittsburgh, PA Abstract The Conjugate Gradient Method is the most prominent iterative method for solving sparse systems of linear equations. In a neighbourhood of every point of the surface which is not a flat point one can introduce a parametrization such that the coordinate lines form a conjugate net. One family can be chosen arbitrarily, even when the lines of this family do not have asymptotic directions. An important example is a net of lines of curvature. References.

A conjugate prior to an exponential family distribution If f(x|θ) is an exponential family, with density as in Definition 3, then a conjugate prior distribution for θ exists. Theorem 9 The prior distribution p(θ) ∝ C(θ)a exp(φ(θ)b) is conjugate to the exponential family distribution likelihood. Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, or more generally are related through Pontryagin duality relations lead naturally to an uncertainty relation—in physics called the Heisenberg uncertainty principle—between them. In mathematical terms, conjugate variables are part of a symplectic . An asymptotic method to calculate the temperature of the fluid-solid interface far away from the heat source is proposed. The method takes into account convection, along with conduction in the fluid as well as in the solid. The asymptotic results are compared with numerical ones and good agreement is : C. F. Stein, P. Johansson. In quantum mechanics, conjugate variables are pairs of quantities that are connected in such a way that if you know one with no error the error in knowing the other.