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2 edition of Properties of surfaces whose asymptotic curves belong to linear complexes. found in the catalog.

Properties of surfaces whose asymptotic curves belong to linear complexes.

Charles Thompson Sullivan

# Properties of surfaces whose asymptotic curves belong to linear complexes.

Written in English

The Physical Object
Paginationpp. 167-196.
Number of Pages196
ID Numbers
Open LibraryOL16646459M

polynomials (I = k). We also consider similar asymptotic properties pertaining to approximation of vector functions by vector splines. We define the latter to be families of vector functions whose components are splines of order k with common knots. ( Academic Press, Inc 0. INTRODUCTION. PROPERTIES OF ATMOSPHERIC GASES whose mass in grams is equal to its molecular mass is called a mole. The volume occupied by a mole of gas at standard atmospheric pressure and 0° C is liters [( ± ) x 2 m' mole-I] and is the same for all gases. Surfaces in Euclidean Space The 2-dimensional analog of a curve is a surface. However, surfaces in general are much more complicated than curves. In this introductory chapter, we give basic deﬁnitions that will be used throughout the rest of the book. The intuitive idea of a surface File Size: 1MB. This paper addresses the problem of solving the Eikonal equation on triangulated domains, which are approximations to either flat regions (subsets of ℜ 2) or curved surfaces in ℜ 3. For many of these applications, there is a need for fast solutions to the Eikonal equation—e.g., run times of fractions of a second on large by:

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### Properties of surfaces whose asymptotic curves belong to linear complexes. by Charles Thompson Sullivan Download PDF EPUB FB2

PROPERTIES OF SURFACES WHOSE ASYMPTOTIC CIJRVES BELONG TO LINEAR COMPLEXES* BY CHARLES T. SULLIVAN INTRODUCTION In this paper a study is made of the geometrical properties of surfaces whose asymptotic curves belong to linear complexes.

The treatment is based on the methods developed by E. WilezSrnski in his book on projective differential. SULLIVAN: SURFACES WHOSE ASYMPTOTIC CURVES [April asymptotic curves.

If the asymptotic curves of only one of the two families belong to linear complexes, this quadric is replaced by a directrix-ruled surface of a higher order. On the other hand, the quadric introduced by Peter is characteristic of the canonical differential equations.

characterise asymptotic directions via the contact of the surface with °at ob- jects (k -planes, k = 1{4), give the equation of the asymptotic curves in terms of the coe–cients of the second fundamental form and study their generic local. We study asymptotic curves on generically immersed surfaces in R 5.

We characterise asymptotic directions via the contact of the surface with flat objects (k-planes, k = 1–4), give the equation.

Meromorphic Function Asymptotic Property Entire Curf These keywords were added by machine and not by the authors.

This process is experimental and the keywords may be updated as the learning algorithm by: 1. Journal of Computational and Applied Mathematics 41 () 57 North-Holland CAM Asymptotic properties of solutions to quasi-linear differential systems Jan Andres Department of Mathematical Analysis, Faculty of Science, Palacky University, Olomouc, Czechoslovakia Received 8 May Abstract Andies, J., Asymptotic properties of solutions to quasi-linear differential Cited by: 5.

1 [] A. Arosio, Asymptotic behavior as t → + ∞ of the solutions of linear hyperbolic equations with coefficients discontinuous in time (on a bounded domain), J.

Differential Equations 39 (), – [] T. Bárta, A generation theorem for hyperbolic equations with coefficients of bounded variation in time, Riv. Mat. Univ. Parma (7) 9 (), 17–Author: Taeko Yamazaki. generalization of the notion of limit linear series to curves which are not necessarily of compact type and prove, among other things, that any degeneration of a gr d in a regular family of semistable curves is a limit gr d on the special ber.

Contents 1. Introduction 2 2. Metrized complexes of algebraic curves 11 3. This enables us to analyse its qualitative properties by use of tools standardly employed in the qualitative investigation of Volterra difference equations.

As the main result, we derive a sharp condition for the asymptotic stability of the studied equation and, moreover, give a precise asymptotic description of its by: In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.

These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different.

For example. Asymptotic oracle properties of SCAD-penalized least squares estimators Huang, Jian and Xie, Huiliang, Asymptotics: Particles, Processes and Inverse Problems, ; Weak convergence of the empirical process of residuals in linear models with many parameters Chen, Gemai and and Lockhart, Richard A., The Annals of Statistics, It follows, of course, from this that these curves are also algebraic for wave surfaces, the Plücker complex-surface, and so on [these being special cases of the Kummer surface].

On a ruled surface whose generator belongs to a linear complex the asymptotic curves can Cited by: surface with the follo wing property: Along each asympto tic curve the corresponding 2nd asympto tic directions are par allel to a plane.

This is a well-known characterization of aﬃne minimal. This banner text can have markup. web; books; video; audio; software; images; Toggle navigation.

ASYMPTOTIC SOLUTIONS OF CERTAIN LINEAR DIFFERENTIAL EQUATIONS IN WHICH THE complex values of the parameter p. The second-order case goes back to Liouville. The essential differences between the present treatment and pre- tions and thus utilize the classical knowledge of their asymptotic properties.

This book shows how to compute a digital model from this point sample. After developing the basics of sampling theory and its connections to various geometric and topological properties, the author describes a suite of algorithms that have been designed for the reconstruction problem, including algorithms for surface reconstruction from dense.

On the asymptotic behaviour and smoothness properties of some positive linear operators for the approximation of continuous functions R. Crawford Wollongong University College Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.

In general there exist two asymptotic directions through P, tangential to two curves such that the tangent at every point of them is an asymptotic direction, and hence those two curves are asymptotic lines of the surface.

Furthermore, the asymptotic lines are curves whose osculating planes coincide with the tangent planes at each point of the curve. iﬁcation Lin M which is a compact surface whose boundary is contained in Kand LnLˆK. There are different types of leaves. A leaf which belongs to the interior of a 1-parameter family of leaves that are all diffeomorphic is regular.

This is in particular the case of pages with Author: Vincent Colin, Pierre Dehornoy, Ana Rechtman. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained.

One of the main features of free boundary value problems for minimal surfaces is that, for principal reasons, it is impossible to derive a priori estimates.

INTERSECTION NORMS ON SURFACES AND BIRKHOFF CROSS SECTIONS MARCOS COSSARINI AND PIERRE DEHORNOY every ﬁnite collection of curves on a surface, we deﬁne an associated (semi-)norm on the ﬁrst homology group of the surface. The unit ball of the dual norm is the convex hull of its integer points.

EINDHOVEN UNIVERSITY OF TECHNOLOGY THE NETHERLANDS DEPARTMENT OF ELECfRICAL ENGINEERING Coden: TEUEDE Eindhoven University of Technology Research Reports (ISSN Cited by: 1. Full text of "Projective Differential Geometry Of Curves And Surfaces" See other formats.

Thanks for contributing an answer to Mathematics Stack Exchange. Please be sure to answer the question. Provide details and share your research. But avoid Asking for help, clarification, or responding to other answers. Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. A linear time-series model is considered to be one for which a stationary time series, which is purely non-deterministic, has the best linear predictor equal to the best predictor.

A general inferential theory is constructed for such models and various estimation procedures are shown to be by: ANALYTIC SURFACES Parametric equations of a surface. Systems of curves on a surface Tangent plane. Normal line Differential of arc Minimal curves Angle between curves.

Differential of surface Radius of normal curvature. Meusnier's theorem Asymptotic tangents. Asymptotic curves Conjugate tangents Taylor Series and Asymptotic Expansions The importance of power series as a convenient representation, as an approximation tool, as a tool for solving diﬀerential equations and so on, is pretty obvious.

What may not be so obvious is that power series can be very useful even when they diverge. Let us start by considering Taylor Size: KB.

This paper aims to study some properties of the linear Boltzmann equation under the action of an absorbing moving surface. This equation represents the time evolution of a population of point particles that interact with the medium through absorption and scattering phenomena by supposing that the mean free path between two consecutive interactions has the same order of magnitude as a.

Covering many aspects of geometry and algebra, this book exposes readers to R geometrical concepts through the use of a modern computing tool — MATLAB.

This work is based on the author’s previous book Geometry of Curves and Surfaces with MAPLE, but it is a greatly expanded version with new chapters and excellent chosen themes. LECTURE NOTES ON CURVES AND SURFACES IN R3 Nigel Hitchin a2 Complex Analysis and Geometry Janu 1 Curves Deﬁnition 1 A smooth parametrized curve in R3 is a map γ: I → R3 from an open interval I ⊆ R such that • γ(t) = (x(t),y(t),z(t)) has derivatives of all orders • γ0(t) 6= 0 for t ∈ I Examples: 1) A straight line:File Size: KB.

In mathematics a translation surface is a surface obtained from identifying the sides of a polygon in the Euclidean plane by translations. An equivalent definition is a Riemann surface together with a holomorphic 1-form.

These surfaces arise in dynamical systems where they can be used to model billiards, and in Teichmüller theory. A particularly interesting subclass is that of Veech surfaces which.

A cardioid (from the Greek καρδία "heart") is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It can also be defined as an epicycloid having a single is also a type of sinusoidal spiral, and an inverse curve of the parabola with the focus as the center of inversion.

The name was coined by de Castillon in Riemann surface explained. In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex surfaces were first studied by and are named after Bernhard n surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite.

linear complexes, 4'7 42; then they belong to every complex of the system 4'l + 42 =?, and all the lines of curvature become rational, being the curve of intersection of the surface with the fundamental spheres sI + Among these complexes are two special ones, whose fundamiental spheres sl, s2 are touched by all the spheres of the congruence.

This paper proposes how to define discrete flat surfaces in hyperbolic 3-space by use of certain discrete integrable systems as well as to define discrete linear Weingarten surfaces.

Asymptotic behavior of the hyperbolic Schwarz map at irregular singular points, coauthor: T. Koike and M. Yoshida, Funkcialaj Ekvacioj 53(), Indeed, dΦ(x, y) is the inﬁmumof lengths of curves connecting x and y in the surface parameterized by f,and the length of any curve in (X, ) connecting x and y is no less than 10 x − y.

Applying Conjecture C to (V, ), A and Φ, we obtain thatVol(f) = Vol(A, Φ) ≥ Vol(A, ) where is the angle in the net. Assuming that the surface is regular, complete and simply connected, and taking account of the Chebyshev nature of the net, it can be proved that take all values: ; these exhaust all of the other words, an asymptotic net in the large is homeomorphic to the Cartesian net on the Euclidean coordinate plane (see).

In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment.

For the sake of applications we derive the self-normalized version of this theorem. The study is motivated by models arising in economical applications where often the linear processes have long memory, and the innovations have heavy by: 3.

Two real Kummer surfaces, belong to the same deformation class if and only if there is a differentiable family, The best-studied class of complex algebraic Kummer surfaces is that of Kummer surfaces coming from the Jacobians of complex curves of genus 2.

be real Kummer surfaces whose real parts are homeomorphic and have singular by: 1. The complex plane C is the most basic Riemann surface.

The map f(z) = z (the identity map) defines a chart for C, and {f} is an atlas for map g(z) = z * (the conjugate map) also defines a chart on C and {g} is an atlas for charts f and g are not compatible, so this endows C with two distinct Riemann surface structures.

In fact, given a Riemann surface X and its atlas A, the. The two curves at any point are equally inclined to the two curves of curvature at that point, or - what is the same thing - the supplementary angles formed by the two asymptotic lines are bisected by the two curves of curvature.

In the case of a quadric surface the asymptotic curves are the two systems of lines on the surface. Geodetic Lines. We analyze the size effect on spin-crossover transition nanoparticles in a 2D Ising-like model subject to a specific ligand-field at the surface.

By anisotropic sampling method applied to the finite 2D square Ising lattices with various sizes, we determined the density of macro states by scanning the spin configurations. This information, which is independent on the system parameters, is used Cited by: 9.Adhesion between rough surfaces is an active field of research where both experimental studies and theoretical modelling are used.

However, it is rather difficult to conduct precise experimental evaluations of adhesive properties of the so-called anti-adhesive materials. Hence, it was suggested earlier by Purtov et al.

() to prepare epoxy resin replicas of surfaces having different Cited by: 5.