pdes differential geometry and robust statistics

... in Robust Statistics: Theoryand Applications” outlines the ongoing research in some topics of robust statistics.It can be considered as an outcome of the International Conference on RobustStatistics ... researchers and practitioners interested inrobust statistics, data analysis and related areas The ICORS meetings create aforum to discuss recent progress and emerging ideas in statistics and encourageinformal ... following areas:robust estimation for high-dimensional data, robust methods for complex data,robustness based on data depth, robust mixture regression, robustness in functionaldata and nonparametrics,

Ngày tải lên: 14/05/2018, 15:12

... Figure 2.7.Suppose α and β are Bertrand mates correspond-c Suppose α is arclength-parametrized and κτ 6= 0 Show that α has a Bertrand mate β ifand only if there are constants r and c so that rκ + ... β so that α and β are Bertrand mates,then there are infinitely many such curves β and this occurs if and only if α is a circularhelix 20 (See Exercise 19.) Suppose α and β are Bertrand mates Prove ... Translation, and Geodesics 64 1 Holonomy and the Gauss-Bonnet Theorem 76 2 An Introduction to Hyperbolic Geometry 88 3 Surface Theory with Differential Forms 97 4 Calculus of Variations and Surfaces

Ngày tải lên: 08/03/2019, 13:08

... 21, 2004 and is survived by hiswife, Ljudmila Pavlovna Goncharova, and three sons Trang 10Differential Geometry of Curves and SurfacesTrang 11Definition 1.1.1 If
a = a1
i + a2
j + a3
k and
b = ... to the Institute of Mathematics and 1 Aleksandr Danilovich Aleksandrov (1912–1999). 2Meyer, W.T Toponogov’s Theorem and Applications Lecture Notes, College on Differential Ge-ometry, Trieste ... of Curves in Three-dimensional Euclidean Space and in the PlaneDefinition 1.1.3 If a map ϕ : M → N is continuous and bijective, and if its and M and N are said to be homeomorphic The Jacobi matrix

Ngày tải lên: 08/03/2019, 13:08

... fromdifferential topology and geometry applied to smooth embedded surfaces The understanding of surfaces embedded in E3 requires local and global concepts, which are respectivelyevocative of differential ... 3 DIFFERENTIAL TOPOLOGY AND GEOMETRY3.3 Umbilics and lines of curvature, principal foliations This section is devoted to second order properties on a surface, and more precisely to umbilics and ... or engineering On one hand,mathematics contribute with classical differential topology and geometry, as well as with combinatorial methodson discrete objects On the other hand, computer science

Ngày tải lên: 08/03/2019, 13:08

... Trang 1Localization, Periodicity, and Galois Symmetry(The 1970 MIT notes) byDennis Sullivan Edited by Andrew Ranicki Trang 2Dennis SullivanDepartment of MathematicsThe Graduate Center ... issued in June1970 and were widely circulated at the time The notes had a jor influence on the development of both algebraic and geometrictopology, pioneering ma-the localization and completion of ... the 1974 Annals of Mathematics papers Genetics of homotopy theory and the Adams conjecture and The transversality istic class and linking cycles in surgery theory2 Many of the ideasoriginating

Ngày tải lên: 16/01/2021, 01:27

... If H and K are separated, then every connected subset M of H U K lies either in H or in K are separated and nonempty (Evidently, if H and K are separated, and H' c Hand K' c K, then H' and K' ... J at P and R, and B 2 touches J at Q and S Then Int B1 and Int B 2 lie in different components of R 2 - J 13 Let J be a !-sphere, and let P E J Then J- Pis homeomorphic toR 14 Let J1 and J2 ... vn E K, then v0v; v~ E L, and conversely Then cp is an isomorphism between K and L If there is such a cp, then K and L are isomorphic If K and L are complexes, and have subdivisions K', L'

Ngày tải lên: 16/01/2021, 01:29

... Translated by R SANDLING 273 Spectral theory and geometry, E.B DAVIES & Y SAFAROV (eds) 274 The Mandelbrot set, theme and variations, T LEI (ed) 275 Descriptive set theory and dynamical systems, ... introduction to noncommutative differential geometry and its physical applications (2nd edition), J MADORE 258 Sets and proofs, S.B COOPER & J.K TRUSS (eds) 259 Models and computability, S.B COOPER ... in random matrix theory and number theory, F MEZZADRI & N.C SNAITH (eds) 323 Poisson geometry, deformation quantisation and group representations, S GUTTet al (eds) 324 Singularities and

Ngày tải lên: 14/03/2014, 10:20

... “contravariant”. Let Ω and
Ω be two domains inR3 and let Θ : Ω→ E3 and
Θ :
Ω→ E3 be two C1-diffeomorphisms such that Θ(Ω) =
Θ(
Ω) and such that the vectors g i (x) := ∂ i Θ(x) and
g i(
x) =
... replaced byRd and E3by a d-dimensional Euclidean space E d This extension only demands that Latinindices and exponents now range in the set{1, 2, , d} and that the sets of ma- trices M3,S3, and S3 ... + o |δx|2 . Note that, here and subsequently, we use standard notations from matrix algebra For instance, δx T stands for the transpose of the column vector δx and∇Θ(x) T designates the transpose

Ngày tải lên: 17/03/2014, 14:24

... Riemannian geometry and, as “inertial frames,” in general relativity. It was this theorem of Gauss, and particularly the very notion of “intrinsic geometry”, which inspired Riemann to develop his geometry. Chapter ... theory of connections on fibe r bundles and then sp e cialize to principal and associated bundles. 0.1. INTRODUCTION 3 Chapter VI returns to Riemannian geometry and discusses Gauss’s lemma which asserts ... introduction to Riemannian geometry and its principal physical application, Einstein’s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus,

Ngày tải lên: 17/03/2014, 14:28

... 3Foreword: MASS and REU at Penn State University vii Chapter 2 Billiard in the Circle and the Square 21Chapter 3 Billiard Ball Map and Integral Geometry 33Chapter 4 Billiards inside Conics and Quadrics ... panorama.Let A and B be the starting and terminal points of the desiredcurve, and let x be the horizontal and y the vertical axes It isconvenient to direct the y axis downward and assume that ... principle, X is a critical point if andonly if ∇f(X) is orthogonal to l The sum of the unit vectors from A to X and from B to X is perpendicular to l if and only if AX and BX make equal angles with

Ngày tải lên: 23/03/2014, 23:20

... texts in Differential Geometry but very few have an early introduction to differential forms and their applications to Physics It is the purpose of these notes to bridge some of these gaps and thus ... of T and B N'=uf+bB Taking the dot product of last equation with T and B respectively, we see that a=N'-T, and b=N'.H Trang 14On the other hand, differentiating the equations N -7T = 0, and N-B=0, ... dependent and mathematicians in general (specially differential geometers) prefer coordinate-free definitions, theorems and proofs And now, a little combinatorics Let us count the number of differential

Ngày tải lên: 27/03/2014, 11:52

... first and second derivatives, normal, metric matrix and curvature matrix for spheres, cones, cylinders, and tori 26 January 1990 Apple Technical Report No KT-23 Trang 2The Differential Geometry ... z] x=F u( ) Trang 3and establishes a metric of differential length:so that the arc length of a curve segment, is given by: The differential surface area enclosed by the differential parallelogram ... respect to the new parameters and , and is the Jacobian matrix of the reparametrization The new Hessian is given by where The new fundamental matrix is given by: and the new curvature matrix

Ngày tải lên: 27/03/2014, 11:53

... and a reference to the <geometry> node for that mesh.The criteria is just that the node not be of type “JOINT”, has an <instance_geometry> node and that the node returns a valid geometry ... continue ; //Get the <instance_geometry> node that corresponds to this //<node> domInstance_geometry* instance_geometry = NULL; instance_geometry = (domInstance_geometry*)nodes[i]->getDescendant( ... (domInstance_geometry*)nodes[i]->getDescendant( "instance_geometry" ); //If there is no <instance_geometry>, this isn't a static //mesh and we will skip it. if (!instance_geometry) continue ; //Get the <geometry> node

Ngày tải lên: 31/03/2014, 10:20

... analytical geometry1»; – «Course of linear algebra and multidimensional geometry»; – «Course of differential geometry» This book is devoted to the first acquaintance with the differential geometry.Therefore ... of modern geometry such as the vectorialand tensorial analysis, covariant differentiation, and the theory of Riemanniancurvature The restriction of the dimension to the cases n = 2 and n = 3 ... determined by themodulus of the velocity and by the geometry of the trajectory (by its curvature) Trang 18ELEMENTS OF VECTORIAL AND TENSORIAL ANALYSIS.§ 1 Vectorial and tensorial fields in the space

Ngày tải lên: 31/03/2014, 15:55

... X 2 X(M) and Y 2 X(N) and X Y 2 X(M N) is given(X Y)(x y) = (X(x) Y(y)), then we have: (2) X Y and X are pr1-related (3) X Y and Y are pr2-related (4) X and X Y are ins(y)-related if and only ... elds Xi 2 X(M) and Yi 2 X(N) for i= 1 2,and a smooth mapping f :M !N If Xi and Yi are f-related for i= 1 2, thenalso 1X1+2X2 and 1Y1+2Y2 are f-related, and also X1 X2] and Y1 Y2] are f-related ... 1("), where f1 f2 : M1 M2 ! N N andwhere " is the diagonal of N N, andf1 f2 is transversal to " if and only if f1 and f2 are transversal Trang 203 Vector Fields and FlowsA vector eld X on

Ngày tải lên: 31/03/2014, 15:55

... dynamical system and discuss bility including the stable manifold and the Hartman–Grobman theorem forboth continuous and discrete systems sta-We prove the Poincar´e–Bendixson theorem and investigate ... the basics foriterated interval maps and ending with the Smale–Birkhoff theorem and theMelnikov method for homoclinic orbits Keywords and phrases Ordinary differential equations, dynamical systems,Sturm-Liouville ... constitutes the lecture notes for my courses nary Differential Equations and Dynamical Systems and Chaos held at theUniversity of Vienna in Summer 2000 (5hrs.) and Winter 2000/01 (3hrs),respectively Ordi-It

Ngày tải lên: 31/03/2014, 15:56

... Equation (1) implies that x and x– lie on the same ray from the origin, and x–i xi = ; r– r– and squaring and adding gives 12 r– That is, project it to the circle, and invert the distance from ... fields X and Y a SMOOTH scalar (field) “X, Y‘, satisfying the following properties Symmetry: “X, Y‘ = “Y, X‘ for all X and Y, Bilinearity: “åX, ∫Y‘ = å∫“X, Y‘ for all X and Y, and scalars å and ∫ ... Equations and Derivation of Newton's Law 114 15 The Schwarzschild Metric and Event Horizons 124 16 White Dwarfs, Neutron Stars and Black Holes, by Gregory C Levine131 References and Further...

Ngày tải lên: 17/03/2014, 14:28

... fields X and Y a scalar (field) “X, Y‘, satisfying the following properties Symmetry: “X, Y‘ = “Y, X‘ for all X and Y, Bilinearity: “åX, ∫Y‘ = å∫“X, Y‘ for all X and Y, and scalars å and ∫ “X, ... be contravariant, and let C and D be covariant Then: ∂x–i k ∂x–j l ∂x–i ∂x–j k l i j W = k lV W, V— W— = k V ∂x ∂xl ∂x ∂x and similarly, ∂x–i ∂xl k i V— C—j = k j V Cl , ∂x ∂x– and ∂xk ∂xl C—iD—j ... presently Definition 4.9 If V and W are contravariant (or covariant) vector fields on M, and if å is a real number, we can define new fields V+W and åV by (V + W)i = Vi + Wi and (åV)i = åVi It is easily...

Ngày tải lên: 12/08/2014, 16:20

... path, and define a new function s (arc length) by s(t) = L(a, t) = length of path from t = a to t Then s is an invertible function of t, and, using s as a parameter, ||dxi/ds||2 is constant, and ... some coordinate neighborhood, and define the length of S by b ⌠  L(a, b) =  ⌡ a 42 dxidxj ± gij dt, dt dt where the sign ±1 is chosen as +1 if the curve is space-like and -1 if it is time-like ... scalar field, so is ||X|| is a scalar field, if it exists, and satisfies ||˙X|| = |˙|·||X|| for every contravariant vector field X and every scalar field ˙ The expected inequality ||X + Y|| ≤...

Ngày tải lên: 12/08/2014, 16:20

... ||V—|| = On the other hand, we can also use G— to compuate ||V—||2, and we get ||V—||2 = , k showing that k = Hence, G— = G, and also D has the desired form This proves (b) (and also (c), by the ... multiplying…) Deduce that x–i(t) = zi + rit for some constants ri and si Finally, set t = and t = to conclude that x–i(t) = x–0i + ∆x–it, and apply (c) above.] 55 If the x–i-system is moving with a ... Lorentz Transformations of Special Relativity If two Lorentz frames x and x– have the same coordinates at (x, y, z, t) = (0, 0, 0, 0), and if the x–-frame is moving in the x-direction with a speed of...

Ngày tải lên: 12/08/2014, 16:20