About the Project

on a point set

AdvancedHelp

(0.009 seconds)

1—10 of 112 matching pages

1: 2.1 Definitions and Elementary Properties
β–ΊLet 𝐗 be a point set with a limit point c . … β–Ί
2.1.16 f ⁑ ( x ) a 0 + a 1 ⁒ ( x c ) + a 2 ⁒ ( x c ) 2 + β‹― , x c in 𝐗 ,
β–ΊIf the set 𝐗 in §2.1(iii) is a closed sector Ξ± ph ⁑ x Ξ² , then by definition the asymptotic property (2.1.13) holds uniformly with respect to ph ⁑ x [ Ξ± , Ξ² ] as | x | . …Suppose u is a parameter (or set of parameters) ranging over a point set (or sets) 𝐔 , and for each nonnegative integer n
2: 1.5 Calculus of Two or More Variables
β–ΊA function is continuous on a point set D if it is continuous at all points of D . … … β–ΊFor f ⁑ ( x , y ) defined on a point set D contained in a rectangle R , let … β–Ίwhere D is the image of D under a mapping ( u , v ) ( x ⁑ ( u , v ) , y ⁑ ( u , v ) ) which is one-to-one except perhaps for a set of points of area zero. …Again the mapping is one-to-one except perhaps for a set of points of volume zero. …
3: 1.6 Vectors and Vector-Valued Functions
β–Ίand S be the closed and bounded point set in the ( x , y ) plane having a simple closed curve C as boundary. … β–ΊSuppose S is a piecewise smooth surface which forms the complete boundary of a bounded closed point set V , and S is oriented by its normal being outwards from V . …
4: 1.9 Calculus of a Complex Variable
β–ΊAn open set in β„‚ is one in which each point has a neighborhood that is contained in the set. β–ΊA point z 0 is a limit point (limiting point or accumulation point) of a set of points S in β„‚ (or β„‚ ) if every neighborhood of z 0 contains a point of S distinct from z 0 . … β–ΊA domain D , say, is an open set in β„‚ that is connected, that is, any two points can be joined by a polygonal arc (a finite chain of straight-line segments) lying in the set. … β–ΊConversely, if at a given point ( x , y ) the partial derivatives u / x , u / y , v / x , and v / y exist, are continuous, and satisfy (1.9.25), then f ⁑ ( z ) is differentiable at z = x + i ⁒ y . … β–Ί
1.9.49 R = lim inf n | a n | 1 / n .
5: 2.8 Differential Equations with a Parameter
β–Ίin which u is a real or complex parameter, and asymptotic solutions are needed for large | u | that are uniform with respect to z in a point set 𝐃 in ℝ or β„‚ . … β–ΊCorresponding to each positive integer n there are solutions W n , j ⁑ ( u , ΞΎ ) , j = 1 , 2 , that depend on arbitrarily chosen reference points Ξ± j , are C or analytic on 𝚫 , and as u
6: 21.3 Symmetry and Quasi-Periodicity
β–ΊThe set of points 𝐦 1 + 𝛀 ⁒ 𝐦 2 form a g -dimensional lattice, the period lattice of the Riemann theta function. …
7: 18.2 General Orthogonal Polynomials
β–ΊLet X be a finite set of distinct points on ℝ , or a countable infinite set of distinct points on ℝ , and w x , x X , be a set of positive constants. …when X is a finite set of N + 1 distinct points. … β–ΊIf the polynomials p n ⁑ ( x ) ( n = 0 , 1 , , N ) are orthogonal on a finite set X of N + 1 distinct points as in (18.2.3), then the polynomial p N + 1 ⁑ ( x ) of degree N + 1 , up to a constant factor defined by (18.2.8) or (18.2.10), vanishes on X . …
8: 26.13 Permutations: Cycle Notation
β–ΊAn element of 𝔖 n with a 1 fixed points, a 2 cycles of length 2 , , a n cycles of length n , where n = a 1 + 2 ⁒ a 2 + β‹― + n ⁒ a n , is said to have cycle type ( a 1 , a 2 , , a n ) . …
9: 22.19 Physical Applications
β–ΊAs a 1 / Ξ² from below the period diverges since a = ± 1 / Ξ² are points of unstable equilibrium. … β–ΊFor an initial displacement with 1 / Ξ² | a | < 2 / Ξ² , bounded oscillations take place near one of the two points of stable equilibrium x = ± 1 / Ξ² . …As a 2 / Ξ² from below the period diverges since x = 0 is a point of unstable equlilibrium. …
10: 3.11 Approximation Techniques
β–ΊHere x j , j = 1 , 2 , , J , is a given set of distinct real points and J n + 1 . …