lists vectors maps and sets

... are called ‘harmonic maps. ’ In this situation, the harmonic maps are precisely the rational maps and their complex conjugates (see [2, (11.5)]) In particular, being conformal maps from a surface, ... Wloc (R2 \S) as n → ∞ REPULSION AND QUANTIZATION IN ALMOST-HARMONIC MAPS 469 We refer to the map u∞ : S → S as a ‘body’ map, and the maps ω i : S → S as ‘bubble’ maps The points {x1 , , xm } ... k ≥ and sufficiently large n Almost-harmonic maps — the proof of Theorem 1.2 The goal of this section is to understand the structure of maps whose tension field is small when measured in L2 , and...

Ngày tải lên: 28/03/2014, 22:20

... Contents of Fordy Wood file:///tmp/index.htm The twistor approach Twistors, nilpotent orbits and harmonic maps, P.Z Kobak, p 295 Index Index of terms used in the articles, p 323 This page is maintained...

Ngày tải lên: 24/04/2014, 16:50

... [0, ) and (3.14) implies (3.15), and the conclusion of Corollary 3.3 follows from Corollary 3.2 (b) Theorems 3.1-3.4 and Corollaries 3.1 and 3.2 all generalize and improve [5, Theorem 3.4] and ... metric space and p: X × X ® [0, ∞) a τ-function For each x Î X and A ⊆ X, let d(x, A) = inf d(x, y), y∈A and p(x, A) = inf p(x, y) y∈A Denote by N (X) the family of all nonempty subsets of X, C ... ∅ Remark 4.2 (a) Corollary 4.3 and Corollary 4.4 are indeed equivalent (b) Theorems 4.1-4.6 and Corollaries 4.1-4.4 all generalize and improve [5, Theorem 2.6] and the primitive Kannan’s fixed...

Ngày tải lên: 20/06/2014, 22:20

... continued by Hussain et al [26], Latif and Al-Mezel [27], and Marín et al [1] In particular, the authors of [27] and [1] have obtained a Rakotch-type and a Bianchini-Grandolfi-type fixed point theorems, ... Given a T0 qpm space (X, d), we denote by 2X and by Clds (X) the collection of all nonempty subsets of X and the collection of all nonempty τds-closed subsets of X, respectively Generalizing the ... < t and limr→t+ sup ϕ(r) < t for all t >0, and such that, for each x, y Î X and each u Î Tx there exists v Î Ty with q(u, v) ≤ (q(x, y)) Theorem 2.6 Let (X, d) be a complete T qpm space and...

Ngày tải lên: 21/06/2014, 02:20

... integers, v ∈ X, and let di j (x) be defined as in (∗ ) Suppose there exist nonnegative real numbers a0 ,a1 ,a2 , ,an−1 and b0 ,b1 ,b2 , Fixed Point Theory and Applications with n −1 i=0 ≤ and ∞ j =0 ... is continuous, and inf x∈X d(x, f (x)) = inf n∈N d(x1n ,x2n ) = inf n∈N 1/n = Let c5 = a7 ≥ be a real number, and let other coefficients , c j , and bk be all 0, then both (A.1) and (A.3) hold ... given (X,d) and f : X → X, since d( f (x), f (y)) ≤ 1, and c5 d( f (x), f (x)) = a7 d( f (x), f (x)) = 1, both (A.2) and (A.4) hold, too However, it is clear that f has no fixed points, and each...

Ngày tải lên: 22/06/2014, 19:20

... 2 Diametrically contractive maps and fixed points references therin; we will call them shrinking We briefly recall some results and properties of maps in this class: (1) the fixed point, ... 1, 81–82 8 Diametrically contractive maps and fixed points [9] B Sims, Examples of fixed point free mappings, Handbook of Metric Fixed Point Theory (W A Kirk and B Sims, eds.), Kluwer Academic, ... diametrically contractive maps are shrinking; (2) if M is a compact set and T is shrinking, then it is diametrically contractive; (3) there are examples of shrinking maps that are not diametrically...

Ngày tải lên: 22/06/2014, 22:20

... et al [9], Jungck and Sessa [12], Khan and Khan [13], O’Regan and Shahzad [15], Rhoades and Saliga [16], Sahab et al [18], Shahzad [19–21], and Singh [22] Common fixed point and approximation ... -commuting maps and invariant approximations Theorem 2.2 Let I and T be self -maps on a q-starshaped subset M of a p-normed space X Assume that cl(T(M)) ⊂ I(M), q ∈ F(I), and I is affine Suppose that T and ... Al-Thagafi and Shahzad’s [2, Theorem 2.2 ], Dotson’s [3, Theorem 1], Guseman and Peters’s [4, Theorem 2], and Hussain and Berinde’s [7, Theorem 3.6] Theorem 3.1 Let T and I be self -maps on a compact...

Ngày tải lên: 22/06/2014, 22:20

... theorem and minimax theorem Theorem 4.1 (Ky Fan’s coincidence theorem) Let X and Y be nonempty convex subsets of topological vector spaces E and F, respectively Let A,B : X → 2Y be two maps satisfying ... ∈ , , if x ∈ 0, otherwise (3.4) Note on KKM maps and applications It is obvious that E is not compact and Tx is convex for all x ∈ E Put y1 = 1/2 and y2 = 3/4 Then it follows that co y1 , y2 ... 1, ,l and t = 1,2, ,k By the convexities of A−1 x and B y, we have y0 ∈ Ax0 and y0 ∈ Bx0 This completes the proof Remark 4.2 The classical Ky Fan’s coincidence theorem assume that both X and Y...

Ngày tải lên: 22/06/2014, 22:20

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:20

... submaps and minors Forbidden submaps In this subsection we study the topological minor inclusion on maps We define for each g ≥ a finite set Fg of forbidden maps, and we use it to characterize maps ... contractible edges Let M − M1 and M −→ M2 → − e e Then e is contractible in M1 and e is contractible in M2 , and we have a map M such that M1 −→ M and M2 − M We say that e and e can be contracted ... 1.1 Preliminaries Graphs and maps All graphs will be undirected and finite They may have multiple edges and loops For a graph G, we will denote by VG its set of vertices and by EG its set of edges...

Ngày tải lên: 07/08/2014, 07:21

... bijection between tree-oriented maps (of size n) and pairs made of a tree and a non-crossing partition (of size n and n + respectively) 3.1 Tree-rooted maps and tree-oriented maps In this subsection, ... corner c and connecting it to h This completes our study of prefix -maps We are now ready to extend the mappings ϕ0 and ϕ1 to prefix maps and to prove Theorem 21 4.4 The trees ϕ0(M T ) and λ0 (w) ... tree-rooted maps of size n and pairs consisting of a tree and a non-crossing partition of size n and n+1 respectively This simple bijection explains why the number of tree-rooted maps of size...

Ngày tải lên: 07/08/2014, 15:22

... behind Alon and Tarsi’s Theorem, combinatorialists always search for purely combinatorial proofs, since this usually helps to understand the situation in more detail Indeed, Alon and Tarsi asked ... Alon and Tarsi’s Theorem We use our strengthening to provide paintability versions of Alon and Tarsi’s bound of the list chromatic number of bipartite and planar bipartite graphs (Theorem 3.3 and ... Fleischner and Stiebitz’ Theorem 3.9 about certain 4-regular Hamiltonian graphs, H¨ggkvist and Janssen’s bound a (Theorem 3.10) for the list chromatic index of the complete graph Kn , and Ellingham and...

Ngày tải lên: 08/08/2014, 11:20

... Hacking Google Maps and Google Earth ® ® Martin C Brown Hacking Google Maps and Google Earth ® ® Hacking Google Maps and Google Earth ® ® Martin C Brown Hacking Google® Maps and Google® Earth ... Google Maps API Google Maps API Documentation Google Maps API Help Google Web API Google Maps Groups Information Sources Google Maps Mania Maplandia.com ... the fundamentals of the Google Maps API, and how to organize and translate existing information into a format that can successfully be used within Google Maps and Google Earth applications The...

Ngày tải lên: 20/10/2014, 01:14

... interface and abstract class (§24.2) To design and implement a dynamic list using an array (§24.3) To design and implement a dynamic list using a linked structure (§24.4) To design and implement ... 0132130807 15 Linked Lists Since MyArrayList is implemented using an array, the methods get(int index) and set(int index, Object o) for accessing and modifying an element through an index and the add(Object ... +remove(index: int) : E Removes the element at the specified index and returns the removed element Sets the element at the specified index and returns the element you are replacing +set(index: int, e:...

Ngày tải lên: 24/10/2014, 01:17