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Two topics on local theta correspondence
... dim span { π(K)v } < ∞ } be the space of K-finite vectors of V, which is a (g, K)-module called the Harish-Chandra module of V By Harish-Chandra’s theory, the HarishChandra module of irreducible ... H Then the restriction induces a linear isomorphism HomH (E ∞ , ρ) ∼ Homh,KH (E, ρ) = where E ∞ denote the Casselman-Wallach globalization of E The next lemma is essentially from Huang and Zhu ... which corresponding to the highest weight under standard basis τSp(m) denote the irreducible Sp(m)-module generated by the highest weight vector (a1 ,··· ,a ,0,···0) in τU(2m) m Note that the...
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Girsanov’s theorem and the risk-neutral measure
... b + T 2 db =p 2T 2 T ,1 2 Z1 y exp , y2 dy (Substitute y = T + b) y = T + b = p 2 T ,1 = 0: CHAPTER 17 Girsanov’s theorem and the risk-neutral measure 191 fe We can also see that I B T ... Under I , the process B t ; t T , is a Brownian motion P Caveat: This theorem requires a technical condition on the size of If IE exp ZT 2 u du 1; everything is OK We make the following ... but here is the beginning of the proof Lemma 1.55 Using the notation of Girsanov’s Theorem, we have the martingale property fe e IE B t jF s = B s ; s t T: e Proof: We first check that...
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Đề tài " Conformal welding and Koebe’s theorem " docx
... (z2 ) = w2 The third definition is the one we gave in the introduction However, the proof of Lemma 24 below shows that the second definition implies h is log-singular, while Theorem 25 below shows ... welding homeomorphism H so that h( x) = H( x) for all x ∈ T \ E If h satisfies the hypothesis of Theorem 3, then h is a conformal welding and there is nothing to So assume otherwise and apply Theorem ... abbildung mehrfach zusammenh¨ngender bereiche auf kreisbereiche etc., Math Z (1 920 ), 23 5–301 a [29 ] O Lehto, Homeomorphisms with a given dilatation, In Proceedings of the Fifteenth Scandinavian...
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abel's theorem in problems and solutions - v.b. alekseev
... conformal mappings 60 62 65 71 74 83 90 96 99 100 105 105 148 20 9 22 1 22 2 22 4 22 8 23 0 23 1 23 2 23 3 23 4 23 5 23 7 23 7 23 8 vii A.10.3 The integrable case A.11 Topological obstructions for the solvability ... the complex numbers v 55 58 vi 2. 5 2. 6 2. 7 2. 8 2. 9 2. 10 2. 11 2. 12 2.13 2. 14 The trigonometric form of the complex numbers Continuity Continuous curves Images of curves: the basic theorem of the ... Sciences (where his manuscript had been either lost or hidden by Cauchy) My 196 4 lectures had been published in 197 6 by one of the pupils of High School audience, V.B Alekseev He has somewhere algebraized...
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Báo cáo hóa học: "Research Article Quasicone Metric Spaces and Generalizations of Caristi Kirk’s Theorem" ppt
... a x , that is, g a x Let H be a family of all mappings h h f Then, 2. 21 yields that d x, h x Thus, by Theorem 2. 6, y is such that g b y ≤ϕ x −ϕ h x , h y for all h ∈ H Hence g b h ∈ H f b for ... We shall show that f y y for all f ∈ F Assume the contrary that there is f ∈ F such that f y / y Then 2. 16 with x y implies that ϕ f y < ϕ y α Thus, by definition of α, there is n ∈ N such that ... then there exits y ∈ X such that ϕ y
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Báo cáo toán học: "Irreducible coverings by cliques and Sperner’s theorem" ppsx
... follows that xi xj ∈ / E(G) since otherwise A ∪ {xi , xj } induces a complete subgraph in G, thus contradicting the hypothesis that ci is a clique This implies that each clique c in G has the form ... Furthermore, I(n, n − 2) = 2n 2 − and the extremal graph (unique up to isomorphism) coincides with K2,n 2 for every n ≥ In [10] it was proved that for sufficiently large n, I(n, n − 3) = 3n−3 − · 2n−3 ... We will show for the first case that max max (s + | s 2 {A1 , ,As } s i=1 the electronic journal of combinatorics (20 02) , #N11 Ai |) = k k /2 , (1) where the second maximum in the left-hand side...
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Báo cáo toán học: "Kocay’s lemma, Whitney’s theorem, and some polynomial invariant reconstruction problems" docx
... graph on fewer than 2v(G) vertices If F has a component 2G 2H isomorphic to G (in which case we write F = G + X) then = If F G+X H +X 2G 2H has no component isomorphic to G then = F F Proof When ... and H are connected nonisomorphic graphs with the same vertex deck, that is, they are a counter example to Ulam’s conjecture Then 2G and 2H are nonisomorphic but N (2G) = N ( 2H) by Lemma 2. 11 Therefore, ... sufficient to show this when at least one of the graphs F1 and F2 has a component isomorphic to G When F2 = 2G, then Equation (10) follows from Lemma 2. 9 and Corollary 2. 10 When F1 = G + X and F2 = G...
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Báo cáo toán học: " Landau’s and Rado’s Theorems and Partial Tournaments" pdf
... suppose that n is odd and that (11) holds Then si = for i = (n + 1) /2, (n + 3) /2, , n Hence, there are no edges in T from a vertex in {(n + 1) /2, (n + 3) /2, , n} to {1, 2, , (n−1) /2} It ... combinatorics 16 (20 09), #N2 As a referee observed, because of the presence of the quantity γ(K), whether or not the inequalities (10) in Theorem 3.1 are satisfied depends on the initial labeling of the vertices ... if the family A = (A1 , , A1 , A2 , , A2 , , An , , An ) r1 r2 the electronic journal of combinatorics 16 (20 09), #N2 rn has an independent transversal: The desired tournament has...
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Báo cáo toán học: "A q-analogue of Graham, Hoffman and Hosoya’s Theorem" pdf
... the mod -2 distance matrix of a graph, where only the parity of each entry of the distance matrix is used We show that if two graphs G1 , G2 have an identical multiset of isomorphic blocks, then ... the mod -2 distance matrices of G1 and G2 have the same determinant value, independent of the tree-like connection of their blocks This shows that the adjacency matrix of several graphs have the ... (Of Theorem 2) Pairs of distinct blocks have at most one vertex in common; the common vertex joining two adjacent blocks is called a cut-vertex Among the blocks of G, let H be a block which has...
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Báo cáo toán học: "Flexible Color Lists in Alon and Tarsi’s Theorem, and Time Scheduling with Unreliable Participants" pot
... classical version (which they use at the end of the proof of [H Ja, Preposition 2. 4]) we get: a Theorem 3.10 The complete graph Kn is edge n-paintable Sketch of the proof The line graph LKn of Kn consists ... around and see who shows up He then suggests that each present player should play against all those other present players against whom he has not played so far Since each player should play only ... Graphs Combinatorica 12 (19 92) , 125 -134 [AlWi] S Alongkorn, C Wichai: Behzad-Vizing Conjecture and Complete Graphs http://math.sci.tsu.ac.th/nmath/download/Alongkorn CompleteGraphs.pdf the electronic...
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Báo cáo toán học: "MacMahon’s theorem for a set of permutations with given descent indices and right-maximal record" ppt
... = 524 13 is I = (1, 2, 2) and = { 123 45, 21 345, 3 124 5, 4 123 5, 5 123 4, 124 35, 21 435, 31 425 , 41 325 , 51 324 , 125 34, 21 534, 31 524 , 41 523 , 51 423 , 13 425 , 23 415, 324 15, 423 15, 523 14, 13 524 , 23 514, 325 14, ... 23 514, 325 14, 425 13, 524 13, 14 523 , 24 513, 345 12, 435 12, 534 12} , DI = {21 435, 21 534, 31 425 , 31 524 , 324 15, 325 14, 41 325 , 41 523 , 423 15, 425 13, 435 12, 51 324 , 51 423 , 523 14, 524 13, 534 12} D I the electronic ... x1 x2 x3 x4 + x1 x2 x3 y1 + x1 x2 x4 y1 + x1 x3 x4 y1 + x1 x3 y1 2 + x1 x2 x3 y1 + x1 x2 x4 y1 + x1 x2 x3 y1 + x1 x2 y2 + x1 x4 y2 + 2x1 x2 y1 y2 + x1 x3 y1 y2 + x1 x4 y1 y2 2 2 + x1 x2 y1 y2 +...
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Oracle Database Backup and Recovery Advanced User’s Guide
... of Backups iv 2- 2 2- 3 2- 4 2- 5 2- 6 2- 7 2- 8 2- 8 2- 9 2- 10 2- 11 2- 12 2- 12 2-14 2- 15 2- 15 2- 16 2- 18 2- 18 2- 20 2- 20 2- 22 2 -24 2- 25 2- 25 2- 26 2- 26 2- 28 2- 30 2- 31 RMAN Backup Types ... Procedure as for Partial TSPITR of Partitioned Tablespaces 20 19- 10 19- 10 19- 12 19- 14 19- 14 19- 14 19- 15 19- 16 19- 17 19- 17 19- 17 19- 18 19- 18 19- 18 19- 18 19- 19 19- 19 19- 19 19- 19 19 -20 19 -20 19 -20 ... 2- 32 2-33 2- 38 2- 39 2- 40 2- 41 2- 43 2- 45 2- 46 2- 47 2- 48 2- 49 2- 49 2- 51 2- 52 2-54 2- 55 2- 55 2- 56 2- 57 2- 58 2- 59 2- 59 2- 60 2- 60 RMAN Recovery Concepts Restoring Files with RMAN Mechanics...
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THE MOUSE, THE BIRD, AND THE SAUSAGE - GRIMM’S FAIRY TALES
... and when the mother heard how she had come by her great riches, she thought she should like her ugly, lazy daughter to go and try her fortune So she made the sister go and sit by the well and ... to her, so that she was covered with it from head to foot ’That is a reward for your industry,’ said Mother Holle, and as she spoke she handed her the spindle which she had dropped into the well ... was homesick, although she was a thousand times better off with Mother Holle than with her mother and sister After waiting awhile, she went to Mother Holle and said, ‘I am so homesick, that I...
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THE FISHERMAN AND HIS WIFE -GRIMM’S FAIRY TALES
... Will have her own will, And hath sent me to beg a boon of thee!’ ’What would she have now?’ said the fish ‘Ah!’ said the fisherman, ‘she wants to be emperor.’ ‘Go home,’ said the fish; ‘she is ... a throne that was two miles high And she had three great crowns on her head, and around her stood all the pomp and power of the Church And on each side of her were two rows of burning lights, ... boon of thee!’ ’What does she want now?’ said the fish ‘Ah!’ said the fisherman, ‘my wife wants to be pope.’ ‘Go home,’ said the fish; ‘she is pope already.’ Then the fisherman went home, and...
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THE OLD MAN AND HIS GRANDSON - GRIMM’S FAIRY TALES
... the mayor, who for his carelessness condemned him to give the peasant a cow for the calf which had run away And now the little peasant and his wife had the cow for which they had so long wished, ... in, and the peasant shut the top down on him; then he took the shepherd’s flock for himself, and drove it away The parson went to the crowd, and declared that the mass had been said Then they came ... more pinched the raven’s head till he croaked loudly The miller asked: ‘What did he say?’ The peasant replied: ‘He says that the Devil is hiding outside there in the closet on the porch.’ The miller...
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Biodegradable Polyurethanes and Poly(ester amide)s
... HOCH2CH2CH2CH2OH 1,3-Propanediamine (1,3-PDA) H2 NCH2CH2CH2NH2 1,3-Butanediol 1 ,2- Propanediamine (1 ,2- PDA) 2, 2-Dimethyl-propanediol 1,4-Butanediamine PhCH2 NH2CHCO–OCH2 1,4-Cyclohexanedimethanol ... = HO[(CH2)mOOC(CH2)4COO]nH Table 6.3 HO[CH2COO]n–R–[OOCCH2]mOH Chain extender raw materials Diols Diamines Ethylene glycol HOCH2CH2OH Ethylene diamine (ED) H2 NCH2CH2NH2 1,4-Butanediol (BDO) HOCH2CH2CH2CH2OH ... 1,4-Cyclohexanedimethanol CH2Ph – CH2OH – HOCH2 H2 NCH2CH2CH2CH2NH2 CH 2O–OCCHNH2 1,4-Cyclohexanedimethanol-L-phenylalanine diester 136 Biodegradable Polyurethanes and Poly(ester amide)s Figure 6.1 Schematic representation...
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THE STRAW, THE COAL, AND THE BEAN- GRIMM’S FAIRY TALES
... in it asleep, with all her court He told, too, how he had heard from his grandfather that many, many princes had come, and had tried to break through the thicket, but that they had all stuck fast ... and as the prince came to the thicket he saw nothing but beautiful flowering shrubs, through which he went with ease, and they shut in after him as thick as ever Then he came at last to the palace, ... break through the thicket into the palace This, however, none of them could ever do; for the thorns and bushes laid hold of them, as it were with hands; and there they stuck fast, and died wretchedly...
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Tài liệu THE ELVES AND THE SHOEMAKER - GRIMM''''S FAIRY TALE pptx
... saved all the trouble, for when he got up in the morning the work was done ready to his hand Soon in came buyers, who paid him handsomely for his goods, so that he bought leather enough for four ... thought pleased the good cobbler very much; and one evening, when all the things were ready, they laid them on the table, instead of the work that they used to cut out, and then went and hid themselves, ... the shoes stood ready for use upon the table This was long before daybreak; and then they bustled away as quick as lightning The next day the wife said to the shoemaker ‘These little wights have...
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