borel serre compactification of locally symmetric spaces and cohomological properties of arithmetic groups
cohomology of arithmetic groups, l-functions and automorphic - t. venkatamarana
... points of split tori in GL2(K) and GL2(F) are the same (as the rank of the unit groups of the rings of integers of K and F are the same) 3.1 Asai L-funct ions We will prove the second part of Theorem ... = OF denote the ring of integers of F , and let IF = { L , w ) denote the two embeddings of F into R The embedding a will also be thought of as the non-trivial element of the Galois group of ... of level one and weight k; respectively, the space of elliptic cusp forms of level D, weight k, and nebentypus XD Finally, let denote the space of holomorphic Hilbert cusp forms of level 1, and...
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proceedings of the international conference on cohomology of arithmetic groups l-functions and automorphic forms mumbai 1998
... points of split tori in GL2(K) and GL2(F) are the same (as the rank of the unit groups of the rings of integers of K and F are the same) 3.1 Asai L-funct ions We will prove the second part of Theorem ... = OF denote the ring of integers of F , and let IF = { L , w ) denote the two embeddings of F into R The embedding a will also be thought of as the non-trivial element of the Galois group of ... of level one and weight k; respectively, the space of elliptic cusp forms of level D, weight k, and nebentypus XD Finally, let denote the space of holomorphic Hilbert cusp forms of level 1, and...
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Báo cáo khoa học: "Generalized Encoding of Description Spaces and its Application to Typed Feature Structures" potx
... unifying the representatives of and , one ( ) for unifying the representatives of and , and one ( ) for unifying the representatives of and Notice that the set of representatives for must be ... structure of the description TFSs actually possess most of the properties of fixed-arity terms when it comes to unification, due to appropriateness Nevertheless, unbounded subtyping chains and acquiring ... inherit their supertypes' features, and with consistent value restrictions The combination of these two properties allows us to annotate a BCPO of types with features and value restrictions only where...
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Báo cáo khoa học: "Efficient Unsupervised Discovery of Word Categories Using Symmetric Patterns and High Frequency Words" ppt
... Discovery of Patterns Our first step is the discovery of patterns that are useful for lexical category acquisition We use two main stages: discovery of pattern candidates, and identification of the symmetric ... the bidirectional arcs and nodes of G(P ): SymG(P ) = {{x}, {(x, y)}|A(x, y) ∧ A(y, x)} The second and third measures count the proportion of the number of symmetric nodes and edges in G(P ), respectively: ... fragments ‘book and newspaper’, ‘newspaper and book’, ‘book and note’, ‘note and book’ and ‘note and newspaper’ In this case the three words are assigned to a category Note that a pair of nodes connected...
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Báo cáo toán học: " Common fixed points and best approximations in locally convex spaces" ppt
... results of Shahzad [20] to locally convex spaces Theorem 3.3 Let T and f be selfmaps of a Hausdorff complete locally convex space X and M ⊂ X such that T(∂M) ⊂ M, where ∂M is the boundary of M in ... [1] and Pant [2], respectively A point x in M is said to be a common fixed point (coincidence point) of f and T if x = fx Î Tx (fx Î Tx) We denote by F(f) and F(T) the set of fixed points of f and ... Hausdorff locally convex topological vector space unless stated otherwise, P the family of continuous seminorms generating the topology of X and K(X) the family of nonempty compact subsets of X For...
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Báo cáo toán học: " Common fixed points and best approximations in locally convex spaces" potx
... results of Shahzad [20] to locally convex spaces Theorem 3.3 Let T and f be selfmaps of a Hausdorff complete locally convex space X and M ⊂ X such that T(∂M) ⊂ M, where ∂M is the boundary of M in ... [1] and Pant [2], respectively A point x in M is said to be a common fixed point (coincidence point) of f and T if x = fx Î Tx (fx Î Tx) We denote by F(f) and F(T) the set of fixed points of f and ... Hausdorff locally convex topological vector space unless stated otherwise, P the family of continuous seminorms generating the topology of X and K(X) the family of nonempty compact subsets of X For...
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Báo cáo hóa học: " Research Article Differences of Weighted Mixed Symmetric Means and Related Results" pdf
... 2.5 Let x and p be positive n-tuples, then for distinct real numbers l and r, different from zero and 1, there exists ξ ∈ a, b , such that ξl−r Proof Taking f x xl and g x from zero and 1, we ... required results by taking limit n i pi 1.19 1.20 xisj in 1.16 and xitj in 1.16 and Journal of Inequalities and Applications We define the quasiarithmetic means with respect to 1.17 as follows: ⎛ Mh,g ... k l 1 r 3.7 Proof Set f x xl/s and g x xr/s , then taking xi → xis in 2.13 , we get 3.7 by the virtue of 1.2 , 1.18 , 1.26 and 1.35 for non zero, distinct real numbers l, r and s Remark 3.4...
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Báo cáo hóa học: " Research Article General Convexity of Some Functionals in Seminormed Spaces and Seminormed Algebras" pdf
... 2 Journal of Inequalities and Applications of Banach spaces as found in 7, Similar statements related to functionals in finitedimensional spaces and countable dimensional spaces have been ... P Chandra and B C Tripathy, “On generalised Kothe-Toeplitz duals of some sequence spaces, ” Indian ¨ Journal of Pure and Applied Mathematics, vol 33, no 8, pp 1301–1306, 2002 B C Tripathy and ... House of the Slovak Academy of Sciences, Sofia, Bulgaria, 1983 T S Stoyanov, “Inequalities for convex combinations of functions,” in Proceedings of the 18th SpringConference of the Union of Bulgarian...
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Báo cáo hóa học: " Research Article Remarks on Cone Metric Spaces and Fixed Point Theorems of Contractive Mappings" pptx
... metric space Fixed Point Theory and Applications The basic properties of convergent and Cauchy sequences may be found at In fact the properties and their proofs are identical to the classical ... following properties: D x, y if and only if x D x, y D y, x , for any x, y ∈ X; D x, y ≤ K D x, z1 1, 2, , n y; D z1 , z2 ··· D zn , y , for any points x, y, zi ∈ X, i Proof The proofs of and are ... for example in References L.-G Huang and X Zhang, “Cone metric spaces and fixed point theorems of contractive mappings,” Journal of Mathematical Analysis and Applications, vol 332, no 2, pp 1468–1476,...
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Báo cáo hóa học: "Research Article Quasicone Metric Spaces and Generalizations of Caristi Kirk’s Theorem" ppt
... Scientific and Technical Research Council of Turkey References L.-G Huang and X Zhang, “Cone metric spaces and fixed point theorems of contractive mappings,” Journal of Mathematical Analysis and Applications, ... metric spaces, ” Hacettepe Journal of Mathematics and Statistics, vol 345, pp 719–724, 2008 Sh Rezapour, M Derafshpour, and R Hamlbarani, “A Review on Topological Properties of Cone Metric Spaces, ” ... 1468–1476, 2007 Sh Rezapour and R Hamlbarani, “Some notes on the paper: “cone metric spaces and fixed point theorems of contractive mappings”,” Journal of Mathematical Analysis and Applications, vol...
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Báo cáo hóa học: " Research Article The Methods of Hilbert Spaces and Structure of the Fixed-Point Set of Lipschitzian Mapping" docx
... has a fixed point in C and Fix T is a retract of C In this paper we shall continue this work Precisely, by means of techniques of asymptotic centers and the methods of Hilbert spaces, we establish ... 2.9 and the properties of δH that T k x0 − T x0 − k z0 z1 − δH √ 2 z0 z1 R − δH √ √ ε0 ε ε, 2.13 ε0 R R R ε ε Multiplying both sides of this inequality by suitable elements of the matrix M and ... Goebel and W A Kirk, “Classical theory of nonexpansive mappings,” in Handbook of Metric Fixed Point Theory, W A Kirk and B Sims, Eds., pp 49–91, Kluwer Academic Publishers, Dordrecht, The Netherlands,...
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Báo cáo hóa học: " Research Article An Order on Subsets of Cone Metric Spaces and Fixed Points of Set-Valued Contractions" docx
... subsequence {xnk } of {xn } is convergent to an element of A Denote N M a collection of all nonempty subsets of M, C M a collection of all nonempty closed subsets of M and K M a collection of all nonempty ... is same as the proof of Theorem 2.5 References L.-G Huang and X Zhang, “Cone metric spaces and fixed point theorems of contractive mappings,” Journal of Mathematical Analysis and Applications, ... of limit we conclude that x y∗ ∈ T x Definition 2.2 Let A and B are subsets of E, we write A B if and only if there exist x ∈ A such that for all y ∈ B, x ≤ y Also for x ∈ E, we write x B if and...
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Báo cáo hóa học: " Research Article Common Fixed Points of Generalized Contractive Hybrid Pairs in Symmetric Spaces" ppt
... where X, d is a symmetric space, x ∈ X and A ⊆ X, d x, A inf{d x, a : a ∈ A}, and B X is the class of all nonempty bounded subsets of X The diameter of A, B ∈ B X is denoted and defined by δ A, ... S, and T T and f Remarks 2.10 Weakly compatible maps are occasionally weakly compatible but converse is not true in general The class of symmetric spaces is more general than that of metric spaces ... mappings in symmetric spaces satisfying a contractive condition of integral type,” Journal of Mathematical Analysis and Applications, vol 322, no 2, pp 796–802, 2006 11 H Chandra and A Bhatt,...
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Báo cáo hóa học: " Research Article On Coincidence and Fixed-Point Theorems in Symmetric Spaces" ppt
... Point Theory and Applications We give another axiom for symmetric spaces and study their relationships in Section We give common fixed-point theorems of four mappings in symmetric spaces and give ... B, S, and T satisfy all conditions of 5, Theorem 2.4 and satisfy also all conditions of 5, Theorem 2.5 But the pairs A, S and B, T have no points of coincidence, and also the pairs A, S and B, ... additional conditions H.E and C.C Theorem 3.4 Let X, d be a symmetric( semimetric) space that satisfies (H.E) and (C.C) and let A, B, S, and T be self-mappings of X such that AX ⊂ T X and BX ⊂ SX, the...
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Báo cáo hóa học: " Research Article Schur-Convexity for a Class of Symmetric Functions and Its Applications" pptx
... follows from Cases 1–4 and the proof of Theorem 3.4 is completed Applications In this section, we establish some inequalities by use of Theorems 3.1, 3.2 and 3.4 and the theory of majorization Theorem ... 567–576, 2006 K.-Z Guan, “Some properties of a class of symmetric functions,” Journal of Mathematical Analysis and Applications, vol 336, no 1, pp 70–80, 2007 F K Hwang and U G Rothblum, “Partition-optimization ... The Netherlands, 1989 22 H Weyl, “Inequalities between the two kinds of eigenvalues of a linear transformation,” Proceedings of the National Academy of Sciences of the United States of America,...
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Báo cáo hóa học: " Research Article The Schur Harmonic Convexity of the Hamy Symmetric Function and Its Applications" pptx
... “Some properties of dual form of the Hamy’s symmetric function,” Journal of Mathematical Inequalities, vol 1, no 1, pp 117–125, 2007 H.-T Ku, M.-C Ku, and X.-M Zhang, “Inequalities for symmetric ... of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003 10 Journal of Inequalities and Applications A W Marshall and I Olkin, Inequalities: Theory of ... Uchiyama, and S.-E Takahasi, “A refinement of various mean inequalities,” Journal of Inequalities and Applications, vol 2, no 4, pp 387–395, 1998 K Guan, “The Hamy symmetric function and its generalization,”...
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Báo cáo hóa học: "Research Article Common Fixed Point and Approximation Results for Noncommuting Maps on Locally Convex Spaces" docx
... subset of a Hausdorff locally convex space E, τ and let T, f, and g be selfmaps of M Suppose that f and g are affine and nonexpansive with q ∈ F f ∩ F g , and T M ⊂ f M ∩ g M If the pairs {T, f} and ... class of Banach operator pairs Our results extend and unify the work of AlThagafi 14 , Chen and Li 23 , Hussain 24 , Hussain and Berinde 25 , Hussain and Jungck , Hussain and Khan , Hussain and ... results of Chen and Li 23 in the setup of a Hausdorff locally convex space Lemma 3.3 Let M be a nonempty τ-bounded subset of Hausdorff locally convex space E, τ , and let ⊆ F f ∩F g , T, f, and g...
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Báo cáo khoa học: "Recurrence patterns of locally advanced head and neck squamous cell carcinoma after 3D conformal (chemo)-radiotherapy" pdf
... of radiotherapy, and of these patients experienced in-field recurrences of the total of 20 cases of LRR occurred in the group of patients who had had a less than CR to nonsurgical treatment and ... fractionated schedules at week intervals, and at a dose of 80 mg/m on day and 28 of the four week hypofractionated radiotherapy schedule Analysis of response to treatment and follow-up Tumour response was ... in 41% of patients, and post-operatively in 59% of patients [17] After a median follow up of 26 months, 17 LRR were noted, of which were in-field, were marginal failures and were outside of the...
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