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Let Rbeacommutativeringwithidentity, Napositiveintegerand A=(aij)
"... overacommutativeringwithidentity ..."
Rigidity of quasiisometries for symmetric spaces and Euclidean buildings
 Inst. Hautes Études Sci. Publ. Math
, 1997
"... 1.1 Background and statement of results An (L, C) quasiisometry is a map Φ: X − → X ′ between metric spaces such that for all x1, x2 ∈ X ..."
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Cited by 193 (28 self)
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1.1 Background and statement of results An (L, C) quasiisometry is a map Φ: X − → X ′ between metric spaces such that for all x1, x2 ∈ X
Numerical Recipes in C: The Art of Scientific Computing. Second Edition
, 1992
"... This reprinting is corrected to software version 2.10 ..."
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Cited by 177 (0 self)
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This reprinting is corrected to software version 2.10
Edmonds polytopes and a hierarchy of combinatorial problems
, 2006
"... Let S be a set of linear inequalities that determine a bounded polyhedron P. The closure of S is the smallest set of inequalities that contains S and is closed under two operations: (i) taking linear combinations of inequalities, (ii) replacing an inequality Σaj xj ≤ a0, where a1,a2,...,an are integ ..."
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Cited by 170 (0 self)
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Let S be a set of linear inequalities that determine a bounded polyhedron P. The closure of S is the smallest set of inequalities that contains S and is closed under two operations: (i) taking linear combinations of inequalities, (ii) replacing an inequality Σaj xj ≤ a0, where a1,a2,...,an are integers, by the inequality Σaj xj ≤ a with a ≥[a0]. Obviously, if integers x1,x2,...,xn satisfy all the inequalities in S, then they satisfy also all inequalities in the closure of S. Conversely, let Σcj xj ≤ c0 hold for all choices of integers x1,x2,...,xn, that satisfy all the inequalities in S. Then we prove that Σcj xj ≤ c0 belongs to the closure of S. To each integer linear programming problem, we assign a nonnegative integer, called its rank. (The rank is the minimum number of iterations of the operation (ii) that are required in order to eliminate the integrality constraint.) We prove that there is no upper bound on the rank of problems arising from the search for largest independent sets in graphs.
Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems
, 1999
"... ..."
Babero’s Hamiltonian derived from a generalized HilbertPalatini action
 Phys.Rev. D
, 1996
"... Barbero recently suggested a modification of Ashtekar’s choice of canonical variables for general relativity. Although leading to a more complicated Hamiltonian constraint this modified version, in which the configuration variable still is a connection, has the advantage of being real. In this artic ..."
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Cited by 104 (0 self)
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Barbero recently suggested a modification of Ashtekar’s choice of canonical variables for general relativity. Although leading to a more complicated Hamiltonian constraint this modified version, in which the configuration variable still is a connection, has the advantage of being real. In this article we derive Barbero’s Hamiltonian formulation from an action, which can be considered as a generalization of the ordinary HilbertPalatini action. In 1986 Ashtekar presented a new pair of canonical variables for the phase spase of general relativity [1]. These variables led to a much simpler Hamiltonian constraint than that in the ADM formulation [2], but had the drawback of introducing complex variables in the phase space action—something that leads to difficulties with reality conditions which then must be imposed. A couple of years later the Lagrangian density corresponding to Ashtekar’s Hamiltonian was given independently by Samuel, and by Jacobson and Smolin [3]. That was seen simply to be the HilbertPalatini (HP) Lagrangian with the curvature tensor replaced by its selfdual part only. Recently Barbero pointed out that it is possible to choose a pair of canonical variables that is closely related to Ashtekars but this time real [4]. The price paid is that the simplicity of Ashtekars Hamiltonian constraint is destroyed. However, some advantages are still present with Barbero’s choice of variables. For example, they provide a real theory of gravity with a connection as configuration variable, and with the usual Gauss and vector constraint, thus fitting into the class of diffeomorphism invariant theories considered in [5] in the context of quantization. In this paper we derive Barbero’s result from an action, and since his formulation includes also that of ADM and Ashtekar via a parameter, the Lagrangian density used as starting point in this paper, also includes these cases. Hence we have found, in a sense, a generalized HP action. We now write down this action, and thereafter we will motivate that it is a good canditate for an action leading to Barbero’s formulation, which then will be explicitly derived from it:
Mode
"... Seen by AALTONEN 09AH in the B + → X K +, X → J/ψφ. Not seen by SHEN 10 in γγ → J/ψφ or AAIJ 12AA in B + → J/ψφK +. ..."
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Seen by AALTONEN 09AH in the B + → X K +, X → J/ψφ. Not seen by SHEN 10 in γγ → J/ψφ or AAIJ 12AA in B + → J/ψφK +.
Tree Insertion Grammar: A CubicTime, Parsable Formalism that Lexicalizes ContextFree Grammar without Changing the Trees Produced
 Computational Linguistics
, 1994
"... this paper, we study the problem of lexicalizing contextfree grammars and show that it enables faster processing. In previous attempts to take advantage of lexicalization, a variety of lexicalization procedures have been developed that convert contextfree grammars (CFGs) into equivalent lexicalize ..."
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Cited by 83 (2 self)
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this paper, we study the problem of lexicalizing contextfree grammars and show that it enables faster processing. In previous attempts to take advantage of lexicalization, a variety of lexicalization procedures have been developed that convert contextfree grammars (CFGs) into equivalent lexicalized grammars. However, these procedures typically suffer from one or more of the following problems
1 Chronic Fatigue Syndrome (CFS) Gene Coexpression Network Analysis R Tutorial
"... This R tutorial describes how to carry out a gene coexpression network analysis using soft thresholding. The network construction is conceptually straightforward: nodes represent genes and nodes are connected if the corresponding genes are significantly coexpressed across appropriately chosen tiss ..."
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This R tutorial describes how to carry out a gene coexpression network analysis using soft thresholding. The network construction is conceptually straightforward: nodes represent genes and nodes are connected if the corresponding genes are significantly coexpressed across appropriately chosen
Higherlevel synchronising devices in Meije–SCCS. Theoretical Computer Science 37(3), pp. 245–267. A Modal Characterisation of ηBisimulation We prove the first part of Thm. 2.5, which states that η is a modal characterisation of ηbisimulation equivalenc
, 1985
"... Abstract. In an algebraic setting for parallelism and synchronisation due to R. Milner, we define a wide variety of synchronising operators on processes. We introduce them by the semantical conditional rules they obey. We prove they are higherlevel nonprimitive operators from the original SCCS calc ..."
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Cited by 71 (0 self)
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Abstract. In an algebraic setting for parallelism and synchronisation due to R. Milner, we define a wide variety of synchronising operators on processes. We introduce them by the semantical conditional rules they obey. We prove they are higherlevel nonprimitive operators from the original SCCS
Results 1  10
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