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A general coefficient of similarity and some of its properties
 Biometrics
, 1971
"... Biometrics is currently published by International Biometric Society. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 107 (0 self)
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Biometrics is currently published by International Biometric Society. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Verifying nonlinear real formulas via sums of squares
 Theorem Proving in Higher Order Logics, TPHOLs 2007, volume 4732 of Lect. Notes in Comp. Sci
, 2007
"... Abstract. Techniques based on sums of squares appear promising as a general approach to the universal theory of reals with addition and multiplication, i.e. verifying Boolean combinations of equations and inequalities. A particularly attractive feature is that suitable ‘sum of squares ’ certificates ..."
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Cited by 19 (2 self)
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Abstract. Techniques based on sums of squares appear promising as a general approach to the universal theory of reals with addition and multiplication, i.e. verifying Boolean combinations of equations and inequalities. A particularly attractive feature is that suitable ‘sum of squares ’ certificates can be found by sophisticated numerical methods such as semidefinite programming, yet the actual verification of the resulting proof is straightforward even in a highly foundational theorem prover. We will describe our experience with an implementation in HOL Light, noting some successes as well as difficulties. We also describe a new approach to the univariate case that can handle some otherwise difficult examples. 1 Verifying nonlinear formulas over the reals Over the real numbers, there are algorithms that can in principle perform quantifier elimination from arbitrary firstorder formulas built up using addition, multiplication and the usual equality and inequality predicates. A classic example of such a quantifier elimination equivalence is the criterion for a quadratic equation to have a real root: ∀a b c. (∃x. ax 2 + bx + c = 0) ⇔ a = 0 ∧ (b = 0 ⇒ c = 0) ∨ a � = 0 ∧ b 2 ≥ 4ac
Closed Form Solutions of Linear Odes having Elliptic Function Coefficients
 ISSAC’04 Proceedings
, 2004
"... We consider the problem of finding closed form solutions of linear differential equations having coefficients which are elliptic functions. For second order equations we show how to solve such an ode in terms of doubly periodic functions of the second kind. The method depends on two procedures, the ..."
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We consider the problem of finding closed form solutions of linear differential equations having coefficients which are elliptic functions. For second order equations we show how to solve such an ode in terms of doubly periodic functions of the second kind. The method depends on two procedures, the first using a second symmetric power of an ode along with a decision procedure for determining when such equations have elliptic function solutions while the second involves the computation of exponential solutions.
unknown title
, 1990
"... Consider the nonhomogeneous recurrence relation k (1.1) Gn = Gn.x + Gn_2 + £ u.nJ ..."
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Consider the nonhomogeneous recurrence relation k (1.1) Gn = Gn.x + Gn_2 + £ u.nJ
AUSTRALASIAN JOURNAL OF COMBINATORICS Volume 46 (2010), Pages 191–202 The plurality strategy on graphs
"... Goldman [Transportation Science 5 (1971), 212–221] proved the classical result on how to find the medians for a set of clients in a tree using majority rule. Here the clients are located at vertices of the tree, and a median is a vertex in the tree that minimizes the sum of the distances to the loca ..."
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Goldman [Transportation Science 5 (1971), 212–221] proved the classical result on how to find the medians for a set of clients in a tree using majority rule. Here the clients are located at vertices of the tree, and a median is a vertex in the tree that minimizes the sum of the distances to the locations of the clients. The majority rule can be rephrased as the Majority Strategy: if we are at vertex v, thenwemovetoneighborw of v if a majority of the clients is closer to w than to v. This strategy can be applied in any connected graph. In Mulder [Discrete Applied Math. 80 (1997), 97–105] the question was answered for which connected graphs the Majority Strategy always produces the set of medians for any given set of clients: these are precisely the median graphs. This class of graphs has been wellstudied in the literature. In this paper we relax the Majority Strategy: instead of requiring a majority of the clients to be This work was done under the DST, Govt. of India grant M/04–1999 awarded to this author. The financial support of the DST, New Delhi is gratefully acknowledged. 192 K. BALAKRISHNAN, M. CHANGAT AND H.M. MULDER closer to w than to v, wemovetow if there are more vertices closer to w than to v (thus ignoring the clients at equal distance from v and w). The main result of the paper is that the Plurality Strategy always produces the median set for any given set of clients if and only if all median sets are connected. We prove a similar result for the Hill Climbing strategy and for the Steepest Ascent Hill Climbing strategy. 1