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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 260 (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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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.
Irreducibility of induced modules for general linear supergroups, arXiv:1309.0284 [math.RT
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The energy of the Mycielskian of a regular graph
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 52 (2012), PAGES 163–171
, 2012
"... Let G be a finite connected simple graph and μ(G) be the Mycielskian of G. We show that for connected graphs G and H, μ(G) is isomorphic to μ(H) if and only if G is isomorphic to H. Furthermore, we determine the energy of the Mycielskian of a connected regular graph G in terms of the energy E(G) of ..."
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Let G be a finite connected simple graph and μ(G) be the Mycielskian of G. We show that for connected graphs G and H, μ(G) is isomorphic to μ(H) if and only if G is isomorphic to H. Furthermore, we determine the energy of the Mycielskian of a connected regular graph G in terms of the energy E(G) of G, where the energy of G is the sum of the absolute values of the eigenvalues of G. The energy of a graph has its origin in chemistry in that the energy of a conjugated hydrocarbon molecule computed using the Hückel theory in quantum chemistry coincides with the graph energy of the corresponding molecular graph. We show that if G is a regular graph of order n with E(G)> 3n, then μ(G) is hyperenergetic.
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"... Investigation of mechanical stability of possible structures of PtN using firstprinciples computations ..."
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Investigation of mechanical stability of possible structures of PtN using firstprinciples computations
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