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Asymptotically flat selfdual solutions to Euclidean gravity
 LETT. B74
, 1978
"... In an attempt to find gravitational analogs of Yang Mills pseudoparticles, we obtain two classes of selfdual solutions to the eucfidean Einstein equations. These metrics are free from singularities and approach a flat metric at infinity. ..."
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Cited by 129 (0 self)
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In an attempt to find gravitational analogs of Yang Mills pseudoparticles, we obtain two classes of selfdual solutions to the eucfidean Einstein equations. These metrics are free from singularities and approach a flat metric at infinity.
The General Selfdual solution of the Einstein Equations
, 1994
"... We obtain the most general explicit (anti)selfdual solution of the Einstein equations. We find that any (anti)selfdual solution can be characterised by three free functions of which one is harmonic. Any stationary (anti)selfdual solution can be characterised by a harmonic function. It turns out t ..."
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We obtain the most general explicit (anti)selfdual solution of the Einstein equations. We find that any (anti)selfdual solution can be characterised by three free functions of which one is harmonic. Any stationary (anti)selfdual solution can be characterised by a harmonic function. It turns out
The selfduality equations on a Riemann surface
 Proc. Lond. Math. Soc., III. Ser
, 1987
"... In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled 'instanton ..."
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Cited by 502 (6 self)
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In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled &apos
Hierarchies from Fluxes in String Compactifications
, 2002
"... Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory a ..."
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Cited by 713 (33 self)
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and Ftheory compactifications on CalabiYau fourfolds. In each case, the hierarchy of scales is fixed by a choice of RR and NS fluxes in the compact manifold. Our solutions involve compactifications of the KlebanovStrassler gravity dual to a confining N = 1 supersymmetric gauge theory
New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 585 (0 self)
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary
Benchmarking Least Squares Support Vector Machine Classifiers
 NEURAL PROCESSING LETTERS
, 2001
"... In Support Vector Machines (SVMs), the solution of the classification problem is characterized by a (convex) quadratic programming (QP) problem. In a modified version of SVMs, called Least Squares SVM classifiers (LSSVMs), a least squares cost function is proposed so as to obtain a linear set of eq ..."
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Cited by 456 (46 self)
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In Support Vector Machines (SVMs), the solution of the classification problem is characterized by a (convex) quadratic programming (QP) problem. In a modified version of SVMs, called Least Squares SVM classifiers (LSSVMs), a least squares cost function is proposed so as to obtain a linear set
Probing the Pareto frontier for basis pursuit solutions
, 2008
"... The basis pursuit problem seeks a minimum onenorm solution of an underdetermined leastsquares problem. Basis pursuit denoise (BPDN) fits the leastsquares problem only approximately, and a single parameter determines a curve that traces the optimal tradeoff between the leastsquares fit and the ..."
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Cited by 352 (4 self)
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. The primaldual solution of this problem gives function and derivative information needed for the rootfinding method. Numerical experiments on a comprehensive set of test problems demonstrate that the method scales well to large problems.
PRIMALDUAL SOLUTION PERTURBATIONS IN CONVEX OPTIMIZATION
 SETVALUED ANALYSIS
, 2001
"... Solutions to optimization problems of convex type are typically characterized by saddle point conditions in which the primal vector is paired with a dual ‘multiplier’ vector. This paper investigates the behavior of such a primaldual pair with respect to perturbations in parameters on which the prob ..."
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Cited by 5 (2 self)
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Solutions to optimization problems of convex type are typically characterized by saddle point conditions in which the primal vector is paired with a dual ‘multiplier’ vector. This paper investigates the behavior of such a primaldual pair with respect to perturbations in parameters on which
RESEARCH ARTICLE Dual Solutions for Nonlinear Flow Using Lie Group Analysis
"... `The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD) flow of an upperconvected Maxwell (UCM) fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and compute ..."
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`The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD) flow of an upperconvected Maxwell (UCM) fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system
DUAL SOLUTIONS FOR AXISYMMETRIC STAGNATION POINT FLOW OVER
"... ABSTRACT. In this note we consider axisymmetric stagnation point flow of one fluid impinging on a disk covered with a second fluid. A similarity reduction is employed to reduce the governing PDEs to a nonlinear ODE boundary value problem. Previous numerical investigations of the problem in the liter ..."
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in the literature indicate the existence of one solution. Here we prove the existence of at least two solutions to the BVP. We also obtain results concerning the possibility of further solutions and present numerical approximations to the solutions. AMS (MOS) Subject Classification. 35B15, 76D03, 76D10 1.
Results 1  10
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