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HigherOrder Energy Expansions And Spike Locations
"... We consider the following singularly perturbed semilinear elliptic problem: (I) \Deltau \Gamma u + f(u) = 0 u ? 0 in\Omega @ = 0 on a small constant and f is some superlinear but subcritical nonlinearity. Associated with (I) is the energy functional J ffl defined by 1 f ..."
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higherorder expansion of J ffl [u ffl ] : I [w] \Gamma c 1 fflH(P ffl ) + ffl where c 2 ; c 3 are generic constants and R(P ffl ) is the Ricci scalar curvature at P ffl . In particular c 3 ? 0. Some applications of this expansion are given.
A higherorder energy expansion to twodimensional . . .
"... Of concern is the following singularly perturbed semilinear elliptic problem { 2∆u − u + up = 0 in Ω u> 0 in Ω and ∂u ∂ν = 0 on ∂Ω, where Ω is a bounded domain in RN with smooth boundary ∂Ω, > 0 is a small constant and 1 < p < ..."
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Cited by 1 (1 self)
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Of concern is the following singularly perturbed semilinear elliptic problem { 2∆u − u + up = 0 in Ω u> 0 in Ω and ∂u ∂ν = 0 on ∂Ω, where Ω is a bounded domain in RN with smooth boundary ∂Ω, > 0 is a small constant and 1 < p <
Statefinders, higherorder energy conditions, and sudden future singularities.
, 2008
"... We link observational parameters such as the deceleration parameter, the jerk, the kerk (snap) and higherorder derivatives of the scale factor, called statefinders, to the conditions which allow to develop sudden future singularities of pressure with finite energy density. In this context, and with ..."
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We link observational parameters such as the deceleration parameter, the jerk, the kerk (snap) and higherorder derivatives of the scale factor, called statefinders, to the conditions which allow to develop sudden future singularities of pressure with finite energy density. In this context
Minimizing Sparse Higher Order Energy Functions of Discrete Variables
"... Higher order energy functions have the ability to encode high level structural dependencies between pixels, which have been shown to be extremely powerful for image labeling problems. Their use, however, is severely hampered in practice by the intractable complexity of representing and minimizing su ..."
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Cited by 74 (13 self)
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Higher order energy functions have the ability to encode high level structural dependencies between pixels, which have been shown to be extremely powerful for image labeling problems. Their use, however, is severely hampered in practice by the intractable complexity of representing and minimizing
HIGHER ORDER ENERGY DECAY RATES FOR DAMPED WAVE EQUATIONS WITH VARIABLE COEFFICIENTS
, 811
"... Abstract. Under appropriate assumptions the energy of wave equations with damping and variable coefficients c(x)utt − div(b(x)∇u) + a(x)ut = h(x) has been shown to decay. Determining the rate of decay for the higher order energies involving the kth order spatial and time derivatives has been an open ..."
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Abstract. Under appropriate assumptions the energy of wave equations with damping and variable coefficients c(x)utt − div(b(x)∇u) + a(x)ut = h(x) has been shown to decay. Determining the rate of decay for the higher order energies involving the kth order spatial and time derivatives has been
Higher order energy decay rates for damped wave equations with variable coefficients,
 Discrete Contin. Dyn. Syst. Ser. S
, 2009
"... Abstract. Under appropriate assumptions the energy of wave equations with damping and variable coefficients c(x)utt − div(b(x)∇u) + a(x)ut = h(x, t) has been shown to decay. Determining the decay rate for the higher order energies of the kth order spatial and time derivatives has been an open probl ..."
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Cited by 4 (2 self)
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Abstract. Under appropriate assumptions the energy of wave equations with damping and variable coefficients c(x)utt − div(b(x)∇u) + a(x)ut = h(x, t) has been shown to decay. Determining the decay rate for the higher order energies of the kth order spatial and time derivatives has been an open
Minimizing dynamic and higher order energy functions using graph cuts
, 2007
"... Over the last few years energy minimization has emerged as an indispensable tool in computer vision. The primary reason for this rising popularity has been the successes of efficient graph cut based minimization algorithms in solving many low level vision problems such as image segmentation, object ..."
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Cited by 5 (1 self)
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Over the last few years energy minimization has emerged as an indispensable tool in computer vision. The primary reason for this rising popularity has been the successes of efficient graph cut based minimization algorithms in solving many low level vision problems such as image segmentation, object
Structured learning of sumofsubmodular higher order energy functions
, 1309
"... Submodular functions can be exactly minimized in polynomial time, and the special case that graph cuts solve with max flow [18] has had significant impact in computer vision [5, 20, 27]. In this paper we address the important class of sumofsubmodular (SoS) functions [2, 17], which can be efficient ..."
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Cited by 3 (1 self)
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be efficiently minimized via a variant of max flow called submodular flow [6]. SoS functions can naturally express higher order priors involving, e.g., local image patches; however, it is difficult to fully exploit their expressive power because they have so many parameters. Rather than trying to formulate
Generalized Higher Order Energy Based Instantaneous Amplitude and Frequency Estimation and Their Applications to Power Disturbance Detection
"... The instantaneous amplitude (IA) based on the higher order differential energy operator is proposed. And its general form for arbitrary order is also proposed. The various definitions of the IA and the instantaneous frequency (IF) estimators are considered. The IA and IF estimators based on the ener ..."
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The instantaneous amplitude (IA) based on the higher order differential energy operator is proposed. And its general form for arbitrary order is also proposed. The various definitions of the IA and the instantaneous frequency (IF) estimators are considered. The IA and IF estimators based
Results 1  10
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5,017