Results 81 to 90 of about 3,785 (249)
Generalizing Generic Differentiability Properties from Convex to Locally Lipschitz Functions
, 1994 David Preiss proved that every locally Lipschitz function on an open subset of a Banach space which has an equivalent norm Gâteaux (Fréchet) differentiable away from the origin is Gâteaux (Fréchet) differentiable on a dense subset of its domain.
Sciffer, S., Giles, J.R.
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CAAI Transactions on Intelligence Technology, EarlyView.ABSTRACT This paper proposes a boundary control method for nonlinear distributed parameter systems (DPSs) with limited boundary measurements (BMs), as typically encountered in networked cyber‐physical processes with spatially distributed dynamics such as thermal and biomedical diffusion systems.
Yanlin Li +5 more
wiley +1 more source
Locally Lipschitz perturbations of bisemigroups
Communications on Pure and Applied Analysis, 2010 In this work we study the ill posed semilinear system $\dot{x}= Lx + f(\xi,t), \dot{y}= Ry + g(\xi,t)$, $\xi=(x,y)$, in Banach spaces where $L$ and $R$ are the infinitesimal generators of two $C_o$ semigroups $\{\mathcal{L}(t), t\geq 0\}$ and $\{\mathcal{R}(-t), t\geq 0\}$ respectively. The nonlinearity $h=(f,g)$
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Asymptotic Behaviour of the Three-Dimensional Á-Navier-Stokes Model with Locally Lipschitz Delay Forcing Terms [PDF]
, 2009 We obtain some results on the existence and uniqueness, and exponential stability of solutions for the three-dimensional ®¡Navier-Stokes model with delays, when the forcing term containing the delay is sub-linear and locally Lipschitz ...
Márquez Durán, Antonio Miguel +2 more
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SDFs from Unoriented Point Clouds using Neural Variational Heat Distances
Computer Graphics Forum, EarlyView.We propose a novel variational approach for computing neural Signed Distance Fields (SDF) from unoriented point clouds. We first compute a small time step of heat flow (middle) and then use its gradient directions to solve for a neural SDF (right). Abstract We propose a novel variational approach for computing neural Signed Distance Fields (SDF) from ...
Samuel Weidemaier +5 more
wiley +1 more source
Conformal Transformation of Uniform Domains Under Weights That Depend on Distance to The Boundary
Analysis and Geometry in Metric Spaces, 2022 The sphericalization procedure converts a Euclidean space into a compact sphere. In this note we propose a variant of this procedure for locally compact, rectifiably path-connected, non-complete, unbounded metric spaces by using conformal deformations ...
Gibara Ryan, Shanmugalingam Nageswari
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Characterization of Strict Convexity for Locally Lipschitz Functions
Rocky Mountain Journal of Mathematics, 2009 It is well known that a smooth function \(f: X\to\mathbb{R}\) is convex iff \(f''(x;h, h)\geq 0\) for all \(x\in X\) and all \(h\in X\). The function \(f\) is strictly convex iff \(f''(x;h,h)> 0\) for ``almost'' all \(x\in X\) and all \(h\in X\). Here \[ f''(x;u,v)= \lim_{t\to 0} \frac{\langle\nabla f(x+ tu)-\nabla f(x),v\rangle}{t}, \] where \(\nabla ...
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A Characterization of bi-Lipschitz embeddable metric spaces in terms of local bi-Lipschitz embeddability [PDF]
Mathematical Research Letters, 2011 We characterize uniformly perfect, complete, doubling metric spaces which embed bi- Lipschitzly into Euclidean space. Our result applies in particular to spaces of Grushin type equipped with Carnot-Carathéodory distance. Hence we obtain the first example of a sub-Riemannian mani- fold admitting such a bi-Lipschitz embedding.
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On Metric Choice in Dimension Reduction for Fréchet Regression
International Statistical Review, EarlyView.Summary Fréchet regression is becoming a mainstay in modern data analysis for analysing non‐traditional data types belonging to general metric spaces. This novel regression method is especially useful in the analysis of complex health data such as continuous monitoring and imaging data.
Abdul‐Nasah Soale +3 more
wiley +1 more source
Multiple Solutions for a Class of Differential Inclusion System Involving the (p(x),q(x))-Laplacian
Abstract and Applied Analysis, 2012 We consider a differential inclusion system involving the (p(x),q(x))-Laplacian with Dirichlet boundary condition on a bounded domain and obtain two nontrivial solutions under appropriate hypotheses.
Bin Ge, Ji-Hong Shen
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