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Showing 1 to 20 of 121 for “"Lipschitz"”.
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Dissipative Lipschitz dynamics
… system when the dynamic satisfies a dissipative Lipschitz condition. We show that when the dynamic is almost upper semicontinuous and satisfies the dissipative Lipschitz property, these conditions can be expressed in terms of approximate Hamilton-Jacobi inequalities, which subsumes the classic …
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A characterization of Bi-Lipschitz embeddable metric spaces in terms of local Bi-Lipschitz embeddability
… complete, doubling metric spaces which embed bi-Lipschitzly into Euclidean space. Our result applies in particular to spaces of Grushin type equipped with Carnot-Carath ́eodory distance. Hence we obtain the first example of a sub-Riemannian manifold admitting such a bi-Lipschitz embedding. Our …
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Macroscopic behaviour of Lipschitz random surfaces
… Gaussian free field, and uniformly random Lipschitz functions. We analyse the specific free energy functional for a class of random fields and for a class of random surfaces. In either case, we are interested in the nature of the minimisers of the specific free energy, and we give a new …
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Lipschitz Geometry of Banach and Metric Spaces
<p>We will investigate Lipschitz and Hölder continuous maps between a Banach space X and its dual space X^*, the space of continuous linear functionals. The existence of these maps is related to the smoothness of the norm of the space and isomorphic invariants called type and cotype will play a …
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Lipschitz and Holder mappings into jet space Carnot groups
… $J^k(\R^n)$, we will prove that there exists a biLipschitz embedding of $\mathbb{S}^n$ into $J^k(\R^n)$ that does not admit a Lipschitz extension to $\mathbb{B}^{n+1}$. This strengthens a result of Rigot and Wenger \cite{RW:LNE} and generalizes a result for $\mathbb{H}^n$ of Dejarnette, …
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Adaptive algorithms for problems involving black-box Lipschitz functions
… the function value at a given point) for a Lipschitz function with a known Lipschitz constant. We consider queries that can be answered about the function by using a finite number of black-box evaluations. Specifically, we study the problems of approximating a Lipschitz function, …
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Lipschitz homotopies of mappings from 3-sphere to 2-sphere
… given homotopic mappings from S^m to S^n of Lipschitz constant L, build the (asymptotically) simplest homotopy between them (meaning having the least Lipschitz constant). The present paper resolves this problem for the first case where Hopf invariant plays a role: m = 3, n = 2, constructing a …
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Intrinsic Lipschitz graphs in Heisenberg groups and non linear sub-elliptic PDEs
In this thesis we study intrinsic Lipschitz functions. In particular we provide a regular approximation result and a Poincarè type inequality for this class of functions. Moreover we study the obstacle problem in the Heisenberg group and we prove a geometric Poincarè inequality for a class of …
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Closed Ideals in Banach Algebras of Analytic Functions Satisfying a Lipschitz Condition
Made available in DSpace on 2014-12-14T13:09:32Z (GMT). No. of bitstreams: 1 7709091.pdf: 980223 bytes, checksum: afab88bb017c48a014899c7f54aaba9a (MD5) Previous issue date: 1976
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Nonconvex optimization algorithm with a new Bi-criteria selection of potential simplices using an estimate of Lipschitz constant /
… (DIviding RECTangles) type algorithms based on Lipschitz objective function models with unknown Lipschitz constant, which are often applied for practical black-box optimization problems, are considered. The main goal of this thesis is set - to propose a global optimization algorithm for …
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Neiškiliojo optimizavimo algoritmas su nauju bikriteriniu potencialiųjų simpleksų išrinkimu naudojant Lipšico konstantos įvertį /
… (DIviding RECTangles) type algorithms based on Lipschitz objective function models with unknown Lipschitz constant, which are often applied for practical black-box optimization problems, are considered. The main goal of this thesis is set - to propose a global optimization algorithm for …
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Duality, Weight Decay, and Metrized Deep Learning
… during training, conferring provable and upfront Lipschitz guarantees for transformers. We find that optimizer dynamics matter: switching from AdamW to Muon improves standard weight regularization methods—weight decay and spectral normalization—allowing models to reach equal performance with a …
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Regularity of solutions and the free boundary for a class of Bernoulli-type parabolic free boundary problems with variable coefficients
… we proceed in Chapter 2 to prove the optimal Lipschitz regularity of viscosity solutions under the main assumption that the free boundary is Lipschitz. In Chapter 3, we prove that Lipschitz free boundaries possess a classical normal in both space and time at each point and that this normal …
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Shared Control Based on Predictability Analysis With Application to Human-SuperLimb Collaboration
… In the second phase of the study, Extended Lipschitz Analysis (ELA) is developed as another method of measuring predictability. ELA evaluates the demonstration data by computing Lipschitz quotients and informs the level of predictability of the desired action independent of the prediction …
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Good Stein Neighborhood Bases for Nonsmooth Pseudoconvex Domains
… in C^∞(Ω̄), even if the boundary of Ω is only Lipschitz. In my thesis, I will show sufficient conditions for the existence of a good Stein neighborhood base on a Lipschitz domain satisfying Property (P).</p>
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Metric Geometry of Finite Subset Spaces
… such as "If a normed space X is an absolute Lipschitz retract, does it follow that X(n) is also an absolute Lipschitz retract?" appears to require considerable effort and will be answered only partially. By the definition of an absolute Lipschitz retract, establishing the existence of …
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Stability of one-dimensional waves in layered media
… of the vertical wave velocity is not locally Lipschitz continuous. This thesis describes a proof that the forward map as a function of the travel tine velocity is Lipschitz continuous, and even differentiable.
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Conformally Flat Spaces of Bounded Curvature
… is bounded below by zero. If the space has Lipschitz conformal factor and curvature bounded below by zero then the two dimensional subspaces have curvature bounded below by K, depending only on the Lipschitz constant and the size of the function.
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