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Littérature scientifique sur le sujet « Higher differentiability »

Auteur : Grafiati
Publié le 9 mars 2023

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Articles de revues sur le sujet "Higher differentiability"

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Menne, Ulrich. « Pointwise differentiability of higher-order for distributions ». Analysis & ; PDE 14, no 2 (20 mars 2021) : 323–54. http://dx.doi.org/10.2140/apde.2021.14.323.

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Esposito, L., F. Leonetti et G. Mingione. « Higher differentiability for minimizers of irregular integrals ». Nonlinear Analysis : Theory, Methods & ; Applications 47, no 7 (août 2001) : 4355–64. http://dx.doi.org/10.1016/s0362-546x(01)00550-8.

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Cellina, Arrigo, et Marco Mazzola. « Higher differentiability of solutions to variational problems ». Calculus of Variations and Partial Differential Equations 45, no 1-2 (14 août 2011) : 11–26. http://dx.doi.org/10.1007/s00526-011-0448-1.

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Menne, Ulrich. « Pointwise differentiability of higher order for sets ». Annals of Global Analysis and Geometry 55, no 3 (14 janvier 2019) : 591–621. http://dx.doi.org/10.1007/s10455-018-9642-0.

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Cameron, Peter, et Piotr T. Chruściel. « Asymptotic flatness in higher dimensions ». Journal of Mathematical Physics 63, no 3 (1 mars 2022) : 032501. http://dx.doi.org/10.1063/5.0083728.

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We show that ( n + 1)-dimensional Myers–Perry metrics, n ≥ 4, have a conformal completion at space-like infinity of C n−3,1 differentiability class and that the result is optimal in even spacetime dimensions. The associated asymptotic symmetries are presented.
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Le Merdy, Christian, et Anna Skripka. « HIGHER ORDER DIFFERENTIABILITY OF OPERATOR FUNCTIONS IN SCHATTEN NORMS ». Journal of the Institute of Mathematics of Jussieu 19, no 6 (13 février 2019) : 1993–2016. http://dx.doi.org/10.1017/s1474748019000033.

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We establish the following results on higher order ${\mathcal{S}}^{p}$-differentiability, $1<p<\infty$, of the operator function arising from a continuous scalar function $f$ and self-adjoint operators defined on a fixed separable Hilbert space:(i)$f$ is $n$ times continuously Fréchet ${\mathcal{S}}^{p}$-differentiable at every bounded self-adjoint operator if and only if $f\in C^{n}(\mathbb{R})$;(ii)if $f^{\prime },\ldots ,f^{(n-1)}\in C_{b}(\mathbb{R})$ and $f^{(n)}\in C_{0}(\mathbb{R})$, then $f$ is $n$ times continuously Fréchet ${\mathcal{S}}^{p}$-differentiable at every self-adjoint operator;(iii)if $f^{\prime },\ldots ,f^{(n)}\in C_{b}(\mathbb{R})$, then $f$ is $n-1$ times continuously Fréchet ${\mathcal{S}}^{p}$-differentiable and $n$ times Gâteaux ${\mathcal{S}}^{p}$-differentiable at every self-adjoint operator.We also prove that if $f\in B_{\infty 1}^{n}(\mathbb{R})\cap B_{\infty 1}^{1}(\mathbb{R})$, then $f$ is $n$ times continuously Fréchet ${\mathcal{S}}^{q}$-differentiable, $1\leqslant q<\infty$, at every self-adjoint operator. These results generalize and extend analogous results of Kissin et al. (Proc. Lond. Math. Soc. (3)108(3) (2014), 327–349) to arbitrary $n$ and unbounded operators as well as substantially extend the results of Azamov et al. (Canad. J. Math.61(2) (2009), 241–263); Coine et al. (J. Funct. Anal.; doi:10.1016/j.jfa.2018.09.005); Peller (J. Funct. Anal.233(2) (2006), 515–544) on higher order ${\mathcal{S}}^{p}$-differentiability of $f$ in a certain Wiener class, Gâteaux ${\mathcal{S}}^{2}$-differentiability of $f\in C^{n}(\mathbb{R})$ with $f^{\prime },\ldots ,f^{(n)}\in C_{b}(\mathbb{R})$, and Gâteaux ${\mathcal{S}}^{q}$-differentiability of $f$ in the intersection of the Besov classes $B_{\infty 1}^{n}(\mathbb{R})\cap B_{\infty 1}^{1}(\mathbb{R})$. As an application, we extend ${\mathcal{S}}^{p}$-estimates for operator Taylor remainders to a broad set of symbols. Finally, we establish explicit formulas for Fréchet differentials and Gâteaux derivatives.
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Carozza, Menita, Jan Kristensen et Antonia Passarelli di Napoli. « Higher differentiability of minimizers of convex variational integrals ». Annales de l'Institut Henri Poincare (C) Non Linear Analysis 28, no 3 (mai 2011) : 395–411. http://dx.doi.org/10.1016/j.anihpc.2011.02.005.

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Tung, L. T. « On higher-order proto-differentiability of perturbation maps ». Positivity 24, no 2 (17 juin 2019) : 441–62. http://dx.doi.org/10.1007/s11117-019-00689-x.

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Gavioli, Chiara. « Higher differentiability of solutions to a class of obstacle problems under non-standard growth conditions ». Forum Mathematicum 31, no 6 (1 novembre 2019) : 1501–16. http://dx.doi.org/10.1515/forum-2019-0148.

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AbstractWe establish the higher differentiability of integer order of solutions to a class of obstacle problems assuming that the gradient of the obstacle possesses an extra integer differentiability property. We deal with the case in which the solutions to the obstacle problems satisfy a variational inequality of the form\int_{\Omega}\langle\mathcal{A}(x,Du),D(\varphi-u)\rangle\,dx\geq 0\quad\text{% for all }\varphi\in\mathcal{K}_{\psi}(\Omega).The main novelty is that the operator {\mathcal{A}} satisfies the so-called {p,q}-growth conditions with p and q linked by the relation\frac{q}{p}<1+\frac{1}{n}-\frac{1}{r},for {r>n}. Here {\psi\in W^{1,p}(\Omega)} is a fixed function, called obstacle, for which we assume {D\psi\in W^{1,2q-p}_{\mathrm{loc}}(\Omega)}, and {\mathcal{K}_{\psi}=\{w\in W^{1,p}(\Omega):w\geq\psi\text{ a.e. in }\Omega\}} is the class of admissible functions. We require for the partial map {x\mapsto\mathcal{A}(x,\xi\/)} a higher differentiability of Sobolev order in the space {W^{1,r}}, with {r>n} satisfying the condition above.
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La Torre et Rocca. « HIGHER ORDER UNIFORM SMOOTHNESS AND DIFFERENTIABILITY OF REAL FUNCTIONS ». Real Analysis Exchange 26, no 2 (2000) : 657. http://dx.doi.org/10.2307/44154068.

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Thèses sur le sujet "Higher differentiability"

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MAZZOLA, MARCO. « Properties of solutions to variational problems ». Doctoral thesis, Università degli Studi di Milano-Bicocca, 2010. http://hdl.handle.net/10281/18339.

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In the context of the variational problems related to integral functionals, we study some necessary conditions for a solution u without standard growth assumptions and strong differentiability conditions on the Lagrangian L. In particular, we investigate the validity of the Euler-Lagrange equation, in its classical and non-classical form, in the cases of functionals with non-differentiable convex Lagrangian or with super-exponential growth for L. Moreover, we investigate the regularity properties for minimizers, concerning higher integrability of the gradient as well as higher differentiability under general growth conditions and mild differentiability assumptions on L.
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Chapitres de livres sur le sujet "Higher differentiability"

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Xiao, Ti-Jun, et Jin Liang. « Differentiability and norm continuity ». Dans The Cauchy Problem for Higher Order Abstract Differential Equations, 199–238. Berlin, Heidelberg : Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-540-49479-9_6.

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Marichal, Jean-Luc, et Naïm Zenaïdi. « Derivatives of Multiple $$\log \Gamma $$ -Type Functions ». Dans A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions, 91–110. Cham : Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95088-0_7.

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AbstractIn this chapter, we discuss the higher order differentiability properties of Σg when g lies in $$\mathcal {C}^r\cap \mathcal {D}^p\cap \mathcal {K}^{\max \{p,r\}}$$ C r ∩ D p ∩ K max { p , r } for any $$p,r\in \mathbb {N}$$ p , r ∈ ℕ . In particular, we show the fundamental fact that Σg also lies in $$\mathcal {C}^r$$ C r and that the sequence $$n \mapsto D^rf^p_n[g]$$ n ↦ D r f n p [ g ] converges uniformly on any bounded subinterval of $$\mathbb {R}_+$$ ℝ + to Dr Σg.
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Mak, Carol, C. H. Luke Ong, Hugo Paquet et Dominik Wagner. « Densities of Almost Surely Terminating Probabilistic Programs are Differentiable Almost Everywhere ». Dans Programming Languages and Systems, 432–61. Cham : Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72019-3_16.

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AbstractWe study the differential properties of higher-order statistical probabilistic programs with recursion and conditioning. Our starting point is an open problem posed by Hongseok Yang: what class of statistical probabilistic programs have densities that are differentiable almost everywhere? To formalise the problem, we consider Statistical PCF (SPCF), an extension of call-by-value PCF with real numbers, and constructs for sampling and conditioning. We give SPCF a sampling-style operational semantics à la Borgström et al., and study the associated weight (commonly referred to as the density) function and value function on the set of possible execution traces.Our main result is that almost surely terminating SPCF programs, generated from a set of primitive functions (e.g. the set of analytic functions) satisfying mild closure properties, have weight and value functions that are almost everywhere differentiable. We use a stochastic form of symbolic execution to reason about almost everywhere differentiability. A by-product of this work is that almost surely terminatingdeterministic(S)PCF programs with real parameters denote functions that are almost everywhere differentiable.Our result is of practical interest, as almost everywhere differentiability of the density function is required to hold for the correctness of major gradient-based inference algorithms.
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Barthe, Gilles, Raphaëlle Crubillé, Ugo Dal Lago et Francesco Gavazzo. « On the Versatility of Open Logical Relations ». Dans Programming Languages and Systems, 56–83. Cham : Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44914-8_3.

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AbstractLogical relations are one among the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be immediately proved by means of logical relations, for instance program continuity and differentiability in higher-order languages extended with real-valued functions. Informally, the problem stems from the fact that these properties are naturally expressed on terms of non-ground type (or, equivalently, on open terms of base type), and there is no apparent good definition for a base case (i.e. for closed terms of ground types). To overcome this issue, we study a generalization of the concept of a logical relation, called open logical relation, and prove that it can be fruitfully applied in several contexts in which the property of interest is about expressions of first-order type. Our setting is a simply-typed $$\lambda $$ λ -calculus enriched with real numbers and real-valued first-order functions from a given set, such as the one of continuous or differentiable functions. We first prove a containment theorem stating that for any collection of real-valued first-order functions including projection functions and closed under function composition, any well-typed term of first-order type denotes a function belonging to that collection. Then, we show by way of open logical relations the correctness of the core of a recently published algorithm for forward automatic differentiation. Finally, we define a refinement-based type system for local continuity in an extension of our calculus with conditionals, and prove the soundness of the type system using open logical relations.
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Lindenstrauss, Joram, David Preiss et Tiˇser Jaroslav. « Asymptotic Fr echet ´Differentiability ». Dans Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179). Princeton University Press, 2012. http://dx.doi.org/10.23943/princeton/9780691153551.003.0015.

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This chapter presents the current development of the first, unpublished proof of existence of points Fréchet differentiability of Lipschitz mappings to two-dimensional spaces. For functions into higher dimensional spaces the method does not lead to a point of Gâteaux differentiability but constructs points of asymptotic Fréchet differentiability. The proof uses perturbations that are not additive, rather than the variational approach, but still provides (asymptotic) Fréchet derivatives in every slice of Gâteaux derivatives. However, it cannot be used to prove existence of points of Fréchet differentiability of Lipschitz mappings of Hilbert spaces to three-dimensional spaces. The results are negative in the sense that an appropriate version of the multidimensional mean value estimate holds.
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Lindenstrauss, Joram, David Preiss et Tiˇser Jaroslav. « Ε‎-Fr ´Echet Differentiability ». Dans Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179). Princeton University Press, 2012. http://dx.doi.org/10.23943/princeton/9780691153551.003.0004.

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This chapter treats results on ε‎-Fréchet differentiability of Lipschitz functions in asymptotically smooth spaces. These results are highly exceptional in the sense that they prove almost Frechet differentiability in some situations when we know that the closed convex hull of all (even almost) Fréchet derivatives may be strictly smaller than the closed convex hull of the Gâteaux derivatives. The chapter first presents a simple proof of an almost differentiability result for Lipschitz functions in asymptotically uniformly smooth spaces before discussing the notion of asymptotic uniform smoothness. It then proves that in an asymptotically smooth Banach space X, any finite set of real-valued Lipschitz functions on X has, for every ε‎ > 0, a common point of ε‎-Fréchet differentiability.
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Actes de conférences sur le sujet "Higher differentiability"

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Surana, K. S., et H. Ngyun. « Solutions of the Right Classes for Laminated Composites Satisfying Interlamina Physics ». Dans ASME 2001 Engineering Technology Conference on Energy. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/etce2001-17156.

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Abstract This paper presents a new theoretical and computational framework for computing solutions of right classes for laminated composites using 2D p-version least squares finite element formulation incorporating the correct physics of interlamina behavior. At the interface between two laminas of dissimilar materials we have continuity of displacements u, v, stresses σyy, τxy, and strain εxx, while the stress σxx and the strains εyy and γxy are discontinuous. Thus, a finite element formulation, incorporating the physics of laminate behavior, would require interpolation of u, v, εxx, σyy and τxy instead of u, v, σxx, σyy and τxy which is generally the case in most mixed formulations. In the p-version LSFEF presented here, we interpolate u, v and σyy, τxy (εxx = ∂u/∂x is used to eliminate εxx as a variable) using appropriate p-version interpolations which would ensure correct interlamina behavior of these components. When the mating lamina properties are different, interlamina discontinuity of σxx, εyy and γxy is automatically generated due to dissimilar material properties of the laminas. In this formulation interlamina jumps in σxx, εyy and γxy do not constitute singularities, hence mesh refinements and higher p-levels are not needed in the vicinity of inter-lamina boundaries. The major thrust of this paper is to construct interpolations for the dependant variables that are of right classes in appropriate spaces so that a sequence of converged solutions in these spaces may be computed which, when converged, would yield a numerical solution that has exactly the same characteristics (in terms of continuity and differentiability) as the analytical or theoretical (strong) solution.
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Surana, K., S. Allu, P. TenPas et J. Reddy. « High-Order Global Differentiability Numerical Solutions in Gas Dynamics Using k-version of Finite Element Method ». Dans 16th AIAA Computational Fluid Dynamics Conference. Reston, Virigina : American Institute of Aeronautics and Astronautics, 2003. http://dx.doi.org/10.2514/6.2003-3686.

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Wang, Menglu, Xueyang Fu, Zepei Sun et Zheng-Jun Zha. « JPEG Artifacts Removal via Compression Quality Ranker-Guided Networks ». Dans Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California : International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/79.

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Existing deep learning-based image de-blocking methods use only pixel-level loss functions to guide network training. The JPEG compression factor, which reflects the degradation degree, has not been fully utilized. However, due to the non-differentiability, the compression factor cannot be directly utilized to train deep networks. To solve this problem, we propose compression quality ranker-guided networks for this specific JPEG artifacts removal. We first design a quality ranker to measure the compression degree, which is highly correlated with the JPEG quality. Based on this differentiable ranker, we then propose one quality-related loss and one feature matching loss to guide de-blocking and perceptual quality optimization. In addition, we utilize dilated convolutions to extract multi-scale features, which enables our single model to handle multiple compression quality factors. Our method can implicitly use the information contained in the compression factors to produce better results. Experiments demonstrate that our model can achieve comparable or even better performance in both quantitative and qualitative measurements.
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Sun, F. P., et Larry D. Mitchell. « Two-Dimensional Velocity Data Smoothing and Structural Angular Velocity Extraction Using a DFT-IDFT Technique ». Dans ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0399.

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Abstract Structure dynamic imaging using a scanning Laser Doppler Velocimeter provides a feasible and efficient means for high-resolution rotational velocity extraction. It shifts the experimentalists’ ground from physical measurement of rotations to mathematical data manipulation and the differentiation of the experimental translational velocity. Consequently, the differentiability of velocity data becomes a major issue since such data are sequences of discrete numbers and are usually noise contaminated. This paper presents an effective method for two-dimensional data set smoothing using one-dimensional Discrete Fourier Transform-Inverse Discrete Fourier Transform (DFT-IDFT) process as a lowpass spatial filter. The angular velocities can then be defined analytically by differentiation in the spatial frequency domain. The technique is prototyped with several real experimental data sets from a steel plate excited at its resonance modes. Special attention is paid to the efforts on making 2-D data set periodic in the data frame as well as to the related error analysis. A preliminary criterion is suggested for determination of “spatial frequency truncation” in IDFT.
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Dallas, James, Yifan Weng et Tulga Ersal. « Combined Trajectory Planning and Tracking for Autonomous Vehicles on Deformable Terrains ». Dans ASME 2020 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/dscc2020-3174.

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Abstract In this work, a novel combined trajectory planner and tracking controller is developed for autonomous vehicles operating on off-road deformable terrains. Common approaches to trajectory planning and tracking often rely on model-dependent schemes, which utilize a simplified model to predict the impact of control inputs to future vehicle response. However, in an off-road context and especially on deformable terrains, accurately modeling the vehicle response for predictive purposes can be challenging due to the complexity of the tire-terrain interaction and limitations of state-of-the-art terramechanics models in terms of operating conditions, computation time, and continuous differentiability. To address this challenge and improve vehicle safety and performance through more accurate prediction of the plant response, in this paper, a nonlinear model predictive control framework is presented that accounts for terrain deformability explicitly using a neural network terramechanics model for deformable terrains. The utility of the proposed scheme is demonstrated on high fidelity simulations for a notional lightweight military vehicle on soft soil. It is shown that the neural network based controller can outperform a baseline Pacejka model based scheme by improving on performance metrics associated with the cost function. In more severe maneuvers, the neural network based controller can achieve sufficient fidelity as compared to the plant to complete maneuvers that lead to failure for the Pacejka based controller. Finally, it is demonstrated that the proposed framework is conducive to real-time implementability.
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Boyle, N., B. Archambault, A. Hagen, C. Meert et R. P. Taleyarkhan. « Detection of Radon-Progeny and Other Alpha-Emitting Radionuclides in Air Using Tensioned Metastable Fluid Detectors ». Dans 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-66805.

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Alpha radiation emitting radon (Rn) gas seepage into homes in the USA leads to over 21,000 annual lung cancer deaths (according to the US-Environmental Protection Agency, EPA) leading to mandatory monitoring for Rn throughout the USA. In the nuclear industry alpha emitting radionuclides in air (e.g., in spent fuel reprocessing) also constitute a major safety and security-safeguards related issues. Purdue University, along with Sagamore Adams Laboratories LLC, is developing the tensioned metastable fluid detector (TMFD) technology for general-purpose alpha-neutron-fission spectroscopy. This paper focuses on rapid, high-efficiency detection of Rn and progeny in air using the novel TMFD technology; Rn and progeny isotopes in air are sparged through the TMFD detection fluid (to entrap the radioactive gas), which is then placed under a metastable state. Through tailoring the metastable fluid state, an audible and visible cavitation detection event is created and readily detected from transient bubble formation. Changing the tensioned state allows for the spectroscopic differentiability of Rn and its daughters which can be used to actively measure the equilibrium between the parent and daughter products. Such a technique can also be used to monitor the atmosphere in critical nuclear facilities for contamination from other alpha emitting isotopes (e.g., Pu, Cm, U...). TMFDs offer the unique ability for high intrinsic efficiency (>95%) alpha-neutron-fission fragment detection, while remaining blind to background beta and gamma radiation (qualified to >3.8×108 Bq m−3 using a dissolved 32P beta source, and also via gammas from a 53 R/hr 137Cs gamma source). Immunity to beta and gamma is beneficial for the discrimination of buildup of beta-emitting Thoron and Rn progeny in the detection fluid allowing for reusability. This paper will discuss the research results pertaining to detection of Radon and progeny in air, for concentrations between 74 Bq m−3 (2 pCi/L) and 740 Bq m−3 (20 pCi/L). The system measures a radon concentration between these levels to within ±15% intrinsic relative error (IRE) within 24 hours meeting the standards outlined by the American Association of Radon Scientists and Technicians-National Radon Proficiency Program (AARST-NRPP) Device Evaluation Program. Precision evaluation was also performed and the relative standard deviation defined by the AARST-NRPP was <5% exceeded the requirement of 25%. Ambient temperature effects were assessed at 10 °C and at 27 °C, which revealed a large increase in collection efficiency with decreasing sampling temperature and slight increase with increasing sampling temperature. Temperature effects on sensitivity thresholds and volumetric expansion were measured and used to compensate for variability in temperature over time. Blind testing with the help of Bowser-Morner Radon Reference Laboratory was performed and succeeded in accurately determining the Rn in air concentration to within 20% within only 6h of sampling. Finally, a 48-hour based collection time has also been developed for use in dwellings where Rn in air concentrations may vary in a day. Overall, the reproducibility and precision of TMFD technology is found to allow for an efficient, cost-effective, reliable, and environmentally friendly means of Rn and progeny detection, and by extension for use for general actinide in air monitoring for the nuclear industry.
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