Relevant bibliographies by topics / Curvature properties

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Curvature properties'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Curvature properties"

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Deszcz, Ryszard, Małgorzata Głogowska, Miroslava Petrovic-Torgasev, and Leopold Verstraelen. "Curvature properties of some class of minimal hypersurfaces in Euclidean spaces." Filomat 29, no. 3 (2015): 479–92. http://dx.doi.org/10.2298/fil1503479d.

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We determine curvature properties of pseudosymmetry type of some class of minimal 2-quasiumbilical hypersurfaces in Euclidean spaces En+1, n ? 4. We present examples of such hypersurfaces. The obtained results are used to determine curvature properties of biharmonic hypersurfaces with three distinct principal curvatures in E5. Those hypersurfaces were recently investigated by Y. Fu in [38].
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Maheshkumar Kankarej, Manisha. "Different Types of Curvature and Their Vanishing Conditions." Academic Journal of Applied Mathematical Sciences, no. 73 (May 2, 2021): 143–48. http://dx.doi.org/10.32861/ajams.73.143.148.

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In the present paper, I studied different types of Curvature like Riemannian Curvature, Concircular Curvature, Weyl Curvature, and Projective Curvature in Quarter Symmetric non-Metric Connection in P-Sasakian manifold. A comparative study of a manifold with a Riemannian connection is done with a P-Sasakian Manifold. Conditions for vanishing for different types of curvature are also a part of the study. Some necessary properties of the Hessian operator are discussed with respect to all curvatures as well.
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Balkan, Y. S., and N. Aktan. "Almost Kenmotsu $f$-manifolds." Carpathian Mathematical Publications 7, no. 1 (July 6, 2015): 6–21. http://dx.doi.org/10.15330/cmp.7.1.6-21.

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In this paper, we consider a generalization of almost Kenmotsu f-manifolds. We get basic Riemannian curvature, sectional curvatures and scalar curvature properties such type manifolds. Finally, we give two examples to clarify some our results.
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Decu, Simona, Stefan Haesen, Leopold Verstraelen, and Gabriel-Eduard Vîlcu. "Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature." Entropy 20, no. 7 (July 14, 2018): 529. http://dx.doi.org/10.3390/e20070529.

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In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of constant ϕ-sectional curvature. For such submanifold, we investigate curvature properties. We establish some inequalities involving the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant). Moreover, we prove that the equality cases of the inequalities hold if and only if the imbedding curvature tensors h and h∗ of the submanifold (associated with the dual connections) satisfy h=−h∗, i.e., the submanifold is totally geodesic with respect to the Levi–Civita connection.
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Peyghan, Esmaeil, and Esa Sharahi. "Vector Bundles and Paracontact Finsler Structures." Facta Universitatis, Series: Mathematics and Informatics 33, no. 2 (September 7, 2018): 231. http://dx.doi.org/10.22190/fumi1802231p.

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Almost paracontact and normal almost paracontact Finsler structures on a vector bundle are defined. Finding some conditions, integrability of these structures are studied. Moreover, we define paracontact metric, para- Sasakian and K-paracontact Finsler structures and study some properties of these structures. For a K-paracontact Finsler structure, we find the vertical and horizontal flag curvatures. Then, defining vertical φ-flag curvature, we prove that every locally symmetric para-Sasakian Finsler structure has negative vertical φ-flag curvature. Finally, we define the horizontal and vertical Ricci tensors of a para-Sasakian Finsler structure and study some curvature properties of them.
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Blaga, Adara M., and Antonella Nannicini. "On curvature tensors of Norden and metallic pseudo-Riemannian manifolds." Complex Manifolds 6, no. 1 (January 1, 2019): 150–59. http://dx.doi.org/10.1515/coma-2019-0008.

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AbstractWe study some properties of curvature tensors of Norden and, more generally, metallic pseudo-Riemannian manifolds. We introduce the notion of J-sectional and J-bisectional curvature of a metallic pseudo-Riemannian manifold (M, J, g) and study their properties.We prove that under certain assumptions, if the manifold is locally metallic, then the Riemann curvature tensor vanishes. Using a Norden structure (J, g) on M, we consider a family of metallic pseudo-Riemannian structures {Ja,b}a,b∈ℝ and show that for a ≠ 0, the J-sectional and J-bisectional curvatures of M coincide with the Ja,b-sectional and Ja,b-bisectional curvatures, respectively. We also give examples of Norden and metallic structures on ℝ2n.
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Wang, Bin, Wenzhe Cai, and Qingxuan Shi. "Simplified Data-Driven Model for the Moment Curvature of T-Shaped RC Shear Walls." Advances in Civil Engineering 2019 (November 3, 2019): 1–16. http://dx.doi.org/10.1155/2019/9897827.

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Sectional deformation quantities, such as curvature and ductility, are of prime significance in the displacement-based seismic design and performance evaluation of structural members. However, few studies on the estimates of curvatures at different limit states have been performed on asymmetric flanged walls. In this paper, a parametric study was performed for a series of T-shaped wall cross-sections based on moment-curvature analyses. By investigating the effects of the axial load ratio, reinforcement content, material properties, and geometric parameters on curvatures at the yield and ultimate limit state, we interpret the variation in curvature with different influencing factors in detail according to the changes of the neutral axis depth. Based on the regression analyses of the numerical results of 4941 T-shaped cross-sections, simple expressions to estimate the yield curvature and ultimate curvature for asymmetric flanged walls are developed, and simplified estimates of the ductility capacity including curvature ductility and displacement ductility are further deduced. By comparing with the experimental results, we verify the accuracy of the proposed formulas. Such simple expressions will be valuable for the determination of the displacement response of asymmetric flanged reinforced concrete walls.
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Duan, Jun-Sheng. "Shrinkage Points of Golden Rectangle, Fibonacci Spirals, and Golden Spirals." Discrete Dynamics in Nature and Society 2019 (December 20, 2019): 1–6. http://dx.doi.org/10.1155/2019/3149602.

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We investigated the golden rectangle and the related Fibonacci spiral and golden spiral. The coordinates of the shrinkage points of a golden rectangle were derived. Properties of shrinkage points were discussed. Based on these properties, we conduct a comparison study for the Fibonacci spiral and golden spiral. Their similarities and differences were looked into by examining their polar coordinate equations, polar radii, arm-radius angles, and curvatures. The golden spiral has constant arm-radius angle and continuous curvature, while the Fibonacci spiral has cyclic varying arm-radius angle and discontinuous curvature.
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Sawicz, Katarzyna. "Curvature properties of some class of hypersurfaces in Euclidean spaces." Publications de l'Institut Math?matique (Belgrade) 98, no. 112 (2015): 165–77. http://dx.doi.org/10.2298/pim141025008s.

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We determine curvature properties of pseudosymmetry type of hypersurfaces in Euclidean spaces En+1, n ? 5, having three distinct nonzero principal curvatures ?1, ?2 and ?3 of multiplicity 1, p and n-p-1, respectively. For some hypersurfaces having this property the sum of ?1, ?2 and ?3 is equal to the trace of the shape operator of M. We present an example of such hypersurface.
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Davidov, Johann, and Oleg Mushkarov. "Curvature Properties of Twistor Spaces." Proceedings of the Steklov Institute of Mathematics 311, no. 1 (December 2020): 78–97. http://dx.doi.org/10.1134/s008154382006005x.

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Dissertations / Theses on the topic "Curvature properties"

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Wisanpitayakorn, Pattipong. "Understanding Mechanical Properties of Bio-filaments through Curvature." Digital WPI, 2019. https://digitalcommons.wpi.edu/etd-dissertations/584.

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Cells are dynamic systems that generate and respond to forces through the complex interplay between biochemical and mechanical regulations. Since cellular processes often happen at the molecular level and are challenging to be observed under in vivo conditions due to limitations in optical microscopy, multiple analysis tools have been developed to gain insight into those processes. One of the ways to characterize these mechanical properties is by measuring their persistence length, the average length over which filaments stay straight. There are several approaches in the literature for measuring the persistence length of the filaments, including Fourier analysis of images obtained using fluorescence microscopy. Here, we show how curvature can be used to quantify local deformations of cell shape and cellular components. We develop a novel technique, called curvature analysis, to measure the stiffness of bio-filaments from fluorescent images. We test our predictions with Monte-Carlo generated filaments. We also apply our approach to microtubules and actin filaments obtained from in vitro gliding assay experiments with high densities of non-functional motors. The presented curvature analysis is significantly more accurate compared to existing approaches for small data sets. To study the effect of motors on filament deformations and velocities observed in gliding assays with functional and non-functional motors, we developed Langevin dynamics simulations of on glass and lipid surfaces. We found that generally the gliding velocity increases with an increase in motor density and a decrease in diffusion coefficient, and that motor density and diffusion coefficient have no clear effect on filament curvatures, except at a very low diffusion coefficients. Finally, we provide an ImageJ plugin to make curvature and persistence length measurements more accessible to everyone.
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Cheung, Leung-Fu. "Geometric properties of stable noncompact constant mean curvature surfaces." Bonn : [s.n.], 1991. http://catalog.hathitrust.org/api/volumes/oclc/26531351.html.

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Trenner, Thomas. "Asymptotic curvature properties of moduli spaces for Calabi-Yau threefolds." Thesis, University of Cambridge, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.609923.

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Renesse, Max-K. von. "Comparison properties of diffusion semigroups on spaces with lower curvature bounds." Bonn : Mathematisches Institut der Universität Bonn, 2003. http://catalog.hathitrust.org/api/volumes/oclc/52348149.html.

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SARACCO, Giorgio. "Fine properties of Cheeger sets and the Prescribed Mean Curvature problem in weakly regular domains." Doctoral thesis, Università degli studi di Ferrara, 2017. http://hdl.handle.net/11392/2487855.

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The two main problems we study are the \emph{Cheeger problem} and the \emph{Prescribed Mean Curvature problem}. The former consists in finding the subsets $E$ of a given ambient set $\Omega$ that realize the Cheeger constant, i.e. such that \[ \frac{P(E)}{|E|} = \inf \left \{ \frac{P(A)}{|A|} \right\} = h_1(\Om)\,, \] where the infimum is sought amongst all subsets of $\Om$ with positive volume; the latter is the non-linear partial differential equation given by \[ \div(Tu) = \div\left( \frac{\grad u}{\sqrt{1+|\grad u|^2}} \right) = H\,, \] which consists in finding functions $u$ whose graph has mean curvature $H$. At a first sight these two problems do not seem to be related but in the special case of a positive, constant prescribed mean curvature $H$ on $\Omega$, a necessary and sufficient condition to existence of solutions and uniqueness up to translations is that $H$ equals the Cheeger constant of $\Omega$ and $\Omega$ is a minimal Cheeger set. On one hand, we study a generalization of the Cheeger problem considering volumes with positive, non-vanishing $L^\infty$ weights and perimeters weighted through a function $g(x,\nu_\Omega (x))$ depending both on the point $x \in \de \Omega$ and the outer normal to $\Om$ at $x$. Then, we prove that any connected minimizer admits a Poincar\'e trace inequality, as well as the standard Sobolev embeddings. On the other hand, in the case of the standard Cheeger problem in dimension $2$ we show that, for simply connected sets $\Om$ that satisfy a ``no-bottleneck'' condition, the maximal Cheeger set $E$ equals the union of all balls contained in $\Om$ whose radius is $r=h_1^{-1}(\Om)$. Moreover, the inner Cheeger formula $|[\Om]^r|=\pi r^2$ holds, where $[\Om]^r$ denotes the set of points of $\Om$ at distance greater or equal than $r$ from $\de \Omega$. This result generalizes a property so far proved only for convex sets and planar strips. Concerning the Prescribed Mean Curvature problem, we show existence and uniqueness of solutions of the PMC equation only assuming that $\Omega$ is a \emph{weakly regular} open set, i.e., when $\Omega$ satisfies a Poincar\'e trace inequality and its perimeter agrees with the $(n-1)$-dimensional Hausdorff measure of the topological boundary. Under these assumptions, we show that uniqueness up to vertical translations is equivalent to several other properties. Namely, that the domain is maximal, i.e. no solutions for the same prescribed datum $H$ can exist in any set $\widetilde \Omega$ strictly containing $\Om$; that $\Om$ is critical, i.e. among all its subsets, it is the only one for which the inequality $|\int_A H| \le P(A)$ becomes an equality; that there exists a solution which solves the capillarity problem in a tube of cross-section $\Om$ with vertical contact angle, i.e. that it satisfies a tangential boundary condition in an integral sense or in a ``weak trace'' sense. Moreover, whenever the perimeter of $\Om$ agrees with the inner Minkowski content of $\Om$, this tangential ``weak trace'' condition assumes the stronger form $Tu(x) \to \nu_\Om (z)$ in a measure-theoretic sense, as $x\in \Omega$ approaches a point $z$ in the ``super-reduced boundary''. Finally, when the prescribed datum $H$ is positive and non-vanishing, we observe again the link between the Cheeger problem and the Prescribed Mean Curvature problem, as being critical corresponds to $\Omega$ being a minimal Cheeger set with Cheeger constant $1$, for the Cheeger problem with the standard perimeter and volume weighted through $H$.
I due principali problemi che studiamo sono il \emph{problema di Cheeger} ed il \emph{problema di curvatura media prescritta}. Il primo consiste nel trovare i sottoinsiemi $E$ di un certo insieme ambiente $\Om$ che realizzano la costante di Cheeger, ovvero tali che \[ \frac{P(E)}{|E|} = \inf \left \{ \frac{P(A)}{|A|} \right\} = h_1(\Om)\,, \] dove l'estremo inferiore \`e fra tutti i sottoinsiemi di $\Omega$ con volume positivo; il secondo problema \`e l'equazione alle derivate parziali non lineare data da \[ \div(Tu) = \div \left ( \frac{\grad u}{\sqrt{1+|\grad u|^2}} \right) = H\,, \] che consiste nel trovare delle funzioni $u$ il cui grafico abbia curvatura media $H$. A prima vista questi due problemi sembrano indipendenti, ma nel caso speciale di una curvatura media prescritta $H$ costante e positiva in $\Omega$, una condizione necessaria e sufficiente all'esistenza di soluzioni e all'unicit\`a a meno di traslazioni, \`e che $H$ sia uguale della costante di Cheeger e che $\Omega$ sia un insieme di Cheeger minimale. Da un lato, studiamo una generalizzazione del problema di Cheeger considerando dei volumi con pesi $L^\infty$ e dei perimetri pesati tramite funzioni $g(x, \nu_\Om (x))$ che dipendono sia dal punto $x\in \de \Omega$ sia dalla normale esterna ad $\Om$ nel punto $x$. Mostriamo che gli insiemi minimi connessi ammettono una disuguaglianza di traccia di Poincar\'e e le classiche immersioni di Sobolev. Dall'altro lato, nel caso del problema di Cheeger classico in $2$ dimensioni, mostriamo che, per insiemi $\Om$ semplicemente connessi che non presentano ``colli di bottiglia'', l'insieme di Cheeger massimale $E$ \`e l'unione di tutte le palle contenute in $\Omega$ di raggio $r= h_1^{-1}(\Om)$. Inoltre, vale la inner Cheeger formula $|[\Om]^r = \pi r^2$, dove $[\Om]^r$ indica l'insieme dei punti di $\Om$ che sono a una distanza maggiore o uguale ad $r$ da $\de \Om$. Questo risultato generalizza una propriet\`a finora dimostrata solo per insieme convessi e strisce. Riguardo al problema di curvatura media prescritta, mostriamo esistenza ed unicit\`a di soluzioni per l'equazione soltanto richiedendo che l insieme $\Om$ sia un aperto ``debolmente regolare'', ovvero che soddisfi una disuguaglianza di traccia di Poincar\'e e che il suo perimetro coincida con la misura di Hausdorff $(n-1)$-dimensionale del suo bordo topologico. Sotto tali ipotesi, dimostriamo che l'unicit\`a, a meno di traslazioni, \`e equivalente a diverse altre propriet\`a. In particolare, alla massimalit\`a del dominio, ovvero non esistono soluzioni per la stessa curvatura prescritta $H$ in nessun insieme $\widetilde \Omega$ che contiene strettamente $\Om$; alla criticalit\`a di $\Omega$, ovvero che $\Om$, fra tutti i suoi sottoinsiemi \`e l'unico per cui la disuguaglianza $|\int_A H| \le P(A)$ diventa un'uguaglianza; all'esistenza di una soluzione che risolve il problema di capillarit\`a in un cilindro di sezione $\Om$ con angolo di contatto verticale, ovvero con una condizione al bordo tangenziale, assunta in un senso integrale o di ``traccia debole''. Inoltre, questa condizione al bordo di ``traccia debole'', quando il perimetro di $\Om$ coincide con il contenuto interno di Minkoswki di $\Om$, assume la forma pi\`u forte $Tu(x) \to \nu_\Om (z)$ in misura, per $x\in \Omega$ che tendono a un punto $z$ nella frontiera ``super-ridotta''. Infine, quando la curvatura prescritta $H$ \`e positiva e non identicamente nulla, si osserva di nuovo il legame fra il problema di Cheeger e di curvatura media prescritta, in quanto la criticalit\`a di $\Om$ \`e equivalente a dire che la costante di Cheeger pesata tramite $H$ e con perimetro classico \`e $1$ e che $\Om$ \`e un insieme minimale di Cheeger.
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McCormick, Timothy M. "Electronic and Transport Properties of Weyl Semimetals." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu153204408441858.

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Miller, Robert William. "Tetrabenzo[8]circulene: Synthesis and Structural Properties of Polycyclic Aromatic Hydrocarbons with Negative Curvature." ScholarWorks @ UVM, 2017. http://scholarworks.uvm.edu/graddis/792.

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Contorted polycyclic aromatic hydrocarbons have found increasing utility in the application of molecular electronics due to the surpamolecular properties that result from these non-planar structures. The [n]circulene series of molecules are particularly attractive members of the contorted aromatic family due to the unique structural implications that result from their changing value of n. For example, when n ≤ 5, the structures adopt a bowl-like shape; when n = 6, a planar structure is observed; and when 7 ≤ n ≤ 16, the compounds assume a saddle-like shape. Very few molecules exhibit the structural contortions that these contorted aromatics do – primarily because aromatic molecules desire to adopt highly planar conformations. Following the model of aromaticity developed by Erich Clar, we set our sights on the synthesis of tetrabenzo[8]circulene, the stabilized form of [8]circulene established through the addition of four fused benzenoid rings around the periphery of the molecule. The initial approach towards this structure employs a Diels-Alder [4 + 2] cycloaddition reaction and a palladium catalyzed arylation reaction as the key transformation steps. The results of these studies were promising, establishing the structural characterization of this new molecule and providing access to functionalized derivatives of the saddle-shaped structure. However, access towards these functionalized derivatives proved limiting, compelling us to investigate alternative synthetic methodologies. In the course of our studies, we established a new methodology towards 2,5-diarylthiophene-1-oxides, a key precursor to the Diels-Alder cycloaddition reaction. These reactive dienes are prepared from readily available arylacetylene precursors via zirconacyclopentadiene intermediates. The isolated yields of the desired thiophene-1-oxides are comparable to those obtained from previously established oxidation strategies while avoiding the formation of over-oxidation products. Of significant importance to scope of our work, this newly established methodology offers broader versatility providing products outfitted with electron-donating or electron-withdrawing groups. These new methodologies provided access to functionalized derivatives of the saddle-shaped molecule tetrabenzo[8]circulene in improved yield when coupled with a revised Diels-Alder/oxidative cyclodehydrogenation approach. This methodology affords products containing both electron-rich and electron-poor functional groups in a more efficient manner. The optoelectronic effects that result from the introduction of this functionality and investigations into the development of larger contorted aromatic systems are also discussed.
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Tewodrose, David. "Some functional inequalities and spectral properties of metric measure spaces with curvature bounded below." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLEE076.

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L’objectif de la thèse est de présenter de nouveaux résultats d’analyse sur les espaces métriques mesurés. Nous étendons d’abord à une certaine classe d’espaces avec doublement et Poincaré des inégalités de Sobolev pondérées introduites par V. Minerbe en 2009 dans le cadre des variétés riemanniennes à courbure de Ricci positives. Dans le contexte des espaces RCD(0,N), nous en déduisons une inégalité de Nash pondérée et un contrôle uniforme du noyau de la chaleur pondéré associé. Puis nous démontrons la loi de Weyl sur les espaces RCD(K,N) compactes à l’aide d’un théorème de convergence ponctuelle des noyaux de la chaleur associés à une suite mGH-convergente d’espaces RCD(K,N). Enfin nous abordons dans le contexte RCD(K,N) un théorème de Bérard, Besson et Gallot fournissant, à l’aide du noyau de la chaleur, une famille de plongements asymptotiquement isométriques d’une variété riemannienne fermée dans l’espace de ses fonctions de carré intégrable. Nous introduisons notamment les notions de métrique RCD, de métrique pull-back, et de convergence faible/forte de métriques RCD sur un espace RCD(K,N) compacte, et nous prouvons un résultat de convergence analogue à celui de Bérard, Besson et Gallot
The aim of this thesis is to present new results in the analysis of metric measure spaces. We first extend to a certain class of spaces with doubling and Poincaré some weighted Sobolev inequalities introduced by V. Minerbe in 2009 in the context of Riemannian manifolds with non-negative Ricci curvature. In the context of RCD(0,N) spaces, we deduce a weighted Nash inequality and a uniform control of the associated weighted heat kernel. Then we prove Weyl’s law for compact RCD(K,N) spaces thanks to a pointwise convergence theorem for the heat kernels associated with a mGH-convergent sequence of RCD(K,N) spaces. Finally we address in the RCD(K,N) context a theorem from Bérard, Besson and Gallot which provides, by means of the heat kernel, an asymptotically isometric family of embeddings for a closed Riemannian manifold into its space of square integrable functions. We notably introduce the notions of RCD metrics, pull-back metrics, weak/strong convergence of RCD metrics, and we prove a convergence theorem analog to the one of Bérard, Besson and Gallot
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Tewodrose, David. "Some functional inequalities and spectral properties of metric measure spaces with curvature bounded below." Doctoral thesis, Scuola Normale Superiore, 2018. http://hdl.handle.net/11384/85734.

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[from the introduction]: The aim of this thesis is to study metric measure spaces with a synthetic notion of Ricci curvature bounded below. We study them from the point of view of Sobolev/Nash type functional inequalities in the non-compact case, and from the point of view of spectral analysis in the compact case. The heat kernel links the two cases: in the first one, the goal is to get new estimates on the heat kernel of some associated weighted structure; in the second one, the heat kernel is the basic tool to establish our results. The topic of synthetic Ricci curvature bounds has known a constant development over the past few years. In this introduction, we shall give some historical account on this theory, before explaining in few words the content of this work. The letter K will refer to an arbitrary real number and N will refer to any finite number greater or equal than 1.
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Ciomaga, Adina. "Analytical properties of viscosity solutions for integro-differential equations : image visualization and restoration by curvature motions." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2011. http://tel.archives-ouvertes.fr/tel-00624378.

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Le manuscrit est constitué de deux parties indépendantes.Propriétés des Solutions de Viscosité des Equations Integro-Différentielles.Nous considérons des équations intégro-différentielles elliptiques et paraboliques non-linéaires (EID), où les termes non-locaux sont associés à des processus de Lévy. Ce travail est motivé par l'étude du Comportement en temps long des solutions de viscosité des EID, dans le cas périodique. Le résultat classique nous dit que la solution u(¢, t ) du problème de Dirichlet pour EID se comporte comme ?t Åv(x)Åo(1) quand t !1, où v est la solution du problème ergodique stationaire qui correspond à une unique constante ergodique ?.En général, l'étude du comportement asymptotique est basé sur deux arguments: la régularité de solutions et le principe de maximumfort.Dans un premier temps, nous étudions le Principe de Maximum Fort pour les solutions de viscosité semicontinues des équations intégro-différentielles non-linéaires. Nous l'utilisons ensuite pour déduire un résultat de comparaison fort entre sous et sur-solutions des équations intégro-différentielles, qui va assurer l'unicité des solutions du problème ergodique à une constante additive près. De plus, pour des équationssuper-quadratiques le principe de maximum fort et en conséquence le comportement en temps grand exige la régularité Lipschitzienne.Dans une deuxième partie, nous établissons de nouvelles estimations Hölderiennes et Lipschitziennes pour les solutions de viscosité d'une large classe d'équations intégro-différentielles non-linéaires, par la méthode classique de Ishii-Lions. Les résultats de régularité aident de plus à la résolution du problème ergodique et sont utilisés pour fournir existence des solutions périodiques des EID.Nos résultats s'appliquent à une nouvelle classe d'équations non-locales que nous appelons équations intégro-différentielles mixtes. Ces équations sont particulièrement intéressantes, car elles sont dégénérées à la fois dans le terme local et non-local, mais leur comportement global est conduit par l'interaction locale - non-locale, par exemple la diffusion fractionnaire peut donner l'ellipticité dans une direction et la diffusion classique dans la direction orthogonale.Visualisation et Restauration d'Images par Mouvements de CourbureLe rôle de la courbure dans la perception visuelle remonte à 1954, et on le doit à Attneave. Des arguments neurologiques expliquent que le cerveau humain ne pourrait pas possiblement utiliser toutes les informations fournies par des états de simulation. Mais en réalité on enregistre des régions où la couleur change brusquement (des contours) et en outre les angles et les extremas de courbure. Pourtant, un calcul direct de courbures sur une image est impossible. Nous montrons comment les courbures peuvent être précisément évaluées, à résolution sous-pixelique par un calcul sur les lignes de niveau après leur lissage indépendant.Pour cela, nous construisons un algorithme que nous appelons Level Lines (Affine) Shortening, simulant une évolution sous-pixelique d'une image par mouvement de courbure moyenne ou affine. Aussi bien dans le cadre analytique que numérique, LLS (respectivement LLAS) extrait toutes les lignes de niveau d'une image, lisse indépendamment et simultanément toutes ces lignes de niveau par Curve Shortening(CS) (respectivement Affine Shortening (AS)) et reconstruit une nouvelle image. Nousmontrons que LL(A)S calcule explicitement une solution de viscosité pour le le Mouvement de Courbure Moyenne (respectivement Mouvement par Courbure Affine), ce qui donne une équivalence avec le mouvement géométrique.Basé sur le raccourcissement de lignes de niveau simultané, nous fournissons un outil de visualisation précis des courbures d'une image, que nous appelons un Microscope de Courbure d'Image. En tant que application, nous donnons quelques exemples explicatifs de visualisation et restauration d'image : du bruit, des artefacts JPEG, de l'aliasing seront atténués par un mouvement de courbure sous-pixelique
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Books on the topic "Curvature properties"

1

Brunnett, Guido. The curvature of plane elastic curves. Monterey, Calif: Naval Postgraduate School, 1993.

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Dhakal, Rajesh P. Curvature ductility of reinforced concrete plastic hinges: Assessment of curvature limits for different forms of plastic hinges in reinforced concrete structures. Saarbrücken: VDM, Verlag Dr. Müller, 2008.

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Dhakal, Rajesh P. Curvature ductility of reinforced concrete plastic hinges: Assessment of curvature limits for different forms of plastic hinges in reinforced concrete structures. Saarbrücken: VDM, Verlag Dr. Müller, 2008.

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1966-, Pérez Joaquín, and Galvez José A. 1972-, eds. Geometric analysis: Partial differential equations and surfaces : UIMP-RSME Santaló Summer School geometric analysis, June 28-July 2, 2010, University of Granada, Granada, Spain. Providence, R.I: American Mathematical Society, 2012.

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Li, Weiping, and Shihshu Walter Wei. Geometry and topology of submanifolds and currents: 2013 Midwest Geometry Conference, October 19, 2013, Oklahoma State University, Stillwater, Oklahoma : 2012 Midwest Geometry Conference, May 12-13, 2012, University of Oklahoma, Norman, Oklahoma. Providence, Rhode Island: American Mathematical Society, 2015.

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Ortaçgil, Ercüment H. The Nonlinear Curvature. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198821656.003.0003.

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Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor. World Scientific Publishing Company, 2001.

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Deruelle, Nathalie, and Jean-Philippe Uzan. Riemannian manifolds. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0064.

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This chapter is about Riemannian manifolds. It first discusses the metric manifold and the Levi-Civita connection, determining if the metric is Riemannian or Lorentzian. Next, the chapter turns to the properties of the curvature tensor. It states without proof the intrinsic versions of the properties of the Riemann–Christoffel tensor of a covariant derivative already given in Chapter 2. This chapter then performs the same derivation as in Chapter 4 by obtaining the Einstein equations of general relativity by varying the Hilbert action. However, this will be done in the intrinsic manner, using the tools developed in the present and the preceding chapters.
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Book chapters on the topic "Curvature properties"

1

Ritoré, Manuel, and Carlo Sinestrari. "Invariance properties." In Mean Curvature Flow and Isoperimetric Inequalities, 16–19. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0213-6_5.

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Busemann, Herbert, and Willy Feller. "Curvature Properties of Convex Surfaces." In Selected Works II, 235–70. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-65624-3_18.

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Garcia-Rio, E., L. Hervella, and R. Vásquez-Lorenzo. "Curvature Properties of Para-Kähler Manifolds." In New Developments in Differential Geometry, 193–200. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-0149-0_14.

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Cheng, Xinyue, and Zhongmin Shen. "Randers Metrics with Special Riemann Curvature Properties." In Finsler Geometry, 77–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-24888-7_6.

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Villani, Cédric. "Weak Ricci curvature bounds II: Geometric and analytic properties." In Grundlehren der mathematischen Wissenschaften, 847–901. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-71050-9_30.

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Pandey, Shashikant, Rajendra Prasad, and Sandeep Kumar Verma. "Concircular Curvature Tensor’s Properties on Lorentzian Para-Sasakian Manifolds." In Springer Proceedings in Mathematics & Statistics, 45–57. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5455-1_4.

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Busemann, Herbert. "Busemann and Feller on Curvature Properties of Convex Surfaces." In Selected Works II, 67–88. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-65624-3_10.

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Barth, Erhardt, Mario Ferraro, and Christoph Zetzsche. "Global Topological Properties of Images Derived from Local Curvature Features." In Lecture Notes in Computer Science, 285–94. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-45129-3_25.

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Presby, Michael J., Rabih Mansour, Manigandan Kannan, Richard K. Smith, Gregory N. Morscher, Frank Abdi, Cody Godines, and Sung Choi. "Influence of Curvature on High Velocity Impact of SIC/SIC Composites." In Mechanical Properties and Performance of Engineering Ceramics and Composites XI, 131–41. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2017. http://dx.doi.org/10.1002/9781119320104.ch12.

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Sakasegawa, D., M. Goto, and A. Suzuki. "Effects of Thickness and Curvature on the Adhesion Properties of Cylindrical Soft Materials by a Point Contact Method." In Gels: Structures, Properties, and Functions, 135–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00865-8_19.

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Conference papers on the topic "Curvature properties"

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Carlsson, Johan M. "Curvature effects on vacancies in nanotubes." In ELECTRONIC PROPERTIES OF NOVEL NANOSTRUCTURES: XIX International Winterschool/Euroconference on Electronic Properties of Novel Materials. AIP, 2005. http://dx.doi.org/10.1063/1.2103903.

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GILKEY, P. "GEOMETRIC PROPERTIES OF THE CURVATURE OPERATOR." In Differential Geometry in Honor of Professor S S Chern. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792051_0005.

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Fan, T. J., G. Medioni, and R. Nevatia. "3-D Surface Description Using Curvature Properties." In OE LASE'87 and EO Imaging Symp (January 1987, Los Angeles), edited by Hua-Kuang Liu and Paul S. Schenker. SPIE, 1987. http://dx.doi.org/10.1117/12.939973.

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Bakar, Suraya Abu, Muhammad Suzuri Hitam, Wan Nural Jawahir Hj Wan Yussof, and Marufa Yeasmin Mukta. "Shape Corner Detection through Enhanced Curvature Properties." In 2020 Emerging Technology in Computing, Communication and Electronics (ETCCE). IEEE, 2020. http://dx.doi.org/10.1109/etcce51779.2020.9350894.

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Barth, Erhardt, Christoph Zetzsche, Mario Ferraro, and Ingo Rentschler. "Fractal properties from 2D curvature on multiple scales." In SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, edited by Baba C. Vemuri. SPIE, 1993. http://dx.doi.org/10.1117/12.146648.

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Chandra, Kambhamettu, and Dmitry B. Goldgof. "Left ventricle wall motion tracking using curvature properties." In SPIE/IS&T 1992 Symposium on Electronic Imaging: Science and Technology, edited by Raj S. Acharya, Carol J. Cogswell, and Dmitry B. Goldgof. SPIE, 1992. http://dx.doi.org/10.1117/12.59561.

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Mokhtarian, F. "Convergence Properties of Curvature and Torsion Scale Space Representations." In British Machine Vision Conference 1995. British Machine Vision Association, 1995. http://dx.doi.org/10.5244/c.9.36.

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Bogaevski, Ilia A., Alexander G. Belyaev, and Tosiyasu L. Kunii. "Qualitative and asymptotic properties of curvature-driven silhouette deformations." In Optical Science, Engineering and Instrumentation '97, edited by Robert A. Melter, Angela Y. Wu, and Longin J. Latecki. SPIE, 1997. http://dx.doi.org/10.1117/12.279659.

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Al Tahhan, Aghyad B., and Mohammad AlKhedher. "Investigating Curvature Effect on Tensile Properties of Carbon Nanotubes." In 2022 Advances in Science and Engineering Technology International Conferences (ASET). IEEE, 2022. http://dx.doi.org/10.1109/aset53988.2022.9735084.

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Yıldırım, Mustafa, and Nesip Aktan. "Some curvature properties of globally framed almost f-cosymplectic manifolds." In II. INTERNATIONAL CONFERENCE ON ADVANCES IN NATURAL AND APPLIED SCIENCES: ICANAS 2017. Author(s), 2017. http://dx.doi.org/10.1063/1.4981658.

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Reports on the topic "Curvature properties"

1

R. Mirzaie. Topological Properties of Some Cohomogeneity on Riemannian Manifolds of Nonpositive Curvature. GIQ, 2012. http://dx.doi.org/10.7546/giq-3-2002-351-359.

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Nakova, Galia. Curvature Properties of Some Three-Dimentional Almost Contact Manifolds with B-Metric II. GIQ, 2012. http://dx.doi.org/10.7546/giq-5-2004-169-177.

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Hart, James, Nasir Zulfiqar, and Carl Popelar. L52289 Use of Pipeline Geometry Monitoring to Assess Pipeline Condition. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), December 2008. http://dx.doi.org/10.55274/r0010254.

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Describes an algorithm is developed for deducing the longitudinal or axial strain from geometry pig measurements of a laterally displaced pipeline; often caused by geohazards. The development is limited to those lateral displacements of the pipeline that results in a predominantly transverse loading; i.e., the induced transverse component of the loading is much greater than its axial component. The emphasis is upon evaluating inelastic straining that accompanies large lateral displacement of the pipeline. The induced extensional strain is found to vary linearly with the change in curvature of the pipeline. The validity of the approach is established through favorable comparisons of the predictions for the extensional strains with those determined from buried pipeline finite element simulations of various displaced pipe configurations, pipe geometries, and loading amplitudes. Since the algorithm relies only upon measurements of the geometry of the displaced pipeline, it is independent of the pipe's and soil's material properties, pipe-soil interaction, and the loading conditions. Benefit: The efficacy of the algorithm is demonstrated by performing a large matrix of finite element simulations of displaced pipelines of different geometries subjected to block subsidence, landslides intersecting the pipeline at varying angles, fault crossings at different angles and different loading states, and comparing the analytical strains with the strains deduced from digital pig measurements of the curvature of the deformed pipeline. In this regard, the finite element simulations serve the role of surrogate geometry pig measurements. These comparisons are used to establish the resolution of the change in curvature measurement required of a geometry pig to produce a reliable estimate for the longitudinal strain in a displaced pipeline. An error analysis is also performed to establish the relative error as a function of the curvature measurement gage length, a characteristic feature-length, and the abruptness of the displaced shape of the pipeline.
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Stuedlein, Armin, Ali Dadashiserej, and Amalesh Jana. Models for the Cyclic Resistance of Silts and Evaluation of Cyclic Failure during Subduction Zone Earthquakes. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, April 2023. http://dx.doi.org/10.55461/zkvv5271.

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This report describes several advances in the cyclic failure assessment of silt soils with immediate and practical benefit to the geotechnical earthquake engineering profession. First, a database of cyclic loading test data is assembled, evaluated, and used to assess trends in the curvature of the CRR-N (cyclic resistance ratio - the number of equivalent cycles) relationship. This effort culminated in a plasticity index-dependent function which can be used to estimate the exponent b in the power law describing cyclic resistance, and may be used to estimate the cyclic resistance of silt soils as well as the number of equivalent loading cycles anticipated for subduction zone earthquakes. Statistical models for the cyclic resistance ratio and cyclic strength ratio are presented in this report. The SHANSEP (Stress History and Normalized Soil Engineering Properties)-inspired functional form of these models have been trained and tested against independent datasets and finalized using a combined dataset to provide reasonable estimates of resistance based on the available data. These models can be used to provide provisional estimates of the CRR-N and cyclic strength ratio power laws for cyclic shear strain failure criteria ranging from 1 to 10%, within certain stated limitations. The ground motion records within the NGA Subduction Project which have been released to the public to-date are implemented to examine the role of subduction zone earthquake characteristics on the number of equivalent loading cycles for a wide range of soils with exponents b ranging from 0.05 (moderate plasticity silt and clay) to 0.35 (dense sand). This analysis shows that the number of loading cycles for a given magnitude subduction zone earthquake is larger than those previously computed, whereas the corresponding magnitude scaling factors for use with the Simplified Method span a smaller range as a result of the ground motion characteristics. Owing to the large variability in the computed equivalent number of loading cycles, consideration of the uncertainty is emphasized in forward analyses. The work described herein may be used to estimate cyclic resistance of intact non-plastic and plastic silt soils and corresponding factor of safety against cyclic failure for a range in cyclic shear strain failure criteria, to plan cyclic laboratory testing programs, and to calibrate models for use in site response and nonlinear deformation analyses in the absence of site-specific cyclic test data. As with any empirical approach, the models presented herein should be revised when additional, high-quality cyclic testing data become available.
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Anderson, Gerald L., and Kalman Peleg. Precision Cropping by Remotely Sensed Prorotype Plots and Calibration in the Complex Domain. United States Department of Agriculture, December 2002. http://dx.doi.org/10.32747/2002.7585193.bard.

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This research report describes a methodology whereby multi-spectral and hyperspectral imagery from remote sensing, is used for deriving predicted field maps of selected plant growth attributes which are required for precision cropping. A major task in precision cropping is to establish areas of the field that differ from the rest of the field and share a common characteristic. Yield distribution f maps can be prepared by yield monitors, which are available for some harvester types. Other field attributes of interest in precision cropping, e.g. soil properties, leaf Nitrate, biomass etc. are obtained by manual sampling of the filed in a grid pattern. Maps of various field attributes are then prepared from these samples by the "Inverse Distance" interpolation method or by Kriging. An improved interpolation method was developed which is based on minimizing the overall curvature of the resulting map. Such maps are the ground truth reference, used for training the algorithm that generates the predicted field maps from remote sensing imagery. Both the reference and the predicted maps are stratified into "Prototype Plots", e.g. 15xl5 blocks of 2m pixels whereby the block size is 30x30m. This averaging reduces the datasets to manageable size and significantly improves the typically poor repeatability of remote sensing imaging systems. In the first two years of the project we used the Normalized Difference Vegetation Index (NDVI), for generating predicted yield maps of sugar beets and com. The NDVI was computed from image cubes of three spectral bands, generated by an optically filtered three camera video imaging system. A two dimensional FFT based regression model Y=f(X), was used wherein Y was the reference map and X=NDVI was the predictor. The FFT regression method applies the "Wavelet Based", "Pixel Block" and "Image Rotation" transforms to the reference and remote images, prior to the Fast - Fourier Transform (FFT) Regression method with the "Phase Lock" option. A complex domain based map Yfft is derived by least squares minimization between the amplitude matrices of X and Y, via the 2D FFT. For one time predictions, the phase matrix of Y is combined with the amplitude matrix ofYfft, whereby an improved predicted map Yplock is formed. Usually, the residuals of Y plock versus Y are about half of the values of Yfft versus Y. For long term predictions, the phase matrix of a "field mask" is combined with the amplitude matrices of the reference image Y and the predicted image Yfft. The field mask is a binary image of a pre-selected region of interest in X and Y. The resultant maps Ypref and Ypred aremodified versions of Y and Yfft respectively. The residuals of Ypred versus Ypref are even lower than the residuals of Yplock versus Y. The maps, Ypref and Ypred represent a close consensus of two independent imaging methods which "view" the same target. In the last two years of the project our remote sensing capability was expanded by addition of a CASI II airborne hyperspectral imaging system and an ASD hyperspectral radiometer. Unfortunately, the cross-noice and poor repeatability problem we had in multi-spectral imaging was exasperated in hyperspectral imaging. We have been able to overcome this problem by over-flying each field twice in rapid succession and developing the Repeatability Index (RI). The RI quantifies the repeatability of each spectral band in the hyperspectral image cube. Thereby, it is possible to select the bands of higher repeatability for inclusion in the prediction model while bands of low repeatability are excluded. Further segregation of high and low repeatability bands takes place in the prediction model algorithm, which is based on a combination of a "Genetic Algorithm" and Partial Least Squares", (PLS-GA). In summary, modus operandi was developed, for deriving important plant growth attribute maps (yield, leaf nitrate, biomass and sugar percent in beets), from remote sensing imagery, with sufficient accuracy for precision cropping applications. This achievement is remarkable, given the inherently high cross-noice between the reference and remote imagery as well as the highly non-repeatable nature of remote sensing systems. The above methodologies may be readily adopted by commercial companies, which specialize in proving remotely sensed data to farmers.
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