Готові списки джерел за темами / Neumann eigenvalues

Добірка наукової літератури з теми "Neumann eigenvalues"

Автор: Grafiati

Опубліковано: 8 червня 2024

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Статті в журналах з теми "Neumann eigenvalues":

Benedikt, Jiří. "On the discreteness of the spectra of the Dirichlet and Neumannp-biharmonic problems." Abstract and Applied Analysis 2004, no. 9 (2004): 777–92. http://dx.doi.org/10.1155/s1085337504311115.

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We are interested in a nonlinear boundary value problem for(|u″|p−2u″)′′=λ|u|p−2uin[0,1],p>1, with Dirichlet and Neumann boundary conditions. We prove that eigenvalues of the Dirichlet problem are positive, simple, and isolated, and form an increasing unbounded sequence. An eigenfunction, corresponding to thenth eigenvalue, has preciselyn−1zero points in(0,1). Eigenvalues of the Neumann problem are nonnegative and isolated,0is an eigenvalue which is not simple, and the positive eigenvalues are simple and they form an increasing unbounded sequence. An eigenfunction, corresponding to thenth positive eigenvalue, has preciselyn+1zero points in(0,1).

Lamberti, Pier Domenico, and Luigi Provenzano. "Neumann to Steklov eigenvalues: asymptotic and monotonicity results." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 147, no. 2 (January 16, 2017): 429–47. http://dx.doi.org/10.1017/s0308210516000214.

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We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of mass concentration at the boundary of a ball. We discuss the asymptotic behaviour of the Neumann eigenvalues and find explicit formulae for their derivatives in the limiting problem. We deduce that the Neumann eigenvalues have a monotone behaviour in the limit and that Steklov eigenvalues locally minimize the Neumann eigenvalues.

Karpukhin, Mikhail A. "The Steklov Problem on Differential Forms." Canadian Journal of Mathematics 71, no. 2 (January 7, 2019): 417–35. http://dx.doi.org/10.4153/cjm-2018-028-6.

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AbstractIn this paper we study spectral properties of the Dirichlet-to-Neumann map on differential forms obtained by a slight modification of the definition due to Belishev and Sharafutdinov. The resulting operator $\unicode[STIX]{x039B}$ is shown to be self-adjoint on the subspace of coclosed forms and to have purely discrete spectrum there. We investigate properties of eigenvalues of $\unicode[STIX]{x039B}$ and prove a Hersch–Payne–Schiffer type inequality relating products of those eigenvalues to eigenvalues of the Hodge Laplacian on the boundary. Moreover, non-trivial eigenvalues of $\unicode[STIX]{x039B}$ are always at least as large as eigenvalues of the Dirichlet-to-Neumann map defined by Raulot and Savo. Finally, we remark that a particular case of $p$-forms on the boundary of a $2p+2$-dimensional manifold shares many important properties with the classical Steklov eigenvalue problem on surfaces.

Diyab, Farah, and B. Surender Reddy. "Comparison of Laplace Beltrami Operator Eigenvalues on Riemannian Manifolds." European Journal of Mathematics and Statistics 3, no. 5 (October 23, 2022): 55–60. http://dx.doi.org/10.24018/ejmath.2022.3.5.143.

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Let $\Delta_{g}$ be the Laplace Beltrami operator on a manifold $M$ with Dirichlet (resp.,Neumann) boundary conditions. We compare the spectrum of on a Riemannian manifold for Neumann boundary condition and Dirichlet boundary condition . Then we construct aneffective method of obtaining small eigenvalues for Neumann's problem.

BARBU, LUMINIŢA, and GHEORGHE MOROŞANU. "On a Steklov eigenvalue problem associated with the (p,q)-Laplacian." Carpathian Journal of Mathematics 37, no. 2 (June 9, 2021): 161–71. http://dx.doi.org/10.37193/cjm.2021.02.02.

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"Consider in a bounded domain \Omega \subset \mathbb{R}^N, N\ge 2, with smooth boundary \partial \Omega, the following eigenvalue problem (1) \begin{eqnarray*} &~&\mathcal{A} u:=-\Delta_p u-\Delta_q u=\lambda a(x) \mid u\mid ^{r-2}u\ \ \mbox{ in} ~ \Omega, \nonumber \\ &~&\big(\mid \nabla u\mid ^{p-2}+\mid \nabla u\mid ^{q-2}\big)\frac{\partial u}{\partial\nu}=\lambda b(x) \mid u\mid ^ {r-2}u ~ \mbox{ on} ~ \partial \Omega, \nonumber \end{eqnarray*} where 1<r<q<p<\infty or 1<q<p<r<\infty; r\in \Big(1, \frac{p(N-1)}{N-p}\Big) if p<N and r\in (1, \infty) if p\ge N; a\in L^{\infty}(\Omega),~ b\in L^{\infty}(\partial\Omega) are given nonnegative functions satisfying \[ \int_\Omega a~dx+\int_{\partial\Omega} b~d\sigma >0. \] Under these assumptions we prove that the set of all eigenvalues of the above problem is the interval [0, \infty). Our result complements those previously obtained by Abreu, J. and Madeira, G., [Generalized eigenvalues of the (p, 2)-Laplacian under a parametric boundary condition, Proc. Edinburgh Math. Soc., 63 (2020), No. 1, 287–303], Barbu, L. and Moroşanu, G., [Full description of the eigenvalue set of the (p,q)-Laplacian with a Steklov-like boundary condition, J. Differential Equations, in press], Barbu, L. and Moroşanu, G., [Eigenvalues of the negative (p,q)– Laplacian under a Steklov-like boundary condition, Complex Var. Elliptic Equations, 64 (2019), No. 4, 685–700], Fărcăşeanu, M., Mihăilescu, M. and Stancu-Dumitru, D., [On the set of eigen-values of some PDEs with homogeneous Neumann boundary condition, Nonlinear Anal. Theory Methods Appl., 116 (2015), 19–25], Mihăilescu, M., [An eigenvalue problem possesing a continuous family of eigenvalues plus an isolated eigenvale, Commun. Pure Appl. Anal., 10 (2011), 701–708], Mihăilescu, M. and Moroşanu, G., [Eigenvalues of -\triangle_p-\triangle_q under Neumann boundary condition, Canadian Math. Bull., 59 (2016), No. 3, 606–616]."

Li, Wei, and Ping Yan. "Various Half-Eigenvalues of Scalarp-Laplacian with Indefinite Integrable Weights." Abstract and Applied Analysis 2009 (2009): 1–27. http://dx.doi.org/10.1155/2009/109757.

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Consider the half-eigenvalue problem(ϕp(x′))′+λa(t)ϕp(x+)−λb(t)ϕp(x−)=0a.e.t∈[0,1], where1<p<∞,ϕp(x)=|x|p−2x,x±(⋅)=max⁡{±x(⋅),0}forx∈𝒞0:=C([0,1],ℝ), anda(t)andb(t)are indefinite integrable weights in the Lebesgue spaceℒγ:=Lγ([0,1],ℝ),1≤γ≤∞. We characterize the spectra structure under periodic, antiperiodic, Dirichlet, and Neumann boundary conditions, respectively. Furthermore, all these half-eigenvalues are continuous in(a,b)∈(ℒγ,wγ)2, wherewγdenotes the weak topology inℒγspace. The Dirichlet and the Neumann half-eigenvalues are continuously Fréchet differentiable in(a,b)∈(ℒγ,‖⋅‖γ)2, where‖⋅‖γis theLγnorm ofℒγ.

Legendre, Eveline. "Extrema of Low Eigenvalues of the Dirichlet–Neumann Laplacian on a Disk." Canadian Journal of Mathematics 62, no. 4 (August 1, 2010): 808–26. http://dx.doi.org/10.4153/cjm-2010-042-8.

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AbstractWe study extrema of the first and the second mixed eigenvalues of the Laplacian on the disk among some families of Dirichlet–Neumann boundary conditions. We show that the minimizer of the second eigenvalue among all mixed boundary conditions lies in a compact 1-parameter family for which an explicit description is given. Moreover, we prove that among all partitions of the boundary with bounded number of parts on which Dirichlet and Neumann conditions are imposed alternately, the first eigenvalue is maximized by the uniformly distributed partition.

Mihăilescu, Mihai, та Gheorghe Moroşanu. "Eigenvalues of −Δp − Δq Under Neumann Boundary Condition". Canadian Mathematical Bulletin 59, № 3 (1 вересня 2016): 606–16. http://dx.doi.org/10.4153/cmb-2016-025-2.

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AbstractThe eigenvalue problem −Δpu − Δqu = λ|u|q−2u with p ∊ (1,∞), q ∊ (2,∞), p ≠ q subject to the corresponding homogeneous Neumann boundary condition is investigated on a bounded open set with smooth boundary from ℝN with N ≥ 2. A careful analysis of this problem leads us to a complete description of the set of eigenvalues as being a precise interval (λ1, ∞) plus an isolated point λ = 0. This comprehensive result is strongly related to our framework, which is complementary to the well-known case p = q ≠ 2 for which a full description of the set of eigenvalues is still unavailable.

Ma, Ruyun, Chenghua Gao, and Yanqiong Lu. "Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/280508.

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We study the spectrum structure of discrete second-order Neumann boundary value problems (NBVPs) with sign-changing weight. We apply the properties of characteristic determinant of the NBVPs to show that the spectrum consists of real and simple eigenvalues; the number of positive eigenvalues is equal to the number of positive elements in the weight function, and the number of negative eigenvalues is equal to the number of negative elements in the weight function. We also show that the eigenfunction corresponding to thejth positive/negative eigenvalue changes its sign exactlyj-1times.

D'AGUÌ, GIUSEPPINA, and GIOVANNI MOLICA BISCI. "THREE NON-ZERO SOLUTIONS FOR ELLIPTIC NEUMANN PROBLEMS." Analysis and Applications 09, no. 04 (October 2011): 383–94. http://dx.doi.org/10.1142/s021953051100190x.

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In this note we obtain a multiplicity result for an eigenvalue Neumann problem. Precisely, a recent critical point result for differentiable functionals is exploited, in order to prove the existence of a determined open interval of positive eigenvalues for which the problem admits at least three non-zero weak solutions.

Більше джерел

Дисертації з теми "Neumann eigenvalues":

Michetti, Marco. "Steklov and Neumann eigenvalues : inequalities, asymptotic and mixed problems." Electronic Thesis or Diss., Université de Lorraine, 2022. http://www.theses.fr/2022LORR0109.

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Cette thèse est consacrée à l'étude des valeurs propres de Neumann, des valeurs propres de Steklov et des relations entre elles. La motivation initiale de cette thèse était de prouver que, dans le plan, le produit entre le périmètre et la première valeur propre de Steklov est toujours inférieur au produit entre l'aire et la première valeur propre de Neumann. Motivés par la recherche de contre-exemples à cette inégalité, nous donnons, dans la première partie de cette thèse, une description complète du comportement asymptotique des valeurs propres de Steklov dans un domaine en haltère constitué de deux ensembles de Lipschitz reliés par un tube mince de largeur qui va à zéro. En utilisant ces résultats dans le cas bidimensionnel, nous trouvons que l'inégalitè n'est pas toujours vraie. Nous étudions l'inégalité dans le cadre convexe, en prouvant une forme plus faible de l'inégalité pour tous les domaines convexes et en prouvant l'inégalité pour une classe spéciale de polygones convexes. Nous donnons également le comportement asymptotique des valeurs propres de Neumann et de Steklov sur des domaines convexes qui s'effondrent, en reliant de cette façcon ces deux valeurs propres aux valeurs propres de type Sturm-Liouville. Dans la deuxième partie de cette thèse, en utilisant les résultats concernant le comportement asymptotique des valeurs propres de Neumann sur les domaines effondrés et une analyse fine des fonctions propres de Sturm-Liouville, nous étudions le problème de maximisation des valeurs propres de Neumann sous contrainte de diamètre. Dans la dernière partie de la thèse, nous étudions le valeurs propres de Steklov-Dirichlet. Après une première discussion sur les propriétés de régularité des fonctions propres de Steklov-Dirichlet, nous obtenons un résultat de stabilité pour les valeurs propres. Nous étudions le problème d'optimisation sous une contrainte de mesure sur l'ensemble dans lequel nous imposons des conditions de Steklov, nous prouvons l'existence d'un minimiseur et la non-existence d'un maximiseur. Dans le plan, nous prouvons un résultat de continuité pour les valeurs propres sous une certaine contrainte topologique
This thesis is devoted to the study of Neumann eigenvalues, Steklov eigenvalues and relations between them. The initial motivation of this thesis was to prove that, in the plane, the product between the perimeter and the first Steklov eigenvalue is always less then the product between the area and the first Neumann eigenvalue. Motivated by finding counterexamples to this inequality, in the first part of this thesis, we give a complete description of the asymptotic behavior of the Steklov eigenvalues in a dumbbell domain consisting of two Lipschitz sets connected by a thin tube with vanishing width. Using these results in the two dimensional case we find that the inequality is not always true. We study the inequality in the convex setting, proving a weaker form of the inequality for all convex domains and proving the inequality for a special class of convex polygons. We then also give the asymptotic behavior for Neumann and Steklov eigenvalues on collapsing convex domains, linking in this way these two eigenvalues with Sturm-Liouville type eigenvalues. In the second part of this thesis, using the results concerning the asymptotic behavior of Neumann eigenvalues on collapsing domains and a fine analysis of Sturm-Liouville eigenfunctions we study the maximization problem of Neumann eigenvalues under diameter constraint. In the last part of the thesis we study the mixed Steklov-Dirichlet. After a first discussion about the regularity properties of the Steklov-Dirichlet eigenfunctions we obtain a stability result for the eigenvalues. We study the optimization problem under a measure constraint on the set in which we impose Steklov boundary conditions, we prove the existence of a minimizer and the non-existence of a maximizer. In the plane we prove a continuity result for the eigenvalues under some topological constraint

Zaveri, Sona. "The second eigenfunction of the Neumann Laplacian on thin regions /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/5748.

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Berger, Amandine. "Optimisation du spectre du Laplacien avec conditions de Dirichlet et Neumann dans R² et R³." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAM036/document.

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Le problème de l'optimisation des valeurs propres du Laplacien est ancien puisqu'à la fin du XIXème siècle Lord Rayleigh conjecturait que la première valeur propre avec condition de Dirichlet était minimisée par le disque. Depuis le problème a été beaucoup étudié. Et les possibilités de recherches sont multiples : diverses conditions, ajout de contraintes, existence, description des optima ... Dans ce document on se limite aux conditions de Dirichlet et de Neumann, dans R^2 et dans R^3. On procède dans un premier temps à un état de l'art. On se focalise ensuite sur les disques et les boules. En effet, ils font partie des rares formes pour lesquelles il est possible de calculer explicitement et relativement facilement les valeurs propres. On verra malheureusement que ces formes ne sont la plupart du temps pas des minimiseurs. Enfin on s'intéresse aux simulations numériques possibles. En effet, puisque peu de calculs théoriques peuvent être faits il est intéressant d'obtenir numériquement des candidats. Cela permet ensuite d'avoir des hypothèses de travail théorique. `{A} cet effet nous donnerons des éléments de compréhension sur une méthode de simulation numérique ainsi que des résultats obtenus
The optimization of Laplacian eigenvalues is a classical problem. In fact, at the end of the nineteenth century, Lord Rayleigh conjectured that the first eigenvalue with Dirichlet boundary condition is minimized by a disk. This problem received a lot of attention since this first study and research possibilities are numerous: various conditions, geometrical constraints added, existence, description of optimal shapes... In this document we restrict us to Dirichlet and Neumann boundary conditions in R^2 and R^3. We begin with a state of the art. Then we focus our study on disks and balls. Indeed, these are some of the only shapes for which it is possible to explicitly and relatively easily compute the eigenvalues. But we show in one of the main result of this document that they are not minimizers for most eigenvalues. Finally we take an interest in the possible numerical experiments. Since we can do very few theoretical computations, it is interesting to get numerical candidates. Then we can deduce some theoretical working assumptions. With this in mind we give some keys to understand our numerical method and we also give some results obtained

Shouman, Abdolhakim. "Comparaison de valeurs propres de Laplaciens et inégalités de Sobolev sur des variétés riemanniennes à densité." Thesis, Tours, 2017. http://www.theses.fr/2017TOUR4034.

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Le but de cette thèse est triple : INÉGALITÉS DE SOBOLEV AVEC DES CONSTANTES EXPLICITES SUR DES VARIÉTÉS RIEMANNIENNES À DENSITÉ ET À BORD CONVEXE : On obtient des inégalités de Sobolev à densité, avec des constantes géométriques explicites pour des variétés à courbure de m-Bakry-Émery Ricci minorée par une constante positive et à bord convexe. Ceci permet de généraliser de nombreux résultats connus dans le cas riemannien aux variétés avec densité. Nous montrons aussi comment déduire des inégalités de Sobolev obtenues, un résultat d’isolement pour les applications f -harmoniques. Nous présenterons également une nouvelle et très simple méthode pour la preuve de l’inégalité de Moser-Trudinger-Onofri [Onofri, 1982] dans le cas du disque euclidien
The purpose of this thesis is threefold: SOBOLEV INEQUALITIES WITH EXPLICIT CONSTANTS ON A WEIGHTED RIEMANNIAN MANIFOLD OF CONVEX BOUNDARY: We obtain weighted Sobolev inequalities with explicit geometric constants for weighted Riemannian manifolds of positive m-Bakry-Emery Ricci curvature and convex boundary. As a first application, we generalize several results of Riemannian manifolds to the weighted setting. Another application is a new isolation result for the f -harmonic maps. We also give a new and elemantry proof of the well-known Moser-Trudinger-Onofri [Onofri, 1982] inequality for the Euclidean disk

Shouman, Abdolhakim. "Comparaison de valeurs propres de Laplaciens et inégalités de Sobolev sur des variétés riemanniennes à densité." Electronic Thesis or Diss., Tours, 2017. http://www.theses.fr/2017TOUR4034.

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Wang, Tai-Ho, and 王太和. "Inequalities between Dirichlet and Neumann Eigenvalues on Sphere." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/31722351819444475448.

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碩士
國立交通大學
應用數學研究所
82
Let M be a compact domain in the n-sphere with smooth boundary. Assume that the mean curvature h of the boundary of M is nonpositive. We prove that the k-th Neumann eigenvalue is less than or equal to the k-th Dirichlet eigenvalue of M. Moreover, these inequalites are strict unless the boundary of M is minimal.

Chang, Yu-Chung, and 張有中. "Inequalities Between Dirichlet and Neumann Eigenvalues in the Hyperbolic Space." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/38484808677084606688.

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碩士
國立交通大學
應用數學研究所
82
In this paper we shall derive an inequality of the form between Dirichlet and Neumann eigenvalues for domains in the hyperbolic space under certain condition which depends upon the mean curvature of boundary.

FU, JUN-JIE, and 傅俊結. "Inequalities between dirichlet and neumann eigenvalues for domains in Sn." Thesis, 1991. http://ndltd.ncl.edu.tw/handle/25752235711685642567.

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Wang, Tai-Ho, and 王太和. "Degree identity for harmonic map heat flow and inequalities between Dirichlet and Neumann eigenvalues." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/23021117619745786986.

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博士
國立交通大學
應用數學系
88
This thesis is divided into two parts. In the first part, we prove that the degree of the solution to the heat equation for harmonic maps between 2-spheres will be increasing or decreasing by the sum of the degrees of the harmonic spheres through each blow-up time. Thus the degree of the harmonic limit will be precisely determined from the degree of the initial map and the amount of the degrees of finite harmonic spheres. The purpose of the second part is to describe some inequalities between Dirichlet and Neumann eigenvalues for smooth domains in the $n$-sphere under certain convex restrictions on the boundary. We prove that if the mean curvature of the boundary is nonpositive, then the $k$th nonzero Neumann eigenvalue is less than or equal to the $k$th Dirichlet eigenvalue for $k = 1, 2, \cdots $. Furthermore, if the second fundamental form of the boundary is nonpositive, then the $(k+\left[\frac{n-1}{2}\right])$th nonzero Neumann eigenvalue is less than or equal to the $k$th Dirichlet eigenvalue for $k = 1, 2, \cdots $.

Marushka, Viktor. "Propriétés des valeurs propres de ballotement pour contenants symétriques." Thèse, 2012. http://hdl.handle.net/1866/8949.

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Le problème d’oscillation de fluides dans un conteneur est un problème classique d’hydrodynamique qui est etudié par des mathématiciens et ingénieurs depuis plus de 150 ans. Le présent travail est lié à l’étude de l’alternance des fonctions propres paires et impaires du problème de Steklov-Neumann pour les domaines à deux dimensions ayant une forme symétrique. On obtient des résultats sur la parité de deuxième et troisième fonctions propres d’un tel problème pour les trois premiers modes, dans le cas de domaines symétriques arbitraires. On étudie aussi la simplicité de deux premières valeurs propres non nulles d’un tel problème. Il existe nombre d’hypothèses voulant que pour le cas des domaines symétriques, toutes les valeurs propres sont simples. Il y a des résultats de Kozlov, Kuznetsov et Motygin [1] sur la simplicité de la première valeur propre non nulle obtenue pour les domaines satisfaisants la condition de John. Dans ce travail, il est montré que pour les domaines symétriques, la deuxième valeur propre non-nulle du problème de Steklov-Neumann est aussi simple.
The study of liquid sloshing in a container is a classical problem of hydrodynamics that has been actively investigated by mathematicians and engineers over the past 150 years. The present thesis is concerned with the properties of eigenfunctions of the two-dimensional sloshing problem on axially symmetric planar domains. Here the axis of symmetry is assumed to be orthogonal to the free surface of the fluid. In particular, we show that the second and the third eigenfunctions of such a problem are, respectively, odd and even with respect to the axial symmetry. There is a well-known conjecture that all eigenvalues of the two-dimensional sloshing problem are simple. Kozlov, Kuznetsov and Motygin [1] proved the simplicity of the first non-zero eigenvalue for domains satisfying the John's condition. In the thesis we show that for axially symmetric planar domains, the first two non-zero eigenvalues of the sloshing problem are simple.

Книги з теми "Neumann eigenvalues":

Edmunds, D. E., та W. D. Evans. Global and Asymptotic Estimates for the Eigenvalues of −Δ‎ + q when q Is Real. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0011.

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This chapter is devoted to the study of the Schrödinger operator −Δ‎ + q with q real, and, in particular, the distribution of its eigenvalues. A general result is established on an open subset Ω‎ of Rn using the Max–Min Principle and covering families of congruent cubes for the Dirichlet problem and a Whitney covering for the Neumann problem. The Cwikel–Lieb–Rosenbljum inequality is proved for q in Ln/2(Rn).

Edmunds, D. E., and W. D. Evans. Generalized Dirichlet and Neumann Boundary-Value Problems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0006.

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In this chapter, the generalized or weak interpretation of the Dirichlet and Neumann problems for general elliptic expressions is motivated and then the Lax–Milgram Theorem is used to set the problems in the framework of eigenvalue problems for operators acting in Hilbert space. Results on variational inequalities in Chapter IV are applied to establish Stampacchia’s weak maximum principle, and this leads to the notion of capacity.

Частини книг з теми "Neumann eigenvalues":

Burdzy, Krzysztof. "Neumann Eigenfunctions and Eigenvalues." In Lecture Notes in Mathematics, 31–39. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04394-4_4.

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Levine, Howard A., and Hans F. Weinberger. "Inequalities between Dirichlet and Neumann Eigenvalues." In Analysis and Continuum Mechanics, 253–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83743-2_13.

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Lamberti, Pier Domenico, and Luigi Provenzano. "Viewing the Steklov Eigenvalues of the Laplace Operator as Critical Neumann Eigenvalues." In Trends in Mathematics, 171–78. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12577-0_21.

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Kleefeld, Andreas. "Shape Optimization for Interior Neumann and Transmission Eigenvalues." In Integral Methods in Science and Engineering, 185–96. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16077-7_15.

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Abele, Daniel, and Andreas Kleefeld. "New Numerical Results for the Optimization of Neumann Eigenvalues." In Computational and Analytic Methods in Science and Engineering, 1–20. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48186-5_1.

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Gol’dshtein, Vladimir, Ritva Hurri-Syrjänen, Valerii Pchelintsev, and Alexander Ukhlov. "Space quasiconformal composition operators with applications to Neumann eigenvalues." In Harmonic Analysis and Partial Differential Equations, 141–60. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-25424-6_6.

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Bercovici, Hari, and Wing Suet Li. "Inequalities for eigenvalues of sums in a von Neumann algebra." In Recent Advances in Operator Theory and Related Topics, 113–26. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8374-0_6.

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Rohleder, Jonathan. "A remark on the order of mixed Dirichlet–Neumann eigenvalues of polygons." In Analysis as a Tool in Mathematical Physics, 570–75. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-31531-3_30.

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Yamada, Susumu, Toshiyuki Imamura, and Masahiko Machida. "High Performance LOBPCG Method for Solving Multiple Eigenvalues of Hubbard Model: Efficiency of Communication Avoiding Neumann Expansion Preconditioner." In Supercomputing Frontiers, 243–56. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-69953-0_14.

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Ricci, Saverio, Piergiulio Mannocci, Matteo Farronato, Alessandro Milozzi, and Daniele Ielmini. "Development of Crosspoint Memory Arrays for Neuromorphic Computing." In Special Topics in Information Technology, 65–74. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-51500-2_6.

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AbstractMemristor-based hardware accelerators play a crucial role in achieving energy-efficient big data processing and artificial intelligence, overcoming the limitations of traditional von Neumann architectures. Resistive-switching memories (RRAMs) combine a simple two-terminal structure with the possibility of tuning the device conductance. This Chapter revolves around the topic of emerging memristor-related technologies, starting from their fabrication, through the characterization of single devices up to the development of proof-of-concept experiments in the field of in-memory computing, hardware accelerators, and brain-inspired architecture. Non-volatile devices are optimized for large-size crossbars where the devices’ conductance encodes mathematical coefficients of matrices. By exploiting Kirchhoff’s and Ohm’s law the matrix–vector-multiplication between the conductance matrix and a voltage vector is computed in one step. Eigenvalues/eigenvectors are experimentally calculated according to the power-iteration algorithm, with a fast convergence within about 10 iterations to the correct solution and Principal Component Analysis of the Wine and Iris datasets, showing up to 98% accuracy comparable to a floating-point implementation. Volatile memories instead present a spontaneous change of device conductance with a unique similarity to biological neuron behavior. This characteristic is exploited to demonstrate a simple fully-memristive architecture of five volatile RRAMs able to learn, store, and distinguish up to 10 different items with a memory capability of a few seconds. The architecture is thus tested in terms of robustness under many experimental conditions and it is compared with the real brain, disclosing interesting mechanisms which resemble the biological brain.

Тези доповідей конференцій з теми "Neumann eigenvalues":

Ledoux, Veerle, Marnix Van Daele, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Efficient Computation of Sturm-Liouville Eigenvalues using Modified Neumann Schemes." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241408.

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Durante, Tiziana. "Waveguides with a box-shaped perturbation: Eigenvalues of the Neumann problem." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992661.

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Báez, G., R. A. Méndez-Sánchez, F. Leyvraz, and T. H. Seligman. "A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions." In SPECIAL TOPICS ON TRANSPORT THEORY: ELECTRONS, WAVES, AND DIFFUSION IN CONFINED SYSTEMS: V Leopoldo García-Colín Mexican Meeting on Mathematical and Experimental Physics. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4862421.

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Sarsenbi, Abdisalam A. "On a Green’s function and eigenvalues of a second-order differential operator with involution and Neumann boundary conditions." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE’16): Proceedings of the 42nd International Conference on Applications of Mathematics in Engineering and Economics. Author(s), 2016. http://dx.doi.org/10.1063/1.4968461.

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Lamberti, Pier Domenico, and Massimo Lanza de Cristoforis. "Lipschitz Type Inequalities for a Domain Dependent Neumann Eigenvalue Problem for the Laplace Operator." In Proceedings of the 4th International ISAAC Congress. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701732_0018.

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Ludvigsen, Arild, and Zhi Yuan Pan. "Extensions and Improvements to the Solutions for Linear Tank Dynamics." In ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/omae2015-41805.

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Linear solvers for the flow exterior to the hull may be used to solve for the fluid dynamics also in the interior of a tank, as discussed in Newman (2005) and Ludvigsen et al. (2013). This introduces extra, erroneous terms in the radiation part of the pressure in the tank, but due to cancellation in restoring and radiation terms, the total representation of the pressure and the global response is correctly obtained. For some kinds of analysis, specific knowledge is needed of the radiation and restoring parts separately. The cancellation of the extra terms can then not be utilized. Examples of this are stability analysis and eigenvalue analysis. In stability analysis we need to know the actual real global restoring coefficients. In eigenvalue analysis, we should have the separately correct representations of the added mass and restoring coefficients, respectively, to be able to conveniently use them as input to standard eigenvalue solvers. Here, we develop the expressions for the corrected, actual terms of the total added mass and restoring coefficients for tanks. This is used in our computer program for performing eigenvalue analysis. Results for peak global response and natural periods of the structure with the influence of tank dynamics are presented. Comparisons are made with results obtained by a quasi-static method for an FPSO and a ship with more largely extensive tanks. For a completely filled tank, the boundary value problem (BVP) for the velocity potential is reduced to Laplace equation in the fluid domain, subject to a Neuman condition on the fixed boundary and it is not closed. The extra condition of having zero pressure at some point in the tank is then added. Direct re-use of the BVP solver for the external flow, gives an undetermined set of linear equations for the velocity potential in the tank fluid. A typical solver for sets of linear equations may still return a solution, but this will contain a random undetermined constant. After imposing zero pressure in the top of the tank, this solution is still unstable, contaminated by numerical noise. An improved method is introduced by imposing algebraically, in the equation system, the constraint of zero pressure in the top of the tank. This gives a non-singular equation system with a stable solution holding zero pressure in some selected point in the tank.

Karadeniz, H. "Uncertainty Modelling and Fatigue Reliability Calculation of Offshore Structures With Deteriorated Members." In ASME 2004 23rd International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2004. http://dx.doi.org/10.1115/omae2004-51403.

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This paper presents formulations and procedure of an efficient calculation of stress spectra and fatigue damage of offshore structures with deteriorated members in the uncertainty space. Calculation modeling of member deteriorations is represented by equivalent spring systems, which can be determined on basis of damage detection and stiffness degradation, with a deterioration uncertainty parameter. Redistributions of the member and system stiffness matrices and the load vectors are expressed in incremental (decremental) forms. The updated system stiffness-matrix is sated in terms of stiffness- and deterioration-uncertainties and the updated system load-vector is stated in terms of deterioration- and loading-uncertainties. Using the Neumann expansion solution technique, the inversion of the updated system stiffness matrix is expressed in terms of uncertainty parameters so that the reliability iteration can be performed without requiring repetitive inversion of the stiffness matrix. The deterioration- and uncertainty-update of the stiffness matrix requires resolution of the eigenvalue problem. This problem is reformulated in terms of uncertainty variables and an efficient solution algorithm is presented. An extra uncertainty parameter is used in structural transfer functions to represent damping uncertainties. Having expressed wave forces as functions of uncertainty variables, formulations of transfer functions of displacements and member internal forces are presented in the uncertainty space, which enable the reliability calculation to be efficient and fast. Apart from uncertainties of structural and loading origins, uncertainties arising from environmental origin, which appear in the spectral-analysis, are summarized. These are related to the modeling of random waves and wave-current interactions as well as to the long-term probability-distribution model of the significant wave height. Uncertainties in SCF, damage model (S-N line), non-narrowness of the stress process, long-term probability distribution of sea states and in the damage at which failure occurs (reference damage) are considered in fatigue-related uncertainties. An example is presented to demonstrate the application of the approximate analysis procedure to the mean value response analysis of deteriorated structures.