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Résumé Une inegalité est derivée et utilisée pour améliorer des limites pour la rigidité torsionelle d'une cylindre orthotropique obtenu dans une étude antérieure.  相似文献   

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We consider the Saint-Venant functional P for the torsional rigidity in an arbitrary plane or spatial domain. The main result of this paper is the sharp estimate P ?? (4/n)m, where n is the dimension of the space, and m is the harmonic mean of moments of inertia of the domain about the coordinate planes. The extremal domains are ellipsoids of a special kind. Thus, we obtain a generalization of the isoperimetric inequality proved by E. Nicolay for the torsional rigidity of simply connected plane domains.  相似文献   

4.
A well‐known problem in elasticity consists in placing two linearly elastic materials (of different shear moduli) in a given plane domain Ω, so as to maximize the torsional rigidity of the resulting rod; moreover, the proportion of these materials is prescribed. Such a problem may not have a classical solution as the optimal design may contain homogenization regions, where the two materials are mixed in a microscopic scale. Then, the optimal torsional rigidity becomes difficult to compute. In this paper we give some different theoretical upper and lower bounds for the optimal torsional rigidity, and we compare them on some significant domains. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

5.
A one-parameter family of variational problems is examined that interpolates between torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. The associated partial differential equation is derived, which is shown to have positive solutions in many cases. Results are obtained regarding extremal domains and regarding variations of the domain or the parameter.  相似文献   

6.
Makai  E. 《Acta Mathematica Hungarica》1966,17(3-4):419-422
Acta Mathematica Hungarica -  相似文献   

7.
We say that a Riemannian manifold M has rank M ≥ k if every geodesic in M admits at least k parallel Jacobi fields. The Rank Rigidity Theorem of Ballmann and Burns–Spatzier, later generalized by Eberlein–Heber, states that a complete, irreducible, simply connected Riemannian manifold M of rank k ≥ 2 (the “higher rank” assumption) whose isometry group Γ satisfies the condition that the Γ-recurrent vectors are dense in SM is a symmetric space of noncompact type. This includes, for example, higher rank M which admit a finite volume quotient. We adapt the method of Ballmann and Eberlein–Heber to prove a generalization of this theorem where the manifold M is assumed only to have no focal points. We then use this theorem to generalize to no focal points a result of Ballmann–Eberlein stating that for compact manifolds of nonpositive curvature, rank is an invariant of the fundamental group.  相似文献   

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In this paper we generalize some classical estimates involving the torsional rigidity and the principal frequency of a convex domain to a class of functionals related to some anisotropic nonlinear operators.  相似文献   

9.
Wide application of polymer composite materials (PCM) in modern technology calls for detailed evaluation of their stress-strain properties in a broad temperature range. To obtain such information, we use the dynamic mechanical analysis and with the help of a reverse torsion pendulum measure the dynamic torsional rigidity of PCM bars of rectangular cross section in the temperature range up to 600 K. It is found that the temperature dependences of the dynamic rigidity of the calculated values of dynamic shear moduli are governed by the percentage and properties of the binder and fibers, the layout of fibers, the phase interaction along interfaces, etc. The principles of dynamic mechanical spectrometry are used to substantiate and analyze the parameters of anisotropy by which the behavior of a composite can be described in the temperature range including the transition of the binder from the glassy into a highly elastic state. For this purpose, the values of dynamic rigidity are measured under low-amplitude vibrations of the PCM specimens with a fiber orientation angle from 0 to 90°. It is shown that for unidirectional composites the dependence between the dynamic rigidity and the fiber orientation angle is of extreme character. The value and position of the peak depend on the type of the binder and fibers and change with temperature. It is found that the anisotropy degree of PCM is dictated by the molecular mobility and significantly changes in the temperature range of transition of the binder and reinforcement from the glassy into a highly elastic state (in the case of SVM fibers). The possibility of evaluating the anisotropy of composites with other reinforcement schemes, in particular, of orthogonally reinforced PCMs, is shown.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 291–308, May–June, 1999.  相似文献   

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Zusammenfassung Für 16 besondere Kreisausschnittwinkel wird die Drillungssteifigkeit eines Stabes mit Kreissektor-Querschnitt durchL-Funktionen ausgedrückt.  相似文献   

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In this paper we prove a sharp upper bound for the first Dirichlet eigenvalue of a class of nonlinear elliptic operators which includes the operator , that is the p‐Laplacian, and , namely the pseudo‐p‐Laplacian. Moreover we prove a stability result by means of a suitable isoperimetric deficit. Finally, we give a sharp lower bound for the anisotropic p‐torsional rigidity.  相似文献   

13.
In the class of convex domains, we define domain perturbation operators which preserve a particular weighted area as well as the convexity property, while (essentially) increasing torsional rigidity. Using these operators, we prove the existence of convex solutions for a related free boundary problem in which the stress function is to satisfy a generalized Bernoulli condition, and we give recursive procedures for computing approximate solutions to this problem. We also define analogous weighted area and convexity preserving domain perturbation operators which (essentially) diminish capacity, and apply them to solve an analogous free boundary problem in which the stream function satisfies a generalized Bernoulli condition.
Zusammenfassung In der Klasse der konvexen Gebiete definieren wir Gebietsstörungsoperatoren, die ein bestimmtes Flächenmaß und die Konvexitätseigenschaft erhalten, während sie (im wesentlichen) die Torsionssteifigkeit vergrößern. Unter Verwendung dieser Operatoren beweisen wir die Existenz von konvexen Lösungen für eine verwandte freie Randwertaufgabe, wobei die Spannungsfunktionen einer verallgemeinerten Bernoulli-Bedingung genügen soll, und geben rekursive Verfahren an, die zu Näherungslösungen führen. Weiter definieren wir analoge flächenmaß- und konvexitätserhaltende Gebietsstörungsoperatoren die (im wesentlichen) die Kapazität vermindern, und verwenden sie zur Lösung einer analogen freien Randwertaufgabe, wo die Strömungsfunktion einer Bernoulli-Bedingung genügt.
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14.
We prove that under certain regularity conditions imposed on the renormalizations of two circle diffeomorphisms with singularities, their C 1-smooth equivalence follows from exponential convergence of those renormalizations. As an easy corollary, any two analytical critical circle maps with the same order of critical points and the same irrational rotation number are C 1-smoothly conjugate.  相似文献   

15.
The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Bounds on the free-surface profiles and on the total head are obtained under minimal assumptions about properties of solutions to the problem and the vorticity distribution.  相似文献   

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In this paper we prove convergence rates for the problem of approximating functions f by neural networks and similar constructions. We show that the rates are the better the smoother the activation functions are, provided that f satisfies an integral representation. We give error bounds not only in Hilbert spaces but also in general Sobolev spaces Wmr(Ω). Finally, we apply our results to a class of perceptrons and present a sufficient smoothness condition on f guaranteeing the integral representation.  相似文献   

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§1Introduction LetMnbeann-dimensionalcompactRiemannianmanifoldisometricallyimmersedinto an(n+p)-dimentionalcompleteandsimplyconnectedRiemannianmanifoldFn+p(c)with constantcurvaturec.DenotebyKMandHthesectionalcurvatureandmeancurvatureofM respectively.In[10],Yauprovedthefollowingstrikingresult.TheoremA.LetMnbeann-dimensionalorientedcompactminimalsubmanifoldin Sn+p(1).IfthesectionalcurvatureofMisnotlessthanp-12p-1,thenMiseitherthetotally geodesicsphere,thestandardimmersionoftheproductoftw…  相似文献   

18.
The Hamiltonian formalism is developed for mechanical systems described by reparametrization-invariant Lagrangians dependent on the external curvatures of a world line. The complete sets of constraints are constructed for the Lagrangians quadratic in the external curvatures, the Lagrangians proportional to an arbitrary external curvature, and the Lagrangians linear in the first two curvatures. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 1, pp. 130–139, October, 1998.  相似文献   

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Let and be a homogeneous -algebra. We establish bounds for the multiplicity of certain homogeneous -algebras in terms of the shifts in a free resolution of over . Huneke and we conjectured these bounds as they generalize the formula of Huneke and Miller for the algebras with pure resolution, the simplest case. We prove these conjectured bounds for various algebras including algebras with quasi-pure resolutions. Our proof for this case gives a new and simple proof of the Huneke-Miller formula. We also settle these conjectures for stable and square free strongly stable monomial ideals . As a consequence, we get a bound for the regularity of . Further, when is not Cohen-Macaulay, we show that the conjectured lower bound fails and prove the upper bound for almost Cohen-Macaulay algebras as well as algebras with a -linear resolution.

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