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91.
In this paper we give the precise index growth for the embedded hypersurfaces of revolution with constant mean curvature
(cmc) 1 in (Delaunay unduloids). When n=3, using the asymptotics result of Korevaar, Kusner and Solomon, we derive an explicit asymptotic index growth rate for finite
topology cmc 1 surfaces with properly embedded ends. Similar results are obtained for hypersurfaces with cmc bigger than 1
in hyperbolic space.
Received: 6 July 2000; in final form: 10 September 2000 / Published online: 25 June 2001 相似文献
92.
Bräuniger T Kempgens P Harris RK Howes AP Liddell K Thompson DP 《Solid state nuclear magnetic resonance》2003,23(1-2):62-76
Beta-sialons are ceramic phases occurring in the SiO(2)-Si(3)N(4)-AlN-Al(2)O(3) system. A series of samples with differing compositions has been investigated by magic-angle spinning nuclear magnetic resonance (NMR) spectroscopy and powder X-ray diffraction (XRD). Although the constituent nitrogen nuclei occupy positions of low symmetry in the beta-sialon structure, 14N NMR spectra could be recorded for the samples examined. The origin of the 14N signal could be traced to the presence of an aluminium nitride (AlN) impurity phase with the help of 27Al NMR and XRD results. Similarly, the existence of Al(2)O(3) grains could be readily detected for a number of samples. Thus, the combination of 14N and 27Al NMR is shown to be an especially effective tool in identifying and characterizing impurity phases in sialon ceramics, complementing the results obtained from standard XRD analysis. 相似文献
93.
Xavier Bonnefond Pierre Maréchal Walter Cedric Simo Tao Lee 《Set-Valued and Variational Analysis》2018,26(2):265-275
Considering a general linear ill-posed equation, we explore the duality arising from the requirement that the discrepancy should take a given value based on the estimation of the noise level, as is notably the case when using the Morozov principle. We show that, under reasonable assumptions, the dual function is smooth, and that its maximization points out the appropriate value of Tikhonov’s regularization parameter. The numerical relevance of our approach is established by means of an illustrative example from nonparametric instrumental regression, a standard problem in statistics. 相似文献
94.
Using the functional renormalization group (FRG) we study the thermal fluctuations of elastic objects (displacement field u, internal dimension d) pinned by a random potential at low temperature T, as prototypes for glasses. A challenge is how the field theory can describe both typical (minimum energy T = 0) configurations, as well as thermal averages which, at any non-zero T as in the phenomenological droplet picture, are dominated by rare degeneracies between low lying minima. We show that this occurs through an essentially non-perturbative thermal boundary layer (TBL) in the (running) effective action Γ [u] at T > 0 for which we find a consistent scaling ansatz to all orders. The TBL describes how temperature smoothes the singularities of the T = 0 theory and contains the physics of rare thermal excitations (droplets). The formal structure of this TBL, which involves all cumulants of the coarse grained disorder, is first explored around d = 4 using a one-loop Wilson RG. Next, a more systematic exact RG (ERG) method is employed, and first tested on d = 0 models where it can be pushed quite far. There we obtain precise relations between TBL quantities and droplet probabilities (those are constrained by exact identities which are then checked against recent exact results). Our analysis is then extended to higher d, where we illustrate how the TBL scaling remains consistent to all orders in the ERG and how droplet picture results can be retrieved. Since correlations are determined deep in the TBL (by derivatives of Γ [u] at u = 0), it remains to be understood (in any d) how they can be retrieved (as u = 0+ limits in the non-analytic T = 0 effective action), i.e., how to recover a T = 0 critical theory. This formidable “matching problem” is solved in detail for d = 0, N = 1 by studying the (partial) TBL structure of higher cumulants when points are brought together. We thereby obtain the β-function at T = 0, all ambiguities removed, displayed here up to four loops. A discussion of the d > 4 case and an exact solution at large d are also provided. 相似文献
95.
Pierre Bérard 《manuscripta mathematica》1990,69(1):261-266
In this note we give an extension of Bochner's vanishing theorem to complete manifolds; this generalizes earlier results of
J. Dodziuk, K.D. Elworthy and S. Rosenberg.
This research was partially done under the E.E.C. Contract # SC 1-0105-C “GADGET” at the C.N.R.S. U.R.A. 188 相似文献
96.
Themistoklis P. Sapsis Pierre F.J. Lermusiaux 《Physica D: Nonlinear Phenomena》2009,238(23-24):2347-2360
In this work we derive an exact, closed set of evolution equations for general continuous stochastic fields described by a Stochastic Partial Differential Equation (SPDE). By hypothesizing a decomposition of the solution field into a mean and stochastic dynamical component, we derive a system of field equations consisting of a Partial Differential Equation (PDE) for the mean field, a family of PDEs for the orthonormal basis that describe the stochastic subspace where the stochasticity ‘lives’ as well as a system of Stochastic Differential Equations that defines how the stochasticity evolves in the time varying stochastic subspace. These new evolution equations are derived directly from the original SPDE, using nothing more than a dynamically orthogonal condition on the representation of the solution. If additional restrictions are assumed on the form of the representation, we recover both the Proper Orthogonal Decomposition equations and the generalized Polynomial Chaos equations. We apply this novel methodology to two cases of two-dimensional viscous fluid flows described by the Navier–Stokes equations and we compare our results with Monte Carlo simulations. 相似文献
97.
We study the quantum nonlinear response to an applied electric field E of a one-dimensional pinned charge-density wave or Luttinger liquid in the presence of disorder. From an explicit construction of low-lying metastable states and of bounce instanton solutions between them, we demonstrate quantum creep v=e(-c/E(1/2)) as well as a sharp crossover at E=E(*) towards a linear response form consistent with variable-range hopping arguments, but dependent only on electronic degrees of freedom. 相似文献
98.
Pierre Gharghouri 《International Journal of Mathematical Education in Science & Technology》2013,44(2):281-285
This note describes a simple method of generating a random sample of N pairs (U i ,?W i ) from a population whose elements have two characteristics U and W associated with a known coefficient of correlation. Although the method described is extremely advantageous when Platonic bodies are used, it can be generalized to include any discrete uniform distribution. 相似文献
99.
We address the question of determining the eigenvalues \({\lambda_{n}}\) (listed in nondecreasing order, with multiplicities) for which Courant’s nodal domain theorem is sharp i.e., for which there exists an associated eigenfunction with \({n}\) nodal domains (Courant-sharp eigenvalues). Following ideas going back to Pleijel (1956), we prove that the only Courant-sharp eigenvalues of the flat equilateral torus are the first and second, and that the only Courant-sharp Dirichlet eigenvalues of the equilateral triangle are the first, second, and fourth eigenvalues. In the last section we sketch similar results for the right-angled isosceles triangle and for the hemiequilateral triangle. 相似文献
100.
In this Letter, we report single-mode fibers made of chalcogenide glasses with low loss in the 5-12μm range. Glasses from the Ge-As-Te-Se system were optimized to prevent nucleation and to exhibit low density of charge carriers. Single-mode fibers were obtained through the rod-in-tube method by substituting 2% Te/Se between the core and cladding glasses. The resulting single-mode fibers had a core diameter of 30μm and exhibited losses of ~6 dB/m at 10.6μm, and as low as 3-4dB/m in the 6-10μm range. 相似文献