Accumulation Point

2008 ◽  
Keyword(s):  
Accumulation Point

scholarly journals ON -K2 FOR NORMAL SURFACE SINGULARITIES

1998 ◽  
Vol 09 (06) ◽  
pp. 653-668 ◽  
Author(s):  
HAO CHEN ◽  
SHIHOKO ISHII
Keyword(s):  
Lower Bound ◽  
Positive Integer ◽  
Rational Number ◽  
Accumulation Point ◽  
Normal Surface ◽  
Accumulation Points ◽  
Surface Singularities

In this paper we show the lower bound of the set of non-zero -K2 for normal surface singularities establishing that this set has no accumulation points from above. We also prove that every accumulation point from below is a rational number and every positive integer is an accumulation point. Every rational number can be an accumulation point modulo ℤ. We determine all accumulation points in [0, 1]. If we fix the value -K2, then the values of pg, pa, mult, embdim and the numerical indices are bounded, while the numbers of the exceptional curves are not bounded.

scholarly journals MORSE SPECTRUM FOR NONAUTONOMOUS DIFFERENTIAL EQUATIONS

2008 ◽  
Vol 08 (03) ◽  
pp. 351-363 ◽  
Author(s):  
FRITZ COLONIUS ◽  
PETER E. KLOEDEN ◽  
MARTIN RASMUSSEN
Keyword(s):  
Differential Equations ◽  
Finite Time ◽  
Accumulation Point ◽  
Morse Decomposition ◽  
Finite Time Lyapunov Exponents ◽  
The Past ◽  
Accumulation Points ◽  
Morse Spectrum ◽  
Nonautonomous Differential Equations ◽  
Linear Cocycle

The concept of a Morse decomposition consisting of nonautonomous sets is reviewed for linear cocycle mappings w.r.t. the past, future and all-time convergences. In each case, the set of accumulation points of the finite-time Lyapunov exponents corresponding to points in a nonautonomous set is shown to be an interval. For a finest Morse decomposition, the Morse spectrum is defined as the union of all of the above accumulation point intervals over the different nonautonomous sets in such a finest Morse decomposition. In addition, Morse spectrum is shown to be independent of which finest Morse decomposition is used, when more than one exists.

Improved Convergence Properties of the Relaxation Schemes of Kadrani et al. and Kanzow and Schwartz for MPEC

2018 ◽  
Vol 35 (01) ◽  
pp. 1850008
Author(s):  
Na Xu ◽  
Xide Zhu ◽  
Li-Ping Pang ◽  
Jian Lv
Keyword(s):  
Linear Dependence ◽  
Constraint Qualification ◽  
Constraint Qualifications ◽  
Accumulation Point ◽  
Stationary Points ◽  
Nondegeneracy Condition ◽  
Equilibrium Constraints ◽  
Convergence Properties ◽  
Constant Rank Constraint Qualification ◽  
Relaxation Schemes

This paper concentrates on improving the convergence properties of the relaxation schemes introduced by Kadrani et al. and Kanzow and Schwartz for mathematical program with equilibrium constraints (MPEC) by weakening the original constraint qualifications. It has been known that MPEC relaxed constant positive-linear dependence (MPEC-RCPLD) is a class of extremely weak constraint qualifications for MPEC, which can be strictly implied by MPEC relaxed constant rank constraint qualification (MPEC-RCRCQ) and MPEC relaxed constant positive-linear dependence (MPEC-rCPLD), of course also by the MPEC constant positive-linear dependence (MPEC-CPLD). We show that any accumulation point of stationary points of these two approximation problems is M-stationarity under the MPEC-RCPLD constraint qualification, and further show that the accumulation point can even be S-stationarity coupled with the asymptotically weak nondegeneracy condition.

scholarly journals Topographic and vegetation effects on snow accumulation in the southern Sierra Nevada: a statistical summary from lidar data

2016 ◽  
Vol 10 (1) ◽  
pp. 257-269 ◽  
Author(s):  
Z. Zheng ◽  
P. B. Kirchner ◽  
R. C. Bales
Keyword(s):  
Sierra Nevada ◽  
Snow Depth ◽  
Point Cloud ◽  
Accumulation Point ◽  
Snow Accumulation ◽  
Slope Aspect ◽  
Conifer Forest ◽  
Vegetation Effects ◽  
Cloud Data ◽  
Depth Measurement

Abstract. Airborne light detection and ranging (lidar) measurements carried out in the southern Sierra Nevada in 2010 in the snow-free and peak-snow-accumulation periods were analyzed for topographic and vegetation effects on snow accumulation. Point-cloud data were processed from four primarily mixed-conifer forest sites covering the main snow-accumulation zone, with a total surveyed area of over 106 km2. The percentage of pixels with at least one snow-depth measurement was observed to increase from 65–90 to 99 % as the sampling resolution of the lidar point cloud was increased from 1 to 5 m. However, a coarser resolution risks undersampling the under-canopy snow relative to snow in open areas and was estimated to result in at least a 10 cm overestimate of snow depth over the main snow-accumulation region between 2000 and 3000 m, where 28 % of the area had no measurements. Analysis of the 1 m gridded data showed consistent patterns across the four sites, dominated by orographic effects on precipitation. Elevation explained 43 % of snow-depth variability, with slope, aspect and canopy penetration fraction explaining another 14 % over the elevation range of 1500–3300 m. The relative importance of the four variables varied with elevation and canopy cover, but all were statistically significant over the area studied. The difference between mean snow depth in open versus under-canopy areas increased with elevation in the rain–snow transition zone (1500–1800 m) and was about 35 ± 10 cm above 1800 m. Lidar has the potential to transform estimation of snow depth across mountain basins, and including local canopy effects is both feasible and important for accurate assessments.

scholarly journals Effect of noise on the dynamics of a complex map at the period-tripling accumulation point

2004 ◽  
Vol 69 (3) ◽  
Author(s):  
Olga B. Isaeva ◽  
Sergey P. Kuznetsov ◽  
Andrew H. Osbaldestin
Keyword(s):  
Accumulation Point

scholarly journals L q-solutions to the Cosserat spectrum in bounded and exterior domains

Analysis ◽  
2006 ◽  
Vol 26 (1) ◽  
Author(s):  
Stephan Weyers
Keyword(s):  
Accumulation Point ◽  
Exterior Domains ◽  
Finite Multiplicity ◽  
Cosserat Spectrum ◽  
Infinite Multiplicity

SummaryIfλ = 1 is an eigenvalue of infinite multiplicity and λ = 2 is an accumulation point of eigenvalues of finite multiplicity. For the

Effect of toroidicity during lower-hybrid mode conversion

1987 ◽  
Vol 38 (1) ◽  
pp. 27-41
Author(s):  
S. Riyopoulos ◽  
S. M. Mahajan
Keyword(s):  
Mode Conversion ◽  
Wide Spectrum ◽  
Perturbation Technique ◽  
Accumulation Point ◽  
Density Fluctuations ◽  
Wave Number ◽  
Lower Hybrid ◽  
Hybrid Mode ◽  
Zeroth Order ◽  
Eigenvalue Spectrum

The effect of toroidicity during lower-hybrid mode conversion is examined by treating the wave propagation in an inhomogeneous medium as an eigenvalue problem for ω2 (m, n), m, n poloidal and toroidal wavenumbers. Since the fre-quency regime near ω = ω2LH is an accumulation point for the eigenvalue spectrum, the degenerate perturbation technique must be applied. The toroidal eigenmodes are constructed by a zeroth-order superposition of monochromatic solutions with different poloidal dependence m; thus they generically exhibit a wide spectrum in k‖ for given fixed ω2 even for small inverse aspect ratio є. When the average 〈k‖〉 is in the neighbourhood of kmin, the minimum wave-number for accessibility of the mode conversion regime, it is possible that excitation of toroidal modes rather than geometrie optics may determine the wave coupling to the plasma. Our results are not changed significantly by a small amount of dissipation. The level of density fluctuations in modem tokamaks, on the other hand, may cause enough k‖ scattering to mask the toroidicity effects. Nevertheless, it is shown that a wide k‖ spectrum excited by a monochromatic pump will persist even with vanishing fluctuation level.

Resonant Decay Near an Accumulation Point

1997 ◽  
Vol 09 (02) ◽  
pp. 227-241
Author(s):  
Christopher King ◽  
Roger Waxler
Keyword(s):  
Quantum Mechanics ◽  
Exponential Decay ◽  
Accumulation Point ◽  
Model System ◽  
Physical Models ◽  
Stable States ◽  
Perturbed System ◽  
Embedded Eigenvalues

We consider the quantum mechanics of a model system in which meta-stable states arise through perturbation of a sequence of embedded simple eigenvalues with an embedded accumulation point. It is shown that the embedded eigenvalues become resonances in the perturbed system. These resonances also accumulate, and the position of the accumulation point is unchanged. The positions of the resonances are estimated uniformly up to the accumulation point. The meta-stable states associated with these resonances have the usual approximately exponential decay with time. Some applications to physical models are discussed.

Regional Differences in Cystine Accumulation Point to a Sutural Delivery Pathway to the Lens Core

2007 ◽  
Vol 48 (3) ◽  
pp. 1253 ◽  
Author(s):  
Ling Li ◽  
Julie Lim ◽  
Marc D. Jacobs ◽  
Joerg Kistler ◽  
Paul J. Donaldson
Keyword(s):  
Regional Differences ◽  
Accumulation Point

scholarly journals Bifurcation for Second-Order Hamiltonian Systems with Periodic Boundary Conditions

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Francesca Faraci ◽  
Antonio Iannizzotto
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Accumulation Point ◽  
Second Order ◽  
Nontrivial Solutions ◽  
Nonautonomous Systems ◽  
Second Order Hamiltonian Systems

Through variational methods, we study nonautonomous systems of second-order ordinary differential equations with periodic boundary conditions. First, we deal with a nonlinear system, depending on a functionu, and prove that the set of bifurcation points for the solutions of the system is notσ-compact. Then, we deal with a linear system depending on a real parameterλ>0and on a functionu, and prove that there existsλ∗such that the set of the functionsu, such that the system admits nontrivial solutions, contains an accumulation point.

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