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81.
许多物理现象可以在数学上描述为受曲率驱动的自由界面运动,例如薄膜和泡沫的演变、晶体生长,等等.这些薄膜和界面的运动常依赖于其表面曲率,从而可以用相应的曲率流来描述,其相关自由界面问题的数值计算和误差分析一直是计算数学领域中的难点.参数化有限元法是曲率流的一类有效计算方法,已经能够成功模拟一些曲面在几类基本的曲率流下的演化过程.本文重点讨论曲率流的参数化有限元逼近,它的产生、发展和当前的一些挑战. 相似文献
82.
《Discrete Mathematics》2022,345(12):113074
It has previously been observed that the limiting gap distribution of the directions to visible points of planar quasicrystals may vanish near zero, that is, there exist planar quasicrystals with a positive limiting minimal normalised gap between the angles of visible points. The exact values of these limiting minimal normalised gaps have not been determined. In this paper we give explicit formulas for the densities of visible points for planar quasicrystals from several families, which include the Ammann–Beenker point set and the vertex sets of some rhombic Penrose tilings. Combining these results with a known characterisation of the limiting minimal gap in terms of a probability measure on an associated homogeneous space of quasicrystals, we give explicit values of the limiting minimal normalised gap between the angles of visible points for several families of planar quasicrystals, in particular, for the Ammann–Beenker point set and for the vertex sets of some rhombic Penrose tilings. We also compare our results with numerical observations. 相似文献
83.
We completely characterize the global phase portraits in the Poincaré disk for all planar Hamiltonian vector fields with linear plus cubic homogeneous terms having a nilpotent saddle at the origin. 相似文献
84.
An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Löwner operator associated with a potential function for the optimization problems with inequality constraints. The favorable properties of both the Löwner operator and the corresponding augmented Lagrangian are discussed. And under some mild assumptions, the rate of convergence of the augmented Lagrange algorithm is studied in detail. 相似文献
85.
New Results on Generalized $c$-Distance Without Continuity in Cone $b$-Metric Spaces over Banach Algebras 下载免费PDF全文
Yan Han & Shaoyuan Xu 《分析论及其应用》2022,38(3):335-350
In this work, some new fixed point results for generalized Lipschitz mappings on generalized $c$-distance in cone $b$-metric spaces over Banach algebras are obtained, not acquiring the condition that the underlying cone should be normal or the
mappings should be continuous. Furthermore, the existence and the uniqueness of the
fixed point are proven for such mappings. These results greatly improve and generalize several well-known comparable results in the literature. Moreover, some examples
and an application are given to support our new results. 相似文献
86.
In this paper, we are interested in the regularity estimates of the nonnegative viscosity super solution of the $β$−biased infinity Laplacian equation $$∆^β_∞u = 0,$$ where $β ∈ \mathbb{R}$ is a fixed constant and $∆^β_∞u := ∆^N_∞u + β|Du|,$ which arises from the random game named biased tug-of-war. By studying directly the $β$−biased infinity Laplacian equation, we construct the appropriate exponential cones as barrier functions to establish a key estimate. Based on this estimate, we obtain the Harnack inequality, Hopf boundary point lemma, Lipschitz estimate and the Liouville property etc. 相似文献
87.
Federico Sánchez-Bringas Ana Irene Ramírez-Galarza 《Annals of Global Analysis and Geometry》1995,13(2):129-140
LetM be a compact orientable surface,I:M R4 an immersion of classC
r
and
a normal unitary smooth vector field. We prove that in the space of pairs (I,
) the family of pairs all whose umbilical points are Darbouxian is generic. 相似文献
88.
On invexity-type nonlinear programming problems 总被引:3,自引:0,他引:3
Z. K. Xu 《Journal of Optimization Theory and Applications》1994,80(1):135-148
In this paper, we propose a new class of nonlinear programing, called SFJ-invex programming. The optimality characterization shows that a problem is SFJ-invex if and only if a Fritz John point together with its multiplier, is a Fritz John saddle point of the problem. Under any constraint qualification assumption, a problem is SFJ-invex if and only if a Kuhn-Tucker point together with its multiplier is a Kuhn-Tucker saddle point of the problem. Furthermore, a generalization of the SFJ-invex, class is developed; the applications to (h, )-convex programming, particularly geometric programming, and to generalized fractional programming provide a relaxation in constraint qualification for differentiable problems to get saddle-point type optimality criteria.The author wishes to thank the referee for helpful comments. 相似文献
89.
The three-component ionic microemulsion system consisting of AOT/water/decane shows an unusual phase behavior in the vicinity
of room temperature. The phase diagram in the temperature-volume fraction (of the dispersed phase) plane exhibits a lower
consolute critical point at about 40 degrees centigrades and 10% volume fraction. A percolation line, starting from the vicinity
of the critical point, cuts across the plane, extending to high volume fraction side at progressively lower temperatures.
In this paper we review the evidence that allows to interpret the phase behavior of our system in terms of interacting spherical
droplets. We also investigate the dynamics of droplets, below and approaching the critical point by dynamic light scattering.
The first cumulant and time evolution of the droplet density correlation function can be quantitatively calculated by assuming
the existence of polydispersed fractal clusters formed by the microemulsion droplets due to attraction. The relaxation phenomena
observed in an extensive set of measurements of electrical conductivity and permittivity close to percolation is also reviewed
and interpreted through the same cluster-forming mechanism, which reproduces the most relevant features of the frequency-dependent
complex dielectric constant of this system.
Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994. 相似文献
90.
Gerard Misiolek 《Proceedings of the American Mathematical Society》1996,124(3):977-982
An example of a geodesic in with conjugate points is given, thus providing an affirmative answer to a question of V.I. Arnold.