In this paper, the well-known nonconforming Morley element for biharmonic equations in two spatial dimensions is extended to any higher dimensions in a canonical fashion. The general -dimensional Morley element consists of all quadratic polynomials defined on each -simplex with degrees of freedom given by the integral average of the normal derivative on each -subsimplex and the integral average...

Hayakawa (1990) has very recently studied the behavior of the power for several large sample tests for the mean direction vector of the Langevin distribution. These tests are not known to possess any non-trivial optimal property. Here we derive some multiparameter locally optimal tests, e.g., best first and second directional derivative tests and locally most mean powerful tests. For the case w...

The proliferation of satellites in the last 30 years has resulted in a similar proliferation of global datasets, not only of the Earth but also of other bodies in the solar system. Measured parameters include topography, temperature, water vapour, electron temperature and density, and the strength of the gravity and magnetic fields, to mention just a few. Directional derivatives and sunshading ...

This work is intended to provide some ideas on the use of a Gaussian-derivative model for visual perception, called the Hermite transform, to extract motion information from an image sequence. Gaussian-derivative operators have long been used in computer vision for feature extraction and are relevant in visual system modeling. A directional energy is defined in terms of the 1-D Hermite transfor...

In this paper, we study the parabolic second-order directional derivative in the Hadamard sense of a vector-valued function associated with circular cone. The The author’s work is supported by National Natural Science Foundation of China (11101248, 11271233), Shandong Province Natural Science Foundation (ZR2012AM016), and Young Teacher Support Program of Shandong University of Technology. The a...

We prove Kantorovich’s theorem on Newton’s method using a convergence analysis which makes clear, with respect to Newton’s Method, the relationship of the majorant function and the non-linear operator under consideration. This approach enable us to drop out the assumption of existence of a second root for the majorant function, still guaranteeing Q-quadratic convergence rate and to obtain a new...

We present a new theory that shows that two images of the same object taken under two different light directions can be made virtually identical by filtering each image by a directional derivative filter. The direction and magnitude of the derivative is generally different for each image, and depends on illumination directions used. The method requires the object surface to be of uniform Lamber...

If φ is an analytic function bounded by 1 on the bidisk D2 and τ ∈ ∂(D2) is a point at which φ has an angular gradient ∇φ(τ) then ∇φ(λ) → ∇φ(τ) as λ → τ nontangentially in D2. This is an analog for the bidisk of a classical theorem of Carathéodory for the disk. For φ as above, if τ ∈ ∂(D2) is such that the lim inf of (1− |φ(λ)|)/(1− ‖λ‖) as λ → τ is finite then the directional derivative D−δφ(τ...

We present an analysis of a recently proposed integral-equation method for the solution of high-frequency electromagnetic and acoustic scattering problems that delivers error-controllable solutions in frequency-independent computational times. Within single scattering configurations the method is based on the use of an appropriate ansatz for the unknown surface densities and on suitable extensi...

This paper is concerned with existence results for inequality problems of type F0(u;v) + Ψ′(u;v) ≥ 0, for all v ∈ X , where X is a Banach space, F : X → R is locally Lipschitz, and Ψ : X → (−∞+∞] is proper, convex, and lower semicontinuous. Here F0 stands for the generalized directional derivative of F and Ψ′ denotes the directional derivative of Ψ. The applications we consider focus on the var...