Fast data extrapolating

Data-extrapolating (extension) technique has important applications in image processing on implicit surfaces and in level set methods. The existing data-extrapolating techniques are inefficient because they are designed without concerning the specialities of the extrapolating equations. Besides, there exists little work on locating the narrow band after data extrapolating—a very important problem in narrow band level set methods. In this paper, we put forward the general Huygens’ principle, and based on the principle we present two efficient data-extrapolating algorithms. The algorithms can easily locate the narrow band in data extrapolating. Furthermore, we propose a prediction–correction version for the data-extrapolating algorithms and the corresponding band locating method for a special case where the direct band locating method is hard to apply. Experiments demonstrate the efficiency of our algorithms and the convenience of the band locating method.     

On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals—III: Clusters of saddle points

It is shown how the recently developed Hadamard expansion procedure can be applied to the hyperasymptotic evaluation of Laplace-type integrals containing a large variable when the phase function has a cluster of close-lying saddle points. The modification to this procedure that is required when the saddles in the cluster coalesce to form a single higher-order saddle is discussed. An example is also considered in which there is both a coalescence of saddles and a Stokes phenomenon as the phase of the large variable is allowed to vary. Numerical examples are given to illustrate the accuracy that can be obtained with this new procedure.     

Transfer and Tate’s theorem

Let H be a subgroup of a finite group G, and assume that p is a prime that does not divide |G : H|. In favorable circumstances, one can use transfer theory to deduce that the largest abelian p-groups that occur as factor groups of G and of H are isomorphic. When this happens, Tate’s theorem guarantees that the largest not-necessarily-abelian p-groups that occur as factor groups of G and H are isomorphic. Known proofs of Tate’s theorem involve cohomology or character theory, but in this paper, a new elementary proof is given. It is also shown that the largest abelian p-factor group of G is always isomorphic to a direct factor of the largest abelian p-factor group of H. Received: 17 June 2008     

Asymptotics of the 1/2-dimension,Discrete Airy Equation and its Approximating Differential Equation

A discrete finite difference model is constructed for the Airy equation using a nonstandard scheme formulated by Mickens and Ramadhani. The method of dominant balance is then applied to obtain a first-order difference equation for the solution that increases sufficiently fast as k→∞. We then calculate the corresponding approximating differential equation and obtain its exact solution as well as its “exact” discrete finite difference representation. The application of various symmetry operations allows the determination of the related rapidly decreasing solution and the oscillatory solutions for negative values of x k>=hk, where h=?x.     

Oxidation state characterization in Cr oxides by means of Cr-Kβ emission spectroscopy

High-resolution Kβ spectra of Cr oxide were measured using a non-conventional spectrometer. Theoretical spectra were obtained using the DV-Xα method in order to interpret the Kβ spectrum structures. Kβ spectrum structures were analyzed and spectral parameters show a great sensitivity to the oxidation state and to the Cr-O distance. High-purity samples of CrO₂ were obtained by means of thermal treatment at 513 °C under oxygen pressure of 200 bar. X-ray diffraction patterns show a typical rutile structure, without spurious phases. The CrO₂ data allowed to confirm the linear dependency of the Kβ_1,3 and Kβ_2,5 energy positions with the oxidation state. The energy of the Kβ_2,5 line relative to the Kβ_1,3 line seems to be a suitable parameter for characterization of the oxidation state. The relative Kβ″ transition probability per Cr-O falls exponentially with Cr-O increasing distance. This behaviour was not found in the literature for Cr oxides.     

Microstructural study of different LDH morphologies obtained via different synthesis routes

In order to better understand the relationship between LDH synthesis parameters and their particle sizes, diverse carbonate intercalated NiAl-LDH phases were prepared using different coprecipitation conditions and their structure, microstructure and morphology were characterized. The samples were synthesized by coprecipitation either at constant pH, in strong alkaline medium or using urea decomposition. The influence of a post-synthesis hydrothermal treatment was also investigated. A well crystalline NiAl-CO₃ phase but containing a high stacking fault density was obtained by combining a strong basic medium and hydrothermal treatment at 120 °C for 24 h. Interestingly, the hydrothermal treatment increases the crystallinity of the samples but does not eliminate stacking faults. The crystallite sizes determined by modeling X-ray diffraction peak broadening with linear combinations of spherical harmonics are fully consistent with TEM observations confirming the validity of the approach used and indicating that the particles are probably small single crystals.     

The a.c. susceptibility third harmonic component of NdO1−0.14F0.14FeAs: A flux dynamic magnetic analysis

In this contribution we present the analysis of the third harmonic susceptibility data of the new superconductor NdFeAs_1−0.14F_0.14. ‘Cole-Cole’ polar plots respect to the magnetic frequency of the exciting field are presented and discussed. Data show that NdFeAs_1−0.14F_0.14 exhibit a ‘bulk pinning’ with a 3D flux dynamic character. A comparison of the responses of high T_c materials and an evaluation of theoretical critical states is also presented.     

On the multiplicity and the Cohen-Macaulayness of fiber cones of graded algebras

Let A be a Noetherian local ring with the maximal ideal m and an m-primary ideal J. Let S=?_n≥0S_n be a finitely generated standard graded algebra over A. Set S⁺=?_n>0S_n. Denote by F_J(S)=?_n≥0→(S_n/JS_n) the fiber cone of S with respect to J. The paper characterizes the multiplicity and the Cohen-Macaulayness of F_J(S) in terms of minimal reductions of S⁺.