32 research outputs found
Low Energy Electron Diffraction with Microscopic Resolution
We report on the development of a Scanning Low Energy Diffraction Microscope, operating in the range of 250 to 1000 eV primary energy. By discriminating against inelastically scattered electrons, low energy electron diffraction (LEED) patterns are obtained from areas of about 100 nm in size. By selecting a particular diffracted beam dark-field images of the surface structure are obtained in the scanning mode. Examples are given for polycrystalline Si and clean and adsorbate covered Si (111) surfaces
Lebesgue regularity for differential difference equations with fractional damping
We provide necessary and sufficient conditions for the existence and unique-ness of solutions belonging to the vector-valued space of sequences ďż˝(Z, X) forequations that can be modeled in the formÎu(n)+Îu(n)=Au(n)+G(u)(n)+ (n), n â Z,,>0,âĽ0,where X is a Banach space, â ďż˝(Z, X), A is a closed linear operatorwith domain D(A) defined on X,andG is a nonlinear function. The oper-ator Îdenotes the fractional difference operator of order >0inthesense of GrĂźnwald-Letnikov. Our class of models includes the discrete timeKlein-Gordon, telegraph, and Basset equations, among other differential differ-ence equations of interest. We prove a simple criterion that shows the existenceof solutions assuming that f is small and that G is a nonlinear term
A Neuroendocrine Carcinoma of Undetermined Origin in a Dog
In this report, we describe a case of neuroendocrine carcinoma of undetermined
origin in a dog. Necropsy revealed scattered small neoplastic nodules in the
bilateral lungs and a small nodule in the parapancreatic lymph node.
Histopathologically, both pulmonary and lymph nodal nodules showed a similar
histologic pattern, with neoplastic cells being arranged in diffusely
proliferating sheet-like cellular nests separated by variable amounts of fibrous
septa, sometimes forming rosettes and duct-like structures. Scattered small
necrotic foci and invasion to fibrous septa were typically observed. Neoplastic
cells showed round to oval-shaped nuclei with prominent nucleoli and abundant
eosinophilic cytoplasm that were positive for Grimeliusâ silver impregnation
staining and immunostaining with cytokeratin, synaptophysin, vasoactive
intestinal peptide and chromogranin A, indicative of the development of a
neuroendocrine carcinoma. However, judging from the distribution of tumors
lacking the portion suggestive of the primary site in any organ examined, as
well as no further indication of differentiation potential of neoplastic cells,
this tumor has so far been diagnosed as neuroendocrine carcinoma of undetermined
origin
Maximal â
[EN] We provide a characterization for the existence and uniqueness of solutions in the space of vector-valued sequences l(p) (Z, X)for the multiterm fractional delayed model in the form
Delta(alpha)u(n) + lambda Delta(beta)u(n) = Lambda u(n) + u(n-tau) + f(n), n is an element of Z, alpha, beta is an element of R+, tau is an element of Z, lambda is an element of R,
where X is a Banach space, A is a closed linear operator with domain D(A) defined on X, f is an element of l(p)(Z,X) and Delta(Gamma) denotes the Grunwald-Letkinov fractional derivative of order Gamma > 0. We also give some conditions to ensure the existence of solutions when adding nonlinearities. Finally, we illustrate our results with an example given by a general abstract nonlinear model that includes the fractional Fisher equation with delay.The second author was supported by MEC, MTM2016-75963-P and PID2019-105011GB-I00 and GVA/2018/110.Girona, I.; Murillo Arcila, M. (2021). Maximal l(p)-regularity of multiterm fractional equations with delay. Mathematical Methods in the Applied Sciences. 44(1):853-864. https://doi.org/10.1002/mma.679285386444