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 �(Z, X) forequations that can be modeled in the formΔu(n)+Δu(n)=Au(n)+G(u)(n)+ (n), n ∈ Z,,>0,≥0,where X is a Banach space, ∈ �(Z, X), A is a closed linear operatorwith domain D(A) defined on X,andG is a nonlinear function. The oper-ator Δdenotes the fractional difference operator of order >0inthesense of Grünwald-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 Grimelius’ 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

The leafminer Liriomyza trifolii (Diptera: Agromyzidae) encapsulates its koinobiont parasitoid Halticoptera circulus (Hymenoptera: Pteromalidae): implications for biological control

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Maximal ℓ

[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