The sdfem on Shishkin meshes for linear convection-diffusion problems

Summary. We consider singularly perturbed linear elliptic problems in two dimensions. The solutions of such problems typically exhibit layers and are difficult to solve numerically. The streamline diffusion finite element method (SDFEM) has been proved to produce accurate solutions away from any layers on uniform meshes, but fails to compute the boundary layers precisely. Our modified SDFEM is implemented with piecewise linear functions on a Shishkin mesh that resolves boundary layers, and we prove that it yields an accurate approximation of the solution both inside and outside these layers. The analysis is complicated by the severe nonuniformity of the mesh. We give local error estimates that hold true uniformly in the perturbation parameter , provided only that , where mesh points are used. Numerical experiments support these theoretical results. Received February 19, 1999 / Revised version received January 27, 2000 / Published online August 2, 2000     

Evolutionary neighborhood discovery algorithm for agricultural routing planning in multiple fields

Annals of Operations Research - In recent years, operations research in agriculture has improved the harvested yield, reduced the cost and time required for field operations, and maintained...     

Nonlinear Optical Properties of Benzylic Amide [2] Catenanes: A Novel Versatile Photonic Material

Abstract

Benzylic amide catenanes are a class of synthetically-accessible interlocked molecular rings which can rotate one through the other depending on the nature of the local environment. The rings contain four phenyl units each and interlocking also affords their packing in novel, highly interacting ways that may lead to unexpected properties thus opening up the possibility of developing new materials. Third harmonic generation in benzylic amide catenane solutions was measured at a wavelength of γ = 1064 nm, with the fundamental and the harmonic wavelengths in the region of transparency of the material. The thoroughly non resonant value of the hyperpolarisability γ(-3ω; ω, ω, ω) was found to be (6.5 ± 0.7) × 10^?35 esu with a negligible imaginary part, in agreement with the value of (6.8 ± 0.9) × 10^?35 esu calculated from a bond-additivity model of hyperpolarisability. The static second order hyperpolarisability predicted by a Molecular Orbital model was about a factor four less than the experimental value. Second hyperpolarizability values of several solvents were also measured at the fundamental wavelength of γ = 1064 nm.     

Information Field Theory and Artificial Intelligence

Information field theory (IFT), the information theory for fields, is a mathematical framework for signal reconstruction and non-parametric inverse problems. Artificial intelligence (AI) and machine learning (ML) aim at generating intelligent systems, including such for perception, cognition, and learning. This overlaps with IFT, which is designed to address perception, reasoning, and inference tasks. Here, the relation between concepts and tools in IFT and those in AI and ML research are discussed. In the context of IFT, fields denote physical quantities that change continuously as a function of space (and time) and information theory refers to Bayesian probabilistic logic equipped with the associated entropic information measures. Reconstructing a signal with IFT is a computational problem similar to training a generative neural network (GNN) in ML. In this paper, the process of inference in IFT is reformulated in terms of GNN training. In contrast to classical neural networks, IFT based GNNs can operate without pre-training thanks to incorporating expert knowledge into their architecture. Furthermore, the cross-fertilization of variational inference methods used in IFT and ML are discussed. These discussions suggest that IFT is well suited to address many problems in AI and ML research and application.     

Maturation of the lantibiotic subtilin: matrix-assisted laser desorption/ionization time-of-flight mass spectrometry to monitor precursors and their proteolytic processing in crude bacterial cultures.

Bacillus subtilis synthesizes the lanthionine containing 32-amino-acid peptide antibiotic (lanti-biotic) subtilin from a ribosomally generated 56-amino-acid precursor pre-propeptide by extensive posttranslational modifications. Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) was used to monitor the production of matured subtilin within crude samples taken from B. subtilis culture media without prior fractionation. The processing reaction of subtilin was blocked with the serine protease inhibitor phenylmethylsulfonyl fluoride and different subtilin precursor peptides in the molecular mass range up to 6220 were observed. Two of these species were isolated by reversed-phase high-performance liquid chromatography (HPLC) and structurally analyzed by post-source decay MALDI-TOFMS. We provide evidence that the precursor species comprise the posttranslational modified C-terminal part of subtilin to which leader peptide moieties with different chain lengths are attached. These antimicrobial-inactive species could be processed to antibiotic-active subtilin by incubation with culture media of different subtilin-nonproducing B. subtilis strains as indicated by a combination of antimicrobial growth assays and MALDI-TOFMS analyses. These achievements are strong evidence for the sensitivity of MALDI-TOFMS methodology that allows straightforward investigations of analytes even in complex mixtures without time-consuming sample preparations.     

Toward an understanding of white-light generation in cubic media - polarization properties across the entire spectral range

We present an extensive investigation of the polarization properties of a femtosecond-laser-induced white-light (WL) continuum generated in a cubic crystal (CaF(2)). The WL spectrum and threshold energies have been examined for input polarizations with various degrees of ellipticity. For linear input polarization, the WL spectrum shows strong depolarization around the input wavelength, while the preservation of the input polarization is pronounced toward the blue spectral region. The observed depolarization effect has been elucidated in the framework of current models for WL generation.     

A Strong Szegö-Widom Limit Theorem for operators with almost periodic diagonal

The classical Strong Szegö-Widom Limit Theorem describes the asymptotic behavior of the determinants of the finite sections PnT(a)Pn of Toeplitz operators, i.e., of operators which have constant entries along each diagonal. We generalize these results to operators which have almost periodic sequences as their diagonals.