Using the Modified Picard Method of Parker and Sochacki [1, 2], we derive a hybrid scheme using the analytical Picard method with approximations to the differential operators. This new method, called Discretized Picard’s Method, uses approximations in the space dimensions to compute derivatives but utilizes a continuous approximation in the time dimension. We illustrate the method using finite ...

The synthesis of functionalized 2-oxo-2H-coumarin derivatives has been studied by a one-pot reaction of o-hydroxybenzaldehyde, ethyl 2-bromoacetate and triphenylphosphine in the presence of catalytic amount of triethyl amine in EtOAc, water or under solvent free conditions. We have found the best results obtained under solvent free condition.

Cellulose sulfuric acid is an efficient metal-free catalyst for the synthesis of 1,3,5-trisubstituted pyrazoles via the condensation of 1,3-diketones and hydrazines. The reaction was carried out in Solvent-free condition at room temperature and the products were isolated in good to excellent yields. Mild reaction conditions, as well as ease of operation and workup are some advantages of the pro...

This work describes a fast, mild, convenient and simple method for preparing of nitrogen heterocyclic derivatives by MCR reaction under solvent-free condition.

In this paper, we propose a new framework to predict visual scanpaths of observers while they freely watch a visual scene. The visual fixations are inferred from bottom-up saliency and several oculomotor biases. Bottom-up saliency is represented by a saliency map whereas the oculomotor biases (saccade amplitudes and saccade orientations) are modeled using public eye tracking datasets. Our exper...

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An important open problem in wormhole routing has been to find a necessary and sufficient condition for deadlock-free adaptive routing. Recently, Duato has solved this problem for a restricted class of adaptive routing algorithms. In this paper, a necessary and sufficient condition is proposed that can be used for any adaptive or nonadaptive routing algorithm for wormhole routing, as long as on...

The goal of this paper is to derive in the two-dimensional case necessary and sufficient minimality conditions in terms of the second variation for the functional v 7→ ∫ Ω ( |∇v| + χ{v>0}Q ) dx, introduced in a classical paper of Alt and Caffarelli. For a special choice of Q this includes water waves. The second variation is obtained by computing the second derivative of the functional along su...

We consider the problem of learning a function from samples with `2-bounded noise. In the simplest agnostic learning setting, the number of samples required for robust estimation depends on a condition number that can be arbitrarily large. We show how to improve this dependence in two natural extensions of the setting: a query access setting, where we can estimate the function at arbitrary poin...