A simple nonconforming quadrilateral finite element

We introduce and analyze a simple nonconforming quadrilateral finite element and then we derive optimal a priori error estimates for arbitrary regular quadrilaterals. The idea of extension to some non-conforming elements for three-dimensional hexahedrons is also presented.     

2‐Arylhydrazono‐3‐oxopropanals in heterocyclic synthesis: Synthesis of arylazopyrazole,arylazoisoxazole and dialkylpyridazine‐5,6‐dicarboxylate derivatives. New one‐step synthesis of arylazopyrimidines

A novel synthesis of arylpyrazole, isoxazole, dialkyl 1,6‐dihydropyridazine 5,6‐dicarboxylate derivatives and a new one‐step synthesis of azolopyrimidines under microwave‐assisted conditions are reported.     

Selective Monoesterification of Unprotected Mono and Disaccharides

Abstract

Under mild conditions, treatment of unprotected methyl-α-D-glucopyranoside, N-acetylglucosamine and maltose with triphenylphosphine, diethylazodicarboxylate and equimolar amount of various carboxylic acids allowed regioselective 6-O-esterifications (6′-O for maltose) of the carbohydrate without esterification of other hydroxyl groups. This reaction found an application in the synthesis of liposoluble, labelled sugars and hydrosoluble polymers.     

Heterocyclic Synthesis with Nitriles: Synthesis of Pyrazolopyrimidine and Pyrazolopyridine Derivatives

The reaction of N ₁-substituted-5-amino-4-cyanopyrazoles with malononitrile and diethylmalonate occurs with formation of 6-substituted pyrazolo[3,4-d]pyrimidines, and pyrazolo[3,4-b]pyridines respectively. The structures of the products and conceivable mechanisms are discussed.     

Augmented hybrid finite element method for domain decomposition

We present an Augmented Hybrid Finite Element Method for Domain Decompositon. In this method, finite element approximations are defined independently on each subdomain and do not match at interface. This dows the user to mda local change of design, of meshes on one aubdomain without modifying other subdomains. Optimal reaults are obtained for a second-order model problem.     

Proximal methods for a class of bilevel monotone equilibrium problems

We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a simple proximal method. Under mild conditions, the weak convergence of the sequences generated by the algorithm is obtained. Using this result we obtain corollaries which improve several corresponding results in this field.     

Moving immersed boundary method

A novel implicit immersed boundary method of high accuracy and efficiency is presented for the simulation of incompressible viscous flow over complex stationary or moving solid boundaries. A boundary force is often introduced in many immersed boundary methods to mimic the presence of solid boundary, such that the overall simulation can be performed on a simple Cartesian grid. The current method inherits this idea and considers the boundary force as a Lagrange multiplier to enforce the no‐slip constraint at the solid boundary, instead of applying constitutional relations for rigid bodies. Hence excessive constraint on the time step is circumvented, and the time step only depends on the discretization of fluid Navier‐Stokes equations, like the CFL condition in present work. To determine the boundary force, an additional moving force equation is derived. The dimension of this derived system is proportional to the number of Lagrangian points describing the solid boundaries, which makes the method very suitable for moving boundary problems since the time for matrix update and system solving is not significant. The force coefficient matrix is made symmetric and positive definite so that the conjugate gradient method can solve the system quickly. The proposed immersed boundary method is incorporated into the fluid solver with a second‐order accurate projection method as a plug‐in. The overall scheme is handled under an efficient fractional step framework, namely, prediction, forcing, and projection. Various simulations are performed to validate current method, and the results compare well with previous experimental and numerical studies.