Synthesis and antiviral activity of novel imidazo[2,1-b]thiazoles coupled with morpholine and thiomorpholines

Herein described the synthesis and antiviral evaluation of a novel series of morpholine and thio-morpholine coupled imidazo[2,1-b]thiazoles. The three-step reaction sequence involving the condensation of 1,3-dichloroacetone with thiourea followed by coupling with morpholine and thiomorpholine and finally cyclization with substituted α-bromoacetophenones yielded the desired imidazothiazoles 7(a–l) . Screening of all the new compounds for their in vitro antiviral activity against influenza virus A/Puerto Rico/8/34 (H1N1) in MDCK cells, resulted in two potent analogs, 7d (IC₅₀: 1.1 μM, C₅₀: >300 μM, SI = 273) and 7e (IC₅₀: 2.0 μM, C₅₀: >300 μM, SI = 150), with a favorable toxicity profile and are the best anti-influenza hit analogs for further structural optimization.     

A New Class of Stabilized WEB-Spline-Based Mesh-Free Finite Elements for the Approximation of Maxwell Equations

The objective of this article is to discuss the existence and the uniqueness of a weighted extended B-spline-(WEB-spline) based discrete solution for the Maxwell equations in low frequency limit. The domain is composed of insulating and conducting regions. This problem has saddle point structure where the electric field in insulating region is the Lagrange multiplier that forces curl-free constraint on the magnetic field.     

WEB‐spline based mesh‐free finite element analysis for the heat equation and the time‐dependent Navier–Stokes equation: A survey

In this article, we give some numerical techniques and error estimates using web‐spline based mesh‐free finite element method for the heat equation and the time‐dependent Navier–Stokes equations on bounded domains. The web‐spline method uses weighted extended B‐splines on a regular grid as basis functions and does not require any grid generation. We demonstrate the method by providing numerical results for the Poisson's and stationary Stokes equation. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Algorithmic analysis of theMAP/PH/1 retrial queue

In this paper the distribution of the maximum number of customers in a retrial orbit for a single server queue with Markovian arrival process and phase type services is studied. Efficient algorithm for computing the probability distribution and some interesting numerical examples are presented.     

Chow-Witt groups and Grothendieck-Witt groups of regular schemes

Let A be a noetherian commutative Z[1/2]-algebra of Krull dimension d and let P be a projective A-module of rank d. We use derived Grothendieck-Witt groups and Euler classes to detect some obstructions for P to split off a free factor of rank one. If d?3, we show that the vanishing of its Euler class in the corresponding Grothendieck-Witt group is a necessary and sufficient condition for P to have a free factor of rank one. If d is odd, we also get some results in that direction. If A is regular, we show that the Chow-Witt groups defined by Morel and Barge appear naturally as some homology groups of a Gersten-type complex in Grothendieck-Witt theory. From this, we deduce that if d=3 then the vanishing of the Euler class of P in the corresponding Chow-Witt group is a necessary and sufficient condition for P to have a free factor of rank one.     

Equipment scheduling problem under disruptions in mail processing and distribution centres

This paper addresses the production and workforce scheduling problem under disruptions in United States Postal Service mail processing facilities. These facilities contain a large variety of equipment and employ a non-homogeneous workforce that work on shifts of various lengths and start times. Disruptions such as demand fluctuation and absenteeism happen and may significantly change demand and the size of workforce. How to adjust production plans and workforce schedules through the use of overtime and flexible employees in the face of these disruptions to meet the service commitment is a challenging problem yet to be solved. This problem is modelled as a large-scale integer program, which contains equipment scheduling, shift scheduling and overtime management, and break assignment modules. Problems of realistic size are solved efficiently through an LP-based decomposition algorithm. Comprehensive experiments have been designed to investigate the effects of the use of overtime, the control of absenteeism, and the importance of integrating equipment and workforce scheduling simultaneously. The model integrates seamlessly with other research studies and provides the necessary and critical tools to manage the resources in a facility on a routine basis.     

Homotopy analysis method with a non-homogeneous term in the auxiliary linear operator

We demonstrate the efficiency of a modification of the normal homotopy analysis method (HAM) proposed by Liao [2] by including a non-homogeneous term in the auxiliary linear operator (this can be considered as a special case of “further generalization” of HAM given by Liao in [2]). We then apply the modified method to a few examples. It is observed that including a non-homogeneous term gives faster convergence in comparison to normal HAM. We also prove a convergence theorem, which shows that our technique yields the convergent solution.     

Subgrid Modeling of Turbulent Premixed Flames in the Flamelet Regime

Large eddy simulation (LES) models for flamelet combustion are analyzed by simulating premixed flames in turbulent stagnation zones. ALES approach based on subgrid implementation of the linear eddy model(LEM) is compared with a more conventional approach based on the estimation of the turbulent burning rate. The effects of subgrid turbulence are modeled within the subgrid domain in the LEM-LES approach and the advection (transport between LES cells) of scalars is modeled using a volume-of-fluid (VOF) Lagrangian front tracking scheme. The ability of the VOF scheme to track the flame as a thin front on the LES grid is demonstrated. The combined LEM-LES methodology is shown to be well suited for modeling premixed flamelet combustion. The geometric characteristics of the flame surfaces, their effects on resolved fluid motion and flame-turbulence interactions are well predicted by the LEM-LES approach. It is established here that local laminar propagation of the flamelets needs to be resolved in addition to the accurate estimation of the turbulent reaction rate. Some key differences between LEM-LES and the conventional approach(es) are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

A constrained optimization approach to finite element mesh smoothing

The quality of a finite element solution has been shown to be affected by the quality of the underlying mesh. A poor mesh may lead to unstable and/or inaccurate finite element approximations. Mesh quality is often characterized by the “smoothness” or “shape” of the elements (triangles in 2-D or tetrahedra in 3-D). Most automatic mesh generators produce an initial mesh where the aspect ratio of the elements are unacceptably high. In this paper, a new approach to produce acceptable quality meshes from a topologically valid initial mesh is presented. Given an initial mesh (nodal coordinates and element connectivity), a “smooth” final mesh is obtained by solving a constrained optimization problem. The variables for the iterative optimization procedure are the nodal coordinates (excluding, the boundary nodes) of the finite element mesh, and appropriate bounds are imposed on these to prevent an unacceptable finite element mesh. Examples are given of the application of the above method for 2- and 3-D meshes generated using automatic mesh generators. Results indicate that the new method not only yields better quality elements when compared with the traditional Laplacian smoothing, but also guarantees a valid mesh unlike the Laplacian method.