Synthesis of Novel α‐(Acyloxy)‐α‐(quinolin‐4‐yl)acetamides by a Three‐Component Reaction between an Isocyanide,Quinoline‐4‐carbaldehyde,and Arenecarboxylic Acids

Novel α‐(acyloxy)‐α‐(quinolin‐4‐yl)acetamides were synthesized by the Passerini three‐component reaction between an isocyanide, quinoline‐4‐carbaldehyde, and arenecarboxylic acids in H₂O. The reactions were carried out in one pot at room temperature with quantitative yields.     

1-Methylimidazolium tetrafluoroborate [Hmim][BF4]: an efficient acidic ionic liquid catalyst for insertion of α-diazo compounds into the N–H bonds of amines

The reusable acidic ionic liquid, 1-methylimidazolium tetrafluoroborate [Hmim][BF₄], was found to be an effective catalyst for the insertion of α-diazoacetate into the N–H bonds of amines. The corresponding products were obtained in good yields and short reaction times via a simple procedure. The catalyst could be recycled and reused without any noticeable decrease in its activity.     

Reversed‐phase vortex‐assisted liquid–liquid microextraction: A new sample preparation method for the determination of amygdalin in oil and kernel samples

A novel, simple, and rapid reversed‐phase vortex‐assisted liquid–liquid microextraction coupled with high‐performance liquid chromatography has been introduced for the extraction, clean‐up, and preconcentration of amygdalin in oil and kernel samples. In this technique, deionized water was used as the extracting solvent. Unlike the reversed‐phase dispersive liquid–liquid microextraction, dispersive solvent was eliminated in the proposed method. Various parameters that affected the extraction efficiency, such as extracting solvent volume and its pH, vortex, and centrifuging times were evaluated and optimized. The calibration curve shows good linearity (r² = 0.9955) and precision (RSD < 5.2%) in the range of 0.07–20 μg/mL. The limit of detection and limit of quantitation were 0.02 and 0.07 μg/mL, respectively. The recoveries were in the range of 96.0–102.0% with relative standard deviation values ranging from 4.0 to 5.1%. Unlike the conventional extraction methods for plant extracts, no evaporative and re‐solubilizing operations were needed in the proposed technique.     

Copper/Graphene/Clay Nanohybrid: A Highly Efficient Heterogeneous Nanocatalyst for the Synthesis of Novel 1,2,3‐Triazolyl Carboacyclic Nucleosides via ‘Click’ Huisgen 1,3‐Dipolar Cycloaddition

A very mild and highly efficient synthesis of some novel 1H‐1,2,3‐triazolyl carboacyclic nucleosides via a ‘Click’ Huisgen cycloaddition of N‐propargyl nucleobases and azido alcohols using Cu/aminoclay/reduced graphene oxide nanohybrid (Cu/AC/r‐GO nanohybrid) as nanocatalyst is described. The preparation and characterization of Cu/AC/r‐GO nanohybrid are discussed. This catalyst was characterized by X‐ray diffraction, FT‐IR, TEM, and energy‐dispersive analysis of X‐ray techniques. Cu/AC/r‐GO nanohybrid is a stable and highly efficient heterogeneous nanocatalyst that can be easily prepared, used, and restored from the reaction mixture by simple filtration, and reused for many consecutive trials without significant decrease in activity.     

A deterministic,multi-item inventory model with supplier selection and imperfect quality

This paper considers the scenario of supply chain with multiple products and multiple suppliers, all of which have limited capacity. We assume that received items from suppliers are not of perfect quality. Items of imperfect quality, not necessarily defective, could be used in another inventory situation. Imperfect items are sold as a single batch, prior to receiving the next shipment, at a discounted price. The demand over a finite planning horizon is known, and an optimal procurement strategy for this multi-period horizon is to be determined. Each of products can be sourced from a set of approved suppliers, a supplier-dependent transaction cost applies for each period in which an order is placed on a supplier. A product-dependent holding cost per period applies for each product in the inventory that is carried across a period in the planning horizon. Also a maximum storage space for the buyer in each period is considered. The decision maker, the buyer, needs to decide what products to order, in what quantities, with which suppliers, and in which periods. Finally, a genetic algorithm (GA) is used to solve the model.     

Artinian cofinite modules over complete Noetherian local rings

Let (R, m) be a complete Noetherian local ring, I an ideal of R and M a nonzero Artinian R-module. In this paper it is shown that if p is a prime ideal of R such that dim R/p = 1 and (0:M p) is not finitely generated and for each i ? 2 the R-module Ext _R ⁱ (M,R/p) is of finite length, then the R-module Ext _R ¹ (M, R/p) is not of finite length. Using this result, it is shown that for all finitely generated R-modules N with Supp(N) ? V (I) and for all integers i ? 0, the R-modules Ext _R ⁱ (N,M) are of finite length, if and only if, for all finitely generated R-modules N with Supp(N) ? V (I) and for all integers i ? 0, the R-modules Ext _R ⁱ (M,N) are of finite length.     

Novel optical polarizer design based on metasurface nano aperture for biological sensing in mid-infrared regime

Since Metasurfaces are playing important roles in optical devices such as optical polarizers and detectors, in this article, we have proposed a novel shape of nano aperture antenna for mid-infrared applications such as bio-sensing and other potential optical applications based on plasmonic characteristic of the gold layer over the SiN substrate. The transmittance tensor is obtained for vertical and horizontal linear polarization and base on boundary condition of the metasurface, the circular polarizations are extracted which are confirmed by the electric field distributions. We have shown by the parametric studies that the phase difference is altered by the gap and slot width and so with the dimension modification, we are able to achieve circular polarizer in the optical range. The biological materials with a thickness of 80 nm have then been placed over the metasurface layer and the figures of merits have been obtained. We have revealed that when the circular polarization is osculated to the metasurface at a special frequency the linear polarization is obtained in the other side of the metasurface. The nano aperture has been modeled and the finite difference time domain calculations are performed in CST Microwave Studio as a commercial full wave simulation software.     

A new HPM for ordinary differential equations

In this paper, we introduce a new version of the homotopy perturbation method (NHPM) that efficiently solves linear and non‐linear ordinary differential equations. Several examples, including Euler‐Lagrange, Bernoulli and Ricatti differential equations, are given to demonstrate the efficiency of the new method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Two-Dimensional Legendre Wavelets for Solving Time-Fractional Telegraph Equation

In this paper, we develop an accurate and efficient Legendre wavelets method for numerical solution of the well known time-fractional telegraph equation. In the proposed method we have employed both of the operational matrices of fractional integration and differentiation to get numerical solution of the time-telegraph equation. The power of this manageable method is confirmed. Moreover, the use of Legendre wavelet is found to be accurate, simple and fast.