The location of median paths on grid graphs

In this paper we consider the location of a path shaped facility on a grid graph. In the literature this problem was extensively studied on particular classes of graphs as trees or series-parallel graphs. We consider here the problem of finding a path which minimizes the sum of the (shortest) distances from it to the other vertices of the grid, where the path is also subject to an additional constraint that takes the form either of the length of the path or of the cardinality. We study the complexity of these problems and we find two polynomial time algorithms for two special cases, with time complexity of O(n) and O(nℓ) respectively, where n is the number of vertices of the grid and ℓ is the cardinality of the path to be located. The literature about locating dimensional facilities distinguishes between the location of extensive facilities in continuous spaces and network facility location. We will show that the problems presented here have a close connection with continuous dimensional facility problems, so that the procedures provided can also be useful for solving some open problems of dimensional facilities location in the continuous case.     

Three component reactions：An efficient and green synthesis of 3, 4-dihydropyrimidin-2-(1H)-ones and thiones using silica gel-supported L-pyrrolidine-2-carboxylic acid-4-hydrogen sulfate

An environmentally benign aqueous protocol for the synthesis of 3,4-dihydropyrimidin-2-(1H)-ones and thiones promoted by a green catalyst,silica gel-supported L-pyrrolidine-2-carboxylic acid-4-hydrogen sulfate,has been developed.The use of nontoxic,thermally stable and inexpensive amino acid catalyst makes the process simple with minimal amount of chemical waste.Compared with classical Biginelli reaction conditions,this new method has the advantages of high yields and simple workup procedures.     

Preparation of a dual-functionalized fumed silica nanoparticle catalysis for synthesis of azaluorenone derivatives

Research on Chemical Intermediates - A dual-functional silica-based catalyst was prepared by treating fumed silica with amino-containing silane then 1,4-butane sultone. The presence of functional...     

Decorations of graphene oxide with cisplatin toward investigation of fluorescence quencher on regulatory sequence of BRCA1 and BRCA2

Journal of the Iranian Chemical Society - Herein, we investigated the interaction of cisplatin loaded on GO (GO@CDDP) with two regulatory sequences, BRCA1 and BRCA2, synthesized from ssDNA based on...     

One‐pot,four‐component synthesis of 1,3,4‐oxadiazole derivatives containing a ferrocene unit and their antimicrobial activity

A four‐component reaction between aromatic carboxylic acids, (N‐isocyanimino)triphenylphosphorane, ferrocenecarbaldehyde and dibenzylamine is reported. This approach is an efficient, simple and high‐yield procedure for the synthesis of 1,3,4‐oxadiazole derivatives containing a ferrocene unit. The antimicrobial activities of the products were investigated against Staphylococcus aureus and Pseudomonas aeruginosa in in vitro and in vivo assays. Copyright © 2015 John Wiley & Sons, Ltd.     

Three-component solvent-free synthesis of 5-substituted-1H-tetrazoles catalyzed by unmodified nanomagnetite with microwave irradiation or conventional heating

Research on Chemical Intermediates - A convenient, rapid, and highly efficient procedure for synthesis of 5-substituted-1H-tetrazoles was developed via multicomponent domino Knoevenagel...     

1,3-Dibromo-5,5-dimethylhydantoin(DBH)/kaolin:An efficient reagent system for the synthesis of 14-aryl-14H-dibenzo[a,j]xanthenes under solvent-free conditions

1,3-Dibromo-5,5-dimethylhydantoin,has been used as an efficient catalyst for the synthesis of 14-aryl-14H-dibenzo[a,j]xanthenes in the presence of kaolin.All reactions are performed in the absence of solvent in relatively short reaction times in good to high yields.