In this paper, several equivalent conditions on the Drazin invertibility of product and difference of idempotents are obtained in a ring. Some results in Banach algebras are extended to the ring case.

This paper introduces a novel feature extraction algorithm called FEUDOR. The features extracted by this method are octagonal homogeneous regions that have different mean square difference compared to their surrounding area. By using integral images we have implemented this algorithm efficiently. We have shown that the repeatability score of FEUDOR under various image transformations is compara...

A cartogram is a type of map used to visualize data. In a map regions are displayed in their true shapes and with their exact relations with the adjacent regions. However, such a map can only be used to demonstrate the actual area values of the regions. Sometimes, we need to display other data on a map, such as population, pollution, electoral votes, production rates, etc. One efficient way to ...

Electrophilic ring opening of spiro-cyclopropanecarboxylated sugars followed by reaction with DBU revealed interesting ring-contraction and ring-expansion reactions depending on the substrate and the kind of hydroxyl protective group present adjacent to the spiro center. A stereoselective method for accessing a new class of carbon chain extended keto-furanoses and C-glycosylated bicyclic compou...

In the title compound, C(30)H(38)O(4)S(2), the centroid of the benzene ring lies on a center of inversion. The thio-phene ring is aligned at 49.8 (1)° with respect to the benzene ring. The alkyl chain adopts an extended zigzag conformation.

In the title mol-ecule, C(29)H(22)ClN(3)S, the quinoline ring system, thio-phene ring and phenyl ring substituents are inclined at angles of 71.70 (7), 59.26 (9) and 81.61 (9)°, respectively, to the 4,5-dihydro-pyrazole ring. In the 4-phenyl-quinoline ring system, the phenyl ring makes a dihedral angle of 62.49 (7)° with mean plane of quinoline ring system. In the crystal structure, mol-ecules ...

We investigate knee-shaped junctions of semiconductor zigzag carbon nanotubes. Two dissimilar octagons appear at such junctions; one of them can reconstruct into a pair of pentagons. The junction with two octagons presents two degenerate localized states at Fermi energy (E(F)). The reconstructed junction has only one state near E(F), indicating that these localized states are related to the oct...