Essential cohomology of finite groups

In this paper we prove that a finite group G with Cohen-Macaulay mod p cohomology will have non-trivial undetectable elements in if and only if G is a p-group such that every element of order p in G is central. Applications and examples are also provided. Received: April 18, 1996     

Application of Adapted-Bubbles to the Helmholtz Equation with Large Wavenumbers in 2D

An adapted-bubbles approach which is a modification of the residual-free bubbles (RFB) method, is proposed for the Helmholtz problem in 2D. A new two-level finite element method is introduced for the approximations of the bubble functions. Unlike the other equations such as the advection-diffusion equation, RFB method when applied to the Helmholtz equation, does not depend on another stabilized method to obtain approximations to the solutions of the sub-problems. Adapted-bubbles (AB) are obtained by a simple modification of the sub-problems. This modification increases the accuracy of the numerical solution impressively. We provide numerical experiments with the AB method up to $ch = 5$ where $c$ is the wavenumber and $h$ is the mesh size. Numerical tests show that the AB method is better by far than higher order methods available in the literature.     

Synthesis,Spectral Characterization and Antimicrobial Activity of Some Transition Metal Complexes of 1,3‐Bis(1H‐benzimidazol‐2‐yl)‐2‐oxapropane

1,3‐Bis(1H‐benzimidazol‐2‐yl)‐2‐oxapropane ( L ) complexes with Fe(NO₃)₃, CoCl₂, Co(NO₃)₂, Ni(NO₃)₂, CuCl₂, Cu(ClO₄)₂, PdCl₂, CdI₂, Hg(NO₃)₂ were synthesized and characterized by elemental analysis, molar conductivity, magnetic moment, TGA, FT‐IR, NMR, ESI‐MS, fluorescence spectroscopy. Also, the crystal structure of 1,3‐bis(1H‐benzimidazol‐2‐yl)‐2‐oxapropane]dichlorocobalt(II), [Co( L )Cl₂], complex is reported that it has distorted trigonal bipyramidal geometry. Antibacterial activities of the compounds were evaluated using the disk diffusion method against six bacteria and Candida albicans. The Hg(II) complex shows superior activity toward S. epidermidis and E. coli whereas the other complexes are ineffective except the Co(NO₃)₂ complex: it showed weak activity toward all of the microorganisms.     

Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method

In this article, the sub‐equation method is presented for finding the exact solutions of a nonlinear fractional partial differential equations. For this, the fractional complex transformation method has been used to convert fractional‐order partial differential equation to ordinary differential equation. The fractional derivatives are described in Jumarie's the modified Riemann–Liouville sense. We apply to this method for the nonlinear time fractional differential equations. With the aid of symbolic computation, a variety of exact solutions for them are obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

The reaction of thiophenoxide with amino-substituted chloro-cyclotriphosphazenes

In the present work, a series of aminocyclotriphosphazene containing sulfur group compounds have been synthesised and characterised by elemental analysis, mass (MS), ¹H and ³¹P NMR spectroscopies. The formation of thiophenoxy-substituted aminocyclotriphosphazenes could be explained by different mechanisms based on primary or secondary amino-substituted cyclotriphosphazenes. Compounds 3, 5 and 7 could be formed by a proton abstraction-chloride elimination and 9, 11 and 13 may be constituted both the S_N² and S_N¹ reaction mechanisms, respectively. These mechanisms are supported by the crystal structures of 5 and 13. Molecular and crystal structures of 5 and 13 have been characterised by X-ray crystallography. The structures of 5 and 13 are monoclinic and have space groups P2₁/n.     

Counting and enumerating aggregate classifiers

We propose a generic model for the “weighted voting” aggregation step performed by several methods in supervised classification. Further, we construct an algorithm to enumerate the number of distinct aggregate classifiers that arise in this model. When there are only two classes in the classification problem, we show that a class of functions that arises from aggregate classifiers coincides with the class of self-dual positive threshold Boolean functions.     

Extremely sensitive sandwich assay of kanamycin using surface-enhanced Raman scattering of 2-mercaptobenzothiazole labeled gold@silver nanoparticles

Herein, we report the development of extremely sensitive sandwich assay of kanamycin using a combination of anti-kanamycin functionalized hybrid magnetic (Fe₃O₄) nanoparticles (MNPs) and 2-mercaptobenzothiazole labeled Au-core@Ag-shell nanoparticles as the recognition and surface-enhanced Raman scattering (SERS) substrate, respectively. The hybrid MNPs were first prepared via surface-mediated RAFT polymerization of N-acryloyl-l-glutamic acid in the presence of 2-(butylsulfanylcarbonylthiolsulfanyl) propionic acid-modified MNPs as a RAFT agent and then biofunctionalized with anti-kanamycin, which are both specific for kanamycin and can be collected via a simple magnet. After separating kanamycin from the sample matrix, they were sandwiched with the SERS substrate. According to our experimental results, the limit of detection (LOD) was determined to be 2 pg mL⁻¹, this value being about 3–7 times more than sensitive than the LOD of previously reported results, which can be explained by the higher SERS activity of silver coated gold nanoparticles. The analysis time took less than 10 min, including washing and optical detection steps. Furthermore, the sandwich assay was evaluated for investigating the kanamycin specificity on neomycin, gentamycin and streptomycin and detecting kanamycin in artificially contaminated milk.     

On weaker forms for concepts in theory of topological groupoids

In this paper, we investigate the topologically weak concepts of topological groupoids by giving the concepts of α-topological groupoid and α-topological subgroupoid. Furthermore, we show the role of the density condition to allow α-topological subgroupoid inherited properties from α-topological groupoid and the irresoluteness property for the structure maps in α-topological groupoid is studied. We also give some results about the fibers of α-topological groupoids.