Convex Sets in Lexicographic Products of Graphs

Geodesic convex sets, Steiner convex sets, and J-convex (alias induced path convex) sets of lexicographic products of graphs are characterized. The geodesic case in particular rectifies Theorem 3.1 in Canoy and Garces (Graphs Combin 18(4):787–793, 2002).     

Performance analysis of modified optical burst switching (OBS) ring network using dummy node

In the present paper an analytical model of an optical burst switching ring network which is capable to handle the variable incoming traffic intelligently is presented. An efficient node architecture and network operating protocol enhances the data throughput in a congested network. Here we propose a node architecture to ease the traffic congestion in a ring network involving a dummy server connected to backbone of the ring topology to ease the traffic flow into the ring by diverting the packets under the congestion situation. An appropriate mathematical model for the proposed node architecture has been developed employing packet queuing control to estimate the amount of carried traffic for different node parameters and the analysis has been further extended to investigate the network performance under different signaling techniques.     

Modeling and performance analysis of optical WDM node architecture using SRR protocol

In order to enhance the data transport capability and overall throughput of an optical wavelength division multiplexing (WDM) system, a proper node architecture design is necessary. In the present paper a simple node architecture model based on media access control protocols for bursty data traffic of variable time slot duration and data rate has been proposed to decrease the packet loss probability and to increase the efficiency of an optical WDM system using synchronous round robin (SRR) protocol. An appropriate mathematical model has been derived to evaluate performance of the proposed node architecture. It has been observed that the network performance is well controlled through implemented model and the corresponding network design parameters.     

Crystal Structure, Absolute Configuration, Conformational Analysis and Molecular Dynamics Study of the Novel Steroidal Tetrazole Derivative: (25R)-3,12a-diaza-A,C-bishomo-5α-spirostano[3,4-d] [12a,12d] bistetrazole [HS-989]

Abstract  

The X-ray crystal structure of the bistetrazole steroid derivative: (25R)-3,12a-diaza-A,C-bishomo-5α-spirostano[3,4-d] [12a,12d] bistetrazole (HS-989) has been determined at room temperature. The crystals are orthorhombic, space group P2₁2₁2₁ with a = 16.855(1) ?, b = 25.048(2) ?, c = 6.402(1) ?, V = 2702.7(5) ?³ Z = 4, Density (calculated) = 1.250 Mg/m³. The tetrazole-modified 7-membered rings A and C have similar modified uniaxial chair conformations, with pseudo-symmetry m through the extra C–N tetrazole bond; the 6-membered rings B and F are symmetrical chairs; of the 5-membered rings, D is in a half-chair and ring E an envelope conformation; tetrazole rings T1 and T2 are both planar and oriented towards the α-face. The spirostan moiety is β-oriented. Overall the modified steroid skeleton is reasonably flat, with a pseudo-torsion angle C(19)–C(10)···C(13)–C(18) of −6.2°. Conformational sampling, using high temperature SYBYL molecular dynamics was used to investigate different arrangements of the steroid skeleton. Predicted low energy conformations were found to compare favourably in some respects with both X-ray crystallographic and NMR observations but with important differences.     

Pyrazine Derivative as Supramolecular Host for Immobilization of Palladium Nanoparticles for Efficient Suzuki Coupling

Palladium nanoparticles (NPs) have been extensively explored as unique catalyst for carbon-carbon coupling reactions. Nonetheless, because of extreme tendency of nanoparticles to undergo agglomeration, the immobilization of these metal NPs on organic frameworks is an important area of research. The present investigation demonstrates the synthesis of pyrazine derivative PYZ - TA as a supramolecular host for holding co-released Pd NPs derived from the original catalyst (Pd(II)) under standard Suzuki coupling. Unprecedent, physical bars are not required to capture Pd NPs within the pores of supramolecular host. The as obtained catalyst PYZ - TA@Pd exhibits high potential to undergo self-assembly in solid as well as in liquid state. The PYZ - TA@Pd ensemble shows high catalytic activity and recyclability (up to seven cycles) in Suzuki-Miyaura coupling reactions using low palladium loading and provides the corresponding products in excellent yields (up to 98 %). Therefore, this study provides an efficient strategy to develop an easy to synthesize palladium centered solid catalyst through coordination between organic host and Pd NPs.