The Anshel-Anshel-Goldfeld (AAG) key-exchange protocol was implemented and studied with the braid groups as its underlying platform. The length-based attack, introduced by Hughes and Tannenbaum, has been used to cryptanalyze the AAG protocol in this setting. Eick and Kahrobaei suggest to use the polycyclic groups as a possible platform for the AAG protocol. In this paper, we apply several known...

This study scrutinizes the complexities of designing and exploring potential energy surfaces systems containing more than twenty atoms with planar tetracoordinate carbons (ptCs). To tackle this issue, we utilized an established design rule to a Naphtho [1,2-b:3,4-b′:5,6-b″:7,8-b′′′]tetrathiophene derivative computationally. process began substituting S CH− units, then replacing three sequential...

The molecule of the title compound, [Na(C(13)H(11)N(3)O)(2)(CH(3)OH)(2)]I, is non-planar, with the Na atom chelated by the O atoms and the N atoms of two N'-(3-pyridylmethyl-ene)benzohydrazide ligands and both O atoms of two methanol ligands. The asymmetric unit consists of one half-mol-ecule. The Na atom is located on a crystallographic centre of inversion. The six-coordinate Na atom adopts a ...

The asymmetric unit of the title compound, C(16)H(14)O(4), consists of one half-mol-ecule of an essentially planar biphenyl-dicarboxylic acid ester, with the complete molecule generated by an inversion centre. The maximum deviation from a least-squares plane through all non-H atoms occurs for the peripheric methyl groups and amounts to 0.124 (2) Å. The solid represents a typical mol-ecular crys...

The investigation of new synthetic routes towards positively charged N-heterocycles is high importance for the further development medicinal chemistry, functional materials, catalysis and other areas application. For accessing acridinium dyes, we previously reported an approach based on aryne-imine-aryne coupling followed by subsequent oxidation acridane intermediates. Herein, now present unusu...

Phytoremediation uses plants and their associated microorganisms in conjunction with agronomic techniques to remove or degrade environmental contaminants. The objective of the field study was to evaluate the effect of vegetation establishment plus fertilizer addition on the biodegradation of alkylated polycyclic aromatic hydrocarbons in a crude oil-contaminated soil. Four replications of the fo...

We describe joint experimental and theoretical studies carried out collaboratively in the authors' labs for understanding the structures and chemical bonding of novel atomic clusters, which exhibit aromaticity. The concept of aromaticity was first discovered to be useful in understanding the square-planar unit of Al4 in a series of MAl4(-) bimetallic clusters that led to discoveries of aromatic...

A classic problem in elastodynamics is the diffraction of time-harmonic stress waves by a pennyshaped crack. It is also a benchmark problem, in that it is the simplest three-dimensional problem for bounded cracks. What happens if the flat circular crack is perturbed? This question motivates the present paper. Recent work is discussed, in which a perturbation theory is developed, based on the go...

Introduction. In this paper the structure of graphs is studied by purely combinatorial methods. The concepts of rank and nullity are fundamental. The first part is devoted to a general study of non-separable graphs. Conditions that a graph be non-separable are given ; the decomposition of a separable graph into its non-separable parts is studied; by means of theorems on circuits of graphs, a me...