The complement of proper power graphs of finite groups

For a finite group $G$, the proper power graph $\mathscr{P}^*(G)$ of $G$ is the graph whose vertices are non-trivial elements of $G$ and two vertices $u$ and $v$ are adjacent if and only if $u \neq v$ and $u^m=v$ or $v^m=u$ for some positive integer $m$. In this paper, we consider the complement of $\mathscr{P}^*(G)$, denoted by ${\overline{\mathscr{P}^*(G)}}$. We classify all finite groups whose complement of proper power graphs is complete, bipartite, a path, a cycle, a star, claw-free, triangle-free, disconnected, planar, outer-planar, toroidal, or projective. Among the other results, we also determine the diameter and girth of the complement of proper power graphs of finite groups.Comment: 29 pages, 14 figures, Lemma 4.1 has been added and consequent changes have been mad

Does Koopmans\u27 Paradigm for 1-Electron Oxidation Always Hold? Breakdown of IP/Eox Relationship for p-Hydroquinone Ethers and the Role of Methoxy Group Rotation

Koopmans’ paradigm states that electron loss occurs from HOMO, thus forming the basis for the observed linear relationships between HOMO/IP, HOMO/Eox, and IP/Eox. In cases where a molecule undergoes dramatic structural reorganization upon 1-electron oxidation, the IP/Eox relationship does not hold, and the origin of which is not understood. For example, X-ray crystallography of the neutral and cation radicals of bicyclo[2.2.1]heptane-annulated p-hydroquinone ethers (THE and MHE) showed that they undergo electron-transfer-induced conformational reorganization and show breakdown of the IP/Eox relationship. DFT calculations revealed that Koopmans’ paradigm still holds true because the electron-transfer-induced subtle conformational reorganization, responsible for the breakdown of IP/Eox relationship, is also responsible for the reordering of HOMO and HOMO-1. Perceived failure of Koopmans’ paradigm in cases of THE and MHE assumes that both vertical and adiabatic electron detachments involve the same HOMO; however, this study demonstrates that the vertical ionization and adiabatic oxidation occur from different molecular orbitals due to reordering of HOMO/HOMO-1. The underpinnings of this finding will spur widespread interest in designing next-generation molecules beyond HQEs, whose electronic structures can be modulated by electron-transfer-induced conformation reorganization

Does Koopmans’ Paradigm for 1-Electron Oxidation Always Hold? Breakdown of IP/E\u3csub\u3eox\u3c/sub\u3e Relationship for \u3cem\u3ep\u3c/em\u3e-Hydroquinone Ethers and the Role of Methoxy Group Rotation

Koopmans’ paradigm states that electron loss occurs from HOMO, thus forming the basis for the observed linear relationships between HOMO/IP, HOMO/Eox, and IP/Eox. In cases where a molecule undergoes dramatic structural reorganization upon 1-electron oxidation, the IP/Eoxrelationship does not hold, and the origin of which is not understood. For example, X-ray crystallography of the neutral and cation radicals of bicyclo[2.2.1]heptane-annulated p-hydroquinone ethers (THE and MHE) showed that they undergo electron-transfer-induced conformational reorganization and show breakdown of the IP/Eox relationship. DFT calculations revealed that Koopmans’ paradigm still holds true because the electron-transfer-induced subtle conformational reorganization, responsible for the breakdown of IP/Eox relationship, is also responsible for the reordering of HOMO and HOMO-1. Perceived failure of Koopmans’ paradigm in cases of THE and MHE assumes that both vertical and adiabatic electron detachments involve the same HOMO; however, this study demonstrates that the vertical ionization and adiabatic oxidation occur from different molecular orbitals due to reordering of HOMO/HOMO-1. The underpinnings of this finding will spur widespread interest in designing next-generation molecules beyond HQEs, whose electronic structures can be modulated by electron-transfer-induced conformation reorganization

Intraradicular Rehabilitation - A Restorative Solution to a non ideal root - A case Report

Aesthetics plays an important role on psychological perspective of an individual. The fracture of an anterior tooth is a common occurrence in young individuals and requires rehabilitation of the affected tooth.This article presents a clinical case of a patient aged 16 years with a structurally compromised, fractured anterior tooth with a short root and open apex reinforced intraradicularly with flowable composite and a light transmitting glass fibre post.KEY WORDS: Trauma, Glass fiber post, Flowable composite, Resin cemen

A Search for Blues Brothers: X-ray Crystallographic/Spectroscopic Characterization of the Tetraarylbenzidine Cation Radical as a Product of Aging of Solid Magic Blue

Magic blue (MB+˙ SbCl6− salt), i.e. tris-4-bromophenylamminium cation radical, is a routinely employed one-electron oxidant that slowly decomposes in the solid state upon storage to form so called ‘blues brothers’, which often complicate the quantitative analyses of the oxidation processes. Herein, we disclose the identity of the main ‘blues brother’ as the cation radical and dication of tetrakis-(4-bromophenyl)benzidine (TAB) by a combined DFT and experimental approach, including isolation of TAB+˙ SbCl6− and its X-ray crystallography characterization. The formation of TAB in aged magic blue samples occurs by a Scholl-type coupling of a pair of MB followed by a loss of molecular bromine. The recognition of this fact led us to the rational design and synthesis of tris(2-bromo-4-tert-butylphenyl)amine, referred to as ‘blues cousin’ (BC: Eox1 = 0.78 V vs. Fc/Fc+, λmax(BC+˙) = 805 nm, εmax = 9930 cm−1 M−1), whose oxidative dimerization is significantly hampered by positioning the sterically demanding tert-butyl groups at the para-positions of the aryl rings. A ready two-step synthesis of BC from triphenylamine and the high stability of its cation radical (BC+˙) promise that BC will serve as a ready replacement for MB and an oxidant of choice for mechanistic investigations of one-electron transfer processes in organic, inorganic, and organometallic transformations

Experimental Investigation on performance of silica fumes as a soil stabilizer for oil contaminated strata

Oil leakage is an environmental issue unnoticed in the present time. The problem of oil leakage and oil contamination is main concern for petroleum harvesting countries. Oil contamination in soil creates health issues in the area surrounding it. The nutrients in the soil get reduced significantly due to oil contamination which makes the land not suitable for cultivation. The oil produces hydrocarbons which makes the civil structures weak and out at risk. The most harmful effects of oil contamination are excessive settlement of structures, breakage of underground pipes, etc. In this project, we are trying to study the effects of oil contamination in the soil and also to find a sustainable solution for it. The soil is contaminated in the percentage from 0 to 20% and the tests on index and engineering properties have been conducted to find the effect of engine oil. In order to stabilize the oil contaminated soil, we use silica fumes as a stabilizing agent. The optimum percentage of silica fume is chosen based on the tests of Index and Engineering properties conducted on the soil with silica fumes. The percentage of oil where the soil properties need stabilization is known and the soil is stabilized with the optimum silica fume percentage

Dynamic Integrated System for Detecting and Fixing Vulnerability Bugs

Bugs are one of the important barriers in the field of software development. Concurrent and frequent bugs are non-deterministic in nature and in the time of vulnerability testing. It is difficult to detect the dynamic bugs with a high representation of vulnerability that causes the damage to the software products. Existing vulnerability testing methods relied on the conventional static testing techniques of finding and fixing the bugs but it does not show a high ratio of they handle or require specific hardware support. It does not include in the clustering approach. To overcome the limitations in the existing techniques, this proposed methods Modified Particle Swarm Optimization (MPSO), Expectation Maximization (EM) Clustering and Variable Neighborhood search. The primary input dataset is preprocessed to obtain the relevant and irrelevant data partition and optimized dataset was given as input to the Modified Particle Swarm Optimization (MPSO) techniqu

Quality in Coriander leaves as influenced by growing conditions

A study was conducted in the plains of Kerala to investigate the performance of coriander leaffor its quality aspects in open and rain shelter conditions. The study suggested that significantlyhigher herbage and biomass yield (g/ plant) was observed from plants grown in rain shelter(9.21 and 12.78) compared to the open field (8.41 and 11.34). Among the varieties, Arka Isharecorded the highest herbage and biomass yield (10.46 and 14.13g/plant) followed by CO-1(8.97and 12.70).There was a significant higher vitamin C content (mg/100g) in open field(189.72) compared to rain shelter ( 124.55) and volatile oil ranging from 0.05-0.06 % in boththe growing conditions and were on par. Total chlorophyll content was recorded more in openfield (1.98) than in rain shelter (1.92) Among the varieties, total chlorophyll was more in CO-4(2.33). However, this need to be confirmed by further studies

Microelectromechnical Systems Inertial Measurement Unit Error Modelling and Error Analysis for Low-cost Strapdown Inertial Navigation System

This paper presents error modelling and error analysis of microelectromechnical systems (MEMS) inertial measurement unit (IMU) for a low-cost strapdown inertial navigation system (INS). The INS consists of IMU and navigation processor. The IMU provides acceleration and angular rate of the vehicle in all the three axes. In this paper, errors that affect the MEMS IMU, which is of low cost and less volume, are stochastically modelled and analysed using Allan variance. Wavelet decomposition has been introduced to remove the high frequency noise that affects the sensors to obtain the original values of angular rates and accelerations with less noise. This increases the accuracy of the strapdown INS. The results show the effect of errors in the output of sensors, easy interpretation of random errors by Allan variance, the increase in the accuracy when wavelet decomposition is used for denoising inertial sensor raw data.Defence Science Journal, 2009, 59(6), pp.650-658, DOI:http://dx.doi.org/10.14429/dsj.59.157