On the critical graph conjecture

Gol'dberg has recently constructed an infinite family of 3-critical graphs of even order. We now prove that if there exists a p(≥4)-critical graph K of odd order such that K has a vertex u of valency 2 and another vertex v ≠ u of valency ≤(p + 2)/2, then there exists a p-critical graph of even order.     

Total Colourings of Graphs

We prove that the TCC (Total Colouring Conjecture) is true forcomplete r-partite graphs, which extends a result of M. Rosenfeld.We also give an alternative, slightly simpler proof of an earlierresult (which says that the TCC is true for graphs having maximumdegree 3) obtained independently by M. Rosenfeld and N. Vijayaditya.     

The Synthesis of a Novel Strained Diyneparacyclophane and Its Dimer by Metal-Mediated Coupling

Relieve strain with a twist! Synthesis of the paracyclophane 1 and its dimer 2 employed a sequence of metal-mediated couplings. The X-ray analysis of 2 revealed a helical twist inherent in this structure, which created extended arms, that trapped a molecule of solvent. A carboxylic acid derivative of 1 was also prepared, and its structure indicated the diyne rod moiety of 1 is distorted more than in analogous compounds.     

Study on transient local entropy generation in pulsating fully developed laminar flow through an externally heated pipe

This study presents the investigation of transient local entropy generation rate in pulsating fully developed laminar flow through an externally heated pipe. The flow inlet to the pipe is considered as pulsating at a constant period and amplitude (only the velocity oscillates). The simulations are extended to include different pulsating flow cases (sinusoidal flow, step flow, and saw-down flow). To determine the effects of the mean velocity, the period and the amplitude of the pulsating flow on the entropy generation rate, the pulsating flow is examined for various cases of these parameters. Two-dimensional flow and temperature fields are computed numerically with the help of the fluent computational fluid dynamics (CFD) code. In addition to this CFD code, a computer program has been developed to calculate numerically the entropy generation and other thermodynamic parameters by using the results of the calculations performed for the flow and temperature fields. In all investigated cases, the irreversibility due to the heat transfer dominates. The step flow constitutes the highest temperature (about 919 K) and generates the highest total entropy rate (about 0.033 W/K) within the pipe. The results of this study indicate that in the considered situations, the inverse of square of temperature (1/T ²) is more dominant on the entropy generation than the temperature gradients, and that the increase of the mean velocity of the pulsating flow has an adverse effect on the ratio of the useful energy transfer rate to irreversibility rate.     

Cell-Penetrating Peptides: Correlation between Peptide-Lipid Interaction and Penetration Efficiency

Cell-penetrating peptides are used in the delivery of peptides and biologics, with some cell-penetrating peptides found to be more efficient than others. The exact mechanism of how they interact with the cell membrane and penetrate it, however, remains unclear. This study attempts to investigate the difference in free energy profiles of three cell-penetrating peptides (TAT, CPP1 and CPP9) with a model lipid bilayer (DOPC) using molecular dynamics pulling simulations with umbrella sampling. Potential mean force (PMF) and free energy barrier between the peptides and DOPC are determined using WHAM analysis and MM-PBSA analysis, respectively. CPP9 is found to have the smallest PMF value, followed by CPP1 and TAT, consistent with the experimental data. YDEGE peptide, however, does not give the highest PMF value, although it is a non-cell-permeable peptide. YDEGE is also found to form water pores, alongside with TAT and CPP9, suggesting that it is difficult to distinguish true water pore formation from artefacts arising from pulling simulations. On the contrary, free energy analysis of the peptide-DOPC complex at the lipid-water interface with MM-PBSA provides results consistent with experimental data with CPP9 having the least interaction with DOPC and lowest free energy barrier, followed by CPP1, TAT and YDEGE. These findings suggest that peptide-lipid interaction at the lipid-water interface has a direct correlation with the penetration efficiency of peptides across the lipid bilayer.     

Expanding the Ligand Framework Diversity of Carbodicarbenes and Direct Detection of Boron Activation in the Methylation of Amines with CO2

A simple and convergent synthetic strategy used to increase the diversity of the carbodicarbene ligand framework through incorporation of unsymmetrical pendant groups is reported. Structural analysis and spectroscopic studies of ligands and their Rh complexes are reported. Reactivity studies reveal carbodicarbenes as competent organocatalysts for amine methylation using CO₂ as a synthon. A unique B? H‐activated boron–carbodicarbene complex was isolated as a reaction intermediate, providing mechanistic insight into the CO₂ functionalization process.     

Structural, spectroscopic, and electrochemical properties of a series of high-spin thiolatonickel(II) complexes

A series of high-spin thiolatonickel(II) complexes, [PhTttBu]Ni(SR) (PhTttBu = phenyltris((tert-butylthio)methyl)borate; 2, R = triphenylmethyl; 3, R = pentafluorophenyl; 4, R = phenyl), were synthesized via the reaction of [PhTttBu]Ni(NO3) (1) with thiols (RSH) in the presence of triethylamine. The [PhTttBu]Ni(SR) products were isolated and characterized by various physicochemical measurements including X-ray diffraction analyses. These thiolatonickel(II) complexes have a distorted trigonal pyramidal geometry with somewhat different tau values: 0.80 and 0.90 for two crystalline phases of 2, 0.74 for 3, and 0.69 for 4, where tau is a normalized measure of pyramidalization (tau = 0 for tetrahedron, tau = 1 for trigonal pyramid). The electronic absorption spectra display characteristic sulfur-to-nickel(II) charge transfer (CT) bands at 532 nm (7500 M(-1) cm(-1)) for 2, 510 nm (4800 M(-1) cm(-1)) for 3, and 569 nm (4100 M(-1) cm(-1)) for 4. The cyclic voltammograms show a quasi-reversible redox couple at E1/2 = -1.11 V for 2, and reversible redox couples at E1/2 = -1.03 V for 3 and E1/2 = -1.17 V for 4 (vs Fc+/Fc). Correlation between the tau value and the CT intensity was observed: the strong CT intensity results from the high tau value, which provides for strong orbital overlap (2 > 3 > 4). Additionally, the CT transition energy correlates with the reduction potential: both the CT transition energy and potential decrease in the order 3 > 2 > 4, consistent with the influence of decreasing electron withdrawing abilities, R = pentafluorophenyl > triphenylmethyl > phenyl. The three thiolatonickel complexes exhibit dramatically different thermal stabilities. Complex 4 is the least stable, undergoing decomposition to [kappa2-PhBttBuSPh]Ni(eta2-CH2SBut) (5) via net exchange of Ni-SPh and B-CH2SBut groups.