Chorded Cycles

A chord is an edge between two vertices of a cycle that is not an edge on the cycle. If a cycle has at least one chord, then the cycle is called a chorded cycle, and if a cycle has at least two chords, then the cycle is called a doubly chorded cycle. The minimum degree and the minimum degree-sum conditions are given for a graph to contain vertex-disjoint chorded (doubly chorded) cycles containing specified elements of the graph, i.e., specified vertices, specified edges as cycle-edges, specified paths, or specified edges as chords. Furthermore, the minimum degree condition is given for a graph to be partitioned into chorded cycles containing specified edges as cycle-edges.     

On vertex-disjoint cycles and degree sum conditions

This paper considers a degree sum condition sufficient to imply the existence of $k$ vertex-disjoint cycles in a graph $G$. For an integer $t\ge 1$, let ${\sigma }_t\left(G\right)$ be the smallest sum of degrees of $t$ independent vertices of $G$. We prove that if $G$ has order at least $7k+1$ and ${\sigma }_4\left(G\right)\ge 8k?3$, with $k\ge 2$, then $G$ contains $k$ vertex-disjoint cycles. We also show that the degree sum condition on ${\sigma }_4\left(G\right)$ is sharp and conjecture a degree sum condition on ${\sigma }_t\left(G\right)$ sufficient to imply $G$ contains $k$ vertex-disjoint cycles for $k\ge 2$.     

A natural bond orbital analysis of aryl‐substituted polyfluorinated carbanions: negative hyperconjugation

Aryl‐substituted polyfluorinated carbanions, ArCHR_f^? where R_f = CF₃ ( 1 ), C₂F₅ ( 2 ), i‐C₃F₇ ( 3 ), and t‐C₄F₉ ( 4 ), were analyzed by means of the natural bond orbital (NBO) theory at the B3LYP/6‐311+G(d,p) computational level. A lone pair NBO at the formal anionic center carbon (Cα) was not found in the Lewis structure. Instead, significant donor/acceptor NBO interactions between π(Cα‐C1) and σ*(Cβ‐F) or σ*(Cβ‐Cγ) were observed for 1 , 2 , 3a (strong electron‐withdrawing substituent, from p‐CF₃ to p‐NO₂), and 4 . Their second‐order donor/acceptor perturbation interaction energy, E(2), values decreased with the increase of the stability of carbanions. A larger E(2) value corresponds to longer Cβ‐F and Cβ‐Cγ bonds and a shorter Cα‐Cβ bond, indicating that the E(2) values can be associated with the negative hyperconjugation of the Cβ‐F and Cβ‐Cγ bonds. In accordance with this, the E(2) values for π(Cα‐C1) → σ*(Cβ‐F) were linearly correlated with the ΔG^o_β‐F values (an empirical measure of β‐fluorine negative hyperconjugation obtained from an increased acidity). In 3b (weak electron‐withdrawing substituents, from H to m‐NO₂) very large E(2) values for LP(Fβ) → π*(Cα‐Cβ) were obtained. This was attributed to the Cβ‐F bond cleavage and the Cα‐Cβ double bond formation in the Lewis structure that is caused by the extremely strong negative hyperconjugation of the Cβ‐F bond.     

CIDEP Created by the Quenching of Photo-Excited Tryptophan at Protein Surface: A Challenge to CIDEP Probing of Protein Structural Changes

Quenching of the triplet excited state of molecular tryptophan by nitroxide radical in 1,4-dioxane and water solutions was investigated by means of time-resolved electron paramagnetic resonance (EPR) and Fourier-transform (FT)-EPR. The chemically induced dynamic electron polarization (CIDEP) signals with net emissive phase were recorded at these quenching events and were analyzed through radical-triplet pair mechanism. The CIDEP time profiles were well reproduced by Bloch and kinetic equations, assuming radical-triplet pair mechanism with the appropriate quenching rate constants. From a comparison of the simulation and the experiment, CIDEP enhancement factor in 1,4-dioxane was determined to be −30 × P _eq, where P _eq is the spin polarization of nitroxide at thermal equilibrium. Net emissive CIDEP was also observed by FT-EPR measurements on the nitroxide quenching of the triplet excited state of tryptophan residue in α-lactalbumin. Magnitude of CIDEP created in α-lactalbumin/nitroxide system depends on the pH condition of α-lactalbumin solution, which is related to protein folding dynamics. We argue the CIDEP mechanism at the α-lactalbumin surface and propose a possibility of a novel CIDEP method to probe a protein surface and structural changes.     

Effective reduction of critical current for current-induced magnetization switching by a Ru layer insertion in an exchange-biased spin valve

Recently, it has been predicted that a spin-polarized electrical current perpendicular to plane directly flowing through a magnetic element can induce magnetization switching through spin-momentum transfer. In this Letter, the first observation of current-induced magnetization switching (CIMS) in exchange-biased spin valves (ESPVs) at room temperature is reported. The ESPVs show the CIMS behavior under a sweeping dc current with a very high critical current density. It is demonstrated that a thin ruthenium (Ru) layer inserted between a free layer and a top electrode effectively reduces the critical current densities for the CIMS. An "inverse" CIMS behavior is also observed when the thickness of the free layer increases.     

Radical polymerizations of 4-pentamethyldisilylstyrenes

Radical polymerization of 4-pentamethyldisilylstyrene ( 1 ) and 4-pentamethyldisilyl-α-methylstyrene ( 2 ) have been conducted. Monomer reactivity ratious (r₁ and r₂) of 1 and 2 with styrene (M₁) were measured with Fineman-Ross plots. The resonance factor (Q) and polar factor (e) of a Q–e scheme for 1 were conculated with the r₁ and r₂ values. The inductive effect (σ_I) resonance effect (σ) of the pentamethyldisily group were monitored with the ₁H- and ₁₃C-NMR spectra of 1 . The magnitudes of σ_I and σ were found to be analogous to those of the trimethylsilyl group, indicating that the disilyl group shows a net electron-withdrawal effect     

A novel tripodal ligand, tris[(4'-methyl-2,2'-bipyridyl-4-yl)methyl]carbinol and its trinuclear Ru(II)/Re(I) mixed-metal complexes: synthesis, emission properties, and photocatalytic CO2 reduction

A novel tripodal ligand, tris[(4'-methyl-2,2'-bipyridyl-4-yl)methyl]carbinol (L), has been synthesized. The spectroscopic, electrochemical, and photocatalytic properties of the new trinuclear complexes (Ru(2)Re and RuRe(2)) linked by the tripodal bridging ligand L are then investigated. In addition, 2-fold-improved photocatalytic activities were obtained in the case of these trinuclear complexes compared to the mixtures of the appropriate monometallic model complexes in the reduction of CO(2) under visible irradiation.     

Relationship between the crystal structures of LiMn1.5Ni0.5O4 and LiMn1.5Ni0.45Fe0.05O4 and their internal resistances as cathode materials for lithium ion batteries

Journal of Solid State Electrochemistry - It has been reported that the partial substitution of Fe for Ni in LiMn1.5Ni0.5O4 improves the rate capability of batteries wherein it is used as a cathode...