Lambda-fold 2-perfect 6-cycle systems in equipartite graphs

A 6-cycle system of a graph G is an edge-disjoint decomposition of G into 6-cycles. Graphs G, for which necessary and sufficient conditions for existence of a 6-cycle system have been found, include complete graphs and complete equipartite graphs. A 6-cycle system of G is said to be 2-perfect if the graph formed by joining all vertices distance 2 apart in the 6-cycles is again an edge-disjoint decomposition of G, this time into 3-cycles, since the distance 2 graph in any 6-cycle is a pair of disjoint 3-cycles.Necessary and sufficient conditions for existence of 2-perfect 6-cycle systems of both complete graphs and complete equipartite graphs are known, and also of λ-fold complete graphs. In this paper, we complete the problem, giving necessary and sufficient conditions for existence of λ-fold 2-perfect 6-cycle systems of complete equipartite graphs.     

Laser-deposited Cu/α–Al2O3 nanocomposite: experiment and modeling

A Nd:YAG laser operating at a wavelength of 266 or 355 nm is used to deposit a thin layer of copper on the (0 0 0 1)α-Al₂O₃ surface. The formation process is precisely controlled by identification of time distribution of two characteristics: energy and flux density of particles incident on the substrate. For this purpose, the Cu-plasma expansion is described by means of an analytical hydrodynamic model whose self-similar solutions are fitted to the experimental plasma images and time-of-flight spectra. The obtained nanocomposite is examined by the aberration-corrected high-resolution transmission electron microscopy (Cs-HRTEM) method. The results reveal that copper crystals assume one main orientation relative to the substrate (1 1 1)[2 ?1 ?1]Cu \(\Vert\) (0 0 0 1)[?1 ?1 2 0]α–Al₂O₃ and the formed interface has a specific microstructure. To reconstruct the phase boundary region, molecular dynamic (MD) and static (MS) simulations are carried out. The results show that strong bonding between copper and sapphire induces structural changes in the (1 1 1) Cu layer nearest the substrate and leads to formation of the system of partially dissociated dislocations in the next layer. In consequence, the Cu/α–Al₂O₃ interface becomes the semicoherent system. The lattice matching regions of the individual Cu layers are significantly lowered, which results in strong deformations along the closed packed planes. The reconstructed interface is used for Cs-HRTEM image simulation. A good accordance with the experimental results indicates that the MD model correctly maps the microstructure at the phase boundary of the synthesized nanocomposite.     

Spasmodic dysphonia and vocal fold paralysis:Outcomes of voice problems on work-related functioning

Patients at a university voice disorder clinic diagnosed with spasmodicdysphonia (SD, n = 68) or vocal fold paralysis (VFP, n = 57) reported vocal symptoms and adverse work outcomes in contrast to a nondisordered group (ND, n = 68). Patients with SD most frequently cited symptoms of effortfulness (57%) and weakness (54%), VFP cited hoarseness (70%) and weakness (60%), while the nondisordered reported hoarseness (28%). SD and VFP produced greater (p<.05) adverse work outcomes than the nondisordered in the past (SD: 65%, VFP: 41%, ND: 3%), potential future (SD: 78%, VFP: 65%, ND: 19%), and current job performance (SD: 64%, VFP: 46%, ND: 2%). These disorders significantly disrupt socioeconomic outcomes and research is needed to improve functional ability and quality of life.     

Investigation by EPR and ENDOR spectroscopy of the novel 4Fe ferredoxin fromPyrococcus furiosus

The hyperthermophilic archaeonPyrococcus furiosus contains a four-Fe ferredoxin (Pf- Fd) that differs from most other 4Fe-Fd’s in that its [Fe₄S₄] cluster is anchored to protein by only three cysteinyl residues.Pf- Fd also is of interest because in its reduced form, [Fe₄S₄]⁺, the cluster exhibits bothS = 1/2 andS = 3/2 spin states. Addition of excess cyanide ion converts the cluster exclusively to anS = 1/2 state (g₁ = 2.09, g₂ = 1.95, g₃ = 1.92), however dialysis restores the EPR signal of native reduced protein indicating that the cluster is not irreversibly altered by cyanide. Both the native protein and protein in the presence of excess cyanide ion (Pf- Fd 4Fe-CN) were investigated here using the techniques of electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) spectroscopy. In particular,Pf- Fd 4Fe-CN was investigated using¹³CN^? and C¹⁵N^? ligands.¹³C and¹⁵N ENDOR indicated that a single cyanide ion bound directly, with the cluster showing an unusually small contact interaction (a_iso(¹³C)～ ?3 MHz, a_iso(¹⁵N) ～ 0). This is in contrast to cyanide bound to monomeric low-spin Fe(III)-containing proteins such as transferrin and myoglobin, for which the¹³C hyperfine coupling has a large isotropic component (a_iso(¹³C) ≈ ?30 MHz). This small contact interaction is not due to low spin density of Fe, as⁵⁷Fe ENDOR of the singly and triply labeledPf- Fd 4FeCN isotopologs, [⁵⁷FeFe₃S₄]⁺ and [Fe⁵⁷Fe₃S₄]⁺, show hyperfine coupling characteristic for [Fe₄S₄]⁺ clusters, particularly for the Fe to which cyanide binds. Thus, the low spin density on¹³C is not due to low spin density on the Fe ion to which it binds. Further theoretical work is needed to explain the contrast between the strong electronic effect of cyanide ion binding with the low spin density on the ligand.     

1H NMR isotope shifts arising from the substitution of 12C by 13C: application to polycyclic aromatic hydrocarbon anions

Isotope shifts are a well-established tool for structural analysis by NMR. The substitution of a protium with a deuterium is the most widely studied of these effects. However, such studies call for specific deuteration that requires complex synthetic techniques owing to the low natural abundance of deuterium. ¹³C occurs at a higher natural abundance and couples strongly with its attached proton. We have developed and refined a method to reliably observe these much smaller shifts without needing to resort to chemical synthesis. We show that carbon induced isotope shifts reflect structural features. Copyright © 2001 John Wiley & Sons, Ltd.     

On the variation of co-ordinates in subspaces

Summary Let1≦k≦n−1, 2≦n. This paper examines the vectors δ_p(L_k), where L_k is a k-dimensional subspace of an n-dimensional space, and the co-ordinates of δ_p(L_k) are given below by (1.1). For fixed k, the set of such vectors as L_k varies is determined for p=2. For general p, information is given on upper and lower bounds for the sum of the co-ordinates of δ_p(L_k). Dedicated to the sixtieth birthday of Prof. Edgar R. Lorch This research was supported in part by the Office of Naval Research under contract number Nonr 3775(09), NR 047040.     

Temperature dependence of the 1H chemical shift of tetramethylsilane in chloroform, methanol, and dimethylsulfoxide

The chemical shift of tetramethylsilane (TMS) is usually taken to be zero. However, it does vary slightly with temperature, having obvious implications for studies of temperature effects on chemical shifts. In this work, we measure the variation in the chemical shift of TMS with temperature in three solvents, CDCl3, CD3OD, and DMSO-d6, relative to the resonant frequency of 3He gas, which can be reasonably assumed to be temperature independent. In all three solvents, the average temperature coefficient over a wide temperature range is about -6 x 10(-4) ppm/degrees C, a factor of five smaller than that previously reported in the literature. Data are included for 3He resonance frequencies over a temperature range of -110 to +180 degrees C, along with new measurements of volume magnetic susceptibilities of the three solvents and estimates of their temperature dependence. A novel method is used to provide temperature measurement via 2H resonances of methanol and ethylene glycol samples, which can concurrently be used for field/frequency locking.     

Sweet success: Ionic liquids derived from non-nutritive sweeteners

The anions of the sweeteners saccharin and acesulfame form ionic liquids when paired with a variety of organic cations.     

Dual propagation inversion of truncated signals

Fourier transforms occur in a variety of chemical systems and processes. A few examples include obtaining spectral information from correlation functions, energy relaxation processes, spectral densities obtained from force autocorrelation functions, etc. In this article, a new functional transform, named the dual propagation inversion (DPI) is introduced. The DPI functional transform can be applied to a variety of problems in chemistry, such as Fourier transforms of time correlation functions, energy relaxation processes, rate theory, etc. The present illustrative application is to generating the frequency representation of a discrete, truncated time-domain signal. The DPI result is compared with the traditional Fourier transform applied to the same truncated time signal. For both noise-free and noise-corrupted time-truncated signals, the DPI spectrum is found to be more accurate, particularly as the signal is more severely truncated. In the DPI, the distributed-approximating-functional free propagator is used to propagate and denoise the signal simultaneously. Received: 30 January 2000 / Accepted: 6 July 2000 / Published online: 23 November 2000