k-Domination and k-Independence in Graphs: A Survey

In 1985, Fink and Jacobson gave a generalization of the concepts of domination and independence in graphs. For a positive integer k, a subset S of vertices in a graph G = (V, E) is k-dominating if every vertex of V − S is adjacent to at least k vertices in S. The subset S is k-independent if the maximum degree of the subgraph induced by the vertices of S is less or equal to k − 1. In this paper we survey results on k-domination and k-independence.     

The cutting stock problem and integer rounding

An integer programming problem is said to have the integer round-up property if its optimal value is given by the least integer greater than or equal to the optimal value of its linear programming relaxation. In this paper we prove that certain classes of cutting stock problems have the integer round-up property. The proof of these results relies upon the decomposition properties of certain knapsack polyhedra.This research was partially supported by National Science Foundation grants ECS-8005350 and 81-13534 to Cornell University.     

Structure and H(2)-Loss Energies of OsHX(H(2))(CO)L(2) Complexes (L = P(t-Bu)(2)Me, P(i-Pr)(3); X = Cl, I, H): Attempted Correlation of (1)J(H-D), T(1min), and DeltaG()

1J(H-D), T(1min) and k(1) for H(2) dissociation from OsHX(H(2))(CO)L(2) have been measured for X = Cl, I, H (L = P(t-Bu)(2)Me or P(i-Pr)(3)), as well as for OsCl(2)(H(2))(CO)(P(i-Pr)(3))(2). For comparison, new data (including previously unobserved coupling constants) have been reported for W(HD)(CO)(3)(P(i-Pr)(3))(2). A comprehensive consideration of T(1min) data for over 20 dihydrogen complexes containing only 1-2 phosphines cis to H(2), together with a consideration of the shortest "conceivable" H-H distance for H(2) bound to a d(4) or d(6) metal, is used to argue that the "fast spinning" model is not appropriate for determining r(H-H) in such complexes. Regarding OsHX(H(2))(CO)L(2), the stronger electron-donor (lighter) halide, when cis to H(2), facilitates loss of H(2). The complete absence of pi-donor ability when X = H renders H(2) loss most difficult. However, a pi-donor trans to H(2) also makes H(2) loss unobservable. Within the series of isoelectronic, structurally analogous Os complexes, a longer H-H bond shows a larger DeltaG() for H(2) loss. However, this correlation does not continue to W(H(2))(CO)(3)(P(i-Pr)(3))(2), which has r(H-H) comparable to that of OsH(halide)(H(2))(CO)(P(i-Pr)(3))(2), but a significantly higher DeltaG(). This may originate from lack of a pi-donor ligand to compensate as H(2) leaves W.     

Enantiospecific synthesis of delta and lambda [Ru(bpy)(2)ppy](+) and [Ru(bpy)(2)quo](+) (bpy = 2,2'-bipyridine,ppy = phenylpyridine-H(+), quo = 8-hydroxyquinolate): (1)H and (13)C NMR studies and X-ray structure determination of rac-[Ru(bpy)(2)quo]PF(6)

In this paper, we describe the enantiospecific synthesis and the complete characterization of the two hexacoordinated ruthenium(II) monocations [Ru(bpy)(2)ppy](+) and [Ru(bpy)(2)quo](+) (bpy = 2,2'-bipyridine, ppy = phenylpyridine-H(+), quo = 8-hydroxyquinolate) in their enantiomeric Delta and Lambda forms. The corresponding enantiomeric excesses (ee's) are determined by (1)H NMR using pure Delta-Trisphat (tris(tetrachlorobenzenedialato)phosphate(V) anion) as a chiral (1)H NMR shift reagent. A complete (1)H and (13)C NMR study has been carried out on rac-[Ru(bpy)(2)ppy]PF(6) and rac-[Ru(bpy)(2)quo]PF(6). Additionally, the X-ray molecular structure of rac-[Ru(bpy)(2)quo]PF(6) is reported; this latter species crystallizes in the monoclinic C2/c space group (a = 22.079 A, b = 16.874 A, c = 17.533 A, alpha = 90 degrees, beta = 109.08 degrees, gamma = 90 degrees ).     

NMR study of Li+ ion dynamics in the perovskite Li(3x)La(1/3-x)NbO3

(7)Li and (6)Li nuclear magnetic resonance (NMR) experiments are carried out on the perovskite Li(3x)La(1/3-x)NbO(3). The results are compared to those obtained on the titanate Li(3x)La(2/3-x)TiO3 (LLTO) in order to investigate the effect, on the lithium ion dynamics, of the total substitution of Nb(5+) for Ti(4+) in the B-site of the ABO(3) perovskites. The XRD patterns analysis reveals that this substitution leads to a change in the distribution of the La(3+) ions in the structure. La(3+) ions distribution is very important, in regard to ionic conductivity, because these immobile ions can be considered as obstacles for the long-range Li+ motion. If compared to the titanates, the compounds of the niobate solid solution have a bigger unit cell volume, a smaller number of La(3+) ions, and a higher number of vacancies. These should favor the motion of the mobile ions into the structure. This is not experimentally observed. Therefore, the interactions between the mobile species and their environment greatly influence their mobility. (7)Li and (6)Li NMR relaxation time experiments reveal that the Li relaxation mechanism is not dominated by quadrupolar interaction. (7)Li NMR spectra reveal the presence of different Li+ ion sites. Some Li+ ions reside in an isotropic environment with no distortion, some others reside in weakly distorted environments. T(1), T(1)(rho), and T(2) experiments allow us to evidence two motions of Li+. As in LLTO, T(1) probes a fast motion of the Li+ ions inside the A-cage of the perovskite structure and T(1)(rho) a slow motion of these ions from A-cage to A-cage. At variance with what has been observed in LLTO, these different Li+ ions can be differentiated through the spin-lattice relaxation times, T(1) and T(1)(rho), as well as through the transverse relaxation time, T(2).     

New route to N-aryl and N-heteroaryl derivatives of 4-hydroxy-3-quinolinecarboxamides

The synthesis of N-aryl and N-heteroaryl substituted 4-hydroxy-3-quinolinecarboxamides 1 is described. The attack of dianions 12 of N-aryl substituted acetamides on the C-4 carbonyl of 4H-3,1-benzoxazin-4-ones 11 gave rise to ketoamides 13 , which smoothly cyclised in the presence of bases to afford quinolinecarboxamides 1 . By this method, a large number of 2-substituted 4-hydroxyquinolinecarboxamides can be prepared.     

Measurements of the Protective Effect of Topically Applied Sunscreens using in vitro Three-dimensional Dermal and Skin Equivalents

Abstract— For preventing or minimizing acute and chronic skin damage caused by UV radiation, the use of sunscreens is probably the most important measure. To screen the protective efficacy of new sunscreen molecules or formulations against UV rays, we evaluated as in vitro testing methods the use of two three-dimensional models, a dermal equivalent (DE) and a skin equivalent (SE). The DE is composed of a porous collagen-glycosaminoglycans-chitosan matrix populated by normal human fibroblasts. The SE is comprised of a fully differentiated epidermis realized by seeding keratinocytes onto the DE. In this study, we demonstrated that the DE and SE models react to the deleterious effects of UVA and UVB. Then, we extended our research to the evaluation of their usefulness for photoprotection trials. Sunscreen agents (Euso-lex 8020 and 6300) and commercially available sunscreens (chemical and physical filter formulations) that protect the skin against either UVA or UVB were evaluated. The tested products were applied (n = 6) topically (10 μL) and incubated for 30 min prior to irradiation over a range of UVA (0-50 J/cm²) or UVB (0-5 J/cm²). The photoprotection provided by the tested sunscreen molecules and formulations was evaluated by measurement of residual cellular viability 24 h postirradiation using the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetra-zolium bromide (MTT) test and assessment of the inflammation response by interleukin-la release assay. When sunscreens were applied prior to UV exposure, a higher residual cellular viability versus control was obtained, demonstrating the photoprotective effects of the tested products. These in vitro models could be used for screening tests to evaluate the protective effects of sunscreen molecules and formulations, especially for UVA trials because there is a lack of consensus for an in vivo method.