Characterisation of k-Variegated Graphs, k greater-than-or-equal-to 3

A graph is said to be k-variegated if its vertex set can be partitioned into k equal parts such that each vertex is adjacent to exactly one vertex from every other part not containing it. Bednarek and Sanders [1] posed the problem of characterizing k-variegated graphs. V.N. Bhat-Nayak, S.A. Choudum and R.N. Naik [2] gave the characterization of 2-variegated graphs. In this paper we characterize k-variegated graphs for k greater-or-equal, slanted 3.

Polarized Ethylenes: Structure of 2-Benzoyl-3-dimethylamino-3-methylthlo-2-propenenitrile

C13H14N2OS, M r = 246, is monoclinic, P21/c, with a = 7.214(1), b = 8.935(5), c = 20.243 (6) A, fl =99.42 (2) °, V = 1304.83 ,~3, Z = 4, D m = 1.23, D x =1.25 Mg m -3, p(Mo Ka, 2 = 0.7107 A) = 0.232 mm -~,F(000) = 520. The structure was solved by direct methods and refined to an R value of 0.042 using 1127 intensity measurements. The C=C and C-N bond distances differ considerably from their normal values. An appreciable rotation [38.3(4) °] about the C=C bond is observed, the bond length being 1.414(5)A.This is due to the combination of push-pull and steric effects.

Inhibition of 3-hydroxy-3-methylglutaryl coenzyme a reductase by cytosolic proteins - real or artifact

The inhibitory effect of FeSO4-dependent cytosolic protein on microsomal HMGCoA reductase is on the enzyme activity and not an artifact of loss of the product, mevalonate, through phosphorylation, unlike that of ATP.Mg effect.

Complexes of lanthanide perchlorates with the open-chain pentadentate ligand n,n,$n^{'},n^{'}$-tetramethyl-3,6,9-trioxaundecane diamide

Complexes of lanthanide perchlorates with the ligand N,N,N,N-tetra-methyl-3,6,9-trioxaundecane diamide (TUD) of the composition Ln(TUD)2-(ClO4)3 (Ln triple bond; length as m-dash La, Nd, Ho, Er, Y) were isolated. Electrical conductivity values indicate that all the perchlorate groups are ionic. IR and nuclear magnetic resonance (1H and 13C) data prove that the ligand coordinates to the metal via the three ether oxygens and the two carbonyl oxygens. A probable coordination number of ten can be assigned for all the complexes.

Molecular-Conformation of 1,3-Pyridylphenylureas by H-1 and C-13 NMR-study

1H and 13C NMR spectra are reported for several 1,3-pyridylphenyl ureas. Analysis of the spectra yielded the chemical shifts. The variations in the chemical shifts have been discussed in terms of the molecular conformations.

Studies in terpenoids. Part 42. Synthesis of 3-(2-hydroxyisopropyl)5,8-dimethyl-1,2-naphthoquinone (emmotin-H)

Emmotin-H, a naturally occurring sesquiterpenoid 1,2-naphthoquinone pigment (1) has been synthesised in a four step sequence starting from the known 5,8-dimethyl-4-oxotetralin-2-carboxylic acid (3a). Selenium dioxide oxidation of its methyl ester (3b) gives 3-methoxycarbonyl-5,8-dimethyl-1,2-naphthoquinone (4) which on reductive acetylation affords the corresponding diacetoxynaphthalene ester (5). Its reaction with excess of methylmagnesium iodide is accompanied by aerial oxidation during work-up and furnishes emmotin-H (1).

Influence of Elastic-Constants on Mode-I Stress-Intensity Factors in 3-Dimensional Crack Problems

Plates with V-through edge notches subjected to pure bending and specimens with rectangular edge-through-notches subjected to combined bending and axial pull were investigated (under live-load and stress-frozen conditions) in a completely nondestructive manner using scattered-light photoelasticity. Stress-intensity factors (SIFs) were evaluated by analysing the singular stress distributions near crack-tips. Improved methods are suggested for the evaluation of SIFs. The thickness-wise variation of SIFs is also obtained in the investigation. The results obtained are compared with the available theoretical solutions.

Dialkyl (3-Aryl- 1,2,4-oxadiazol-5-yl)phosphonates: Synthesis and Thermal Behavior-Evidence for Monomeric Alkyl Metaphosphate

Dialkyl (3-aryl-l,2,4-oxadiazol-5-yl)phosphonate6sa -h have been obtained by 1,3-dipolar cycloaddition of arenenitrile oxides 5a-f to dialkyl phosphorocyanidates (4a and 4b) in yields ranging between 30% and 58%. A standardized method for obtaining cyanidates 4a and 4b has been established. The diethyl thiophosphorocyanidate (4c) is less reactive than 4a and 4b, only the 3-(4'-nitrophenyl) derivative 6i being obtainable. While the IR and NMFt spectra of 6a-i were unexceptional, their UV spectra showed evidence of conjugative interaction in high degrees between the phosphonate and heterocyclic moieties as well as a varying conjugative interaction between the heterocyclic and aryl moieties. The oxadiazoles 6a-h are thermally labile and yield trialkyl phosphates 7 as the only identifiable products. A mechanism based on the intermediacy of monomeric alkyl metaphosphate 11 in the formation of trialkyl phosphate was postulated, and supportive evidence in the form of trapping the metaphosphate with acetophenone has been obtained.

Structure Of 5'-Deoxy-5',6-Epithio-5,6-Dihydro-2',3'-O-Isopropylideneuridine, C12h16n2o5s

Mr=300.33 , triclinic, P1, a=5.635 (2), b=11.077(2), c=11.582(2)A, a= 70.48 (1), fl= 88.16 (3), y=80.56(3) ° , V= 670.325 A3, Z=2, D x = 1.49 Mg m -3, Cu Ka, n= 1.54184 ,A, g = 2.308mm -1, F(000)=316, T=301K, R=0.054, R w = 0.093 for 1944 observed counter reflections. The sulphur position with respect to the dihydrouracil ring, which is of possible relevance to the action of thymidylate synthetase, is axial in molecule A and equatorial in B. Both molecules show the anti conformation about the glycosidic bond [torsion angle C(6)-N(1)-C(1')-O(4'), 2'CN = 21.6 (9) and 29.4 (10) °] and have the C(4')-endo, O(4')-exo (40T) sugar conformation. The dioxolane-ring conformation is O(2')-endo in A and C(7)-endo in B. The dihydrouracil rings show self base pairing with hydrogen bondsN(3A)...O(ZB) and N(3B)...O(ZA).

A polarized, twisted, ethylene: structure of methyl 2-(1,3-dimethyl-2-imidazolidinylidene)-3-oxobutyrate dihydrate, C10H16N2O3.2H2O

Mr = 248, monoclinic, P21/n, a = 12.028 (2), b=7.168(2), c= 15.187(5)A, fl=91.88(2) °, Z= 4, V= 1308.6,~3, Din= 1.26, Dx= 1.263 Mgm -3, 2 (Cu Ka) = 1.5418 .A, g = 0.86 mm -1, F(000) = 536, T= 293 K. Final R = 5.6% for 2120 observed reflexions. Owing to the push-pull effect, the C=C bond distance is as long as 1.464 (2)/k with the twist angle about the bond 62.6.

Structure of a thionucleoside: 5'-deoxy-5',6-epithio-5,6-dihydro-2',3'-O-isopropylidene-3-methyluridine

C13HlsN205 S, M r = 314.35, orthorhombic, P212121 with a = 39.526 (4), b = 6.607 (2), c = 5.661 (2) A, Z = 4, V = 1478.36 A 3, D c = 1.412 Mg m -3, Cu Ka radiation. Final R = 0.073 for 1154 observed counter reflections. The sulphur atom is in a pseudo-equatorial position with respect to the dihydrouracil ring. The sugar pucker is predominantly O(l')-exo unlike the C(3')-exo,C(4')-endo observed for 2',3'-O-isopropylideneuridine (ISPU). The fivemembered dioxolane ring has C(7) displaced by 0.497 (7)A from the best plane through atoms 0(2'), C(2'), C(3'), 0(3'), in contrast to ISPU where 0(3') shows the maximum deviation.

Paraxial-wave optics and relativistic front description .1. The scalar theory

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

Zeeman effect of chlorine nuclear quadrupole resonance and hydrogen bonding in 2,6-, 2,5- and 3,5-dichlorophenols

The Zeeman effect of chlorine nuclear quadrupole resonance in polycrystalline samples of 2,6-, 2,5 and 3,5-dichlorophenol has been investigated at room temperature in order to study the effect of hydrogen bonding on the electric field gradient asymmetry parameter n. While the two n.q.r. lines in 3,5-dichlorophenol gave an asymmetry parameter of 10%, those in 2,6- and 2,5-dichlorophenol gave different values of n for the two chlorines. The chlorine atom which is ortho to the OH group and involved in hydrogen bonding (i.e., corresponding to the low frequency line) gave an asymmetry parameter of 0.21 in 2,6-dichlorophenol and 0.17 in 2,5-dichlorophenol while the other chlorine (i.e., corresponding to the high frequency line) gave a lower value of 0.12 in 2,6-dichlorophenol and 0.11 in 2,5-dichlorophenol. These values of n are discussed in terms of hydrogen bonding and bond parameters.