On the Arrangement of Cliques in Chordal Graphs with respect to the Cuts

A cut (A, B) (where B = V - A) in a graph G = (V, E) is called internal if and only if there exists a vertex x in A that is not adjacent to any vertex in B and there exists a vertex y is an element of B such that it is not adjacent to any vertex in A. In this paper, we present a theorem regarding the arrangement of cliques in a chordal graph with respect to its internal cuts. Our main result is that given any internal cut (A, B) in a chordal graph G, there exists a clique with kappa(G) + vertices (where kappa(G) is the vertex connectivity of G) such that it is (approximately) bisected by the cut (A, B). In fact we give a stronger result: For any internal cut (A, B) of a chordal graph, and for each i, 0 <= i <= kappa(G) + 1 such that vertical bar K-i vertical bar = kappa(G) + 1, vertical bar A boolean AND K-i vertical bar = i and vertical bar B boolean AND K-i vertical bar = kappa(G) + 1 - i. An immediate corollary of the above result is that the number of edges in any internal cut (of a chordal graph) should be Omega(k(2)), where kappa(G) = k. Prompted by this observation, we investigate the size of internal cuts in terms of the vertex connectivity of the chordal graphs. As a corollary, we show that in chordal graphs, if the edge connectivity is strictly less than the minimum degree, then the size of the mincut is at least kappa(G)(kappa(G)+1)/2 where kappa(G) denotes the vertex connectivity. In contrast, in a general graph the size of the mincut can be equal to kappa(G). This result is tight.

A thermodynamic interpretation of the zonal arrangement of minerals in the bedded manganese deposits of the Noda tamagawa mine, Japan

Calculated phase relations in the system MnOSi02-C02-02 were used to propose a thermodynamic explanation for the thermal metamorphism of rhodochrosite beds lying between chert strata. The metamorphic MnOS i 0 2 minerals are arranged in order quartz(chert), rhodonite. tephroite and manganosite-hausmannite-pyrochroite rhodonite across the ore bed. The calculation covered temperatures up to 1000 K and pressures up to 5 kb. The zoning was interpreted as the result of a continuous rise in metamorphic temperature. The equilibrium partner of rhodochrosite changed from rhodonite through manganosite. Across the ore bed there are gradients in the chemical potential of MnO and SiO2 but fugacities of volatlle components such as C02. 02 and H20 were probably uniform at any given time and location during formation of the zones. Assuming that the total pressure and the fugacity of C02 were at 1.4 kb and 1.0 1 b. respectively. rhodonite. tephroite and manganosite would have formed at 472. 478 and 629 K.

A need for re-examination of the fibre diffraction data of A-DNA

A-DNA pattern, obtained using a flat plat camera, was indexed by Fuller Image on the basis of a c-face centred monoclinic cell with A = 22.24 Å, B = 40.62 Å, C = 28.15 Å and β = 97.0°. A precession photograph of A-DNA which gives an undistorted picture of the lattice, showed that the unit cell parameters as given by Fuller Image were not quite correct. The precession photograph showed a strong meridional reflection (R = 0.00 Å−1) on the 11th layer line. But the occurrence of the meridional reflection on the 11th layer line could not be explained on the basis of the cell parameters given by Fuller Image ; using those cell parameters the reflection which comes closest to the meridian on 11th layer line is at R = 0.025 Å−1. However, a simple interchange of a and b values accounted for the meridional reflection on 11th layer line. The corrected cell parameter refined against 28 strong spots are A = 40.75 Å, B = 22.07 Å, C = 28.16 Å and β = 97.5°. In the new unit cell of A-DNA, the packing arrangement of the two molecules is different from that in the old one. Nonetheless, our earlier contention is again reaffirmed that both right and left-handed A-DNA are stereochemically allowed and consistent with the observed fibre pattern.

Effect of Alkyl Chain Arrangement on Conformation and Dynamics in a Surfactant Intercalated Layered Double Hydroxide: Spectroscopic Measurements and MD Simulations

The anionic surfactant dodecyl sulfate (DDS) has been intercalated in an Mg-Al layered double hydroxide (LDH). Monolayer and bilayer arrangements of the alkyl chains of the intercalated surfactant can be engineered by tuning the Al/Mg ratio of the LDH. In both arrangements the anionic headgroup of the surfactant is tethered to the LDH sheets, and consequently translational mobility of the chains is absent. The degrees of freedom of the confined alkyl chains are restricted to changes in conformation. The effects of the arrangement of the intercalated surfactant chains on conformational order and dynamics have been,investigated by spectroscopic measurements and molecular dynamics simulations. Infrared, Raman, and C-13 NMR spectroscopies were used to investigate conformation of the alkyl chains in the monolayer and bilayer arrangements and variable contact time cross-polarization magic angle spinning (VCT CPMAS) NMR measurements to probe molecular motion. The alkyl chains in the monolayer arrangement of the intercalated DDS chains showed considerably greater conformational disorder and faster dynamics as compared to chains in the bilayer arrangement, in spite of the fact that the volume available per chain in the monolayer is smaller than that in the bilayer. Atomistic MD simulations of the two arrangements of the intercalated surfactant were carried out using an isothermal-isobaric ensemble. The simulations are able to reproduce the essential results of the experiment-greater conformational disorder and faster dynamics for the alkyl chains in the monolayer arrangement of the intercalated surfactant. The MD simulations show that these results are a consequence of the fact that the nature of conformational disorder in the two arrangements is different. In the monolayer arrangement the alkyl chains can sustain isolated gauche defects, whereas in the bilayer arrangement gauche conformers occur only as part of a kink a gauche(+) trans gauche(-) sequence.

An Efficient Load Distribution Strategy for a Distributed Linear Network of Processors with Communication Delays

In this paper, we present an improved load distribution strategy, for arbitrarily divisible processing loads, to minimize the processing time in a distributed linear network of communicating processors by an efficient utilization of their front-ends. Closed-form solutions are derived, with the processing load originating at the boundary and at the interior of the network, under some important conditions on the arrangement of processors and links in the network. Asymptotic analysis is carried out to explore the ultimate performance limits of such networks. Two important theorems are stated regarding the optimal load sequence and the optimal load origination point. Comparative study of this new strategy with an earlier strategy is also presented.

An asymmetric homodinuclear complex containing the mu-x-oxobis(mu-x-carboxylato)diruthenium(III) core: X-ray structure of [Ru20(o2ec6H4-p-OMe)3(en) (PPh3)2] (C104)" 3CHC13

Asymmetric tri-bridged diruthenium(III) complexes, [Ru2O(O(2)CR)(3)(en) (PPh(3))(2)](ClO4) (R = C6H4-p-X: X = OMe (1a), Me (1b); en=1,2-diaminoethane), were prepared and structurally characterized. Complex 1a 3CHCl(3), crystallizes in the triclinic space group P (1) over bar with a = 14.029(5), b = 14.205(5), c = 20.610(6) Angstrom, alpha= 107.26(3), beta = 101.84(3), gamma= 97.57(3)degrees, V= 3756(2) Angstrom(3) and Z = 2. The complex has an {Ru-2(mu-O)(mu-O(2)CR)(2)(2+)} core and exhibits [O4PRu(mu-O)RuPO2N2](+) coordination environments for the metal centers. The novel structural feature is the asymmetric arrangement of ligands at the terminal sites of the core which shows an Ru... Ru separation of 3.226(3) Angstrom and an Ru-O-Ru angle of 119.2(5)degrees. An intense visible band observed near 570 nm is assigned to a charge transfer transition involving the d pi-Ru(III) and p pi-mu-O Orbitals. Cyclic voltammetry of the complexes displays a reversible Ru-2(III,III) reversible arrow Ru-2(III,IV) couple near 0.8 V (versus SCE) in MeCN-0.1 M TBAP.

Solid state stacked trimers of 1,10-phenanthroline in a supramolecular tubular motif of C-methyl calix[4]resorcinarene

The self-assembly of bidentate ligand, 1,10-phenanthroline with C-methyl calix[4]resorcinarene (CMCR) in presence of coumarin results in a unique trimer stacking arrangement of phenanthroline molecules in a nanotubular motif generated by the supramolecular assembly of the host.

Immunochemical approach to the mapping of an assembled epitope of human chorionic gonadotropin: Proximity of CTP-alpha to the receptor binding region of the beta-subunit

A single-step solid-phase RIA (SS-SPRIA) developed in our laboratory using hybridoma culture supernatants has been utilised for the quantitation of epitope-paratope interactions. Using SS-SPRIA as a quantitative tool for the assessment of epitope stability, it was found that several assembled epitopes of human chorionic gonadotropin (hCG) are differentially stable to proteolysis and chemical modification. Based on these observations an approach has been developed for identifying the amino acid residues constituting an epitopic region. This approach has now been used to map an assembled epitope at/near the receptor binding region of the hormone. The mapped site forms a part of the seat belt region and the cystine knot region (C34-C38-C88-C90-H106). The carboxy terminal region of the alpha-subunit forms a part of the epitope indicating its proximity to the receptor binding region. These results are in agreement with the reported receptor binding region identified through other approaches and the X-ray crystal structure of hCG.

X-ray Topographic Assessment of Dislocations in Crystals Grown from Solution

Crystals growing from solution, the vapour phase and from supercooled melt exhibit, as a rule, planar faces. The geometry and distribution of dislocations present within the crystals thus grown are strongly related to the growth on planar faces and to the different growth sectors rather than the physical properties of the crystals and the growth methods employed. As a result, many features of generation and geometrical arrangement of defects are common to extremely different crystal species. In this paper these commoner aspects of dislocation generation and configuration which permits one to predict their nature and distribution are discussed. For the purpose of imaging the defects a very versatile and widely applicable technique viz. x-ray diffraction topography is used. Growth dislocations in solution grown crystals follow straight path with strongly defined directions. These preferred directions which in most cases lie within an angle of ±15° to the growth normal depend on the growth direction and on the Burger's vector involved. The potential configuration of dislocations in the growing crystals can be evaluated using the theory developed by Klapper which is based on linear anisotropic elastic theory. The preferred line direction of a particular dislocation corresponds to that in which the dislocation energy per unit growth length is a minimum. The line direction analysis based on this theory enables one to characterise dislocations propagating in a growing crystal. A combined theoretical analysis and experimental investigation based on the above theory is presented.

A study in Crystal engineering: Solid-state photodimerization of chloro- and methyl-coumarins

Use of chloro and methyl substitution in crystal engineering and their interchangeability in terms of mode of packing have been examined in a series of substituted coumarins. Photoreactivity in the solid state lists been correlated with the crystallograhic structures of these coumarins. The packing of chloro-substituted aromatic compounds has been investigated by analysing the arrangement of 132 compounds. Results substantiate the use of the chloro group as a steering agent and show that the chloro and methyl groups are not always interchangeable.

Structure and dynamics of two-dimensional sheared granular flows

The structure and dynamics of the two-dimensional linear shear flow of inelastic disks at high area fractions are analyzed. The event-driven simulation technique is used in the hard-particle limit, where the particles interact through instantaneous collisions. The structure (relative arrangement of particles) is analyzed using the bond-orientational order parameter. It is found that the shear flow reduces the order in the system, and the order parameter in a shear flow is lower than that in a collection of elastic hard disks at equilibrium. The distribution of relative velocities between colliding particles is analyzed. The relative velocity distribution undergoes a transition from a Gaussian distribution for nearly elastic particles, to an exponential distribution at low coefficients of restitution. However, the single-particle distribution function is close to a Gaussian in the dense limit, indicating that correlations between colliding particles have a strong influence on the relative velocity distribution. This results in a much lower dissipation rate than that predicted using the molecular chaos assumption, where the velocities of colliding particles are considered to be uncorrelated.

Quasi-2D XY Magnetic Properties and Slow Relaxation in a Body Centered Metal Organic Network of [Co-4] Clusters

Octahedral Co2+ centers have been connected by mu(3)-OH and mu(2)-OH2 units forming [Co-4] clusters which are linked by pyrazine forming a two-dimensional network. The two-dimensional layers are bridged by oxybisbenzoate (OBA) ligands giving rise to a three-dimensional structure. The [Co-4] clusters bond with the pyrazine and the OBA results in a body-centered arrangement of the clusters, which has been observed for the first time. Magnetic studies reveal a noncollinear frustrated spin structure of the bitriangular cluster, resulting in a net magnetic moment of 1.4 mu B per cluster. For T > 32 K, the correlation length of the cluster moments shows a stretched-exponential temperature dependence typical of a Berezinskii-Kosterlitz-Thouless model, which points to a quasi-2D XY behavior. At lower temperature and down to 14 K, the compound behaves as a soft ferromagnet and a slow relaxation is observed, with an energy barrier of ca. 500 K. Then, on further cooling, a hysteretic behavior takes place with a coercive field that reaches 5 Tat 4 K. The slow relaxation is assigned to the creation/annihilation of vortex-antivortex pairs, which are the elementary excitations of a 2D XY spin system.

Reversal of handedness in DNA: A stable link between RU and LZ helices

Two types of left-handed zig-zag (LZ) helices were obtained following stereochemical guideline. They are referred to as LZ1 and LZ2 helices. LZ1 helices have conformations similar to those found in the single crystals of d(C-G)3 and d(C-G)25,6. Z-character is more prominent in LZ2 than in LZ1 helix. The conformations of a stable link between RU and LZ helical fragments are given. The link involves inverted stacking arrangement of the bases: a characteristic feature of all RL models proposed by us

X-Ray Studies On Crystalline Complexes Involving Amino-Acids And Peptides .11. Peptide Aggregation And Water-Structure In The Crystals Of A Hydrated 1-1 Complex Between L-Histidyl-L-Serine And Glycyl-L-Glutamic Acid

The hexahydrate of a 1:1 complex between L-histidyl-L-serine and glycyl-L-glutamic acid crystallizes in space group P1 with a = 4.706(1), b= 8.578(2), c= 16.521(3) ÅA; α= 85.9(1), β= 89.7(1)°, = 77.4(1). The crystal structure, solved by direct methods, has been refined to an R value of 0.046 for 2150 observed reflections. The two peptide molecules in the structure have somewhat extended conformations. The unlike molecules aggregate into separate alternating layers. Each layer is stabilized by hydrogen bonded head-to-tail sequences as well as sequences of hydrogen bonds involving peptide groups. The arrangement of molecules in each layer is similar to one of the plausible idealized arrangements of L-alanyl-L-alanine worked out from simple geometrical considerations. Adjacent layers in the structure are held together by interactions involving side chains as well as water molecules. The water structure observed in the complex provides a good model, at atomic resolution, for that in protein crystals. An interesting feature of the crystal structure is the existence of two water channels in the interfaces between adjacent peptide layers.

Crystal structure of the amino acid-vitamin complex lysine pantothenatestar, open

L-Lysine d-pantothenate, a 1:1 amino acid-vitamin complex, crystallizes in the monoclinic space group P21 with Image Full-size image (1K) .The structure has been solved by direct methods and refined to an R value of 0.053 for 1868 observed reflections. The zwitterionic positively charged lysine molecules in the structure assume the sterically most favourable conformation with an all-trans side chain trans to the α-carboxylate group. The pantothenate anion has a somewhat folded conformation stabilised by an intramolecular bifurcated hydrogen bond. The unlike molecules aggregate into separate alternating layers. The molecules in the lysine layers form a head-to-tail sequence parallel to the a-axis. The interactions which hold the adjacent layers together include those between the side chain amino group of lysine and the carboxylate group in the pantothenate anion. The geometry of these interactions is such that each carboxylate group is sandwiched between two amino groups in a periodic arrangement of alternating carboxylate and amino groups.