Splittings of free groups, normal forms and partitions of ends

Splittings of a free group correspond to embedded spheres in the 3-manifold M = # (k) S (2) x S (1). These can be represented in a normal form due to Hatcher. In this paper, we determine the normal form in terms of crossings of partitions of ends corresponding to normal spheres, using a graph of trees representation for normal forms. In particular, we give a constructive proof of a criterion determining when a conjugacy class in pi (2)(M) can be represented by an embedded sphere.

Theoretical Treatment of Interaction Parameters in Multicomponent Metallic Solutions

A new theoretical equation for interaction parameter in multicomponent metallic solutions is developed using the pseudopotential formalism coupled with the free energy of the hard sphere system. The approximate expression for the pseudopotential term is given in terms of the heat of solution at infinite dilution, to allow easy evaluation of the interaction parameter in various multicomponent systems. This theory has been applied to 23 non-ferrous alloys based on Pb, Sn, Bi and indium. Comparison with the results of previous theoretical calculations using only the hard sphere model suggests that the inclusion of the pseudopotential term yields a quantitatively more correct prediction of interaction parameters in multicomponent metallic solutions. Numerical calculations were also made for 320 Fe-base solutions relevant to steelmaking and the agreement between calculation and experimental data appears reasonable, with 90% reliability in predicting the correct sign.

Unsteady mixed convection over two-dimensional and axisymmetric bodies

The unsteady laminar incompressible mixed convection flow over a two-dimensional body (cylinder) and an axisymmetric body (sphere) has been studied when the buboyancy forces arise from both thermal and mass diffusion and the unsteadiness in the flow field is introduced by the time dependent free stream velocity. The nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The results indicate that for the thermally assisting flow the local skin friction, heat transfer and mass diffusion are enhanced when the buoyancy force from mass diffusion assists the thermal buoyancy force. But this trend is opposite for the thermally opposing flow. The point of zero skin friction moves upstream due to unsteadiness. No singularity is observed at the point of zero skin friction for unsteady flow unlike steady flow. The flow reversal is observed after a certain instant of time. The velocity overshoot occurs for assisting flows.

Euclideanization of Majorana and Weyl Fermions

A continuous procedure is presented for euclideanization of Majorana and Weyl fermions without doubling their degrees of freedom. The Euclidean theory so obtained is SO(4) invariant and Osterwalder-Schrader (OS) positive. This enables us to define a one-complex parameter family of the N=1 supersymmetric Yang-Mills (SSYM) theories which interpolate between the Minkowski and a Euclidean SSYM theory. The interpolating action, and hence the Euclidean action, manifests all the continous symmetries of the original Minkowski space theory.

Roofed polyquinanes: synthesis and electronic structure

Starting from readily available norbornenobenzoquinone 7 and employing a photothermal metathesis reaction as the main strategy, novel "roofed" polyquinane bisenones 3 and 13 have been synthesized. Among these, the former is potentially serviceable for further elaboration to dodecahedrane 1. Catalytic hydrogenation of 3 provided the dione 12, which fully inscribes the circumference of dodecahedrane sphere. The "roofed" C-16-bisenone 3 has been successfully annulated to C19-bisenone 24 and C19-trisenone 26 by employing the Greene methodology and Pauson-Khand reaction, respectively. The molecular structures of 3 and 13 were computed using molecular mechanics and semiempirical MO methods. The nonbonded distances between the double bonds vary strongly with the method employed. The interactions between the pi-MO's were, therefore, probed by means of photoelectron (PE) spectroscopy. Comparison with the PE spectra of a series of model systems with increasing complexity enabled an unambiguous assignment of the observed peaks. The symmetric and antisymmetric combinations of the pi-MO's of the enone moieties of 3 and 13 show large splittings, characteristic of propano-bridged systems in which through-space and through-bond effects act in concert.

Improving the phenomenology of Kl3 form factors with analyticity and unitarity

The shape of the vector and scalar K-l3 form factors is investigated by exploiting analyticity and unitarity in a model-independent formalism. The method uses as input dispersion relations for certain correlators computed in perturbative QCD in the deep Euclidean region, soft-meson theorems, and experimental information on the phase and modulus of the form factors along the elastic part of the unitarity cut. We derive constraints on the coefficients of the parameterizations valid in the semileptonic range and on the truncation error. The method also predicts low-energy domains in the complex t plane where zeros of the form factors are excluded. The results are useful for K-l3 data analyses and provide theoretical underpinning for recent phenomenological dispersive representations for the form factors.

Magnetic, electric, and dielectric properties of FeCo alloy nanoparticles dispersed in amorphous matrix

Nanocrystalline Fe53Co47 alloy was synthesized by a single-step transmetallation chemical method at room temperature. The Fe53Co47 alloy nanoparticles of 77 and 47 wt% were dispersed in silica matrix by the sol-gel process using tetraethyl orthosilcate. Structural studies reveal that the as-prepared alloy powders are in bcc phase and silica is in an amorphous state. The phase-transition temperature and Mossbauer spectra analysis of the Fe-Co alloy establishes the homogeneous alloy formation. A saturation magnetization of 218 emu/g was obtained for pure FeCo alloy at room temperature. Scanning electron microscopic analysis demonstrates the hollow-sphere morphology for FeCo alloy particles. Magnetic nanocomposite consisting of 47 wt% FeCo-silica shows enhanced thermal stability over the native FeCo alloy. Electrical and dielectric properties of 47 wt% FeCo-silica nanocomposites were investigated as a function of frequency and temperature. It was found that the dielectric constants and dielectric loss were stable throughout the measured temperature (310-373 K). Our results indicate that FeCo-silica nanocomposite is a promising candidate for high-frequency applications. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

A divisive scheme for constructing minimal spanning trees in coordinate space

An algorithm to generate a minimal spanning tree is presented when the nodes with their coordinates in some m-dimensional Euclidean space and the corresponding metric are given. This algorithm is tested on manually generated data sets. The worst case time complexity of this algorithm is O(n log2n) for a collection of n data samples.

Random-Restart Reactive Tabu Search Algorithm for Detection in Large-MIMO Systems

We present a low-complexity algorithm based on reactive tabu search (RTS) for near maximum likelihood (ML) detection in large-MIMO systems. The conventional RTS algorithm achieves near-ML performance for 4-QAM in large-MIMO systems. But its performance for higher-order QAM is far from ML performance. Here, we propose a random-restart RTS (R3TS) algorithm which achieves significantly better bit error rate (BER) performance compared to that of the conventional RTS algorithm in higher-order QAM. The key idea is to run multiple tabu searches, each search starting with a random initial vector and choosing the best among the resulting solution vectors. A criterion to limit the number of searches is also proposed. Computer simulations show that the R3TS algorithm achieves almost the ML performance in 16 x 16 V-BLAST MIMO system with 16-QAM and 64-QAM at significantly less complexities than the sphere decoder. Also, in a 32 x 32 V-BLAST MIMO system, the R3TS performs close to ML lower bound within 1.6 dB for 16-QAM (128 bps/Hz), and within 2.4 dB for 64-QAM (192 bps/Hz) at 10(-3) BER.

Crystal structures, spectral and magnetic properties of (µ-hydroxo)(µ-acetato)dicopper(II) complexes containing chelating amines

The reaction of [Cu2(O2CMe)4(H2O)2] with N, N, N′, N′-tetramethylethane- 1,2-diamine (tmen) in ethanol yielded the dicopper(II) complex [Cu2(OH)(O2CMe)(tmen)2][ClO4]21. A similar reaction with N, N- dimethylethane- 1,2-diamine (dmen) afforded a crystalline product 2 in which two dicopper(II) complexes, [Cu2(OH)(O2CMe)(dmen)2][ClO4]22a and [Cu2(OH)(O2CMe)(H2O)2(dmen)2][ClO4]22b, are cocrystallized in a 1 : 1 molar ratio along with 2NaClO4. The crystal structures of 1 and 2 have been determined. The complexes have an asymmetrically dibridged [Cu2(µ-OH)(µ-O2CMe)]2+ core. The co-ordination geometry of the metal is square planar (CuO2N2). The copper atoms in 2b have a square-pyramidal CuO3N2 co-ordination sphere. The Cu Cu distances and Cu–O–Cu angles in 1, 2a and 2b are 3.339(2), 3.368(3), 3.395(7)Å, 120.1(2), 116.4(1) and 123.6(2)°, respectively. Complex 1 exhibits an axial ESR spectrum in a methanol glass giving g∥= 2.26 (A∥= 164 × 10–4 cm–1) and g⊥= 2.04. The ESR spectra obtained from the bulk material of the dmen product are indicative of the presence of two dimers, viz. complex 2a(g∥= 2.25, A∥= 165 × 10–4 cm–1; g⊥= 2.03) and 2b(g∥= 2.19, A∥= 184 × 10–4 cm–1; g⊥= 2.0). Variable-temperature magnetic susceptibility measurements on these complexes show an intramolecular antiferromagnetic coupling in the dimeric core. The fitting parameters are J=–27.8 cm–1, g= 2.1 for complex 1 and J=–10.1 cm–1, g= 2.0 for 2. The magnetostructural properties of the complexes are discussed. There is a linear correlation of the –2J values with the Cu Cu distances among dibridged complexes having square-planar copper(II) centres.

Reactions of copper(I) aryloxides with phenyl isothiocyanate: steric and ligand control in the oligomerization of [N-phenylimino(aryloxy)methanethiolato]copper(I) complexes

The preparation of five different copper(I) complexes [CuSC(=NPh)(OAr)}L(n)]m (1-5) formed by the insertion of PhNCS into the Cu-OAr bond and the crystal structure analyses of three of them have been carried out. A monomeric species 1 (OAr = 2,6-dimethylphenoxide) is formed in the presence of excess PPh3 (n = 2, m = 1) and crystallizes as triclinic crystals with a = 12.419(4) angstrom, b = 13.298(7) angstrom, c = 15.936(3) angstrom, alpha = 67.09(3)-degrees, beta = 81.63(2)-degrees, gamma = 66.54(3)-degrees, V = 2224(2) angstrom3, and Z = 2. The structure was refined by the least-squares method to final R and R(w) values of 0.038 and 0.044, respectively, for 7186 unique reflections. Copper(I) 2,5-di-tert-butyl-4-methylphenoxide results in the formation of a dimeric species 2 in the presence of P(OMe)3 (n = 1, m = 2), where the coordination around Cu is trigonal. Crystals of 2 were found to be orthorhombic with a = 15.691(2) angstrom, b = 18.216(3) angstrom, c = 39.198(5) angstrom, v = 11204(3) angstrom3, and Z = 8. Least-squares refinement gave final residuals of R = 0.05 and R(w) = 0.057 with 6866 unique reflections. A tetrameric species 3 results when PPh3 is replaced by P(OMe)3 in the coordination sphere of copper(I) 2,6-dimethylphenoxide. It crystallizes in the space group P1BAR with a = 11.681 (1) angstrom, b = 13.373(2) angstrom, c = 20.127(1) angstrom, a = 88.55(l)-degrees, beta = 89.65(l)-degrees, gamma = 69.28(1)-degrees, V = 2940(l) angstrom3, and Z = 2. Least-squares refinement of the structure gave final values of 0.043 and 0.05 for R and R(w) respectively using 12214 unique reflections. In addition, a dimeric species 4 is formed when 1 equiv of PPh3 is added to the copper(I) 4-methylphenoxide, while with an excess of PPh3 a monomeric species 5 is isolated. Some interconversions among these complexes are also reported.

On Two-User Gaussian Multiple Access Channels With Finite Input Constellations

Constellation Constrained (CC) capacity regions of two-user Single-Input Single-Output (SISO) Gaussian Multiple Access Channels (GMAC) are computed for several Non-Orthogonal Multiple Access schemes (NO-MA) and Orthogonal Multiple Access schemes (O-MA). For NO-MA schemes, a metric is proposed to compute the angle(s) of rotation between the input constellations such that the CC capacity regions are maximally enlarged. Further, code pairs based on Trellis Coded Modulation (TCM) are designed with PSK constellation pairs and PAM constellation pairs such that any rate pair within the CC capacity region can be approached. Such a NO-MA scheme which employs CC capacity approaching trellis codes is referred to as Trellis Coded Multiple Access (TCMA). Then, CC capacity regions of O-MA schemes such as Frequency Division Multiple Access (FDMA) and Time Division Multiple Access (TDMA) are also computed and it is shown that, unlike the Gaussian distributed continuous constellations case, the CC capacity regions with FDMA are strictly contained inside the CC capacity regions with TCMA. Hence, for finite constellations, a NO-MA scheme such as TCMA is better than FDMA and TDMA which makes NO-MA schemes worth pursuing in practice for two-user GMAC. Then, the idea of introducing rotations between the input constellations is used to construct Space-Time Block Code (STBC) pairs for two-user Multiple-Input Single-Output (MISO) fading MAC. The proposed STBCs are shown to have reduced Maximum Likelihood (ML) decoding complexity and information-losslessness property. Finally, STBC pairs with reduced sphere decoding complexity are proposed for two-user Multiple-Input Multiple-Output (MIMO) fading MAC.

New Approximation Algorithms for Minimum Cycle Bases of Graphs

We consider the problem of computing an approximate minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. Although in most such applications any cycle basis can be used, a low weight cycle basis often translates to better performance and/or numerical stability. Despite the fact that the problem can be solved exactly in polynomial time, we design approximation algorithms since the performance of the exact algorithms may be too expensive for some practical applications. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k >= 1, we give (2k - 1)-approximation algorithms with expected running time O(kmn(1+2/k) + mn((1+1/k)(omega-1))) and deterministic running time O(n(3+2/k) ), respectively. Here omega is the best exponent of matrix multiplication. It is presently known that omega < 2.376. Both algorithms are o(m(omega)) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the Theta(m(omega) ) bound. We also present a 2-approximation algorithm with expected running time O(M-omega root n log n), a linear time 2-approximation algorithm for planar graphs and an O(n(3)) time 2.42-approximation algorithm for the complete Euclidean graph in the plane.

Glass Transition in the Density Functional Theory of Freezing

A mean-field description of the glass transition in the hard-sphere system is obtained by numerically locating "glassy" minima of a model free-energy functional. These minima, characterized by inhomogeneous but aperiodic density distributions, appear as the average density is increased above the value at which equilibrium crystallization takes place. Investigations of the density distribution and local bond-orientational order at these minima yield results similar to those obtained from simulations.

Binding of active site directed ligands to phospholipase A2: Implications on the molecular constraints and catalytic mechanism

Molecular constraints for the localization of active site directed ligands (competitive inhibitors and substrates) in the active site of phospholipase A2 (PLA2) are characterized. Structure activity relationships with known inhibitors suggest that the head : group interactions dominate the selectivity as well as a substantial part of the affinity. The ab initio fitting of the amide ligands in the active site was carried out to characterize the head group interactions. Based on a systematic coordinate space search, formamide is docked with known experimental constraints such as coordination of the carbonyl group to Ca2+ and hydrogen bond between amide nitrogen and ND1 of His48. An optimal position for a bound water molecule is identified and its significance for the catalytic mechanism is postulated. Unlike the traditional ''pseudo-triad'' mechanism, the ''Ca-coordinatedoxyanion'' mechanism proposed here invokes activation of the catalytic water to form the oxyanion in the coordination sphere of calcium. As it attacks the carbonyl carbon of the ester, a near-tetrahedral intermediate is formed. As the second proton of the catalytic water is abstracted by the ester oxygen, its reorientation and simultaneous cleavage form hydrogen bond with ND1 of His48. In this mechanism of esterolysis, a catalytic role for the water co-ordinated to Ca2+ is recognised.