Popular Matchings with Variable Job Capacities

We consider the problem of matching people to jobs, where each person ranks a subset of jobs in an order of preference, possibly involving ties. There are several notions of optimality about how to best match each person to a job; in particular, popularity is a natural and appealing notion of optimality. However, popular matchings do not always provide an answer to the problem of determining an optimal matching since there are simple instances that do not adroit popular matchings. This motivates the following extension of the popular rnatchings problem:Given a graph G; = (A boolean OR J, E) where A is the set of people and J is the set of jobs, and a list < c(1), c(vertical bar J vertical bar)) denoting upper bounds on the capacities of each job, does there exist (x(1), ... , x(vertical bar J vertical bar)) such that setting the capacity of i-th, job to x(i) where 1 <= x(i) <= c(i), for each i, enables the resulting graph to admit a popular matching. In this paper we show that the above problem is NP-hard. We show that the problem is NP-hard even when each c is 1 or 2.

Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.

Diruthenium(III) compounds, Ru2O(O2CAr)2(MeCN)4(PPh3)2(ClO4)2.cntdot.H2O and Ru2O(O2CAr)4(PPh3)2, with an (Ru2(.mu.-O)(.mu.-O2CAr)22+) core as model systems for the diiron centers in hemerythrin

Diruthenium(II1) compounds, Ru20(02CAr)2(MeCN)4(PPh3)2(C104)(z1~) Hazn0d R U ~ O ( O ~ C A ~ ) ~(2() P(PA~r ~= )P~h,C6H4-p-OMe), were prepared by reacting R U ~ C I ( O ~ CaAnd~ P)P~h 3 in MeCN and characterized by analytical and spectral data. The molecular structures of 1 with Ar = Ph and of 2 with Ar = C&p-OMe were determined by X-ray crystallography. Crystal data for Ru~~(~~CP~)~(M~CN),(PP~(~la)):~ m(oCnIoc~lin,ic), n~/~cH, ~a O= 27.722 (3) A, b = 10.793 (2) A, c = 23.445 ( 2 )A , fi = 124.18 (l)', V = 5803 A3, and 2 = 4. Cr stal data for Ru~O(O~CC~H~-~-O(M2b~): )o~rth(orPhoPm~bi~c, )Pn~n a, a = 22.767 (5) A, b = 22.084 (7) A, c = 12.904 (3) 1, V = 6488 AS; and 2 = 4. Both 1 and 2 have an (Ruz0(02CAr)z2t1 core that is analogous to the diiron core present in the oxidized form of the nonheme respiratory protein hemerythrin. The Ru-Ru distances of 3.237 (1) and 3.199 ( I ) A observed in 1 and 2, respectively, are similar to the M-M distances known in other model systems. The essentially diamagnetic nature of 1 and 2 is due to the presence of two strongly interacting t22 Ru"' centers. The intense colors of 1 (blue) and 2 (purple) are due to the charge-transfer transition involving an ( R ~ ~ ( f i - 0m)o~ie~ty.) The presence of labile MeCN and carboxylato ancillary ligands in I and 2, respectively, makes these systems reactive toward amine and heterocyclic bases.

Geometry and quadratic nonlinearity of charge transfer complexes in solution using depolarized hyper-Rayleigh scattering

We report large quadratic nonlinearity in a series of 1:1 molecular complexes between methyl substituted benzene donors and quinone acceptors in solution. The first hyperpolarizability, beta(HRS), which is very small for the individual components, becomes large by intermolecular charge transfer (CT) interaction between the donor and the acceptor in the complex. In addition, we have investigated the geometry of these CT complexes in solution using polarization resolved hyper-Rayleigh scattering (HRS). Using linearly (electric field vector along X direction) and circularly polarized incident light, respectively, we have measured two macroscopic depolarization ratios D = I-2 omega,I-X,I-X/I-2 omega,I-Z,I-X and D' = I-2 omega,I-X,I-C/I-2 omega,I-Z,I-C in the laboratory fixed XYZ frame by detecting the second harmonic scattered light in a polarization resolved fashion. The experimentally obtained first hyperpolarizability, beta(HRS), and the value of macroscopic depolarization ratios, D and D', are then matched with the theoretically deduced values from single and double configuration interaction calculations performed using the Zerner's intermediate neglect of differential overlap self-consistent reaction field technique. In solution, since several geometries are possible, we have carried out calculations by rotating the acceptor moiety around three different axes keeping the donor molecule fixed at an optimized geometry. These rotations give us the theoretical beta(HRS), D and D' values as a function of the geometry of the complex. The calculated beta(HRS), D, and D' values that closely match with the experimental values, give the dominant equilibrium geometry in solution. All the CT complexes between methyl benzenes and chloranil or 1,2-dichloro-4,5-dicyano-p-benzoquinone investigated here are found to have a slipped parallel stacking of the donors and the acceptors. Furthermore, the geometries are staggered and in some pairs, a twist angle as high as 30 degrees is observed. Thus, we have demonstrated in this paper that the polarization resolved HRS technique along with theoretical calculations can unravel the geometry of CT complexes in solution. (C) 2011 American Institute of Physics. doi:10.1063/1.3514922]

Popular matchings with variable item copies

We consider the problem of matching people to items, where each person ranks a subset of items in an order of preference, possibly involving ties. There are several notions of optimality about how to best match a person to an item; in particular, popularity is a natural and appealing notion of optimality. A matching M* is popular if there is no matching M such that the number of people who prefer M to M* exceeds the number who prefer M* to M. However, popular matchings do not always provide an answer to the problem of determining an optimal matching since there are simple instances that do not admit popular matchings. This motivates the following extension of the popular matchings problem: Given a graph G = (A U 3, E) where A is the set of people and 2 is the set of items, and a list < c(1),...., c(vertical bar B vertical bar)> denoting upper bounds on the number of copies of each item, does there exist < x(1),...., x(vertical bar B vertical bar)> such that for each i, having x(i) copies of the i-th item, where 1 <= xi <= c(i), enables the resulting graph to admit a popular matching? In this paper we show that the above problem is NP-hard. We show that the problem is NP-hard even when each c(i) is 1 or 2. We show a polynomial time algorithm for a variant of the above problem where the total increase in copies is bounded by an integer k. (C) 2011 Elsevier B.V. All rights reserved.

Novel photo-crosslinkable flame retardant polyvanillylidene arylphosphate esters

A new class of photo-crosslinkable flame retardant arylphosphate ester polymers based on diarylidenecycloalkanone groups has been synthesized by polymerizing 2,5-divanillylidene cyclopentanone and 2,6-divanillylidenecyclohexanone with various arylphosphorodichloridates by interfacial polycondensation using a phase transfer catalyst. The resulting polymers were characterized by inherent viscosity, g.p.c., i.r., H-1, C-13, P-31 n.m.r. spectroscopy. These polymers were studied for their photochemical and flame retardant properties. The divanillylidene cycloalkanone group in the chain function as photoactive centres while arylphosphate ester groups impart flame retardancy. The photo-crosslinking proceeds via 2 pi + 2 pi cycloaddition reaction of the divanillylidene cycloalkanone moieties. The crosslinking rate, thermal stability and flammability characteristics of the polymers increase with decrease in the size of the cycloalkanone ring. (C) 1997 Elsevier Science Ltd.

Raman evidence for the superconducting gap and spin-phonon coupling in the superconductor Ca( Fe0.95Co0.05)(2)As-2

Inelastic light scattering studies on a single crystal of electron-doped Ca(Fe0.95Co0.05)(2)As-2 superconductor, covering the tetragonal-to-orthorhombic structural transition as well as the magnetic transition at T-SM similar to 140 K and the superconducting transition temperature T-c similar to 23 K, reveal evidence for superconductivity-induced phonon renormalization. In particular, the phonon mode near 260 cm(-1) shows hardening below T-c, signaling its coupling with the superconducting gap. All three Raman active phonon modes show anomalous temperature dependence between room temperature and T-c, i.e. the phonon frequency decreases with lowering temperature. Further, the frequency of one of the modes shows a sudden change in temperature dependence at TSM. Using first-principles density functional theory based calculations, we show that the low temperature phase (T-c < T < T-SM) exhibits short-ranged stripe antiferromagnetic ordering, and estimate the spin-phonon couplings that are responsible for these phonon anomalies.

Structure of 2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9-hexadecafluorodecyl 1,10-ditosylate by X-ray crystallography and F-19-NMR spectroscopy

2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9-hexadecafluorodecyl 1,10-ditosylate and its precursors were synthesized and characterized by H-1- and F-19-NMR spectroscopic methods and X-ray crystallography. These compounds are building blocks for the syntheses of the surfactants containing polyperfluoromethylene spacer. The molecule has extended all-trans conformation with molecular symmetry (1) over bar (C-i). There is a reasonably strong C-H ... O interaction in the crystal and there are two F ... F intermolecular contact distances less than the sum of van der Waals radii. (C) 1999 Elsevier Science B.V. All rights reserved.

Self-assembled molecular films of tetraamino metal (Co, Cu, Fe) phthalocyanines on gold and silver. Electrochemical and spectroscopic characterization

The formation of molecular films of 2,9,16,23-tetraamino metal phthalocyanines [TAM(II)Pc; M (II) = Co, Cu, and TAM(III)Pc; M = Fe] by spontaneous adsorption on gold and silver surfaces is described. The properties of these films have been investigated by cyclic voltammetry, impedance, and FT-Raman spectroscopy. The charge associated with Co(II) and Co(I) redox couple in voltammetric data leads to a coverage of (0.35+/-0.05) x 10(-10) mol cm(-2), suggesting that the tetraamino cobalt phthalocyanine is adsorbed as a monolayer with an almost complete coverage. The blocking behavior of the films toward oxygen and Fe(CN)(6)(3-/4-) redox couple have been followed by cyclic voltammetry and impedance measurements. This leads to an estimate of the coverage of about 85 % in the case of copper and the iron analogs. FT-Raman studies show characteristic bands around 236 cm(-1) revealing the interaction between the metal substrate and the nitrogen of the -NH2 group on the phthalocyanine molecules.

Almost quarter-pinched Kähler metrics and Chern numbers

Given n is an element of Z(+) and epsilon > 0, we prove that there exists delta = delta(epsilon, n) > 0 such that the following holds: If (M(n),g) is a compact Kahler n-manifold whose sectional curvatures K satisfy -1 -delta <= K <= -1/4 and c(I)(M), c(J)(M) are any two Chern numbers of M, then |c(I)(M)/c(J)(M) - c(I)(0)/c(J)(0)| < epsilon, where c(I)(0), c(J)(0) are the corresponding characteristic numbers of a complex hyperbolic space form. It follows that the Mostow-Siu surfaces and the threefolds of Deraux do not admit Kahler metrics with pinching close to 1/4.

Appraisal of Bishop's method of slope stability analysis

The stability of slopes is a major problem in geotechnical engineering. Of the methods available for the analysis of soil slopes such as limit equilibrium methods, limit analysis and numerical methods such as FEM and FDM, limit equilibrium methods are popular and generally used, owing to their simplicity in formulation and in evaluating the overall factor of safety of slope. However limit equilibrium methods possess certain disadvantages. They do not consider whether the slope is an embankment or natural slope or an excavation and ignore the effect of incremental construction, initial stress, stress strain behavior etc. In the work reported in this paper, a comparative study of actual state of stress and actual factor of safety and Bishop's factor of safety is performed. The actual factor of safety is obtained by consideration of contours of mobilised shear strains. Using Bishop's method of slices, the critical slip surfaces of a number of soil slopes with different geometries are determined and both the factors of safety are obtained. The actual normal stresses and shear stresses are determined from finite difference formulation using FLAG (Fast Lagrangian Analysis of Continuaa) with Mohr-Coulomb model. The comparative study is performed in terms of parameter lambda(c phi) (= gamma H tan phi/c). I is shown that actual factor of safety is higher than Bishop's factor of safety depending on slope angle and lambda(c phi).

Band-Structure Lineup at In0.2Ga0.8N/Si Heterostructures by X-ray Photoelectron Spectroscopy

In0.2Ga0.8N layers were directly grown on Si(111) substrate by plasma-assisted molecular beam epitaxy (PAMBE). Structural characteristics of the as-grown InGaN epilayers were evaluated high resolution X-ray diffraction and composition of InGaN was estimated from photoluminescence spectra using the standard Vegard's law. High-resolution X-ray photoemission spectroscopy measurements were used to determine the band offset of wurtzite-In0.2Ga0.8N/Si(111) heterojunctions. The valence band of InGaN is found to be 2.08 +/- 0.04 eV below that of Si. The conduction band offset (CBO) of InGaN/Si heterojunction is found similar to 0.74 eV and a type-II heterojunction. (C) 2012 The Japan Society of Applied Physics

Regioselective Deiodination of Thyroxine by Iodothyronine Deiodinase Mimics: An Unusual Mechanistic Pathway Involving Cooperative Chalcogen and Halogen Bonding

Iodothyronine deiodinases (IDs) are mammalian selenoenzymes that catalyze the conversion of thyroxine (T4) to 3,5,3'-triiodothyronine (T3) and 3,3',5'-triiodothyronine (rT3) by the outer- and inner-ring deiodination pathways, respectively. These enzymes also catalyze further deiodination of T3 and rT3 to produce a variety of di- and monoiodo derivatives. In this paper, the deiodinase activity of a series of pen-substituted naphthalenes having different amino groups is described. These compounds remove iodine selectively from the inner-ring of T4 and T3 to produce rT3 and 3,3'-diiodothyronine (3,3'-T2), respectively. The naphthyl-based compounds having two selenols in the pen-positions exhibit much higher deiodinase activity than those having two thiols or a thiol selenol pair. Mechanistic investigations reveal that the formation of a halogen bond between the iodine and chalcogen (S or Se) and the pen-interaction between two chalcogen atoms (chalcogen bond) are important for the deiodination reactions. Although the formation of a halogen bond leads to elongation of the C-I bond, the chalcogen bond facilitates the transfer of more electron density to the C-I sigma* orbitals, leading to a complete cleavage of the C-I bond. The higher activity of amino-substituted selenium compounds can be ascribed to the deprotonation of thiol/selenol moiety by the amino group, which not only increases the strength of halogen bond but also facilitates the chalcogen chalcogen interactions.

Determination of MBE grown wurtzite GaN/Ge3N4/Ge heterojunctions band offset by X-ray photoelectron spectroscopy

Hexagonal Ge3N4 layer was prepared on Ge surface by in situ direct atomic source nitridation and it is promising buffer layer to grow GaN on Ge (111). The valence band offset (VBO) of GaN/Ge3N4/Ge heterojunctions is determined by X-ray photoemission spectroscopy. The valence band (VB) of Ge3N4 is found to be 0.38?+/-?0.04?eV above the GaN valance band and 1.14?+/-?0.04?eV below the Ge. The GaN/Ge3N4 and Ge3N4/Ge are found type-II and type-I heterojunctions, respectively. The exact measurements of the VBO and conduction band offset (CBO) are important for use of GaN/Ge3N4/Ge (111) heterosystems.

Threshold voltage modeling under size quantization for ultra-thin silicon double-gate metal-oxide-semiconductor field-effect transistor

We report on the threshold voltage modeling of ultra-thin (1 nm-5 nm) silicon body double-gate (DG) MOSFETs using self-consistent Poisson-Schrodinger solver (SCHRED). We define the threshold voltage (V th) of symmetric DG MOSFETs as the gate voltage at which the center potential (Φ c) saturates to Φ c (s a t), and analyze the effects of oxide thickness (t ox) and substrate doping (N A) variations on V th. The validity of this definition is demonstrated by comparing the results with the charge transition (from weak to strong inversion) based model using SCHRED simulations. In addition, it is also shown that the proposed V t h definition, electrically corresponds to a condition where the inversion layer capacitance (C i n v) is equal to the oxide capacitance (C o x) across a wide-range of substrate doping densities. A capacitance based analytical model based on the criteria C i n v C o x is proposed to compute Φ c (s a t), while accounting for band-gap widening. This is validated through comparisons with the Poisson-Schrodinger solution. Further, we show that at the threshold voltage condition, the electron distribution (n(x)) along the depth (x) of the silicon film makes a transition from a strong single peak at the center of the silicon film to the onset of a symmetric double-peak away from the center of the silicon film. © 2012 American Institute of Physics.