Spin-1 Kitaev model in one dimension

We study a one-dimensional version of the Kitaev model on a ring of size N, in which there is a spin S > 1/2 on each site and the Hamiltonian is J Sigma(nSnSn+1y)-S-x. The cases where S is integer and half-odd integer are qualitatively different. We show that there is a Z(2)-valued conserved quantity W-n for each bond (n, n + 1) of the system. For integer S, the Hilbert space can be decomposed into 2N sectors, of unequal sizes. The number of states in most of the sectors grows as d(N), where d depends on the sector. The largest sector contains the ground state, and for this sector, for S=1, d=(root 5+1)/2. We carry out exact diagonalization for small systems. The extrapolation of our results to large N indicates that the energy gap remains finite in this limit. In the ground-state sector, the system can be mapped to a spin-1/2 model. We develop variational wave functions to study the lowest energy states in the ground state and other sectors. The first excited state of the system is the lowest energy state of a different sector and we estimate its excitation energy. We consider a more general Hamiltonian, adding a term lambda Sigma W-n(n), and show that this has gapless excitations in the range lambda(c)(1)<=lambda <=lambda(c)(2). We use the variational wave functions to study how the ground-state energy and the defect density vary near the two critical points lambda(c)(1) and lambda(c)(2).

Error-free matrix symmetrizers and equivalent symmetric matrices

A symmetrizer of the matrix A is a symmetric solution X that satisfies the matrix equation XA=AprimeX. An exact matrix symmetrizer is computed by obtaining a general algorithm and superimposing a modified multiple modulus residue arithmetic on this algorithm. A procedure based on computing a symmetrizer to obtain a symmetric matrix, called here an equivalent symmetric matrix, whose eigenvalues are the same as those of a given real nonsymmetric matrix is presented.

1, 2-Bis (diphenylphosphino) etane bridged dinuclear copper (I) complexes: Investigations of solid state and solution structures by CP/MAS31P NMR spectroscopy, X-ray crystallography, IR spectroscopy and solution 31P NMR and 63Cu NMR spectroscopy

Three different complexes of copper (I) with bridging 1, 2-bis(diphenylphosphino)ethane (dppe), namely [Cu2 (mu-dppe) (CH3CN)6] (ClO4)2 (1), [Cu2 (mu-dppe)2 (CH3 CN)2] (ClO4)2 (2), and [Cu2 (mu-dppe) (dppe)2 (CH3CN)2] (ClO4)2 (3) have been prepared. The structure of [Cu2 (mu-dppe) (dPPe)2 (CH3CH)2] (ClO4)2 has been determined by X-ray crystallography. It crystallizes in the space group PT with a=12.984(6) angstrom, b=13.180(6) angstrom, c=14.001(3) angstrom, alpha=105.23(3), beta=105.60(2), gamma=112.53 (4), V=1944 (3) angstrom3, and Z=1. The structure was refined by least-squares method with R=0.0365; R(w)=0.0451 for 6321 reflections with F0 greater-than-or-equal-to 3 sigma (F0). The CP/MAS P-31 and IR spectra of the complexes have been analysed in the light of available crystallographic data. IR spectroscopy is particularly helpful in identifying the presence of chelating dppe. P-31 chemical shifts observed in solid state are very different from those observed in solution, and change significantly with slight changes in structure. In solution, complex 1 remains undissociated but complexes 2 and 3 undergo extensive dissociation. With a combination of room temperature H-1, Cu-63, and variable temperature P-31 NMR spectra, it is possible to understand the various processes occurring in solution.

Support vector machine for evaluating seismic-liquefaction potential using shear wave velocity

The use of the shear wave velocity data as a field index for evaluating the liquefaction potential of sands is receiving increased attention because both shear wave velocity and liquefaction resistance are similarly influenced by many of the same factors such as void ratio, state of stress, stress history and geologic age. In this paper, the potential of support vector machine (SVM) based classification approach has been used to assess the liquefaction potential from actual shear wave velocity data. In this approach, an approximate implementation of a structural risk minimization (SRM) induction principle is done, which aims at minimizing a bound on the generalization error of a model rather than minimizing only the mean square error over the data set. Here SVM has been used as a classification tool to predict liquefaction potential of a soil based on shear wave velocity. The dataset consists the information of soil characteristics such as effective vertical stress (sigma'(v0)), soil type, shear wave velocity (V-s) and earthquake parameters such as peak horizontal acceleration (a(max)) and earthquake magnitude (M). Out of the available 186 datasets, 130 are considered for training and remaining 56 are used for testing the model. The study indicated that SVM can successfully model the complex relationship between seismic parameters, soil parameters and the liquefaction potential. In the model based on soil characteristics, the input parameters used are sigma'(v0), soil type. V-s, a(max) and M. In the other model based on shear wave velocity alone uses V-s, a(max) and M as input parameters. In this paper, it has been demonstrated that Vs alone can be used to predict the liquefaction potential of a soil using a support vector machine model. (C) 2010 Elsevier B.V. All rights reserved.

On Computation of Minimum Distance of Linear Block Codes Above 1/2 Rate Coding

The minimum distance of linear block codes is one of the important parameter that indicates the error performance of the code. When the code rate is less than 1/2, efficient algorithms are available for finding minimum distance using the concept of information sets. When the code rate is greater than 1/2, only one information set is available and efficiency suffers. In this paper, we investigate and propose a novel algorithm to find the minimum distance of linear block codes with the code rate greater than 1/2. We propose to reverse the roles of information set and parity set to get virtually another information set to improve the efficiency. This method is 67.7 times faster than the minimum distance algorithm implemented in MAGMA Computational Algebra System for a (80, 45) linear block code.

On Network-Error Correcting Convolutional Codes under the BSC Edge Error Model

Convolutional network-error correcting codes (CNECCs) are known to provide error correcting capability in acyclic instantaneous networks within the network coding paradigm under small field size conditions. In this work, we investigate the performance of CNECCs under the error model of the network where the edges are assumed to be statistically independent binary symmetric channels, each with the same probability of error pe(0 <= p(e) < 0.5). We obtain bounds on the performance of such CNECCs based on a modified generating function (the transfer function) of the CNECCs. For a given network, we derive a mathematical condition on how small p(e) should be so that only single edge network-errors need to be accounted for, thus reducing the complexity of evaluating the probability of error of any CNECC. Simulations indicate that convolutional codes are required to possess different properties to achieve good performance in low p(e) and high p(e) regimes. For the low p(e) regime, convolutional codes with good distance properties show good performance. For the high p(e) regime, convolutional codes that have a good slope ( the minimum normalized cycle weight) are seen to be good. We derive a lower bound on the slope of any rate b/c convolutional code with a certain degree.

Effective action and adiabatic expansions for the 1-D and 2-D hubbard models at half-filling

We analyze here the occurrence of antiferromagnetic (AFM) correlations in the half-filled Hubbard model in one and two space dimensions using a natural fermionic representation of the model and a newly proposed way of implementing the half-filling constraint. We find that our way of implementing the constraint is capable of enforcing it exactly already at the lowest levels of approximation. We discuss how to develop a systematic adiabatic expansion for the model and how Berry's phase contributions arise quite naturally from the adiabatic expansion. At low temperatures and in the continuum limit the model gets mapped onto an O(3) nonlinear sigma model (NLsigma). A topological, Wess-Zumino term is present in the effective action of the ID NLsigma as expected, while no topological terms are present in 2D. Some specific difficulties that arise in connection with the implementation of an adiabatic expansion scheme within a thermodynamic context are also discussed, and we hint at possible solutions.

Exact free-surface flows for shallow-water equations .1. - the incompressible case

A comprehensive exact treatment of free surface flows governed by shallow water equations (in sigma variables) is given. Several new families of exact solutions of the governing PDEs are found and are shown to embed the well-known self-similar or traveling wave solutions which themselves are governed by reduced ODEs. The classes of solutions found here are explicit in contrast to those found earlier in an implicit form. The height of the free surface for each family of solutions is found explicitly. For the traveling or simple wave, the free surface is governed by a nonlinear wave equation, but is arbitrary otherwise. For other types of solutions, the height of the free surface is constant either on lines of constant acceleration or on lines of constant speed; in another case, the free surface is a horizontal plane while the flow underneath is a sine wave. The existence of simple waves on shear flows is analytically proved. The interaction of large amplitude progressive waves with shear flow is also studied.

Computing Fractal Dimension of Signals using Multiresolution Box-counting Method

In this paper, we have developed a method to compute fractal dimension (FD) of discrete time signals, in the time domain, by modifying the box-counting method. The size of the box is dependent on the sampling frequency of the signal. The number of boxes required to completely cover the signal are obtained at multiple time resolutions. The time resolutions are made coarse by decimating the signal. The loglog plot of total number of boxes required to cover the curve versus size of the box used appears to be a straight line, whose slope is taken as an estimate of FD of the signal. The results are provided to demonstrate the performance of the proposed method using parametric fractal signals. The estimation accuracy of the method is compared with that of Katz, Sevcik, and Higuchi methods. In ddition, some properties of the FD are discussed.

Structure of N-nitroso-r-2,c-7-diphenylhexahydro-1,4-diazepin-5-one

C17H17N3O2, M(r) = 295.34, orthorhombic, P2(1)2(1)2(1), a = 7.659 (1), b = 12.741 (1), c = 15.095 (1) angstrom, V = 1473.19 (2) angstrom 3, Z = 4, D(m) = 1.33, D(x) = 1.32 Mg m-3, lambda(Cu K-alpha) = 1.5418 angstrom, mu = 0.68 mm-1, F(000) = 624, T = 295 K, R = 0.031 for 1549 unique observed reflections with I > 2.5-sigma(I). The seven-membered heterocyclic ring adopts a boat conformation flattened at the nitroso end of the ring. The substituent phenyl rings occupy pseudo-axial positions and the nitroso group is coplanar with the C(2), N(1), C(7) plane of the central ring. The crystal structure is stabilized by intermolecular N-H...O and weak C-H...O hydrogen bonds.

Organometallic Chemistry of Diphosphazanes. 11. Reactions of fac-[Mo(CO)3(MeCN){.eta.2-Ph2PN(Pri)PPh(DMP)}] (DMP = 3,5-Dimethyl-1-Pyrazolyl) with Diphosphazanes and Diphosphinoalkanes and Oxidative Addition with Iodine

The use of fac-[Mo(CO)(3)(MeCN)(eta(2)-L(1))] (1a) {L(1) = Ph(2)PN(Pr-i)PPh(DMP)}(2) as a precursor to metalloligands and bimetallic, heterotrimetallic, and heptacoordinated complexes is reported. The reaction of 1a with diphosphazane, dppa, or a diphosphinoalkane such as dppm or dppe yields the fac-eta(1)-diphosphine substituted metalloligands, fac-[Mo(CO)(3)(eta(2)-L(1))(eta(1)-PXP)] {PXP = dppa (2), dppm (3), and dppe (4)}. These undergo isomerization to yield the corresponding mer-diphosphine complexes (5-7). Oxidation of the uncoordinated phosphorus atom of the mer-eta(1)-dppm-substituted complex eventually provides mer-[Mo(CO)(3)-(eta(2)-L(1)){eta(1)-Ph(2)PCH(2)P(O)Ph(2)}](8). The structure of the latter complex has been confirmed by single crystal X-ray diffraction {triclinic system, P ($) over bar 1; a = 11.994(3), b = 14.807(2), c = 15.855(3) Angstrom; alpha = 114.24(1), beta = 91.35(2), and gamma = 98.95(1)degrees; Z = 2, 4014 data (F-0 > 5 sigma(F-0)), R = 0.066, R(W) = 0.069}. Treatment of the dppe metalloligand 7 with [PtCl2(COD)] yields the heterotrimetallic complex cis-[PtCl2{mer-[Mo(CO)(3)(eta(2)-L(1))(eta(1)-dppe]}(2)] (9). Attempts to prepare a related trimetallic complex with the dppm-containing metalloligand were unsuccessful; only the tetracarbonyl complex cis-[Mo(CO)(4)(eta(2)-L(1))] (1b) and cis-[PtCl2(eta(2)-dppm)] were obtained. Reaction of la with dppe in the ratio 2:1 yields the mer-mer dinuclear complex [{mer-[Mo(CO)(3)(eta(2)-L(1))]}(2)(mu-dppe)] (10) bridged by dppe. Oxidation of 1a with iodine yields the Mo(II) heptacoordinated complex [MoI2(CO)(2)(eta(3)-L(1))] (11) with tridentate PPN coordination. The same Mo(II) complex 11 is also obtained by the direct oxidation of the tetracarbonyl complex cis-[Mo(CO)(4)(eta(2)-L(1))] (1b) with iodine. The structure of 11 has been confirmed by X-ray diffraction studies {monoclinic system, Cc; a = 10.471(2), b = 19.305(3), c = 17.325(3) Angstrom; beta = 95.47(2)degrees; Z = 4, 3153 data (F-0 > 5 sigma(F-0)), R = 0.049, R(W) = 0.051}. This complex exhibits an unusual capped-trigonal prismatic geometry around the metal. A similar heptacoordinated complex 12 with a chiral diphosphazane ligand {L(3) = (S,R)-P(h)2PN-(*CHMePh)*PPh(DMP)} has also been synthesized.

Photolysis of arene chromium tricarbonyl complexes in presence of amine-boranes: Observation of sigma-borane complexes in solution

Activation of the B-H sigma-bond of amine-boranes on the chromium(0) center of arene chromium tricarbonyl complexes (eta(6)-arene) Cr(CO)(3) (arene = fluorobenzene, 1a; benzene, 1b and mesitylene, 1c) has been studied. Photolysis of 1b in presence of ammonia-borane (H3N center dot BH3, AB) and tert-butylamine-borane ((BuH2N)-Bu-t center dot BH3, TBAB) resulted in H-2 evolution and precipitation of a BNHx polymer. On the other hand, photolysis in the presence of trimethylamine-borane (Me3N center dot BH3, TMAB) resulted in the formation of a sigma-borane complex (2) along with Cr(CO)(5)(eta(1)-HBH2 center dot NMe3) (3). The sigma-borane complexes (eta(6)-arene) Cr-( CO)(2)(eta(1)-HBH2 center dot NMe3) (arene = fluorobenzene, 2a; benzene, 2b and mesitylene, 2c) were characterized in solution by H-1, B-11, and C-13 NMR spectroscopy. Electron withdrawing substituents on the arene ring provide the more stable sigma-borane moiety in this series of complexes. (C) 2011 Elsevier B.V. All rights reserved.

Unified approach to the constraint counting theory of glasses

An approach to the constraint counting theory of glasses is applied to many glass systems which include an oxide, chalcohalide, and chalcogenides. In this, shifting of the percolation threshold due to noncovalent bonding interactions in a basically covalent network and other recent extensions of the theory appear natural. This is particularly insightful and reveals that the chemical threshold signifies another structural transition along with the rigidity percolation threshold, thus unifying these two seemingly disparate toplogical concepts. [S0163-1829(99)11441-3].

A current error space vector based hysteresis controller with constant switching frequency and simple online boundary computation for VSI fed IM drive

This paper proposes a simple current error space vector based hysteresis controller for two-level inverter fed Induction Motor (IM) drives. This proposed hysteresis controller retains all advantages of conventional current error space vector based hysteresis controllers like fast dynamic response, simple to implement, adjacent voltage vector switching etc. The additional advantage of this proposed hysteresis controller is that it gives a phase voltage frequency spectrum exactly similar to that of a constant switching frequency space vector pulse width modulated (SVPWM) inverter. In this proposed hysteresis controller the boundary is computed online using estimated stator voltages along alpha and beta axes thus completely eliminating look up tables used for obtaining parabolic hysteresis boundary proposed in. The estimation of stator voltage is carried out using current errors along alpha and beta axes and steady state model of induction motor. The proposed scheme is simple and capable of taking inverter upto six step mode operation, if demanded by drive system. The proposed hysteresis controller based inverter fed drive scheme is simulated extensively using SIMULINK toolbox of MATLAB for steady state and transient performance. The experimental verification for steady state performance of the proposed scheme is carried out on a 3.7kW IM.

Network Error Correction for Unit-Delay, Memory-Free Networks Using Convolutional Codes

A single source network is said to be memory-free if all of the internal nodes (those except the source and the sinks) do not employ memory but merely send linear combinations of the symbols received at their incoming edges on their outgoing edges. In this work, we introduce network-error correction for single source, acyclic, unit-delay, memory-free networks with coherent network coding for multicast. A convolutional code is designed at the source based on the network code in order to correct network- errors that correspond to any of a given set of error patterns, as long as consecutive errors are separated by a certain interval which depends on the convolutional code selected. Bounds on this interval and the field size required for constructing the convolutional code with the required free distance are also obtained. We illustrate the performance of convolutional network error correcting codes (CNECCs) designed for the unit-delay networks using simulations of CNECCs on an example network under a probabilistic error model.