Solving linear programming problems exactly

A linear programming problem in an inequality form having a bounded solution is solved error-free using an algorithm that sorts the inequalities, removes the redundant ones, and uses the p-adic arithmetic. (C) Elsevier Science Inc., 1997

The complexity of certain incremental code generation problems

This paper looks at the complexity of four different incremental problems. The following are the problems considered: (1) Interval partitioning of a flow graph (2) Breadth first search (BFS) of a directed graph (3) Lexicographic depth first search (DFS) of a directed graph (4) Constructing the postorder listing of the nodes of a binary tree. The last problem arises out of the need for incrementally computing the Sethi-Ullman (SU) ordering [1] of the subtrees of a tree after it has undergone changes of a given type. These problems are among those that claimed our attention in the process of our designing algorithmic techniques for incremental code generation. BFS and DFS have certainly numerous other applications, but as far as our work is concerned, incremental code generation is the common thread linking these problems. The study of the complexity of these problems is done from two different perspectives. In [2] is given the theory of incremental relative lower bounds (IRLB). We use this theory to derive the IRLBs of the first three problems. Then we use the notion of a bounded incremental algorithm [4] to prove the unboundedness of the fourth problem with respect to the locally persistent model of computation. Possibly, the lower bound result for lexicographic DFS is the most interesting. In [5] the author considers lexicographic DFS to be a problem for which the incremental version may require the recomputation of the entire solution from scratch. In that sense, our IRLB result provides further evidence for this possibility with the proviso that the incremental DFS algorithms considered be ones that do not require too much of preprocessing.

The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear flow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear how of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

EPR and photoluminescence studies of ZnO:Mn nanophosphors prepared by solution combustion route

Nanocrystalline ZnO:Mn (0.1 mol%) phosphors have been successfully prepared by self propagating, gas producing solution combustion method. The powder X-ray diffraction of as-formed ZnO:Mn sample shows, hexagonal wurtzite phase with particle size of similar to 40 nm. For Mn doped ZnO, the lattice parameters and volume of unit cell (a=3.23065 angstrom, c=5.27563 angstrom and V=47.684 (angstrom)(3)) are found to be greater than that of undoped ZnO (a=3.19993 angstrom, c=5.22546 angstrom and V=46.336 (angstrom)(3)). The SEM micrographs reveal that besides the spherical crystals, the powders also contained several voids and pores. The TEM photograph also shows the particles are approximately spherical in nature. The FTIR spectrum shows two peaks at similar to 3428 and 1598 cm(-1) which are attributed to O-H stretching and H-O-H bending vibration. The PL spectra of ZnO:Mn indicate a strong green emission peak at 526 nm and a weak red emission at 636 nm corresponding to T-4(1) -> (6)A(1) transition of Mn2+ ions. The EPR spectrum exhibits fine structure transition which will be split into six hyperfine components due to Mn-55 hyperfine coupling giving rise to all 30 allowed transitions. From EPR spectra the spin-Hamiltonian parameters have been evaluated and discussed. The magnitude of the hyperfine splitting (A) constant indicates that there exists a moderately covalent bonding between the Mn2+ ions and the surrounding ligands. The number of spins participating in resonance (N), its paramagnetic susceptibility (chi) have been evaluated. (C) 2011 Elsevier B.V. All rights reserved.

Robust Relay Precoder Design for MIMO-Relay Networks

In this paper, we consider a robust design of MIMO-relay precoder and receive filter for the destination nodes in a non-regenerative multiple-input multiple-output (MIMO) relay network. The network consists of multiple source-destination node pairs assisted by a single MIMO-relay node. The source and destination nodes are single antenna nodes, whereas the MIMO-relay node has multiple transmit and multiple receive antennas. The channel state information (CSI) available at the MIMO-relay node for precoding purpose is assumed to be imperfect. We assume that the norms of errors in CSI are upper-bounded, and the MIMO-relay node knows these bounds. We consider the robust design of the MIMO-relay precoder and receive filter based on the minimization of the total MIMO-relay transmit power with constraints on the mean square error (MSE) at the destination nodes. We show that this design problem can be solved by solving an alternating sequence of minimization and worst-case analysis problems. The minimization problem is formulated as a convex optimization problem that can be solved efficiently using interior-point methods. The worst-case analysis problem can be solved analytically using an approximation for the MSEs at the destination nodes. We demonstrate the robust performance of the proposed design through simulations.

Analysing Message Sequence Graph Specifications

We give a detailed construction of a finite-state transition system for a com-connected Message Sequence Graph. Though this result is well-known in the literature and forms the basis for the solution to several analysis and verification problems concerning MSG specifications, the constructions given in the literature are either not amenable to implementation, or imprecise, or simply incorrect. In contrast we give a detailed construction along with a proof of its correctness. Our transition system is amenable to implementation, and can also be used for a bounded analysis of general (not necessarily com-connected) MSG specifications.

An iterative auction mechanism for combinatorial exchanges

Combinatorial exchanges are double sided marketplaces with multiple sellers and multiple buyers trading with the help of combinatorial bids. The allocation and other associated problems in such exchanges are known to be among the hardest to solve among all economic mechanisms. In this paper, we develop computationally efficient iterative auction mechanisms for solving combinatorial exchanges. Our mechanisms satisfy Individual-rationality (IR) and budget-nonnegativity (BN) properties. We also show that our method is bounded and convergent. Our numerical experiments show that our algorithm produces good quality solutions and is computationally efficient.

Developments in quantum information processing by nuclear magnetic resonance: Use of quadrupolar and dipolar couplings

Use of dipolar and quadrupolar couplings for quantum information processing (QIP) by nuclear magnetic resonance (NMR) is described. In these cases, instead of the individual spins being qubits, the 2(n) energy levels of the spin-system can be treated as an n-qubit system. It is demonstrated that QIP in such systems can be carried out using transition-selective pulses, in (CHCN)-C-3, (CH3CN)-C-13, Li-7 (I = 3/2) and Cs-133 (I = 7/2), oriented in liquid crystals yielding 2 and 3 qubit systems. Creation of pseudopure states, implementation of logic gates and arithmetic operations (half-adder and subtractor) have been carried out in these systems using transition-selective pulses.

Difference in spin state and covalence between La1-xSrxCoO3 and La2-xSrxLi0.5Co0.5O4

We present a comparative study of the spin states and electronic properties of La1-xSrxCoO3 and La2-xSrxLi0.5Co0.5O4 using X-ray absorption near-edge structure spectroscopy at both the O-K and Co-L-2.3 thresholds. In the La2-xSrxLi0.5Co0.5O4 system the CoO6 octahedra are isolated, the holes induced by Sr doping are trapped in the isolated Co(IV)O-6 octahedra, and a low-spin state is found for the Co ions, which does not change upon Sr doping. In the La1-xSrxCoO3 system, the interconnected CoO6 octahedra, with a 180degrees Co-O-Co bond angle, give rise to a transition from low-spin to intermediate-spin state with a ferromagnetic alignment of the Co spins. The double-exchange, ferromagnetic coupling between Co ions mediated by the 180degrees bond angle is responsible for suppressing the low spin-state. We find that the branching ratio of spectral intensities at the L-2 and L-3 thresholds in the Co-L-2.3 X-ray absorption spectra is sensitive to the spin state of the Co ions allowing its direct spectroscopic determination. (C) 2002 Published by Elsevier Science B.V.

Weakly non-linear stability of a hydrodynamic accretion disc

When the cold accretion disc coupling between neutral gas and a magnetic field is so weak that the magnetorotational instability is less effective or even stops working, it is of prime interest to investigate the pure hydrodynamic origin of turbulence and transport phenomena. As the Reynolds number increases, the relative importance of the non-linear term in the hydrodynamic equation increases. In an accretion disc where the molecular viscosity is too small, the Reynolds number is large enough for the non-linear term to have new effects. We investigate the scenario of the `weakly non-linear' evolution of the amplitude of the linear mode when the flow is bounded by two parallel walls. The unperturbed flow is similar to the plane Couette flow, but with the Coriolis force included in the hydrodynamic equation. Although there is no exponentially growing eigenmode, because of the self-interaction, the least stable eigenmode will grow in an intermediate phase. Later, this will lead to higher-order non-linearity and plausible turbulence. Although the non-linear term in the hydrodynamic equation is energy-conserving, within the weakly non-linear analysis it is possible to define a lower bound of the energy (alpha A(c)(2), where A(c) is the threshold amplitude) needed for the flow to transform to the turbulent phase. Such an unstable phase is possible only if the Reynolds number >= 10(3-4). The numerical difficulties in obtaining such a large Reynolds number might be the reason for the negative result of numerical simulations on a pure hydrodynamic Keplerian accretion disc.

Quantum spin models with exact dimer ground states

Inspired by the exact solution of the Majumdar-Ghosh model, a family of one-dimensional, translationally invariant spin Hamiltonians is constructed. The exchange coupling in these models is antiferromagnetic, and decreases linearly with the separation between the spins. The coupling becomes identically zero beyond a certain distance. It is rigorously proved that the dimer configuration is an exact, superstable ground-state configuration of all the members of the family on a periodic chain. The ground state is twofold degenerate, and there exists an energy gap above the ground state. The Majumdar-Ghosh Hamiltonian with a twofold degenerate dimer ground state is just the first member of the family. The scheme of construction is generalized to two and three dimensions, and illustrated with the help of some concrete examples. The first member in two dimensions is the Shastry-Sutherland model. Many of these models have exponentially degenerate, exact dimer ground states.

Synthesis of acicular hydrogoethite (alpha-FeOOH center dot xH(2)O; 0.1 < x < 0.22) particles using morphology controlling cationic additives and magnetic properties of maghemite derived from hydrogoethite

A method for the preparation of acicular hydrogoethite (alpha -FeOOH.xH(2)O, 0.1 < x < 0.22) particles of 0.3-1 mm length has been optimized by air oxidation of Fe( II) hydroxide gel precipitated from aqueous (NH4)(2)Fe(SO4)(2) solutions containing 0.005-0.02 atom% of cationic Pt, Pd or Rh additives as morphology controlling agents. Hydrogoethite particles are evolved from the amorphous ferrous hydroxide gel by heterogeneous nucleation and growth. Preferential adsorption of additives on certain crystallographic planes thereby retarding the growth in the perpendicular direction, allows the particles to acquire acicular shapes with high aspect ratios of 8-15. Synthetic hydrogoethite showed a mass loss of about 14% at similar to 280 degreesC, revealing the presence of strongly coordinated water of hydration in the interior of the goethite crystallites. As evident from IR spectra, excess H2O molecules (0.1- 0.22 per formula unit) are located in the strands of channels formed in between the double ribbons of FeO6 octahedra running parallel to the c- axis. Hydrogoethite particles constituted of multicrystallites are formed with Pt as additive, whereas single crystallite particles are obtained with Pd (or Rh). For both dehydroxylation as well as H-2 reduction, a lower reaction temperature (similar to 220 degreesC) was observed for the former (Pt treated) compared to the latter (Pd or Rh) (similar to 260 degreesC). Acicular magnetite (Fe3O4) was prepared either by reducing hydrogoethite (magnetite route) or dehydroxylating hydrogoethite to hematite and then reducing it to magnetite (hematite- magnetite route). According to TEM studies, preferential dehydroxylation of hydrogoethite along < 010 > leads to microporous hematite. Maghemite (gamma -Fe2O3 (-) (delta), 0 < < 0.25) was obtained by reoxidation of magnetite. The micropores are retained during the topotactic transformation to magnetite and finally to maghemite, whereas cylindrical mesopores are formed due to rearrangement of the oxygen sublattice from hexagonal to cubic close packing during the conversion of hydrogoethite to magnetite and then to maghemite. Accordingly, three different types of maghemite particles are realized: strongly oriented multicrystalline particles, single crystalline acicular particles with micropores or crystallites having mesopores. Higher values of saturation magnetization ((s) = 74 emu g(-1)) and coercivity (H-c = 320 Oe) are obtained for single crystalline mesoporous particles. In the other cases, the smaller size of particles and larger distribution of micropores decreases sigma (s) considerably ( < 60 emu g(-1)) due to relaxation effects of spins on the surface atoms as revealed by Mossbauer spectroscopy.

An adaptive cascade compensator for a wide class of stable minimum or nonminimum phase plants through time moment estimation

Model Reference Adaptive Control (MRAC) of a wide repertoire of stable Linear Time Invariant (LTI) systems is addressed here. Even an upper bound on the order of the finite-dimensional system is unavailable. Further, the unknown plant is permitted to have both minimum phase and nonminimum phase zeros. Model following with reference to a completely specified reference model excited by a class of piecewise continuous bounded signals is the goal. The problem is approached by taking recourse to the time moments representation of an LTI system. The treatment here is confined to Single-Input Single-Output (SISO) systems. The adaptive controller is built upon an on-line scheme for time moment estimation of a system given no more than its input and output. As a first step, a cascade compensator is devised. The primary contribution lies in developing a unified framework to eventually address with more finesse the problem of adaptive control of a large family of plants allowed to be minimum or nonminimum phase. Thus, the scheme presented in this paper is confined to lay the basis for more refined compensators-cascade, feedback and both-initially for SISO systems and progressively for Multi-Input Multi-Output (MIMO) systems. Simulations are presented.

On an oscillatory point force in a rotating stratified fluid

The forced oscillations due to a point forcing effect in an infinite or contained, inviscid, incompressible, rotating, stratified fluid are investigated taking into account the density variation in the inertia terms in the linearized equations of motion. The solutions are obtained in closed form using generalized Fourier transforms. Solutions are presented for a medium bounded by a finite cylinder when the oscillatory forcing effect is acting at a point on the axis of the cylinder. In both the unbounded and bounded case, there exist characteristic cones emanating from the point of application of the force on which either the pressure or its derivatives are discontinuous. The perfect resonance existing at certain frequencies in an unbounded or bounded homogeneous fluid is avoided in the case of a confined stratified fluid.

The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear ow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear flow of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.