Computational experience with an interior point algorithm on the satisfiability problem

We apply the zero-one integer programming algorithm described in Karmarkar [12] and Karmarkar, Resende and Ramakrishnan [13] to solve randomly generated instances of the satisfiability problem (SAT). The interior point algorithm is briefly reviewed and shown to be easily adapted to solve large instances of SAT. Hundreds of instances of SAT (having from 100 to 1000 variables and 100 to 32,000 clauses) are randomly generated and solved. For comparison, we attempt to solve the problems via linear programming relaxation with MINOS.     

Pseudo Complex Cepstrum Using Discrete Cosine Transform

Two new algorithms are proposed, which obtain pseudo complex cepstrum using Discrete Cosine Transform (DCT). We call this as the Discrete Cosine Transformed Cepstrum (DCTC). In the first algorithm, we apply the relation between Discrete Fourier Transform (DFT) and DCT. Computing the complex cepstrum using Fourier transform needs the unwrapped phase. The calculation of the unwrapped phase is difficult whenever multiple zeros and poles occur near or on the unit circle. Since DCT is a real function, its phase can only be 0 or π and the phase is unwrapped by representing the negative sign by exp (−jπ) and the positive sign by exp (j0) . The second algorithm obviates the need for DFT and obtains DCTC by representing the DCT sequence itself by magnitude and phase components. Phase is unwrapped in the same way as the first algorithm. We have tested DCTC on a simulated system that has multiple poles and zeros near or on the unit circle. The results show that DCTC matches the theoretical complex cepstrum more closely than the DFT based complex cepstrum. We have explored possible uses for DCTC in obtaining the pitch contour of syllables, words and sentences. It is shown that the spectral envelope obtained from the first few coefficients matches reasonably with the envelope of the signal spectrum under consideration, and thus can be used in applications, where faithful reproduction of the spectral envelope is not critical. We also examine the utility of DCTC as feature set for speaker identification. The identification rate with DCTC as feature vector was higher than that with linear prediction-derived cepstral coefficients.     

Infrared and Raman spectra of aquamolybdenum (VI) oxide hydrate (MoO3·2H2O)

The infrared and Raman spectra of MoO₃·2H₂O are recorded and analysed on the basis of vibrations due to MoO₆ octahedra and H₂O molecules. Considerable changes in the frequencies of the octahedra have been observed due to strong distortion in the octahedral arrangement. The inactivev ₆ vibration of O _h symmetry became active in the Raman spectrum. Co-ordinated (aquated) and hydrated (interlayer) water molecules give rise to different frequencies.     

An interior point algorithm to solve computationally difficult set covering problems

We present an interior point approach to the zero–one integer programming feasibility problem based on the minimization of a nonconvex potential function. Given a polytope defined by a set of linear inequalities, this procedure generates a sequence of strict interior points of this polytope, such that each consecutive point reduces the value of the potential function. An integer solution (not necessarily feasible) is generated at each iteration by a rounding scheme. The direction used to determine the new iterate is computed by solving a nonconvex quadratic program on an ellipsoid. We illustrate the approach by considering a class of difficult set covering problems that arise from computing the 1-width of the incidence matrix of Steiner triple systems.     

Photo-Fries and Fries reaction of 5,8-dihydro-1-naphthyl esters

Systematic studies were performed on the photo-Fries and the Fries reaction of aliphatic, aliphatic unsaturated, aromatic and aromatic unsaturated esters of 5,8-dihydro-1-naphthol. The Fries reaction of 5,8-dihydro-1-naphthyl acetate in various solvents is also reported.     

Clustering and mechanics in dense depletion and thermal gels

We report on the microstructure and mechanical properties (elastic modulus) of concentrated depletion and thermal gels of octadecyl-coated silica particles for different values of the strength of interaction--polymer concentration for depletion gels and temperature for thermal gels. The depletion gels are composed of dense clusters and voids, while the thermal gels are devoid of clusters. Shear breaks up clusters in depletion gels while it induces clustering in the thermal gels. In both of these gels, the microstructure recovers to the presheared state upon cessation of shear. The recovery of the elastic modulus mimics the microstructure in the sense that the elastic modulus recovers to the presheared sheared state after shearing is stopped. Calculations of the gel boundary by modeling the interactions with an effective one-component square-well model reveals that suspensions with similar ranges of attraction gel at the same volume fraction at a fixed strength of attraction. Calculations of the elastic modulus using the na?ve mode coupling theory for depletion gels are in good agreement with experimental measurements provided clustering is taken into account and have the same magnitude as the elastic moduli of thermal gels with similar strengths of attraction. These calculations, in addition to the experimental observations reinforce the point that the microscopic parameter determining the elastic modulus of dense gels and its recovery is the localization length which is only a fraction of the particle diameter and not the structure on the length scale of the particle diameter and larger.     

Synthesis of phenazine derivatives for use as precursors to electrochemically generated bases

1,6-Disubstituted phenazine derivatives for use as precursors to electrochemically generated bases have been synthesized from readily available starting materials. Reaction of 1,6-dihydroxyphenazine with 1,10-diododecane, 1,11-diiodo-3,6,9-trioxaundecane or (R,R)-(-)-1,2-bis(3-iodopropoxy)cyclohexane gave planar chiral phenazinophanes containing ether-linked bridges; molecular structures of all these compounds have been determined by X-ray crystallography. Substituted 1,6-diaminophenazines were prepared by palladium-mediated amination of 1,6-dichlorophenazine and acylation of 1,6-diaminophenazine followed by reduction. Reaction of 1,6-bis(alkylamino)phenazines with sebacoyl chloride gave planar chiral phenazinophanes containing amide-linked bridges.     

Binding of Acridinedione Dyes with α, β and γ-Cyclodextrins: Fluorescence Quenching and Estimation of Thermodynamic Parameters

Using absorption and fluorescence spectroscopy, acridinedione (ACD) was found to be included into the -cyclodextrin (-CD) cavity to form a 1 : 1 inclusion complex. As a consequence of inclusion, the fluorescence of ACD is strongly quenched. Lifetime data confirm that the quenching is purely static. The association constant for the formation of the complex was calculated using linear and non-linear equations. H and S values obtained from the temperature dependent association constants of the -CD/ACD(B) system are reported. It was also observed that these dyes complexed very weakly with and -CD.