Biased random walks

How much can an imperfect source of randomness affect an algorithm? We examine several simple questions of this type concerning the long-term behavior of a random walk on a finite graph. In our setup, at each step of the random walk a “controller” can, with a certain small probability, fix the next step, thus introducing a bias. We analyze the extent to which the bias can affect the limit behavior of the walk. The controller is assumed to associate a real, nonnegative, “benefit” with each state, and to strive to maximize the long-term expected benefit. We derive tight bounds on the maximum of this objective function over all controller's strategies, and present polynomial time algorithms for computing the optimal controller strategy.     

Synthesis,characterization and biological analysis of transition metal complexes with macro cyclic ligands derived from adipic acid,ethylenediamine with diethyloxalate and diethylmalonate

Macro-cyclic ligands from adipic acid, ethylenediamine with diethyloxalate and diethylmalonate and their respective metal complexes of Mn(II), Co(II), Ni(II), Cu(II), and Zn(II) with macro cyclic ligands (LO) and (LM) L [N,N′-bis(2-aminoethyl)hexanediamide] were synthesized successfully. These metal complexes were characterized by Fourier transform infrared, ultraviolet visible spectrometry, proton nuclear magnetic resonance spectroscopy, and mass Spectrometry, CHNS and thermogravimetric analysis. The elemental analysis confirms the structures for Mn(II), Co(II) and Ni(II) complexes similar to octahedral geometry, Cu(II) complexes as a square planar geometry and Zn(II) complexes in the tetrahedral geometry. The molar conductivities of all the metal complexes were taken in 10^?3 M DMSO, and values of all the metal complexes showed their electrolytic nature which indicates the presence of chloride ions. Thermal analysis supports as the metal complexes are thermally stable. The result of antimicrobial activity against various microorganisms confirms that the metal complexes are potent bactericides and fungicides than the ligand. Metal complexes of LO with Cu(II) and Zn(II) were found to be highly active against S. typhimurium than the complexes of LM.

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Universal binary Hermitian forms

We will determine (up to equivalence) all of the integral positive definite Hermitian lattices in imaginary quadratic fields of class number 1 that represent all positive integers.

     

Correction to: Unbounded order continuous operators on Riesz spaces

Positivity - In page 838, line 7, we should write: For sequences in a Dedekind complete Riesz space E, if and only if there exists a sequence such that and for each (see [1, Page 17–18]).     

Unbounded order continuous operators on Riesz spaces

In this paper, using the concept of unbounded order convergence in Riesz spaces, we define new classes of operators, named unbounded order continuous (uo-continuous, for short) and boundedly unbounded order continuous operators. We give some conditions under which uo-continuity will be equivalent to order continuity of some operators on Riesz spaces. We show that the collection of all uo-continuous linear functionals on a Riesz space E is a band of \(E^\sim \).     

Molecularly imprinted polymer Based PVC-Membrane-Coated graphite electrode for the determination of metoprolol

A PVC-based membrane containing metoprolol molecularly imprinted polymer (MIP) coated directly on graphite electrode for the determination of metoprolol in real samples is reported. This potentiometric sensor was designed by dispersing the MIP particles in dioctylphthalate plasticizer as solvent mediator and then embedded in polyvinyl chloride matrix. The electrode exhibited a near-Nernstian slope of 55.4 ± 1 mV decade^-1 for metoprolol over a wide concentration range between 2.0 × 10^-7-8.0 × 10^-3 M and a detection limit of 1.3 × 10^-7 M. With a response time of about 14 s it could be used for at least 6 months without any divergence in potential. The proposed electrode can be used in the pH range of 3.5-10.5 and can reveal good selectivities for metoprolol over a wide variety of ions. Finally, the designed sensor was successfully applied as an indicator electrode to determine the concentration of metoprolol in tablets, human urine and plasma. The results were compared favorably with those obtained by HPLC method and showed satisfactory agreements with them.     

Solid-Phase Extraction of Metoprolol onto(Methacrylic acid-ethylene glycol dimethacrylate)-based Molecularly Imprinted Polymer and Its Spectrophotometric Determination

A new adsorbent for molecularly imprinted solid phase extraction (MISPE) of metoprolol was synthesized using methacrylic acid (MAA) as functional monomer and ethylene glycol dimethacrylate (EGDMA) as cross‐linking agent causing a non‐covalent, bulk, thermal radical‐polymerization. Control polymer (non‐imprinted polymer) was prepared under well defined conditions without the use of metoprolol. The synthesized polymers were characterized by IR spectroscopy, X‐ray diffraction and thermal analysis techniques. This polymer was used for the rapid extraction and preconcentration of metoprolol from real samples prior to spectrophotometric determination. Extraction efficiency and the influence of flow rates of sample and stripping solutions, pH, type of eluent for elution of metoprolol from polymer, break through volume and limit of detection were studied. The detection limit of the proposed method is 0.4 ng·mL^?1. The method was applied successfully to the recovery and determination of metoprolol in tablets, human urine and plasma samples.     

Efficient “On‐the‐Fly” calculation of Raman Spectra from Ab‐Initio molecular dynamics: Application to hydrophobic/hydrophilic solutes in bulk water

We present a novel computational method to accurately calculate Raman spectra from first principles. Together with an extension of the second‐generation Car‐Parrinello method of Kühne et al. (Phys. Rev. Lett. 2007, 98, 066401) to propagate maximally localized Wannier functions together with the nuclei, a speed‐up of one order of magnitude can be observed. This scheme thus allows to routinely calculate finite‐temperature Raman spectra “on‐the‐fly” by means of ab‐initio molecular dynamics simulations. To demonstrate the predictive power of this approach we investigate the effect of hydrophobic and hydrophilic solutes in water solution on the infrared and Raman spectra. © 2015 Wiley Periodicals, Inc.