Cosmological Constraints on Polytropic Gas Model

We study the polytropic gas scenario as the unification of dark matter and dark energy. We fit the model parameters by using the latest observational data including type Ia supernovae, baryon acoustic oscillation, cosmic microwave background, and Hubble parameter data. At 68.3 % and 95.4 % confidence levels, we find the best fit values of the model parameters as $\tilde{K}=0.742_{-0.024}^{+0.024}(1\sigma)_{-0.049}^{+0.048}(2\sigma)$ and $n=-1.05_{-0.08}^{+0.08}(1\sigma)_{-0.16}^{+0.15}(2\sigma)$ . Using the best fit values of the model, we obtain the evolutionary behaviors of the equation of state parameters of the polytropic gas model and dark energy, the deceleration parameter of the universe, the dimensionless density parameters of dark matter and dark energy as well as the growth factor of structure formation. Then, we investigate different energy conditions in the polytropic gas model and obtain that only the strong energy condition is violated for the special ranges of the redshift. We also conclude that in the this model, the universe starts from the matter dominated epoch and approaches a de Sitter phase at late times, as expected. Further, the universe begins to accelerate at redshift z _t=0.74. Furthermore, in contrary to the ΛCDM model, the cosmic coincidence problem is solved naturally in the polytropic gas scenario. Moreover, this model fits the data of the growth factor well as the ΛCDM model.     

Application of He's variational iteration method and Adomian's decomposition method to Sawada–Kotera–Ito seventh‐order equation

In this article, the Sawada–Kotera–Ito seventh‐order equation is studied. He's variational iteration method and Adomian's decomposition method (ADM) are applied to obtain solution of this equation. We compare these methods together. The study highlights the significant features of the employed methods and its capability of handling completely integrable equations. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 887–897, 2011     

Maximizing non-monotone submodular set functions subject to different constraints: Combined algorithms

We study the problem of maximizing constrained non-monotone submodular functions and provide approximation algorithms that improve existing algorithms in terms of either the approximation factor or simplicity. Different constraints that we study are exact cardinality and multiple knapsack constraints for which we achieve (0.25−?)-factor algorithms.We also show, as our main contribution, how to use the continuous greedy process for non-monotone functions and, as a result, obtain a 0.13-factor approximation algorithm for maximization over any solvable down-monotone polytope.     

Three-Component,One-Pot Synthesis of 2,4,5-Trisubstituted Imidazoles Catalyzed by TiCl4-SiO2 Under Conventional Heating Conditions or Microwave Irradiation

In this study, silica-supported titanium tetrachloride was prepared and used as a novel catalyst for rapid and efficient synthesis of 2,4,5-trisubstituted imidazoles by a three-component, one-pot condensation of 1,2-diketones and aryl aldehydes in excellent yield under solvent-free conditions using conventional heating or microwave irradiation.

Dinuclear copper complexes of pyridylphenylphosphine ligands: Characterization of a mixed-valence Cu/Cu dimer

Homo bi-copper complexes [Cu₂{PhP(2-py)₂}₂(NO₃)₃] (1) and [Cu₂{P(2-py)₃}₂Cl₂] (2), were synthesized from the reaction of Cu(NO₃)₂·3H₂O and CuCl₂·2H₂O with their corresponding 2-pyridylphosphine ligands. Compound 1 has a mixed valence Cu(I)-Cu(II) core with electron acceptor phosphine atoms and two NO₃⁻ anions coordinated in a monodentate fashion to Cu(I), giving it a distorted tetrahedral geometry. The environment of Cu(II) in 1 is composed of four nitrogen atoms from pyridyl and another NO₃⁻ anion in a square pyramidal geometry. This complex shows luminescence and a low energy absorption band at 969 nm corresponding to intermetallic electron transfer between the copper centers. Complex 2 was prepared from the treatment of copper(II) chloride with tris(2-pyridyl)phosphine, producing a binuclear copper complex which possesses a crystallographic inversion center. The copper geometry in this complex is distorted tetrahedral with coordination of one Cl⁻, two nitrogens from one bridging tris(2-pyridyl)phosphine ligand and one P atom from the other bridging tris(2-pyridyl)phosphine ligand, in a similar way observed in related complexes. The products have been characterized by spectroscopic methods and also by the single-crystal X-ray diffraction method.