Experimental Determination of the Electronic Polarizability of Quinoline and Isoquinoline in Solution by Three New Strategies

The values of electronic polarizability of quinoline and isoquinoline in extremely diluted liquid solution are reported in this paper. These were obtained by means of three new strategies based on UV-visible-NIR spectroscopy, the Kramers-Krönig relations, high precision densitometry and high exactitude refractometry, which are called here Arakawa’s Approximation (AA), Optical Substractive Approximation (OSA) and Optical Differential Approximation (ODA). In general the static electronic polarizability values of solute molecules obtained by ODA and OSA are in excellent agreement with the reported theoretical values at the Density Functional Theory (DFT) level and the Atom monopole-dipole model, but strong discrepancies were observed with the experimental values previously reported for quinoline and isoquinoline using refractometric and electro-optic methods. These differences were interpreted and analyzed in terms of dielectric intermolecular forces, resonant and pre-resonant effects. The AA method is shown to fail in predicting the polarizability of the quinoline and isoquinoline molecules.     

Embedding into l ∞2 Is Easy, Embedding into l ∞3 Is?NP-Complete

We give a new algorithm for enumerating all possible embeddings of a metric space (i.e., the distances between every pair within a set of n points) into ℝ² Cartesian space preserving their l _∞ (or l ₁) metric distances. Its expected time is (i.e., within a poly-log of the size of the input) beating the previous algorithm. In contrast, we prove that detecting l _∞³ embeddings is NP-complete. The problem is also NP-complete within l ₁² or l _∞² with the added constraint that the locations of two of the points are given or alternatively that the two dimensions are curved into a three-dimensional sphere. We also refute a compaction theorem by giving a metric space that cannot be embedded in l _∞³; however, it can be embedded if any single point is removed. This research is partially supported by NSERC grants. I would like to thank Steven Watson for his extensive help on this paper.     

Functional inequalities for the Wright functions

In this paper, our aim is to show some mean value inequalities for the Wright function, such as Turán-type inequalities, Lazarevi?-type inequalities, Wilker-type inequalities and Redheffer-type inequalities. Moreover, we prove monotonicity of ratios for sections of series of Wright functions, the result is also closely connected with Turán-type inequalities. In the end of the paper, we present some other inequalities for the Wright function.     

On the calculation of group characters

It is known that characters of irreducible representations of finite Lie algebras can be obtained using the Weyl character formula including Weyl group summations which make actual calculations almost impossible except for a few Lie algebras of lower rank. By starting from the Weyl character formula, we show that these characters can be re-expressed without referring to Weyl group summations. Some useful technical points are given in detail for the instructive example of G₂ Lie algebra.     

Erdős–Gallai stability theorem for linear forests

The Erd?s–Gallai Theorem states that every graph of average degree more than $l?2$ contains a path of order $l$ for $l\ge 2$. In this paper, we obtain a stability version of the Erd?s–Gallai Theorem in terms of minimum degree. Let $G$ be a connected graph of order $n$ and $F=\left({?}_{i=1}^k{P}_{2a_i}\right)?\left({?}_{i=1}^l{P}_{2b_i+1}\right)$ be $k+l$ disjoint paths of order $2a_1,\dots ,2a_k,2b_1+1,\dots ,2b_l+1,$ respectively, where $k\ge 0$, $0\le l\le 2$, and $k+l\ge 2$. If the minimum degree $\delta \left(G\right)\ge {\sum }_{i=1}^k{a}_i+{\sum }_{i=1}^l{b}_i?1$, then $F?G$ except several classes of graphs for sufficiently large $n$, which extends and strengths the results of Ali and Staton for an even path and Yuan and Nikiforov for an odd path.     

Stability for parametric implicit vector equilibrium problems

In this paper, we consider a class of parametric implicit vector equilibrium problems in Hausdorff topological vector spaces where a mapping f and a set K are perturbed by parameters and λ, respectively. We establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution set mapping S:Λ₁×Λ₂→2^X for such parametric implicit vector equilibrium problems.     

Synthesis and characterization of aluminum and zinc complexes supported by pyrrole-based ligands and catalysis of the aluminum complexes toward the ring-opening polymerization of ?-caprolactone

Reaction of quinolin-8-amine with 1H-pyrrole-2-carbaldehyde or 5-tert-butyl-1H-pyrrole-2-carbaldehyde catalyzed by HCO₂H forms N-((1H-pyrrol-2-yl)methylene)quinolin-8-amine (≡ HL, 3a) or N-((5-tert-butyl-1H-pyrrol-2-yl)methylene)quinolin-8-amine (≡ HL′, 3b). Treatment of 3a and 3b respectively with AlMe₃ or AlEt₃ in toluene affords corresponding aluminum complexes LAlMe₂ (4a), L′AlMe₂ (4b) and LAlEt₂ (4c). Reaction of 3a and 3b with an equivalent of ZnEt₂ in toluene generates L₂Zn and L′₂Zn, respectively. A related compound N-((1H-pyrrol-2-yl)methylene)-2-(3,5-dimethyl-1H-pyrazol-1-yl)benzenamine (≡ HL″, 7) was prepared by reaction of 2-(3,5-dimethyl-1H-pyrazol-1-yl)benzenamine with 1H-pyrrole-2-carbaldehyde in the presence of HCO₂H. Reaction of 7 with AlMe₃ gives L″₂AlMe (8), and with ZnEt₂ yields L″₂Zn (9). All new compounds were characterized by NMR spectroscopy and elemental analysis. The structures of complexes 4b, 5b and 8 were additionally characterized by single crystal X-ray diffraction analyses. Complexes 4a-4c, and 8 were proved to be active catalysts for the ring-opening polymerization (ROP) of ?-caprolactone (?-CL) in the presence of BnOH. The kinetic study of the polymerization reactions catalyzed by 4a and 8 was performed.     

The Characterization of FeZSM-5 by 57Fe Mössbauer Spectroscopy: Sensitivity Towards Nitrogen

Hyperfine Interactions - Mössbauer spectra were recorded at 4.2 K of an FeZSM-5 zeolite that has been treated with nitrogen at 623 K. Changes in the sample environment clearly show the...     

Thermoanalytical studies on complexes of clotrimazole with cyclodextrins

γ-Cyclodextrin and dimethyl-β-cyclodextrin were used as solubilizing agents for a very poorly water-soluble drug, an imidazole derivative antifungal agent, clotrimazole; with the aim of improving the physicochemical properties of the drug. Solid products were prepared by physical mixing, kneading, precipitation and spray-drying methods in 1:1 and 1:2 drug:cyclodextrin molar ratios. Drug interactions were studied by thermoanalytical methods such as DSC, DTA, TG and DTG, X-ray diffractometry and Fourier transformation-infrared spectroscopy. The results demonstrated the formation of inclusion complexes in some products. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the perturbations of spectra of upper triangular operator matrices

In this paper we investigate perturbations of the regular spectrum of an upper triangular operator matrix such as acting on a Hilbert space H⊕K.