Derivatives of a finite class of orthogonal polynomials related to inverse Gamma distribution

In this work, we consider derivatives of a finite class of orthogonal polynomials with respect to weight function which is related to the probability density function of the inverse gamma distribution over the positive real line. General properties for this derivative class such as orthogonality, Rodrigues’ formula, recurrence relation, generating function and various other related properties such as self-adjoint form and normal form are indicated. The corresponding Gaussian quadrature formulae are introduced with examples. These examples are provided to support the advantages of considering the derivatives class of the finite class of orthogonal polynomials related to inverse gamma distribution. The orthogonality property related to the Fourier transform of the derivative class under discussion is also given.     

Synthesis and anticancer activity studies of alpha-aminoalkylated conjugated nitroalkenes

Novel alpha-aminoalkylated conjugated nitroalkenes which inhibit human cervical cancer (HeLa) cell proliferation by binding to tubulin were synthesized by imidazole/LiCl-mediated reaction of conjugated nitroalkenes with N-tosylimines.     

Crystal structure of homo-DNA and nature's choice of pentose over hexose in the genetic system

An experimental rationalization of the structure type encountered in DNA and RNA by systematically investigating the chemical and physical properties of alternative nucleic acids has identified systems with a variety of sugar-phosphate backbones that are capable of Watson-Crick base pairing and in some cases cross-pairing with the natural nucleic acids. The earliest among the model systems tested to date, (4' --> 6')-linked oligo(2',3'-dideoxy-beta-d-glucopyranosyl)nucleotides or homo-DNA, shows stable self-pairing, but the pairing rules for the four natural bases are not the same as those in DNA. However, a complete interpretation and understanding of the properties of the hexapyranosyl (4' --> 6') family of nucleic acids has been impeded until now by the lack of detailed 3D-structural data. We have determined the crystal structure of a homo-DNA octamer. It reveals a weakly twisted right-handed duplex with a strong inclination between the hexose-phosphate backbones and base-pair axes, and highly irregular values for helical rise and twist at individual base steps. The structure allows a rationalization of the inability of allo-, altro-, and glucopyranosyl-based oligonucleotides to form stable pairing systems.     

Multiscale simulation of viscoelastic free surface flows

A micro–macro approach based on combining the Brownian configuration fields (BCF) method [M.A. Hulsen, A.P.G. van Heel, B.H.A.A. van den Brule, Simulation of viscoelastic flow using Brownian configuration fields, J. Non-Newtonian Fluid Mech. 70 (1997) 79–101] with an Arbitrary Lagrangian–Eulerian (ALE) Galerkin finite element method, using elliptic mesh generation equations coupled with time-dependent conservation equations, is applied to study slot coating flows of polymer solutions. The polymer molecules are represented by dumbbells with both linear and non-linear springs; hydrodynamic interactions between beads are incorporated. Calculations with infinitely extensible (Hookean) and pre-averaged finitely extensible (FENE-P) dumbbell models are performed and compared with equivalent closed-form macroscopic models in a conformation tensor based formulation [M. Pasquali, L.E. Scriven, Free surface flows of polymer solutions with models based on the conformation tensor, J. Non-Newtonian Fluid Mech. 108 (2002) 363–409]. The BCF equation for linear dumbbell models is solved using a fully implicit time integration scheme which is found to be more stable than the explicit Euler scheme used previously to compute complex flows. We find excellent agreement between the results of the BCF based formulation and the macroscopic conformation tensor based formulation. The computations using the BCF approach are stable at much higher Weissenberg numbers, (where λ is the characteristic relaxation time of polymer, and is the characteristic rate of strain) compared to the purely macroscopic conformation tensor based approach, which fail beyond a maximum Wi. A novel computational algorithm is introduced to compute complex flows with non-linear microscopic constitutive models (i.e. non-linear FENE dumbbells and dumbbells with hydrodynamic interactions) for which no closed-form constitutive equations exist. This algorithm is fast and computationally efficient when compared to both an explicit scheme and a fully implicit scheme involving the solution of the non-linear equations with Newton’s method for each configuration field.     

Advertising strategies in a franchise system

The main question of this research is: Who should undertake promotional and brand-image advertising if the franchisor and franchisees act so as to maximize their respective profits? To address this question, we study a two-stage advertising game between a franchisor and two adjacent franchisees. In the first stage of the game, the franchisor chooses between three advertising models – centralizing or delegating the two types of advertising to the franchisees or delegating only promotional advertising. In the second stage, given the franchisor’s choice of an advertising model, the two franchisees decide whether or not to cooperate. Our main findings are that (1) the franchisees should cooperate if the franchisor delegates either both brand-image and promotional advertising or promotional advertising, although cooperation between franchisees does not necessary improve the franchisor’s profits. (2) The choice of an advertising arrangement critically depends on the margins as well as the costs of performing both promotional and brand-image advertising. We also discuss the conditions under which the three advertising models should be implemented.     

Molecular Architecture of Multi‐Block Polymer Synthesized in a Dual‐Catalyst Single CSTR

This work aims at deriving analytical solutions for the molecular architecture of multi‐block polymer synthesized in a dual‐catalyst single CSTR. While the relevant equations are developed for homopolymerization, they can easily be extended to copolymerization. Special emphasis is placed on the quantities associated with each catalyst rather than the overall ones. However, if all rate parameters are available, the expressions can be used to calculate the properties of the material made by each catalyst as well as the overall ones under various process conditions. Given the reasonable assumption of large residence time, the solutions are simplified to elucidate the kinetics of chain‐shuttling involving two catalysts. It is shown that systems with low chain‐shuttling ability, if DP^P_n,0 ≠ DP^Q_n,0, may exhibit significant deviation from Flory's most probable distribution. Furthermore, systems with high chain‐shuttling ability produce macromolecules with more uniform architecture and polydispersity index close to 2.

     

High-resolution Fourier transform infrared absorption spectroscopy of the ν6 band of c-C3H2

The gas-phase high-resolution absorption spectrum of the ν(6) band of cyclopropenylidene (c-C(3)H(2)) has been observed using a Fourier transform infrared spectrometer for the first time. The molecule has been produced by microwave discharge in an allene (3.3 Pa) and Ar (4.0 Pa) mixture inside a side arm glass tube. The observed spectrum shows a pattern of c-type ro-vibrational transitions in which the Q-branch lines strongly and distinctly stand out in the spectrum. A combined least-squares analysis of the observed 216 ro-vibrational transitions together with 28 millimeter-wave rotational transitions from the previous study has resulted in an accurate determination of the molecular constants in the ν(6) state. The band center is found to be at 776.11622(13) cm(-1) with one standard deviation in parentheses, which is 2.3% lower than the matrix isolation value. The intensity ratio I(3)(ν(3))/I(6)(ν(6)) obtained from the observed ν(3) and ν(6) bands, 1.90(9), is somewhat lower than the ratio estimated from ab initio (2.4-2.6) and DFT (2.8) calculations.     

Polymeric catalysts for chemo- and enantioselective epoxidation of olefins: New crosslinked chiral transition metal complexing polymers

Polymeric analogs of well-known chiral Mn(III)-salen complexes were synthesized and were used as recyclable catalysts for asymmetric epoxidation of olefins. For this purpose two different monomers, 2 and 3 , bearing chiral Mn(III)-salen moieties were synthesized. The monomer 3 carries a bulky substituent closer to the Schiff base moiety, while monomer 2 lacks such a substituent. These metal complexed chiral monomers were subsequently copolymerized with ethylene glycol dimethacrylate producing insoluble crosslinked functional matrices that possess macroporous morphology. Chemo- and enantioselective catalytic activities of these two polymers were evaluated for epoxidation of olefins. Both polymers catalyzed the epoxidation of a variety of olefins at room temperature in the presence of iodosylbenzene (PhIO) as the terminal oxidant with yields comparable to the homogenous system. In terms of their enantioselective catalytic activity, polymer P-2 (obtained from 3 ) performed better than polymer P-1 (obtained from 2 ). Unfortunately, while the homogeneous systems are reported to offer over 80% enantioselectivity, with the present polymeric catalysts, enantioselectivity to a maximum of 30% were observed. Unlike the homogeneous system, use of an external nitrogenous donor played a very insignificant role in influencing enantioselectivity. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 1809–1818, 1997     

Adsorption of formaldehyde and butynediol from aqueous solutions on a Cu2C2-silica gel catalyst

The effect of equilibrium concentration on adsorption has been studied at different temperatures and the nature of isotherms is discussed. For the formaldehyde-Cu₂C₂-silica gel system, Freundlich type equations describe the data satisfactorily.

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. . -Cu₂C₂- .

     

Density functional study of hydrogen‐bonded acetonitrile–water complex

We report the interaction of acetonitrile with one, two, and three water molecules using the Density Functional Theory method and the 6‐31+G* basis set. Different conformers were studied and the most stable conformer of acetonitrile–(water)_n complex has total energies –209.1922504, –285.6224478, and –362.068728 hartrees with one, two, and three water molecules, respectively. The corresponding binding energy for these three structures is 4.52, 8.34, and 22.48 kcal/mol. The hydrogen‐bonding results in blue, blue, and redshift in C?N stretching mode in acetonitrile with one, two, and three water molecules, respectively, whereas there was a redshift in O? H symmetric stretching mode of water. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005