Ab initio studies on several species of the formula X3YO and X3YOH

Ab initio molecular orbital calculations using both minimal and extended basis sets have been applied to two isoelectronic sets of molecules. One set corresponds to the 18 electron species H₃NO, H₃CO^– and H₃COH while the second set contains the 42 electron fluorinated molecules F₃NO, F₃CO^– and F₃COH. The geometries of these molecules have been optimized, using both the minimal STO-3G and the extended 4-31G basis sets. These comparative calculations reveal that the 4-31G basis produced structural parameters in much better agreement with experiment. The effect of includingd-orbitals in the basis set was also investigated. For the fluorinated oxides it has been found that the optimized 4-31G structures were only slightly altered by the addition ofd-orbitals. For H₃NO, on the other hand, the inclusion ofd-orbitals considerably shortens the N-O bond distance. Both H₃NO and CF₃OH, which are unknown experimentally, are theoretically predicted to be capable of existence. The electronic structures of these molecules have also been examined using electronic partitioning according to the Mulliken scheme.     

An Algorithm for Computing the Singularity of the Generic Germ of a Pencil of Plane Curves

Abstract

We give an algorithm that describes the singularity of all but finitely-many germs in a pencil generated by two arbitrary germs of plane curve.     

Well‐defined non‐linear polyethylene‐based macromolecular architectures

Polyethylene (PE)‐based 3‐ and 4‐miktoarm star [PE(PCL)₂, PE(PCL)₃] and H‐type [(PCL)₂PE(PCL)₂] block copolymers [polycaprolactone (PCL)] were synthesized by a combination of polyhomologation, chlorosilane chemistry, and ring opening polymerization (ROP). The following steps were used for the synthesis of the miktoarm stars: (a) reaction of a hydroxy‐terminated polyethylene (PE‐OH), prepared by polyhomologation of dimethylsulfoxonium methylide with a monofunctional boron initiator followed by oxidation/hydrolysis, with chloromethyl(methyl)dimethoxysilane or chloromethyltrimethoxysilane; (b) hydrolysis of the produced ω‐di(tri)methoxysilyl‐polyethylenes to afford ω‐dihydroxy‐polyethylene (difunctional initiator) and ω‐trihydroxy‐polyethylene (trifunctional initiator); and (c) ROP of ɛ‐caprolactone with the difunctional (3‐miktoarm star) or trifunctional macroinitiator (4‐miktoarm star), in the presence of 1‐tert‐butyl‐2,2,4,4,4‐pentakis(dimethylamino)‐2λ⁵,4λ⁵‐catenadi(phosphazene) (t‐BuP₂). The H‐type block copolymers were synthesized using the same strategy, but with a difunctional polyhomologation initiator. All intermediates and final products were characterized by HT‐GPC, ¹H NMR and FTIR analyses. Thermal properties of the PE precursors and all final products were investigated by DSC and TGA. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2129–2136     

Uniform persistence for population interaction models with time delay

In this paper uniform persistence is establised for kolmogorov type Prey‐Predator and competion models with per capitals ent growth rates that are dependent on time‐lagged population densities.     

Beta-type means

Abstract

Based on the relationship between the Beta and the Euler Gamma function, beta-type functions of several variables, generated by a single variable function, are introduced. Applying the method of iterative functional equations, all means of beta-type are determined and some of their properties are discussed.     

Higher-order time integration with a local Lax–Wendroff procedure for a central scheme on an overlapping grid

We have implemented a high-order Lax–Wendroff type time integration for a central scheme on an overlapping grid for conservation law problems. Using a local iterative approach presented by Dumbser et al. (JCP, 2008) [12], we extend a local high-order spatial reconstruction on each cell to a local higher-order space–time polynomial on the cell. We rewrite the central scheme in a fully discrete form to avoid volume integration in the space–time domain. The fluxes at cell interfaces are calculated directly via integrating a higher-order space–time reconstruction of the flux. We compare this approach with the corresponding multi-stage Runge–Kutta time integration (RK). Numerical results show that the new time integration is more cost-effective.     

The Kirchhoff type Schrödinger problem with critical growth

In this paper, we study the Kirchhoff type problem with critical growth. By using the variational method, the existence and multiplicity of solutions are obtained.     

Projective Reed–Muller type codes on rational normal scrolls

In this paper we study an instance of projective Reed–Muller type codes, i.e., codes obtained by the evaluation of homogeneous polynomials of a fixed degree in the points of a projective variety. In our case the variety is an important example of a determinantal variety, namely the projective surface known as rational normal scroll, defined over a finite field, which is the basic underlining algebraic structure of this work. We determine the dimension and a lower bound for the minimum distance of the codes, and in many cases we also find the exact value of the minimum distance. To obtain the results we use some methods from Gröbner bases theory.     

Co-precipitation synthesis,humidity sensing and photoluminescence properties of nanocrystalline Co2+ substituted zinc(II)molybdate (Zn1–xCoxMoO4; x = 0, 0.3, 0.5, 0.7, 1)

Zinc-cobalt molybdate composites (Zn_1–xCo_xMoO₄; x = 0, 0.3, 0.5, 0.7, 1) were synthesised by a simple co-precipitation method and characterised by thermogravimetric/differential thermal analysis (TG/DTA), Fourier transform-infrared (FT-IR), Fourier transform Raman (FT-Raman) spectroscopy, X-ray diffraction spectroscopy (XRD), scanning electron microscopy (SEM/EDAX) and transmission electron microscopy (TEM). The surface area was calculated by BET analysis in the adsorption/desorption isotherm. The humidity sensing properties of zinc-cobalt molybdates were tested by dc electrical measurements at different relative humidity environments (RH = 5–98%). The electrical resistance of the composites linearly decreases and the maximum sensitivity of 3672 ± 110 was observed for the Zn_0.3Co_0.7MoO₄ (ZnCM-4) composite towards humidity, which is calculated by the relation S_f = R_5%/R_98%, where the response time is 200 s and the recovery time is 100 s. Photoluminescence (PL) measurement at the room temperature of ZnM-1 composite exhibited a blue emission peak at 475 nm (λ_em) when excited at a wavelength (λ_ex) of 430 nm. During Co²⁺ substitution in Zn²⁺ matrix, a green and red emission peak was observed when excited at a wavelength (λ_ex) of 520 nm.