Nonlinear transformation methods for accelerating the convergence of Coulomb integrals over exponential type functions

It is well known that in any ab initio molecular orbital (MO) calculation, the major task involves the computation of molecular integrals, among which the computation of Coulomb integrals are the most frequently encountered. As the molecular system gets larger, computation of these integrals becomes one of the most laborious and time consuming steps in molecular systems calculation. Improvement of the computational methods of molecular integrals would be indispensable to a further development in computational studies of large molecular systems. The atomic orbital basis functions chosen in the present work are Slater type functions. These functions can be expressed as finite linear combinations of B functions which are suitable to apply the Fourier transform method. The difficulties of the numerical evaluation of the analytic expressions of the integrals of interest arise mainly from the presence of highly oscillatory semi-infinite integrals. In this work, we present a generalized algorithm based on the nonlinear transformation of Sidi, for a precise and fast numerical evaluation of molecular integrals over Slater type functions and over B functions. Numerical results obtained for the three-center two-electron Coulomb and hybrid integrals over B functions and over Slater type functions. Comparisons with numerical results obtained using alternatives approaches and an existing code are listed.     

Implementation of pi-pi interactions in molecular dynamics simulation

No explicit pi-pi interaction term has been incorporated in the conventional molecular dynamics (MD) simulation programs in spite of its significant role in the folding of biomolecules and the clustering of organic chemicals. In this article, we propose a technique to emphasize the effect of pi-pi interactions using a function of energy and implement it into an MD simulation program. Several trial calculations show that the pi-pi incorporated program gives improved results consistent with experimental data on atom geometry and has no unfavorable interference with the conventional computational framework. This indicates an importance of the explicit consideration of pi-pi interactions in MD simulation.     

Biosynthesis and biodegradability of copolythioesters from 3,3'-thiodipropionic acid and plant oils by Cupriviadus necator

To prepare sulfur-containing natural polymers effectively, several plant oils and 3,3'-thiodipropionic acid (TDP) have been used as carbon sources for the biosynthesis of copolymer poly[(3-hydroxybutyrate)-co-(3-mercaptopropionate)] [poly(3HB-co-3MP)] by a wild-type bacterium Cupriviadus necator H16. By using the plant oils, copolymer accumulation and incorporation of 3MP units are greater than those of cases using sugars. The 3MP fraction is controllable over a range of 1-39 mol-% by adjusting the cultivation conditions. Microbial degradability of the copolymers has been examined in an activated sludge supernatant. The biodegradation proceeded by two mechanisms: surface erosion and auto-catalytic hydrolysis, depending on the 3MP unit fraction, and show preferential degradation of 3HB unit sequences.     

On the norm of a Hilbert's type linear operator and applications

In this paper, the norm of a Hilbert's type linear operator is given. As applications, a new operator inequality and the equivalent forms with the norm are obtained, and particularly some new extended Hilbert's type inequalities and the equivalent forms with the best constant factors are established.     

Weighted weak type inequalities for modified Hardy operators and geometric means operators in dimensions one and greater

We characterize the pairs of weights (u,v) such that the geometric mean operator G₁, defined for positive functions f on (0,∞) by

     

Pointwise estimates for relative fundamental solutions of heat equations in $${\mathbb{R} \times \mathbb{C}}$$

Let be a subharmonic, nonharmonic polynomial and a parameter. Define , a closed, densely defined operator on . If and , we solve the heat equations , u(0,z) = f(z) and , . We write the solutions via heat semigroups and show that the solutions can be written as integrals against distributional kernels. We prove that the kernels are C ^∞ off of the diagonal {(s, z, w) : s = 0 and z = w} and find pointwise bounds for the kernels and their derivatives.      

The class of mappings with bounded specific oscillation,and integrability of mappings with bounded distortion on Carnot groups

This paper is the first of the author’s three articles on stability in the Liouville theorem on the Heisenberg group. The aim is to prove that each mapping with bounded distortion of a John domain on the Heisenberg group is close to a conformal mapping with order of closeness \(\sqrt {K - 1} \) in the uniform norm and order of closeness K ? 1 in the Sobolev norm L _p ¹ for all \(p < \tfrac{C}{{K - 1}}\).In the present article we study integrability of mappings with bounded specific oscillation on spaces of homogeneous type. As an example, we consider mappings with bounded distortion on the Heisenberg group. We prove that a mapping with bounded distortion belongs to the Sobolev class W _p,loc ¹ , where p → ∞ as the distortion coefficient tends to 1.     

Elliptic enumeration of nonintersecting lattice paths

We enumerate lattice paths in the planar integer lattice consisting of positively directed unit vertical and horizontal steps with respect to a specific elliptic weight function. The elliptic generating function of paths from a given starting point to a given end point evaluates to an elliptic generalization of the binomial coefficient. Convolution gives an identity equivalent to Frenkel and Turaev's summation. This appears to be the first combinatorial proof of the latter, and at the same time of some important degenerate cases including Jackson's and Dougall's summation. By considering nonintersecting lattice paths we are led to a multivariate extension of the summation which turns out to be a special case of an identity originally conjectured by Warnaar, later proved by Rosengren. We conclude with discussing some future perspectives.     

Coupled In/Te and Ni/vacancy ordering and the modulated crystal structure of a B8 type, Ni3±xIn1−yTe2+y solid solution phase

The commensurate superstructures of a NiAs/Ni₂In type parent structure, Ni_3.32InTe₂ and Ni_3.12In_0.86Te_2.14 (q=γ[0 0 1]^*, γ=2/3) as well as one dimensionally incommensurate structure of Ni₃InTe₂ (γ=0.71) were refined from neutron powder diffraction data (R_wp=4.77%, 4.53% and 4.91% for the three structures, respectively, at 298 K). The commensurate structures were refined in the P6₃/mmc space group (c=3c_NiAs). The stacking sequence at the hcp array is -In/Te/Te/- and the trigonal bipyramidal site within the In layer, Ni(2), is partially occupied while it is empty in the Te layers. The octahedral position in between the In and Te layers, Ni(1a), is fully occupied while the octahedral position in between two adjacent Te layers, Ni(1b), is partially occupied. With decreasing In and Ni content, the modulation wave vector, γ, was found to increase continuously until γ=1. From this, crenel functions to describe the whole homogeneity range of the solid solution were constructed with the length of the atomic domains Δ^Te=γ (and hence Δ^In=Δ^Ni=1−γ) and Δ^Ni(1b)=γ/2 (and hence Δ^Ni(1a)=1−γ/2) which were then used for the refinement of the incommensurate structure of Ni₃InTe₂. The corresponding effect in real space is that the single In layers separating double layers of Te occur less frequent when γ in increasing until at γ=1 the CdI₂ type structure of Ni_1+xTe₂ is reached.     

1H and 13C NMR assignments for two new angular furanocoumarin glycosides from Peucedanum praeruptorum

Two novel angular-type furanocoumarin glycosides, peucedanoside A (1) and peucedanoside B (2), along with a known compound apterin (3), were isolated from the roots of Peucedanum praeruptorum Dunn. Their chemical structures were determined by MS, NMR spectroscopy and chemical analysis. Complete assignments of the 1H and 13C NMR spectroscopic data were achieved by 1D and 2D NMR experiments including DEPT, HSQC, HMBC and ROESY.