Efficient electronic integrals and their generalized derivatives for object oriented implementations of electronic structure calculations

For the new parallel implementation of electronic structure methods in ACES III (Lotrich et al., in preparation) the present state-of-the-art algorithms for the evaluation of electronic integrals and their generalized derivatives were implemented in new object oriented codes with attention paid to efficient execution on modern processors with a deep hierarchy of data storage including multiple caches and memory banks. Particular attention has been paid to define proper integral blocks as basic building objects. These objects are stand-alone units and are no longer tied to any specific software. They can hence be used by any quantum chemistry code without modification. The integral blocks can be called at any time and in any sequence during the execution of an electronic structure program. Evaluation efficiency of these integral objects has been carefully tested and it compares well with other fast integral programs in the community. Correctness of the objects has been demonstrated by several application runs on real systems using the ACES III program.     

On the oriented chromatic index of oriented graphs

A homomorphism from an oriented graph G to an oriented graph H is a mapping from the set of vertices of G to the set of vertices of H such that is an arc in H whenever is an arc in G. The oriented chromatic index of an oriented graph G is the minimum number of vertices in an oriented graph H such that there exists a homomorphism from the line digraph LD(G) of G to H (the line digraph LD(G) of G is given by V(LD(G)) = A(G) and whenever and ). We give upper bounds for the oriented chromatic index of graphs with bounded acyclic chromatic number, of planar graphs and of graphs with bounded degree. We also consider lower and upper bounds of oriented chromatic number in terms of oriented chromatic index. We finally prove that the problem of deciding whether an oriented graph has oriented chromatic index at most k is polynomial time solvable if k ≤ 3 and is NP‐complete if k ≥ 4. © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 313–332, 2008     

A note on some embedding problems for oriented graphs

We conjecture that every oriented graph G on n vertices with δ⁺(G), δ^?(G)≥5n/12 contains the square of a Hamilton cycle. We also give a conjectural bound on the minimum semidegree which ensures a perfect packing of transitive triangles in an oriented graph. A link between Ramsey numbers and perfect packings of transitive tournaments is also considered. © 2011 Wiley Periodicals, Inc. J Graph Theory 69: 330–336, 2012     

A management oriented approach to reduce a project duration and its risk (variability)

The effects of different activities on risk and the expected completion time of a project are not the same; various activities have various effects on the successful completion of a project. Based on this fact, one of the most important issues in project management is to determine important activities and the amount of effort that should be assigned to control them, thereby completing the project successfully. In this paper, one index and one method are proposed to satisfy this necessity. Our main hypothesis is, expending effort on activities and controlling them actively results in activities risk reduction. Based on this hypothesis, the proposed index and method are compared to existing indices in the literature. Comparison results show that the proposed index and method strongly surpass other indices.     

Diversity-oriented approach to biologically relevant molecular frameworks starting with beta-naphthol and using the Claisen rearrangement and olefin metathesis as key steps

A diversity-oriented approach for the synthesis of various structurally different molecular frameworks from readily accessible and common precursors is described. A Claisen rearrangement followed by ring-closing metathesis or ethylene-promoted ring-closing enyne metathesis has been utilized as the key synthetic transformation to generate naphthoxepine derivatives. The ring-closing metathesis approach has also been used to generate spirocyclic compounds and the pleiadene framework.     

Two geometric representation theorems for separoids

Summary {\it Separoids\/} capture the combinatorial structure which arises from the separations by hyperplanes of a family of convex sets in some Euclidian space. Furthermore, as we prove in this note, every abstract separoid <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>S$ can be represented by a family of convex sets in the $(|S|-1)$-dimensional Euclidian space. The {\it geometric dimension\/} of the separoid is the minimum dimension where it can be represented and the upper bound given here is tight. Separoids have also the notions of {\it combinatorial dimension\/} and {\it general position\/} which are purely combinatorial in nature. In this note we also prove that: {\it a separoid in general position can be represented by a family of points if and only if its geometric and combinatorial dimensions coincide\/}.     

Synthesis of Unprecedented Scaffold Diversity

Building a better library : The synthesis of a library of natural‐product‐like small molecules with unprecedented scaffold diversity has been reported (see scheme; Ns=nosylate). The library represents a significant advancement in the capability of synthetic chemists to generate structurally diverse and complex small molecules in a rapid manner.

     

Application of the Low Frequency Raman Spectroscopy for Studying Ultra-High Molecular Weight Polyethylenes

In the frequency range below ∼150 cm⁻¹, the longitudinal acoustic modes (LAM) localized along straight chain segments (SCS) of macromolecules emerge in the Raman spectra of linear semicrystalline polymers. The LAM frequency is inversely proportional to the SCS length; therefore, the LAM band contour reflects the SCS length distribution in a sample. The opportunities given one by the low-frequency Raman spectroscopy for studying the ordered structures in polyethylene are demonstrated and discussed. The illustrating material consists of both previously published and original data on nucleation and transformation of the ensemble of SCS in powder-like, gelled, and drawn ultra-high molecular weight polyethylene.     

The spectral dispersion curves of highly oriented fibres

Spectral dispersion curves of the refractive indices and birefringence of highly oriented fibres [poly(ethylene 2,6-naphthalene-dicarboxylate) (1000 denier/248 filaments, PEN-Q50M4; PEN), poly(ethylene terephthalate) (PET), Seun yarn (meta-aramid fibres, Teijin Japan; CONEX) and Technora T-240 (1000 denier/667 filaments aramid fibres, Teijin Japan; TECHNORA)] have investigated using the automatic variable-wavelength interferometric (VAWI) technique. This technique is especially recommended for measuring the refractive indices of highly oriented fibres. The polarizabilities per unit volume are calculated for these fibres and the molecular orientation function of PEN and PET are determined. Microinterferograms are given for illustration.