Topological calculus for separating points from closed sets by maps

Pointfree formulas for three kinds of separating points for closed sets by maps are given. These formulas allow controlling the amount of factors of the target product space so that it does not exceed the weight of the embeddable space. In literature, the question of how many factors of the target product are needed for the embedding has only been considered for specific spaces. Our approach is algebraic in character and can thus be viewed as a contribution to Kuratowski’s topological calculus.     

Charge gating and electronic delocalization over a denderimeric assembly of trinuclear ruthenium clusters

A zeroth-order dendrimer was formed using a tridentate bridging ligand, 2,4,6-tri-4-pyridyl-S-triazine, and the redox-active trinuclear ruthenium cluster Ru3O(OAc)6(CO)(py)(H2O). The electronic properties of this dendrimer were probed using cyclic voltammetry. IR spectroelectrochemistry was performed at both low (-30 degrees C) and room temperature. The IR spectroelectrochemical response at -30 degrees C was straightforward, but at room temperature, the dendrimer exhibits an unusual and complex series of electronic behaviors, including intramolecular cluster-to-bridging-ligand charge transfer, gated electron transfer, and dynamic exchange on the IR time scale.     

The X-ray revision of the structure of bis(4-hydroxybenzhydrazide)copper(II) sulfate(VI) dihydrate and its vibrational spectroscopy

The structure of known copper(II) complex with 4-hydroxybenzoic acid hydrazide has been corrected on the basis of a new X-ray analysis. It has been found, that the sulfate(VI) ion is bonded in apical position of Cu(II) coordination pyramid having two organic ligands at the base. Two water molecules are not coordinated as has been postulated before, but stabilizes the sulfate(VI) group orientation and link the layers of complex molecules by strong hydrogen bonds. The detailed interpretation of the measured IR and Raman spectra has been performed with aid of both: quantum calculations as well as H/D and ⁶³Cu–⁶⁵Cu isotope substitution.     

Cyclic Just-In-Time Sequences Are Optimal

Consider the Product Rate Variation problem. Given n products 1,...,i,...,n, and n positive integer demands d ₁,..., d_i,...,d_n. Find a sequence =₁,...,_T, T = _i=1 ⁿ d _i, of the products, where product i occurs exactly d _i times that always keeps the actual production level, equal the number of product i occurrences in the prefix ₁,..., _t, t=1,...,T, and the desired production level, equal r _i t, where r _i=d_i/T, of each product i as close to each other as possible. The problem is one of the most fundamental problems in sequencing flexible just-in-time production systems. We show that if is an optimal sequence for d ₁,...,d_i,...,d_n, then concatenation ^m of m copies of is an optimal sequence for md ₁,..., md_i,...,md_n.     

Comprehensive and uniform synthesis of all naturally occurring phosphorylated phosphatidylinositols

Studies of cellular signal transduction mechanisms involving receptor-mediated generation of inositol phosphates and phosphorylated phosphatidylinositols require easy access to these naturally occurring products. Although numerous synthetic methods have been developed during the past decade, most of these methods suffer from excessive length and lack of generality. In this work we describe the comprehensive and uniform synthesis of all naturally occurring phosphatidylinositols such as phosphatidylinositol, phosphatidylinositol 3-phosphate, 4-phosphate, 5-phosphate, 3,4-bisphosphate, 3,5-bisphosphate, 4,5-bisphosphate, and 3,4,5-trisphosphate, featuring both saturated and unsaturated fatty acid chains.     

A Fully Polynomial Approximation Scheme for Minimizing Makespan of Deteriorating Jobs

A fully polynomial approximation scheme for the problem of scheduling n deteriorating jobs on a single machine to minimize makespan is presented. Each algorithm of the scheme runs in O(n ⁵ L ⁴³) time, where L is the number of bits in the binary encoding of the largest numerical parameter in the input, and is required relative error. The idea behind the scheme is rather general and it can be used to develop fully polynomial approximation schemes for other combinatorial optimization problems. Main feature of the scheme is that it does not require any prior knowledge of lower and/or upper bounds on the value of optimal solutions.     

Reinvestigation of zinc(II) complexation by 2-thiophenecarboxylic hydrazide: X-ray structure of tris(2-thiophenecarboxyhydrazide)zinc(II) tetrachlorozincate(II) di(ethanol) and vibrational spectroscopy of its decomposition product

Reaction of ZnCl₂ and 2-thiophenecarboxylic hydrazide (tch), in ethanol resulted in the crystalline product [Zn(tch)₃][ZnCl₄] · 2EtOH, which slowly decomposes losing solvent molecules. The structure of the first compound has been determined by the single crystal X-ray method. Analysing the IR spectra of both compounds it has been found that the complex [Zn(tch)₃]²⁺ cation and [ZnCl₄]²⁻ anion are preserved after crystal decomposition. Vibrational spectra of the obtained substances were interpreted with the assistance of DFT calculations and metal isotope as well as deuterium replacement.