On Center Cycles in Grid Graphs

Finding good cycles in graphs is a problem of great interest in graph theory as well as in locational analysis. We show that the center and median problems are NP-hard in general graphs. This result holds both for the variable cardinality case (i.e., all cycles of the graph are considered) and the fixed cardinality case (i.e., only cycles with a given cardinality p are feasible). Hence it is of interest to investigate special cases where the problem is solvable in polynomial time. In grid graphs, the variable cardinality case is, for instance, trivially solvable if the shape of the cycle can be chosen freely. If the shape is fixed to be a rectangle one can analyze rectangles in grid graphs with, in sequence, fixed dimension, fixed cardinality, and variable cardinality. In all cases a complete characterization of the optimal cycles and closed form expressions of the optimal objective values are given, yielding polynomial time algorithms for all cases of center rectangle problems. Finally, it is shown that center cycles can be chosen as rectangles for bounded cardinalities such that the center cycle problem in grid graphs is in these cases completely solved.     

High-throughput analysis in catalysis research using novel approaches to transmission infrared spectroscopy

This study has demonstrated that high-throughput FTIR transmission measurements using a newly designed array-based support formed using silicon wells and a silicon wafer is a very useful and robust tool for the characterization of polymer composition for combinatorial materials research. The comonomer content in copolymers can be measured accurately with a fully automated throughput of >300 samples/day (8 h). The transmission measurement is more robust, reliable, and easier to automate than other spectroscopic methods. The support itself provides excellent resistance to aggressive organic solvents at elevated temperatures and allows the unattended deposition and preparation of polymer films for infrared analysis. Because of the excellent durability of the support with respect to the solvent, the support can be rinsed and reused many times. This high-throughput approach to infrared transmission spectroscopy can be used for measuring a wide array of polymer characteristics: vinyl content, geometrical isomers, crystallinity, and tacticity. As well, this IR approach can be used to predict the oxidative stability of the antioxidant packages. Because the support provides a means of containing hot polymer solutions while the solvent evaporates, the support is also suitable for high-throughput nanoindentation methods for the determination of modulus and other physical properties of the polymer.     

Structural analysis of nine-coordinate lanthanide complexes: steric control of the metal-water distance across the series

The structures of 10 isomorphous lanthanide (Ln) complexes of a chiral DOTA tetra-amide ligand (L(1)), [LnL(1)(H(2)O)](CF(3)SO(3))(3).3H(2)O, crystallizing in space group P2(1), have been studied by single-crystal X-ray diffraction. The Ln coordination is a O(4)N(4) square antiprism, the O(4) base of which is capped by an aqua ligand. The sterically demanding position of the latter results in the lengthening of the Ln-OH(2) distance along the Pr to Lu series by 0.06 A (after allowing for the lanthanide contraction). In parallel, the distance between the bound water oxygen and the second-sphere water oxygen is reduced from 3.17 A (Pr) to 3.04 A (Lu), consistent with the enhanced hydrogen bond acceptor ability of the coordinated water oxygen across the series. A Cambridge Structural Database survey of [Ln(H(2)O)(9)](CF(3)SO(3))(3) salts (space group P6(3)/m) and of six reported isostructural complexes of DOTA [L(2)] revealed a similar trend. The implications of the resultant destabilization of the ground state structure for the water interchange process are discussed.     

Enumeration of probiotic bacilli spores in animal feed: interlaboratory study

Fourteen out of 17 laboratories completed an interlaboratory study comparing 2 pretreatment protocols of feed samples containing authorized probiotic bacilli spores. Both methods used tryptone soy agar for enumeration. Pretreatment A involved preparation of a suspension of the feed sample in 50% ethanol. For pretreatment B, the sample was suspended in peptone salt solution and heated at 80 degrees C for 10 min. Each laboratory analyzed 12 samples (6 per pretreatment), which represented duplicates of a high (10(9) colony-forming units [CFU]/g) and low (10(5) CFU/g) level of bacilli spores or a blank that contained vegetative probiotic bacteria only. For pretreatment A, the repeatability relative standard deviation (RSD(r)) was 2.9% for the low level and 2.5% for the high. The reproducibility relative standard deviation (RSDR) values were 7.8 and 5.9%, respectively. Pretreatment B revealed RSD(r) values of 1.1 and 1.0%, and RSDR values of 5.8 and 3.4%, respectively. The heat treatment (pretreatment B) of feed samples had better precision data, resulted in higher viable bacilli counts, and was more effective in deactivating vegetative background flora. It is therefore recommended for adoption for official control purposes and for CEN and ISO standards.     

A Refinement of Carleman's Inequality

We prove a new sharpening of the inequalitywhich is due to T. Carleman.     

Convergent Outer Approximation Algorithms for Solving Unary Programs

Interesting cutting plane approaches for solving certain difficult multiextremal global optimization problems can fail to converge. Examples include the concavity cut method for concave minimization and Ramana's recent outer approximation method for unary programs which are linear programming problems with an additional constraint requiring that an affine mapping becomes unary. For the latter problem class, new convergent outer approximation algorithms are proposed which are based on sufficiently deep l-norm or quadratic cuts. Implementable versions construct optimal simplicial inner approximations of Euclidean balls and of intersections of Euclidean balls with halfspaces, which are of general interest in computational convexity. Computational behavior of the algorithms depends crucially on the matrices involved in the unary condition. Potential applications to the global minimization of indefinite quadratic functions subject to indefinite quadratic constraints are shown to be practical only for very small problem sizes.     

Constraint decomposition algorithms in global optimization

Many global optimization problems can be formulated in the form min{c(x, y): x X, y Y, (x, y) Z, y G} where X, Y are polytopes in ^p , ⁿ , respectively, Z is a closed convex set in ^p+n, while G is the complement of an open convex set in ⁿ . The function c: ^p+n is assumed to be linear. Using the fact that the nonconvex constraints depend only upon they-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in ⁿ . Computational experiments show that the resulting algorithms work well for problems with smalln.     

Beiträge zum thermischen Verhalten von Sulfaten. XII. Zum chemischen Transport von In2(SO4)3 mit Cl2 und mit HCl. Experimente und Modellrechnungen

Contributions on the Thermal Behaviour of Sulfates XII. The Chemical Vapour Transport of In₂(SO₄)₃ with Cl₂ and HCl. Experimental Results and Calculations By means of CVT (T₁ between 500°C and 825°C; ΔT = 50°C), well shaped crystals of anhydrous In₂(SO₄)₃ can be grown in the less hot region of a closed silica ampoule. We investigated the dependence of the deposition rate on the variation of the concentration of the transport agent (system In₂(SO₄)₃/Cl₂) and on the variation of the transport temperature (In₂(SO₄)₃/Cl₂ as well as In₂(SO₄)₃/HCl). A comparison of the experimental results with thermodynamical calculations shows a satisfying agreement. The influence of the variation of some additional parameters (H₂O from the wall of the ampoule; Δ_BH(In₂(SO₄)₃)) on the deposition rate is discussed.