Finite-time implications of relaxation times for stochastically monotone processes

Summary For a continuous-time finite state Markov process with stationary distribution , it is well-known thatP ⁱ (X ^t =j)- ^j isO(e ^-t ) ast, for a certain . For a stochastically monotone process for which the reversed process is also stochastically monotone, one can obtain bounds valid for allt. Precisely, exp(-t). The proof exploits duality for stochastically monotone processes.Research supported by National Science Foundation Grant MCS 84-03239     

Establishing order in planar subdivisions

A planar subdivision is the partition of the plane induced by an embedded planar graph. A representation of such a subdivision isordered if, for each vertexv of the associated graphG, the (say) clockwise sequence of edges in the embedding ofG incident withv appears explicitly.The worst-case complexity of establishing order in a planar subdivision, i.e., converting an unordered representation into an ordered one, is shown to be (n + log (G)), wheren is the size (number of vertices) of the underlying graphG and (G) is (essentially) the number of topologically distinct embeddings ofG in the plane.This work was supported by the National Science and Engineering Research Council of Canada under Grant A3583. A preliminary version of this paper appeared in theProceedings of the Third Annual ACM Symposium on Computational Geometry.     

On the large order behavior of Φ 4 4

We continue the rigorous study of the large order behavior of the perturbation series for the ⁴ model in 4 dimensions started in [1]. In this paper we prove a result announced in [1]. We show that the exact radius of convergence of the Borel transform of the renormalized perturbation series for ₄ ⁴ is greater than or equal to the expected value given by the position of the first renormalon [2]. This result holds for any vector (²)² model withN components, and makes use of the Lipatov bound of [1]. This result is based on a partial resummation of counterterms similar to the one of [3], but in a phase-space analysis of the renormalized series.     

Large area bolometers for millimeter-wave power calibration

An accurate monolithic power meter has been developed for millimeter-wave applications. The detector is a large-area Bismuth bolometer, integrated on a fused-Quartz substrate. It simply measures the temperature change caused by the absorption of millimeter-wave radiation. The power meter is simple to fabricate, inexpensive, and can be easily calibrated using a low-frequency network. The measured responsivity for a 50 bolometer, with an area of 1×1cm, at a bias of 1V. and a video modulation of 100Hz, is 1mV/W. The noise spectrum exhibits a 1/f rolloff till 1KHz, and is limited by the Johnson noise for higher frequencies. The NEP of the detector is 3WHz^–1/2 at a video modulation of 1KHz. It is possible to decrease the current NEP by fabricating bolometers with higher responsivities. Possible application areas are absolute power calibration and localized power density measurements at millimeter and submillimeter wavelengths.     

Monotone Chemical Reaction Networks

We analyze certain chemical reaction networks and show that every solution converges to some steady state. The reaction kinetics are assumed to be monotone but otherwise arbitrary. When diffusion effects are taken into account, the conclusions remain unchanged. The main tools used in our analysis come from the theory of monotone dynamical systems. We review some of the features of this theory and provide a self-contained proof of a particular attractivity result which is used in proving our main result.     

Self-assembly of a hydrophobic groove

Heptakis(2,6-di-O-methyl)-β-cyclodextrin interacts with 5,15-diphenylporphine to produce a 2:1 complex in dimethyl sulfoxide. This complex possesses a hydrophobic groove that circumscribes the metal binding site of the porphyrin moiety.     

Synthesis,crystal structures and electrochemical properties of group 6 metal carbonyl anion complexes

A series of [M(CO)₅I]⁻ and [M₂(CO)₁₀I]⁻ anion complexes have been synthesized by the photochemical reaction of PhCH₂N(CH₃)₃I or FcCH₂N(CH₃)₃I (Fc=ferrocenyl) with M(CO)₆ (M = Cr, Mo or W), and characterized by elemental analyses, i.r., ¹H-n.m.r. and ¹³C-n.m.r. spectra in the case of the molybdenum and tungsten complexes. These complexes exhibit considerably different electrochemical behavior, when investigated by cyclic voltammetry. The crystal structures of [PhCH₂N(CH₃)₃][Cr(CO)₅I] and [FcCH₂N(CH₃)₃][W₂(CO)₁₀I] have been determined by X-ray diffraction, indicating that only weak contacts maybe exist between anions and cations by the I...H bond in the former, and there are no direct interactions between anions and cations in the latter.     

Transition metal complexes with Girard reagent-based ligands

The ligand, salicylaldehyde Girard-T hydrazonium chloride, [H₂SalGT]Cl (1), and two complexes [Cu(HSalGT)X₂]·H₂O (X = Br(2); Cl(3)) were synthesized and their crystal structures were determined by single-crystal X-ray analysis. In the two isostructural complexes, the Cu(II) is located in a square-pyramidal environment, with the chelating ligand and one halogen atom in the basal plane and the second halogen in the apical position. The most apparent structural difference between the 1 and its complexes 2 and 3 is the orientation of the N(CH₃)₃ group: in 1, it is practically coplanar to the rest of the molecule, while in 2 and 3 it is oriented to the side of the axially bonded halogen, which can be explained by the C–H…X intramolecular interactions. The compounds were characterized by elemental analysis, molar conductivity, magnetic susceptibility and electronic absorption spectra.     

Restricted rotation about the boron---nitrogen bond in aminoboranes

The application of variable temperature ¹³C NMR to the study of a series of chlorodialkylaminophenylboranes has enabled G values for the rotational barrier, about the boron---nitrogen bond, to be determined.     

Synthesis,crystal structure and ferro-magnetic interaction of a binuclear copper(II) complex with the 1,4-dinitro-2,3,5,6-tetracarboxylatobenzenic anion as bridging ligand

A binuclear complex [Cu₂(DTB)(DMF)₄(H₂O)]·2DMF (DTB = 1,4-dinitro-2,3,5,6-tetracarboxylatobenzenic anion; DMF = N,N-dimethylformamide) has been synthesized and its crystal structure determined by X-ray crystallography. In the complex Cu ion is located in a distorted square pyramidal environment with two oxygen atoms O(1) and O(3) from two carboxylate groups, another two oxygen atoms O(7) and O(8) from terminal ligands of two DMF molecules, and a fifth coordinated oxygen atom O(9) from the terminal ligand of one H₂O molecule, in which the O(8) atom is situated in the apex of the pyramid. DTB as bridging ligand coordinates two Cu ions through its four carboxylate groups. The variable-temperature magnetic susceptibility of the complex was measured in the 5–300 K range. The magnetic coupling parameter is consistent with a ferromagnetic exchange between the two copper(II) centers and the data fit a binuclear magnetic exchange model based on the Hamiltonian operator ( = -2J₁₂, ₁ = ₂= 1/2), giving the ferromagnetic coupling parameter of 2J = 1.80 cm^{- 1}. This is the first example of a tetracarboxylatobenzenic bridging complex exhibiting ferromagnetic interaction.