Kruskal-Katona type theorems for clique complexes arising from chordal and strongly chordal graphs

A forest is the clique complex of a strongly chordal graph and a quasi-forest is the clique complex of a chordal graph. Kruskal-Katona type theorems for forests, quasi-forests, pure forests and pure quasi-forests will be presented.     

Copper-catalyzed addition reactions of aromatics and ketones to 2-aza-2,4-cyclopentadienone: facile and efficient transformation of carbonyl-ene-nitriles to 1H-pyrrolin-2(5H)-ones

Copper-catalyzed reactions of carbonyl-ene-nitriles with carbon nucleophiles, such as aromatics and ketones, afforded pyrrolin-2-ones (gamma-lactam) in excellent yield. The reaction mechanism involves addition reactions with a ketimine moiety of the 2-aza-2,4-cyclopentadienone intermediate, which is formed via hydration of a nitrile moiety followed by dehydrative cyclization.     

Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. III

By extending the methodology given in Parts I and II of this series of articles, certain dynamical systems of chemical kinetic equations are analyzed in the setting of the Banach algebra B(ℬ︁) of all bounded operators acting on a Banach space ℬ︁. In this article, we proceed from the general setting of B(ℬ︁), which played a central role in Part II, toward its specific application to the dynamical systems. In our analysis, crucial initial steps are taken by (i) equipping the abstract space ℬ︁ with the “positive quadrant,” which we denote by Γ(ℝ⁺ⁿ), and by (ii) investigating the asymptotic behavior of the solution χ_ϵ(t) of the initial-value problem is suitably specified for our application purposes. The main theorem and its two specialized versions, together with the notions of Γ-semipositive operators and semipositive matrices presented here, serve as fundamental tools for the analysis of a class of dynamical systems of chemical kinetic equations whose examples were illustratively treated in the previous parts of this series of articles. The techniques developed here for an asymptotic analysis of chemical kinetic dynamical systems will be linked and unified with those for the asymptotic analysis of quantum mechanical systems in a forthcoming part of this series of articles. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 149–163, 1997     

Linear viscoelastic analysis using frequency-domain algorithm on oscillating circular shear flows for bubble suspensions

To achieve a stable evaluation of the linear viscoelasticity of bubble suspensions, which have difficulties for conventional rheometers from spatial distributions of rheological properties with bubble deformations, we proposed a novel rheometry based on spatio-temporal velocity data obtained by ultrasonic velocity profiling (UVP). A frequency-domain algorithm was adopted to overcome a critical influence of measurement noise on the rheological assessment, which is inferred from error propagation characteristics through the equations of motion in discretized form. Applicability and advantage of the present rheometry with the frequency-domain algorithm were verified by two kinds of fluids: high viscous oil as a Newtonian fluid and polyacrylamide aqueous solution as a shear thinning, viscoelastic fluid. The rheometry was finally adopted for bubble suspensions subject to high oscillatory shear, and it could validly extract elasticity-originated momentum transfer as a function of space.     

Liver function assessment with three (13)C breath tests by two-point measurements

In this study, we performed three breath tests - l-[1-(13)C ]phenylalanine breath test (PBT), l-[1-(13)C ] methionine breath test, and [(13)C]methacetin breath test (MethaBT) - in patients with chronic liver disease to determine the optimal timing of expired air collection for diagnosing chronic liver disease and evaluating the grade of fibrosis. The subjects were 61 adults with normal livers, 98 chronic hepatitis patients, and 91 liver cirrhosis patients. We investigated the relationships of breath test results with routine biochemical tests and the Child-Pugh score, as well as the diagnostic capacities of the breath tests for liver dysfunction/cirrhosis and grade of liver fibrosis. For the diagnosis of liver cirrhosis and correlations with liver fibrosis, the accuracy of the PBT at 30 min (PBT30) was similar to that of the MethaBT at 15 min (Metha15). For liver function assessment by two-point measurement with (13)C breath tests, we recommend the PBT30 and the Metha15.     

Comparisons of O-acylation and Friedel-Crafts acylation of phenols and acyl chlorides and Fries rearrangement of phenyl esters in trifluoromethanesulfonic acid: effective synthesis of optically active homotyrosines

Reactions involving phenol derivatives and acyl chlorides have to be controlled for competitive O-acylations and C-acylations (Friedel-Crafts acylations and Fries rearrangements) in acidic condition. The extent for these reactions in trifluoromethanesulfonic acid (TfOH), which is used as catalyst and solvent, is examined. Although diluted TfOH was needed for effective O-acylation, concentrated TfOH was required for effective C-acylations in mild condition. These results have been applied to the novel synthesis of homotyrosine derivatives. Both Fries rearrangement of N-TFA-Asp(OBn)-OMe and Friedel-Crafts acylation of phenol with N-TFA-Asp(Cl)-OMe in TfOH afforded the homotyrosine skeleton, followed by reduction and deprotection afforded homotyrosines maintaining stereochemistry of Asp as an optically pure form.     

Synthetic studies on β-lactam antibiotics. Part 16. synthesis of 1-carba-2-penem-3-carboxylic acid esters from penicillins utilizing a carbon-carbon coupling reaction

Allylazetidinones $\text{9}$, $\text{10}$, prepared by coupling of allylcoppers $\text{8}$ with chloroazetidinones $\text{6}$, $\text{7}$, were converted into carbapenem esters $\text{16}$, $\text{28}$–$\text{31}$ using an Emmons-Horner reaction to introduce the 6-side chain and an intramolecular Wittig reaction to form the carbapenem ring system.