Fixed points and matching points in partitions

The Ramanujan Journal - We study fixed points in integer partitions viewed, respectively, as weakly increasing or weakly decreasing structures. A fixed point is a point with value i in position i....     

Epicardial development in the rat: a new perspective.

Development of the epicardium is critical to proper heart formation. It provides all of the precursor cells that form the coronary system and supplies signals that stimulate cardiac myocyte proliferation. The epicardium forms from mesothelial cells associated with the septum transversum and is referred to as the proepicardium (PE). Two different methods by which these PE cells colonize the developing heart have been described. In avians, PE cells form a bridge to the heart over which PE cells migrate onto the heart. In fish and mammals, PE cells form vesicles of cells that detach from the mesothelium, float through the pericardial cavity, and attach to the heart. A previous study of rat PE development investigated this process at the histological level. Protein markers have been developed since this study. Thus, we investigated this important developmental process coupled with these new markers using other visualization techniques such as scanning electron microscopy (SEM) and confocal microscopy. Finally, a novel, three-dimensional (3-D) culture system was used to confirm the identity of the PE cells. In this study, we found convincing evidence that the rat PE cells directly attach to the heart in a manner similar to that observed in avians.     

Correlations of13C chemical shifts and geometry modifications

The effect of geometry modifications of¹³C chemical shifts has been investigated in a small subset of molecules using both LO-INDO and Gaussian 70 (4–31) calculations. The Gaussian calculations, while known to give poor absolute shifts, compare well to the reparameterized semi-empirical INDO determinations in calculated shift changes. In virtually all cases the signs of the shift changes were found to be opposite to that of the changes in the calculated electronic energy.     

The different steric environments of the 5-exo- and 5-endo- substituent for a pair of isomeric tricarbonyl(methoxycyclohexa-1,-diene)irons

A shift reagent has been employed to demonstrate the sterically-hindered environment of the methoxy group in tricarbonyl(5-endo-methoxycyclohexa-1,-diene)iron relative to that of the methoxy group in the 5-exo analogue.     

Determination of higher molecular weight aliphatic aldehydes and ketones

The visible absorption spectra have been measured for the reaction products formed by aldehydes and ketones with p-nitrobenzenediazonium fluoborate in a phosphoric acid-2-methoxyethanol solvent medium. The absorption maxima for the reaction products of higher molecular weight aldehydes and ketones are much more intense than those formed by formaldehyde, acetaldehyde and acetone. This intensity effect has been used to analyze for propionaldehyde in mixtures also containing formaldehyde, acetaldehyde or acetone. The nature of the reaction products are considered.     

Extended Peptide Nucleic Acid Nucleobases Based on Isoorotic Acid for the Recognition of A–U Base Pairs in Double-Stranded RNA

Peptide nucleic acids (PNA) with extended isoorotamide containing nucleobases ( I _o ) were designed for binding A–U base pairs in double-stranded RNA. Isothermal titration calorimetry and UV thermal melting experiments revealed improved affinity for A–U using the Io scaffold in PNA. PNAs having four sequential Io extended nucleobases maintained high binding affinity.     

Viscoelasticity of rubber-resin mixtures

The dynamic viscoelastic response of blends in various proportions of natural rubber with each of two tackifier resins, a poly(β-pinene) and a pentaerythritol ester of hydrogenated rosin, has been investigated. Results are presented in the form of master curves of the modulus G′_r and the viscosity η′_r against frequency. The two resins show remarkably similar behavior in modifying the viscoelastic behavior of the rubber; the most obvious effects of increasing resin concentration are (a) a displacement of the transition zone toward lower frequencies, (b) a reduction in width and eventual elimination of the “rubbery plateau,” and (c) a displacement of the terminal zone in the direction of higher frequencies. The effect (a) is interpreted in molecular terms as a restriction of segmental motion and may be quantitatively evaluated in terms of reduced fractional free volume and increased monomeric friction coefficient. Effects (b) and (c) are explicable in terms of reduced average molecular weight, with consequent reduction in entanglement coupling and resistance to viscous flow. Quantitative analysis of the results, using relaxation time spectra, lends support to the iso-free-volume theory of the glassy state and shows a correlation between fractional free volume and monomeric friction coefficient.     

Bifurcations in parametric nonlinear programming

Bifurcation and continuation techniques are introduced as a class of methods for investigating the parametric nonlinear programming problem. Motivated by the Fritz John first-order necessary conditions, the parametric programming problem is first reformulated as a closed system of nonlinear equations which contains all Karush-Kuhn-Tucker and Fritz John points, both feasible and infeasible solutions, and relative minima, maxima, and saddle points. Since changes in the structure of the solution set and critical point type can occur only at singularities, necessary and sufficient conditions for the existence of a singularity are developed in terms of the loss of a complementarity condition, the linear dependence constraint qualification, and the singularity of the Hessian of the Lagrangian on a tangent space. After a brief introduction to elementary bifurcation theory, some simple singularities in this parametric problem are analyzed for both branching and persistence of local minima. Finally, a brief introduction to numerical continuation and bifurcation procedures is given to indicate how these facts can be used in a numerical investigation of the problem.This research was supported by the Air force Office of Scientific Research through grant number AFOSR-88-0059.