Uniqueness of Positive Solutions of Δu+f(u)=0 in ℝN, N≦3

We study the uniqueness of radial ground states for the semilinear elliptic partial differential equation in ℝ ^N . We assume that the function f has two zeros, the origin and u ₀>0. Above u ₀ the function f is positive, is locally Lipschitz continuous and satisfies convexity and growth conditions of a superlinear nature. Below u ₀, f is assumed to be non-positive, non-identically zero and merely continuous. Our results are obtained through a careful analysis of the solutions of an associated initial‐value problem, and the use of a monotone separation theorem. It is known that, for a large class of functions f, the ground states of (*) are radially symmetric. In these cases our result implies that (*) possesses at most one ground state. (Accepted July 3, 1996)     

The Fukui potential and the capacity of charge and the global hardness of atoms

In the course of a reaction it is the shape of the Fukui potential that guides a distant reagent toward the site where an electrophile/nucleophile is willing to accept/donate charge. In this paper we explore the mathematical characteristics of the Fukui potential and demonstrate its relationship to the hardness and the ability of an atom in a molecule to change its charge. The Fukui potential not only determines the active site for electron transfer, but it also approximates the distribution of hardness of a molecule: it is the Coulomb contribution to the frontier local hardness. The Fukui potential at the position of the nuclei is equal to the variation of the chemical potential with the nuclear charge and therefore measures the sensitivity of the system to changes in atom type. In the specific case of atoms and slightly charged ions, the Fukui potential at the nucleus measures the hardness. The strong correlation between the hardness and the Fukui potential at the nucleus suggests that the Fukui potential at the nucleus is an alternative definition for the chemical hardness.     

In vitro cytotoxic evaluation of a novel phosphinyl derivative of boldine

2,9-Dimethoxymethylboldine (2), 2,9-dimethoxymethyl-3-bromoboldine (3) and 2,9-dimethoxymethyl-3-diphenylphosphinylboldine (4) have been synthesized in an effort to find compounds with potential pharmacological applications. The cytotoxic activities of the natural precursor 1 and these three derivatives have been measured as IC?? inhibitory growth. The diphenylphosphinyl derivative 4 showed a significant cytotoxic activity on two breast cancer cell lines, namely MCF-7 and MDA-MB-231, with IC?? values of 55.5 and 62.7 [μM], respectively. These results suggest that the kind of structural modifications introduced to synthesize compound 4 represent a promising way to enhance the cytotoxic activity of boldine derivatives.     

A note on a question of Dimca and Greuel

In this note, we give a positive answer to a question of Dimca and Greuel about the quotient between the Milnor and Tjurina numbers of an isolated plane curve singularity in the cases of one Puiseux pair and semi-quasi-homogeneous singularities.     

Topological defects with axial symmetry: a disk + a string

The superimposed gravitational field of a string and a family of axisymmetric walls is analysed. The resulting axisyrnmetric system is a topological defect. A striking observational feature is the appearance of a double-ring image from a distant point source.     

ESR study of Gd and Nd in RNi2 and RCo2 laves phase compounds

We report ESR study of Gd and Nd in RCo₂ and RNi₂ (R = Sc, Y, Zr, Lu, Ce) compounds. The variation of the Gd g shift from RCo₂ to RNi₂ compounds is consistent with a recent calculation of the density of states and also with the systematic behaviour demonstrated previously by us for transition metal intermetallic compounds. The Nd resonance in CeNi₂ and LuNi₂ indicate Γ₆ ground state crystalline field splitting; the Nd g value in YNi₂:Nd and LuNi₂: Nd is anomallous. Several possibilities for this anomally are discussed.     

Coupling of a sheep anti-T3 IgG to a solid phase for a triiodothyronine radioimmunoassay

Optimal conditions for coupling sheep anti-T₃ IgG to a solid phase are presented. We found that the optimal activation of microcrystalline cellulose was achieved with 0.15M 1,1-carbonyldiimidazol (CDI) in acetone. We also found that using a 25 mg/cm³ anti-T₃ IgG solution, in barbitone buffer 0.05M, pH 8.0, we could get a reasonable yield of coupling and a remaining solution of anti-T₃ IgG (first supernatant) with a suitable concentration (10 mg/cm³) for another coupling. The solid phase anti-T₃ obtained in these two couplings present similar characteristics which make possible their use in a total T₃ RIA.     

Radiopharmaceuticals for renal studies: Evaluation of protein binding

Determination of total in vitro protein binding was evaluated for the following radiopharmaceuticals:^99mTc-diethylenetriaminepentaacetic acid (DTPA),^99mTc-dimercaptosuccinic acid (DMSA),^99mTc-glucoheptonate (GH) and^99mTc-fosfomycin (PHO). For that they were incubated wtih human serum at 37°C. After three and sixty minutes of incubation, the bound fraction was evaluated by two different methods: gel filtration and precipitation with trichloroacetic acid (TCA). The percentage of the^99mTc-kidney agents bound by human serum proteins is different for each one. Determination by TCA precipitation always leads to higher results. For renal imaging agents (DMSA, GH and PHO) the percentage of binding by each serum proteic constituent was also evaluated by electrophoretic analysis. All proteic constituents of human serum bind with those radiopharmaceuticals but the percentage of binding is different in accordance with both the radiopharmaceutical and the proteic constituent.