Determination of Very Slow Diffusion of Paramagnetic Ions by NMR Spectroscopy

In this paper, we propose a new method of measuring the very slow paramagnetic ion diffusion coefficient using a commercial high-resolution spectrometer. If there are distinct paramagnetic ions influencing the hydrogen nuclear magnetic relaxation time differently, their diffusion coefficients can be measured separately. A cylindrical phantom filled with Fricke xylenol gel solution and irradiated with gamma rays was used to validate the method. The Fricke xylenol gel solution was prepared with 270 Bloom porcine gelatin, the phantom was irradiated with gamma rays originated from a ⁶⁰Co source and a high-resolution 200 MHz nuclear magnetic resonance (NMR) spectrometer was used to obtain the phantom ¹H profile in the presence of a linear magnetic field gradient. By observing the temporal evolution of the phantom NMR profile, an apparent ferric ion diffusion coefficient of 0.50 μm²/ms due to ferric ions diffusion was obtained. In any medical process where the ionizing radiation is used, the dose planning and the dose delivery are the key elements for the patient safety and success of treatment. These points become even more important in modern conformal radio therapy techniques, such as stereotactic radiosurgery, where the delivered dose in a single session of treatment can be an order of magnitude higher than the regular doses of radiotherapy. Several methods have been proposed to obtain the three-dimensional (3-D) dose distribution. Recently, we proposed an alternative method for the 3-D radiation dose mapping, where the ionizing radiation modifies the local relative concentration of Fe²⁺/Fe³⁺ in a phantom containing Fricke gel and this variation is associated to the MR image intensity. The smearing of the intensity gradient is proportional to the diffusion coefficient of the Fe³⁺ and Fe²⁺ in the phantom. There are several methods for measurement of the ionic diffusion using NMR, however, they are applicable when the diffusion is not very slow.     

On the asymptotic behavior of solutions of certain integro-differential equations

The authors present conditions under which every positive solution $x(t)$ of the integro--differential equation $x^{\prime \prime }(t)=a(t)+\int_{c}^{t}(t-s)^{\alpha-1}[e(s)+k(t,s)f(s,x(s))]ds, \quad c>1, \ \alpha >0,$ satisfies $x(t)=O(tA(t))\textrm{ as }t\rightarrow \infty,$ i.e, $\limsup_{t\rightarrow \infty }\frac{x(t)}{tA(t)}<\infty, \textrm{where} \ A(t)=\int_{c}^{t}a(s)ds.$ From the results obtained, they derive a technique that can be applied to some related integro--differential equations that are equivalent to certain fractional differential equations of Caputo type of any order.     

Use of 4-bromo pyridazine 3,6-dione for building 3-amino pyridazine libraries

An efficient method for preparation of 4,6 or 5,6 disubstituted 3-aminopyridazines was easily carried out starting from easily available 4-bromo-pyridazine-3,6-dione, and using combination of both amination and Pd(0) cross-coupling reactions under microwave irradiation.     

Global Existence,Decay, and Blow up of Solutions of a Singular Nonlocal Viscoelastic Problem

In this work we consider a nonlinear hyperbolic one-dimensional viscoelastic nonlocal problem with a nonlocal boundary condition. We establish a blow up result for large initial data and a decay result for small enough initial data.     

Mixed nonlocal problem for a nonlinear singular hyperbolic equation

In this paper, we study a nonlocal mixed problem for a nonlinear hyperbolic equation. Based on some a priori estimates and some density arguments, we prove the well posedness of the associated linear problem. The existence and uniqueness of the weak solution of the nonlinear problem are then established by applying an iterative process based on the obtained results for the linear problem. Copyright © 2009 John Wiley & Sons, Ltd.     

1H and C-13 Nuclear Magnetic Resonance of Tiaprofenic Acid

¹H-NMR spectrum of tiaprofenic acid in CDCI3 was obtained and proton chemical shifts from tetramethylsilane were assigned to each proton and set of equivalent protons of the molecule. The hydroxy proton of the carboxylic acid group was confirmed by deuterium exchange. The natural abundance C-13 nuclear magnetic resonance spectrum of the compound in CDCI3 was recorded using Fourier transorm technique. The chemical shifts of carbon resonances have been assigned on the basis of the chemical shift additivity theory and the signal multiplicity observed in the single frequency off-resonance decoupled (SFORD) spectrum. Also comparison with carbon chemical shifts of model compounds were useful.     

Lie algebras admitting a unique quadratic structure

We prove that any Lie algebra g over a field K of characteristic zero admitting a unique up to a constant quadratic structure is necessarily a simple Lie algebra. If the field K is algebraically closed, such condition is also sufficient.

Further, a real Lie algebra g admits a unique quadratic structure if and only if its complexification g^C is a simple Lie algebra over C     

Injective Modules over Prüfer v-Multiplication Domains

Let R be an integral domain with quotient field F. It is shown that R is a strongly discrete Prüfer v-multiplication domain if and only if there exists a bijection between the set of the prime w-ideals and the set of isomorphism classes of GV-torsionfree indecomposable injective R-modules and every indecomposable injective R-module, viewed as a module over its endomorphism ring, is uniserial. It is also shown that the w-closure of any GV-torsionfree homomorphic image of F is injective if and only if R is a Prüfer v-multiplication domain satisfying an almost maximality-type property.     

Direct Synthesis of Multi‐functional Pyrimidine,Pyrazine, and Pyridine Scaffolds via Inter‐ and Intramolecular Annulations of 3‐Amino‐thieno[2,3‐b]pyridine‐2‐carboxylate

The synthesis of a new series of annulated thieno[2,3‐b]pyridines was performed. Ester compound 1 underwent heterocyclization upon reaction with phenylisothiocyanate and formamide to afford pyrimidines 2 and 3 , respectively. Thienopyrimidine 5 was resulted via reaction of amino derivative 1 with triethyl orthoformate to afford the non‐isolable intermediate 4 , which allowed hydrazinolysis with hydrazine hydrate to afford the target compound. Pyrimidine type 5 was condensed with p‐nitrobenzaldehyde to afford Schiff base 6 . Refluxing of ester 1 with ethyl cyanoacetate and diethyl malonate followed by base‐mediated heterocyclization afforded condensed pyridines 8 and 9 , respectively. The tetracyclic pyrazine derivative 14 was obtained from the reaction of amino compound 1 with 2,5‐dimethoxytetrahydrofuran followed by hydrazinolysis to give carbohydrazide 11 , which undergo diazotization followed by Curtius rearrangement. The antibacterial results illustrated no significant results for the investigated compounds except compound 5 , which has moderate activity against Gram‐positive bacteria.