Positive solutions of $\Delta u+u^p = 0$ whose singular set is a manifold with boundary

The aim of this paper is to prove the existence of weak solutions to the equation , with , which are positive in a domain and which are singular along a k-dimensional submanifold with smooth boundary. Here, the exponent p is required to lie in the interval , where is the dimension of the singular set. In the particular case where and , solutions correspond to solutions of the singular Yamabe problem. Received: 7 October 2001 / Accepted: 7 March 2002 / Published online: 6 August 2002     

Synthesis, Characterization, and Biological Activity of n-Tributyltin Derivatives of Pharmaceutically Active Carboxylates

Summary.  Tributyltin(IV) derivatives of six different pharmaceutically active carboxylates were synthesized. The complexes were characterized by different analytical techniques (elemental analysis; infrared, NMR, and mass spectroscopy). ¹¹⁹Sn NMR data were also recorded in six different coordinating and non-coordinating solvents. The antibacterial activities of the compounds were tested using ten different bacteria relative to the reference drugs ampicillin and cephalexin. Received September 20, 2001. Accepted (revised) December 6, 2001     

New adsorbents from oil shales: Preparation, characterization and U, Th isotope adsorption tests

New activated adsorbents for radionuclides have been produced from Moroccan oil shales by pyrolysis of the natural material at 550 °C flowed by a KMnO₄ activation. The texture and composition of the native rock and the adsorbents were studied before their use in tests for adsorption of radionuclides from standard solutions prepared from uranylnitrate and thorium nitrate in equilibrium with their daughters. The distribution coefficients between solutions containing U, Th and Ra and the adsorbents were evaluated by means of specific activities, measured by g-ray spectrometry. The adsorbents were observed to eliminate U, Th, Ra, Ac and Tl from aqueous solutions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Spectrophotometeric determination of someN-substituted phenothiazine derivatives usingN-bromophthalimide

A simple, rapid and sensitive spectrophotometric method is described for the quantitative determination ofN-substituted phenothiazines. The method depends on the formation of a stable phenothiazine free radical cation by the use ofN-bromophthalimide as oxidising agent in a strong acid medium (methanol/ sulphuric acid 1 1 v/v). The produced red or violet color possesses absorption maximum range from 500 to 530 nm. A linear relationship exists between the absorbance at (_max) and concentration in the range 5 to 40 g ml^–1 with apparent molar absorptivities range from 6 × 10³ to 12 × 10³1 mol^–1 cm^–1. The color is developed instantaneously for all the studied phenothiazines except for thioproperazine mesylate, trifluoperazine dihydrochloride and prochlorperazine mesylate that require 25, 15 and 25 min, respectively, for complete reaction. The developed colors are stable over 24 h. The average % recovery is 99.85±0.61 to 100.28±0.95. The method was applied successfully to the microdetermination of chlorpromazine HCl, promethazine HCl, pericyazine, thioproperazine mesylate, perphenazine, prochlorperazine mesylate, trimeprazine tartrate and trifluoperazine 2HCl either in pure form or incorporated in their pharmaceutical preparations. The results of analysis are in good agreement with those of the official B.P. 1988 and USP XXII.     

Spectrophotometric Determination of Pyrithioxin in Pharmaceutical Preparations

Rapid direct and induced difference spectrophotometric methods for determination of pyrithioxin in single dosage forms (tablets and syrups) are reported. The direct methods depend upon measurement of the absorbance of pyrithioxin in different media at λ_max i-e at 296 nm in 0.1 M hydrochloric acid, at 328 nm in citric acid-phosphate buffer of pH 7 and at 314 nm in 0.1 M sodium hydroxide. The mean percentage recovery of the authentic samples were 100.55±0.43, 101.21±0.58 and 100.29±0.64 respectively (P=0.05). The absorbance difference methods are based upon either measurement of the difference between the acid and the alkaline solutions i-e. Δ A (Alk-Acid) at 318 nm with an accuracy of 100.72±0.88 or the absorbance difference between the acid and neutral solutions i-e Δ A (pH 7-acid) at 328 nm with an accuracy of 100.31±0.68.     

Volatiles,color characteristics and other physico–chemical parameters of commercial Moroccan honeys

Seven commercial Moroccan honeys were considered for chemical characterisation. Volatile fraction, total polyphenols content, antioxidant and antiradical activities were evaluated by employing different analytical methodologies. Several physical parameters such as refractive index, pH, water content, solids content and colour were measured. Volatile fraction revealed an abundant presence of cis- and trans-linalool oxide in the seven studied samples. The presence of high levels of compounds related to the Maillard reaction, like furfural and hydroxymethylfurfural, could be the result of thermal treatments used to liquefy commercial honeys or of long storage times. The CIE L^*a^*b^*C_ab^*h_ab° chromatic coordinates confirmed the advanced stage of the Maillard reaction, showing L^* values lower than the common values found for honey of similar typologies.     

The Influence of the Calcination and Water Washing Treatments on the Uranium Content in Sedimentary Phosphate Samples Using Solid State Nuclear Track Detectors and Gamma-Ray Spectrometry

The uranium and thorium contents were evaluated in the 100–400 µm granulometric fraction of different sedimentary phosphate samples by using a method based on determining the mean critical angles of etching of the CR-39 and LR-115 type II solid state nuclear track detectors (SSNTD) for detecting -particles emitted by the nuclei of the uranium-238 and thorium-232 series. Data obtained were compared with the results of -ray spectrometry measurements performed on the same samples. The influence of the calcination and water washing treatments as well as the lithology and stratigraphy on the uranium concentration of the phosphate samples was investigated.     

Study of the partitioning of uranium and thorium in moroccan black shale

Moroccan black shale was analysed for uranium and thorium isotopes using alpha-spectrometry. A sequential leaching procedure was used to define the speciation of isotopes of the actinides in the material. As in most other organic rich rocks, uranium is highly enriched in the black shale. This actinide is associated predominantly with humic acids. Thorium (²³²Th) is a less mobile radionuclide in this environment as was expected from its chemical properties, and in agreement with the most widely adopted views in the published literature. It is partitioned between silicate minerals, pyrite and kerogen.     

Spectrophotometric Determination of Some Phenolic Antibiotics in Dosage Forms

 A simple and sensitive spectrophotometric method is described for the determination of some phenolic antibiotics namely: cefadroxil, amoxicillin and vancomycin. The method is based on the measurement of the orange yellow species produced when the drugs are coupled with diazotized benzocaine in triethylamine medium. The method is applicable over the range of 0.8–12 μg/ml for cefadroxil, 2–16 μg/ml for amoxicillin and 2–18 μg/ml for vancomycin. The formed compounds absorb at 455 nm for both cefadroxil and amoxicillin and at 442 nm for vancomycin. The proposed method has detection limits of 0.018 μg for cefadroxil, 0.0034 μg for amoxicillin and 0.0156 μg for vancomycin. The stoichiometric ratio for the studied compounds was found to be 1:1 and a proposal of the reaction pathway was made. The proposed method was applied for the analysis of the cited drugs in their pharmaceutical preparations. The results are in good agreement with those obtained by the official methods. Received February 7, 2000. Revision June 14, 2000.     

Neutron activation analysis of Th via233Pa

A method is described for the analysis of thorium by neutron activation. The sample is brought into solution and quantitative extraction of²³³Pa is carried out in 1M HNO₃ using 0.5M HTTA in benzene. Extraction mechanisms are discussed. The use of a low-power reactor (100 kW_th) enables determination of thorium at a lower concentration limit of 50 ng for periods of irradiation, cooling and measurement of 3 hours, 24 hours and 300 seconds, respectively.