Radial solutions for the Brezis-Nirenberg problem involving large nonlinearities

Let us consider the problem

(0.1)     

Nodal solutions for an elliptic problem involving large nonlinearities

Let us consider the problem

(0.1)     

Highly shifted LIPOCEST agents based on the encapsulation of neutral polynuclear paramagnetic shift reagents

Improved LIPOCEST MRI contrast agents with highly shifted intraliposomal water protons were prepared by entrapping neutral polynuclear Tm(III)-based paramagnetic shift reagents in phospholipidic vesicles.     

Representation Formulae for Solutions to Some Classes of Higher Order Systems and Related Liouville Theorems

Let m ≥ 1 be an integer and N > 2m. Let μ be a positive Radon measure on . We study necessary and sufficient conditions on possible distributional solutions of , that guarantee the validity of the representation formula a.e. on , where and c(2m) is a positive constant depending on m and N. Several consequences are derived. In particular we prove Liouville theorems for systems of higher order elliptic inequalities and weighted form of Hardy-Littlewood-Sobolev systems of integral equations. Received: March 2008     

On the Green Function of the Annulus

Using the Gegenbauer polynomials and the zonal harmonics functions we give some representation formula of the Green function in the annulus. We apply this result to prove some uniqueness results for some nonlinear elliptic problems.     

Development of a CZE method for the determination of mizolastine and its impurities in pharmaceutical preparations using response surface methodology

A fast and selective CZE method for the determination of mizolastine and related impurities is described. Response surface methodology was applied to study the influence of phosphate/triethanolamine (TEA) buffer concentration, heptakis(2,3,6-tri-O-methyl)-beta-CD (TMbetaCD) concentration, voltage and temperature. The optimum conditions were: 105 mM phosphate/TEA buffer (pH 3.0) containing 10 mM TMbetaCD, temperature 19 degrees C and voltage 30 kV. Validation of the method was performed in drug substance and drug product. Robustness was evaluated using a Plackett-Burman design, including pH among the considered factors. Applying the optimal conditions, the nine peaks were baseline separated in about 10 min. The method was applied to the quality control of mizolastine in controlled-release tablets.     

Monitoring the traceability of the pH of a primary tetraborate buffer: comparison of results from primary and secondary apparatus

This paper reports evaluation of the behaviour of different combined glass electrodes applied to measurement of the pH of a primary, 0.01 mol kg⁻¹, tetraborate buffer. Measurements were first performed by use of a primary Harned cell (at 15, 25, and 37 °C); these results were then compared with those obtained for the same solution by use of three combined glass electrodes (25 °C) with different membranes and liquid-junction designs, calibrated by use of commercial pH-metric buffers. The pH of the same solution was also measured in terms of the molal concentration of hydrogen ions, using acid–base titration to evaluate the formal potential difference K of each cell at fixed ionic strength, I, adjusted by addition of KCl or Et₄NI (tetraethylammonium iodide). The reference value from primary measurement, paH = 9.171, was slightly closer to the mean value obtained by determination of concentration, rather than that obtained by direct measurement of activity; the differences were smaller than the extended uncertainty characteristics of the secondary measurements. The importance of evaluation of the ionic strength of the solution under study is emphasised. We verified that for tetraborate buffer slight modification of the value of I used to calculate γ _i (the activity coefficient of a single ion) in the calculation of paH from the acidity function at zero molality of chloride can significantly affect the reference value of the calibrator tool. This is true, in general, for low values of the ionic strength, such as those considered in this work; an approximate value of I can then cause distortions along the pH traceability chain. Application of the concepts of thermodynamics to this traceability chain is discussed.     

A multifunctional nanoassembly of mesogen-bearing amphiphiles and porphyrins for the simultaneous photodelivery of nitric oxide and singlet oxygen

We report a molecular nanoassembly able to supply simultaneously, in the same region of space and under the exclusive control of visible light, nitric oxide and singlet oxygen, two species playing a key role in the therapy of cancer; the considerable fluorescence of this nanoaggregate and its reduced size (ca. 40 nm) represent additional advantages that make this photoactive vehicle an appealing candidate to be tested in biological systems.     

Improved Dynamic Text Indexing

In the dynamic text indexing problem, a text string has to be maintained under string insertions and deletions in order to answer on-line queries about arbitrary pattern occurrences. By means of some new techniques and data structures, we achieve improved worst-case bounds. We show that finding allpoccoccurrences of a pattern of lengthpin the current text of lengthntakesO(p + pocc + updlog p + log n) time, whereupdis the number of text uptakes performed so far; inserting or deleting a string of lengthsfrom the current text takesO(s log(s + n)) time.     

Iterated processes and their applications to higher order differential equations

In this paper we construct models obtained by suitably combining Brownian motions and telegraphs in such a way that their transition functions satisfy higher-order parabolic or hyperbolic equations of different types. Equations with time-varying coefficients are also derived by considering processes endowed either with drift or with suitable modifications of their structure. Finally the distribution of the maximum of the iterated Brownian motion (along with some other properties) is presented. This work is partially supported by the Natural Science Foundation of Guangdong Province, National Natural Science Foundation of China grant No. 19501026 and the Alexander von Humbodlt Foundation