On the degree of iterates of automorphisms¶of the affine plane

For a polynomial automorphism f of ?² _ℂ, we set τ = deg f ²)/(deg f). We prove that τ≤ 1 if and only if f is triangularizable. In this situation, we show (by using a deep result from number theory known as the theorem of Skolem–Mahler–Lech) that the sequence (deg f ⁿ ) _{n ∈ℕ} is periodic for large n. In the opposite case, we prove that τ is an integer (τ≥ 2) and that the sequence (deg f ⁿ ) _{n ∈ℕ} is a geometric progression of ratio τ. In particular, if f is any automorphism, we obtain the rationality of the formal series . Received: 1 December 1997     

Effects of Curcumin Analogues DMC and EF24 in Combination with the Cytokine TRAIL against Kidney Cancer

The natural compound curcumin has been shown to have therapeutic potential against a wide range of diseases such as cancer. Curcumin reduces cell viability of renal cell carcinoma (RCC) cells when combined with TNF-related apoptosis-inducing ligand (TRAIL), a cytokine that specifically targets cancer cells, by helping overcome TRAIL resistance. However, the therapeutic effects of curcumin are limited by its low bioavailability. Similar compounds to curcumin with higher bioavailability, such as demethoxycurcumin (DMC) and 3,5-bis(2-fluorobenzylidene)-4-piperidone (EF24), can potentially have similar anticancer effects and show a similar synergy with TRAIL, thus reducing RCC viability. This study aims to show the effects of DMC and EF24 in combination with TRAIL at reducing ACHN cell viability and ACHN cell migration. It also shows the changes in death receptor 4 (DR4) expression after treatment with these compounds individually and in combination with TRAIL, which can play a role in their mechanism of action.     

Time-dependent density functional theory molecular dynamics simulation of doubly charged uracil in gas phase

We use time-dependent density functional theory and Born-Oppenheimer molecular dynamics methods to investigate the fragmentation of doubly ionized uracil in gas phase. Different initial electronic excited states of the dication are obtained by removing electrons from different inner-shell orbitals of the neutral species. We show that shape-equivalent orbitals lead to very different fragmentation patterns revealing the importance of the intramolecular chemical environment. The results are in good agreement with ionion coincidence measurements of uracil collision with 100 keV protons.     

Reactivity between CuxV2O5 and AgyV2O5 bronzes studied by spark plasma sintering

A method based on the analysis of reaction layers that form in Cu_xV₂O₅–Ag_yV₂O₅ interdiffusion couples annealed by spark plasma sintering to quickly explore the Cu–Ag–V₂O₅ ternary system at high pressure is presented. Through use of microanalysis profiling, the phases occurring in this system have been obtained much faster than by conventional techniques of solid-state chemistry. Microdiffraction profiling has also been used to properly identify the Cu_0.5Ag_0.5V₂O₅ phase in the reaction layer between CuV₂O₅ and Ag_0.8V₂O₅. The stability domains of the phases have been approximately determined and interpreted. In most cases, reaction kinetics occurs quickly, as expected by the high diffusion coefficient of Cu and Ag in V₂O₅. Though the experiments have been carried out under high pressure (75 MPa), the same phases are obtained than with sealed quartz tubes experiments.     

Criteria to define the standard deviation for proficiency assessment for the determination of essential trace elements in serum: comparison of Z-scores based on the Horwitz function or on biological variability

A critical issue in the organisation of Proficiency Testing/External Quality Assessment Schemes is the definition of the criteria against which the performance of individual laboratories should be evaluated. Organisers of EQAS in Occupational and Environmental Laboratory Medicine (http://www.occupational-environmental-laboratory.com) collaborate to define common acceptable levels of performance. The aim of this study was to compare the Horwitz function to the Fraser’s approach. Sets of results obtained from the distribution of test materials in the Network schemes (for the measurands: copper, selenium or zinc in serum) were used to calculate Z-scores according to both approaches. Quality specifications derived from both approaches were also compared to the standard deviations obtained. Except for selenium, Horwitz criteria suggests a more stringent evaluation than Fraser criteria, the latter being very stringent as regard the participant analytical variability.     

Oxidation and chlorination reactions of perfluoroketene-N,S-acetals

The paper presents the results of the investigation of oxidation and chlorination reactions of perfluoroketene-N,S-acetals. Oxidation reactions of perfluoroketene-N,S-acetals proved to be dependent on the nature of oxidizing agent and led to the formation of corresponding sulfone in the case of m-chloroperbenzoic acid or amides of α-H-perfluoroalkane carboxylic acids in the case of tert-butyl hydroperoxide or hydrogen peroxide. Reaction of 1-tert-butylsulfanyl-2,3,3,4,4,4-hexafluoro-1-[N-methyl,N-((S)-α-methylbenzyl)amino]-but-1-ene with sulfuryl chloride demonstrated the chlorination of perfluoroketene-N,S-acetals as a new approach in the synthesis of chiral α-chloro perfluoroalkane carboxylic acid amides.     

Ultrafast laser processing of drug particles in water for pharmaceutical discovery

The laser fragmentation technique has been extensively used to produce inorganic nanoparticles, but its practice on organic materials, especially on drugs, is less common. Here, we briefly review the recent advances in laser micro-/nanonization of organic materials and the rationale of using laser fragmentation for drug discovery. We present our case studies of two drug models: fenofibrate and naproxen. Both drugs were fragmented in water with femtosecond (fs) laser and characterized in terms of particle size distribution and physicochemical properties. Effects of fs laser fragmentation were also compared with nanosecond (ns) laser fragmentation and with conventional media milling technique. Fs laser was more suitable to produce sub-micron size drug particles than ns laser, but degradation of drugs after nanonization was also more pronounced than micronization. Physicochemical transformations such as oxidation, hydration and amorphisation might occur during the laser–material interactions. Laser nanonization showed improved dissolution kinetics, similar to media milling. Unlike the conventional milling techniques, laser fragmentation enabled the treatment of minute amount (as small as several milligrams) of drugs with high efficiency, thus is a useful tool for particle size reduction during the early phases of drug discovery.     

Computer Assisted Proof of Transverse Saddle-to-Saddle Connecting Orbits for First Order Vector Fields

In this paper we introduce a computational method for proving the existence of generic saddle-to-saddle connections between equilibria of first order vector fields. The first step consists of rigorously computing high order parametrizations of the local stable and unstable manifolds. If the local manifolds intersect, the Newton–Kantorovich theorem is applied to validate the existence of a so-called short connecting orbit. If the local manifolds do not intersect, a boundary value problem with boundary values in the local manifolds is rigorously solved by a contraction mapping argument on a ball centered at the numerical solution, yielding the existence of a so-called long connecting orbit. In both cases our argument yields transversality of the corresponding intersection of the manifolds. The method is applied to the Lorenz equations, where a study of a pitchfork bifurcation with saddle-to-saddle stability is done and where several proofs of existence of short and long connections are obtained.     

Unraveling complex small-molecule binding mechanisms by using simple NMR spectroscopy

Heteronuclear NMR spectroscopy provides a unique way to obtain site-specific information about protein-ligand interactions. Usually, such studies rely on the availability of isotopically labeled proteins, thereby allowing both editing of the spectra and ligand signals to be filtered out. Herein, we report that the use of the methyl SOFAST correlation experiment enables the determination of site-specific equilibrium binding constants by using unlabeled proteins. By using the binding of L- and D-tryptophan to serum albumin as a test case, we determined very accurate dissociation constants for both the high- and low-affinity sites present at the protein surface. The values of site-specific dissociation constants were closer to those obtained by isothermal titration calorimetry than those obtained from ligand-observed methods, such as saturation transfer difference. The possibility of measuring ligand binding to serum albumin at physiological concentrations with unlabeled proteins may open up new perspectives in the field of drug discovery.