Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions

In this paper, we show that the maximum principle holds for quasilinear elliptic equations with quadratic growth under general structure conditions.Two typical particular cases of our results are the following. On one hand, we prove that the equation (1) {ie77-01} where {ie77-02} and {ie77-03} satisfies the maximum principle for solutions in H ¹()L(), i.e., that two solutions u ₁, u ₂H¹() L() of (1) such that u ₁u₂ on , satisfy u ₁u₂ in . This implies in particular the uniqueness of the solution of (1) in H ₀ ¹ ()L().On the other hand, we prove that the equation (2) {ie77-04} where fH^–1() and g(u)>0, g(0)=0, satisfies the maximum principle for solutions uH¹() such that g(u)¦Du|{²L¹(). Again this implies the uniqueness of the solution of (2) in the class uH ₀ ¹ () with g(u)¦Du|{²L¹().In both cases, the method of proof consists in making a certain change of function u=(v) in equation (1) or (2), and in proving that the transformed equation, which is of the form (3) {ie77-05}satisfies a certain structure condition, which using ((v₁ -v ₂)⁺)ⁿ for some n>0 as a test function, allows us to prove the maximum principle.     

Stereochemistry and reactivity of F- and H-vinyldiazocarbonyl compounds and their phosphazines: synthesis of pyrazoles and pyridazines

3-(Trifluoromethyl)-substituted (F) 2-vinyl-2-diazocarbonyl compounds, having cis-relationship of functional groups (AlkO₂C, CN₂), do not undergo 1,5-electrocyclization, but readily take part in the tandem Staudinger-diaza-Wittig reactions to produce trifluoromethyl-substituted pyridazines, whereas their non-fluorinated analogs (H), with trans-configuration, easily cyclize to pyrazoles, but remain intact under Staudinger-diaza-Wittig reaction conditions. The difference in the reactivity of H- and F-vinyldiazoketones, vinyldiazoacetates, and derived phosphazines is apparently caused by the different stereochemical arrangements of the AlkO₂C and CN₂ groups.     

Ruthenium complexes of aminophosphine ligands and their use as pre-catalysts in the transfer hydrogenation of aromatic ketones: X-ray crystal structure of thiophene-2-(N-diphenylthiophosphino)methylamine

Reaction of thiophene-2-methylamine with one or two equivalents of PPh₂Cl in the presence of NEt₃, proceeds in thf to give thiophene-2-(N-diphenylphosphino)methylamine, 1a and thiophene-2-(N,N-bis(diphenylphosphino))methylamine, 2a respectively, under anaerobic conditions. Oxidations of 1a and 2a with aqueous hydrogen peroxide, elemental sulfur or gray selenium in thf gives the corresponding oxides, sulfides and selenides [Ph₂P(E)NHCH₂-C₄H₃S] (E: O 1b, S 1c, Se 1d) and [(Ph₂P(E))₂NCH₂-C₄H₃S], (E: O 2b, S 2c, Se 2d) respectively, in high yield. Furthermore, two novel Ru(II) complexes with the P-N ligands 1a and 2a were synthesized starting with the complex [Ru(η⁶-p-cymene)(μ-Cl)Cl]₂. The complexes were fully characterized by analytical and spectroscopic methods. ³¹P-{¹H} NMR, DEPT, ¹H-¹³C HETCOR or ¹H-¹H COSY correlation experiments were used to confirm the spectral assignments. The molecular structure of thiophene-2-(N-diphenylthiophosphino)methylamine was also elucidated by single-crystal X-ray crystallography. Following activation by NaOH, compounds 3 and 4 catalyze the transfer hydrogenation of acetophenone derivatives to 1-phenylethanol derivatives in the presence of iso-PrOH as the hydrogen source. [Ru(Ph₂PNHCH₂-C₄H₃S)(η⁶-p-cymene)Cl₂], 3 and [Ru((PPh₂)₂NCH₂-C₄H₃S)(η⁶-p-cymene)Cl]Cl, 4 complexes are suitable catalyst precursors for the transfer hydrogenation of acetophenone derivatives in 0.1 M iso-PrOH solution. Notably 4 acts as an excellent catalyst giving the corresponding alcohols in excellent conversions up to 99% (TOF ? 744 h⁻¹). This transfer hydrogenation is characterized by low reversibility under the experimental conditions.     

Spectral measurements of inductively coupled and helicon discharge modes of a laboratory argon plasma source

An experimental study was conducted to investigate the effects of several operational parameters in the emission spectra, in the 400-850 nm wavelength region, of a laboratory Argon plasma source. In particular, the emission spectra of the inductively coupled plasma and the Helicon plasma modes of operation were compared. Comparisons of spectra point to a significant increase in the ionization fraction of the plasma for the Helicon mode of operation. The spectral measurements allow one to determine the major trends in the plasma electron density for various parameters such as power delivered to the helical antenna, propellant mass flow rate, and applied external magnetic field intensity.Analysis of a prominent Argon single ion line, at 434.8 nm, points out that the plasma electron density increases linearly with the power delivered to the helical antenna, and that there is an optimum propellant mass flow rate for maximum ionization fraction. Additional analysis of the same line shows that above a minimum applied axial magnetic field intensity, the variation in the magnetic field strength has little effect on the plasma electron density.     

Monosize microbeads for pseudo-affinity adsorption of human insulin

Affinity adsorption technique is increasingly used for protein purification, separation and other biochemical applications. Therapeutic molecules such as antibodies, cytokines, therapeutic DNA and plasma proteins must be purified before characterization and utilization. The aim of this study was to prepare micronsized spherical polymeric beads and to investigate the extent of their human insulin adsorption capability. Monosize poly(ethylene glycol dimethacrylate-N-methacryloyl-(L)-histidine) [poly(EDMA-MAH)] beads were prepared by modified suspension copolymerization. Functional monomer (MAH) was synthesized using methacryloyl chloride and L-histidine. The beads were characterized using scanning electron microscopy (SEM), Fourier transform infrared spectroscopy, swelling test and elemental analysis. MAH incorporation into monosize polymeric beads, having an average size around 2-3 μm, was estimated as 55.3 μmol MAH/g bead. Equilibrium swelling ratios of poly(EDMA-MAH) and poly(EDMA) beads were 65% and 55%, respectively. Adsorption experiments were performed under different conditions (i.e., pH, temperature, protein concentration and ionic strength). It was found that adsorption characteristics are strongly depend on these conditions. Maximum insulin adsorption capacity was achieved as 24.7 mg insulin/g poly(EDMA-MAH) beads. Results were well fitted to the Langmuir isotherm model. Compared with poly(EDMA-MAH), nonspecific insulin adsorption onto poly(EDMA) beads was very low (0.61 mg insulin/g bead) and can be negligible. It was observed that insulin could be repeatedly adsorbed and desorbed (at least 10 times) without significant loss in adsorption capacity.     

Versatile introduction of azido moiety into oligonucleotides through diazo transfer reaction

The use of a diazo transfer (DZT) reagent enables clean and efficient conversion of aminated oligodeoxyribonucleotides (ODNs) into their azido counterparts under mild conditions. ODNs bearing an amino tether at the 3', 5', or any internal position could be modified in this manner thus demonstrating the versatility of this reaction. Easy access to such azido-modified ODNs is of great interest for conjugation in particular through copper catalyzed 1,3-dipolar cycloaddition (CuAAC reaction).     

An Interactive Algorithm for Multi-objective Route Planning

We address the route selection problem for Unmanned Air Vehicles (UAV) under multiple objectives. We consider a general case for this problem, where the UAV has to visit several targets and return to the base. We model this problem as a combination of two combinatorial problems. First, the path to be followed between each pair of targets should be determined. We model this as a multi-objective shortest path problem. Additionally, we need to determine the order of the targets to be visited. We model this as a multi-objective traveling salesperson problem (MOTSP). The overall problem is a combination of these two problems, which we define as a generalized MOTSP. We develop an exact interactive approach to identify the best paths and the best tour of a decision maker under a linear utility function.     

Principal functions of non-selfadjoint matrix Sturm-Liouville equations

In this paper we investigate the principal functions corresponding to the eigenvalues and the spectral singularities of the boundary value problem

     

High‐order finite difference schemes for numerical solutions of the generalized Burgers–Huxley equation

In this article, up to tenth‐order finite difference schemes are proposed to solve the generalized Burgers–Huxley equation. The schemes based on high‐order differences are presented using Taylor series expansion. To establish the numerical solutions of the corresponding equation, the high‐order schemes in space and a fourth‐order Runge‐Kutta scheme in time have been combined. Numerical experiments have been conducted to demonstrate the high‐order accuracy of the current algorithms with relatively minimal computational effort. The results showed that use of the present approaches in the simulation is very applicable for the solution of the generalized Burgers–Huxley equation. The current results are also seen to be more accurate than some results given in the literature. The proposed algorithms are seen to be very good alternatives to existing approaches for such physical applications. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1313‐1326, 2011