A refinement of the Brascamp–Lieb–Poincaré inequality in one dimension

In this short note, we give a refinement of the Brascamp–Lieb inequality in the style of the Houdré–Kagan extension for the Poincaré inequality in one dimension. This is inspired by works by Helffer and by Ledoux.     

Cycloaddition versus amidation in reactions of 2-amino-2-oxoethyl-phenanthrolinium ylides to activated alkynes and alkenes

A comparative study regarding cycloaddition versus amidation reactions of 2-amino-2-oxoethyl-phenanthrolinium ylides to activated alkynes and alkenes is presented. The reaction pathway is different, depending on dipolarophile (with triple or double bond) and ylide structures. The monoenamidation reaction proved to be stereoselective leading to a Z-stereochemistry on the acrylate double bond. The structures of all newly synthesized compounds have been proved by spectral analysis (NMR and IR) and in some cases by X-ray diffraction.     

NMR parameters in gapped graphene systems

We calculate the nuclear spin-lattice relaxation time and the Knight shift for the case of gapped graphene systems. Our calculations consider both the massive and massless gap scenarios. Both the spin-lattice relaxation time and the Knight shift depend on temperature, chemical potential, and the value of the electronic energy gap. In particular, at the Dirac point, the electronic energy gap has stronger effects on the system nuclear magnetic resonance parameters in the case of the massless gap scenario. Differently, at large values of the chemical potential, both gap scenarios behave in a similar way and the gapped graphene system approaches a Fermi gas from the nuclear magnetic resonance parameters point of view. Our results are important for nuclear magnetic resonance measurements that target the ¹³C active nuclei in graphene samples.     

Water soluble complexes of methyl β-cyclodextrin and sulconazole nitrate

Complexation between methyl β-cyclodextrin (Me βCD) and sulconazole nitrate (SULC) was realized both under freeze drying and ultrasonication conditions. The process was carried out in solution and in solid state. In solution, the complexation was evaluated using solubility studies, nuclear magnetic resonance spectroscopy (¹H-NMR) and UV–Vis absorption studies. In the solid state, differential scanning calorimetry (DSC), and X-ray diffraction studies were used. Solubility studies indicate the existence of inclusion complexes between SULC and Me βCD. ¹H-NMR data showed that the inclusion complexes have different structures, according with the method we used for synthesis: for the freeze dried method the complex is obtained by complexation of dichlorobenzene ring of SULC into inner cavity of CD while for ultrasonication method the complex is obtained by complexation of imidazole graph of SULC into the CD molecule. DSC and X-ray studies bring supplementary information concerning the formation of complex Me βCD–SULC. As a result of the inclusion process into Me βCD, the solubility of SULC increase significant, being 10 times more comparative with the pure drug. We anticipate that these modifications will have a significant impact on the biological effects of the drug, making the SULC–Me βCD complex an appropriate candidate for a new drug delivery system.     

Comparative rheological study of ionic semi-IPN composite hydrogels based on polyacrylamide and dextran sulphate and of polyacrylamide hydrogels

Ionic semi-interpenetrating polymer networks composite hydrogels were synthesized by free-radical polymerization using dextran sulphate (DxS), acrylamide as monomer and N,N′-methylene(bis)acrylamide as cross-linking agent. The viscoelastic properties of these composite hydrogels were investigated by oscillatory shear measurements under small deformation conditions comparative with those of polyacrylamide gels. Changes of the rheological properties of composite hydrogels have been studied in terms of polymerization temperature, cross-linker ratio, initial monomer concentration and molar mass of DxS. The results showed that the stability of the composite hydrogels obtained at room temperature (22?°C) was relatively low because the storage modulus (G′) was only eight times higher than the loss modulus (G″), while for those obtained by cryopolymerization (?18?°C), the stability was improved, the G′ values being about 30 times higher than those of G″. This behaviour indicated that, by conducting the synthesis of hydrogels below the freezing point of the reaction solutions, an enhancement of the hydrogels elasticity was achieved. The network parameters, i.e. the average molecular weight between two cross-links and the cross-link density of the composite hydrogels prepared at ?18?°C, were estimated from rheological data.     

Heat-treatment influence on Ni–Fe–Cu–Mo nanocrystalline alloy obtained by mechanical alloying

The 77Ni14Fe5Cu4Mo (wt%) powders have been obtained by dry mechanical alloying of elemental powders in a planetary mill under argon atmosphere for milling durations ranging from 2 to 28?h. The alloy formation is obtained after 12?C16?h of milling, as shown by the X-ray diffraction and magnetic studies. The crystallite mean size is 13?±?2?nm after 28?h of milling. An optimal heat-treatment temperature was chosen after the analysis of the DSC signals. and the samples were heated at 350?°C for different durations ranging from 0.5 to 4?h. The heat treatment was continued to enhance the alloy formation and to eliminate the internal stresses induced during the milling process. The evolution of the phases amount during the heat treatment was calculated from the X-ray patterns using the Rietveld procedure.     

Displacement immunoassay for the detection of ochratoxin A using ochratoxin B modified glass beads

We report here the development of a new assay for the detection of ochratoxin A (OTA) based on the use of its dechlorinated analogue, ochratoxin B (OTB), in a displacement immunoassay. OTB was immobilised on controlled-pore glass beads followed by the binding of anti-OTA antibody, with anti-IgG antibody peroxidase conjugate used as a label. In this manner, an original bio-sensing material was obtained. Upon incubation of this material with OTA, the toxin competes with OTB for the binding sites of the anti-OTA antibodies and releases the antibody-tagged peroxidase complex into the solution. Compared to classic competitive immunoassays, this newly developed displacement immunoassay presents a similar detection limit and assay time. Moreover, the detection, based on the activity of the horseradish peroxidase, is performed for the first time in situ using wine samples.     

Analyticity of the Planar Limit of a Matrix Model

Using Chebyshev polynomials combined with some mild combinatorics, we provide an alternative approach to the analytical and formal planar limits of a random matrix model with a 1-cut potential V. For potentials ${V(x)=x^{2}/2-\sum_{n\ge1}a_{n}x^{n}/n}$ , as a power series in all a _n , the formal Taylor expansion of the analytic planar limit is exactly the formal planar limit. In the case V is analytic in infinitely many variables {a _n } _n ≥ 1 (on the appropriate spaces), the planar limit is also an analytic function in infinitely many variables and we give quantitative versions of where this is defined. Particularly useful in enumerative combinatorics are the gradings of ${V,V_{t}(x)=x^{2}/2-\sum_{n\ge1}a_{n}t^{n/2}x^{n}/n}$ and ${V_{t}(x)=x^{2}/2-\sum_{n\ge3}a_{n}t^{n/2 -1}x^{n}/n}$ . The associated planar limits F(t) as functions of t count planar diagram sorted by the number of edges respectively faces. We point out a method of computing the asymptotic of the coefficients of F(t) using the combination of the wzb method and the resolution of singularities. This is illustrated in several computations revolving around the important extreme potential ${V_{t}(x)=x^{2}/2+\log(1-\sqrt{t}x)}$ and its variants. This particular example gives a quantitative and sharp answer to a conjecture of ’t Hooft’s, which states that if the potential is analytic, the planar limit is also analytic.