The Jacobi-Dunkl transform on ℝ and the convolution product on new spaces of distributions

In this work, we consider the Jacobi-Dunkl operator Λ _α,β , a 3 b 3 \frac-12\alpha\geq\beta\geq\frac{-1}{2} , a 1 \frac-12\alpha\neq\frac{-1}{2} , on ℝ. The eigenfunction Y_l^a,b\Psi_{\lambda}^{\alpha,\beta} of this operator permits to define the Jacobi-Dunkl transform. The main idea in this paper is to introduce and study the Jacobi-Dunkl transform and the Jacobi-Dunkl convolution product on new spaces of distributions     

A conductometric biosensor for the estimation of the number of cleaving sites in peptides and proteins

A conductometric enzyme biosensor using proteinase K was developed and then tested to relate its electrical signal to the number of proteinase K hydrolysis sites in bovine serum albumin (BSA) and angiotensin, a ten amino acid peptide, with one cleaving site.The conductometric sensor presents a large linear range of response for BSA and angiotensin ranging from 0.5 to 8 mg/l and from 4 to 8 mg/l, respectively. For a same tested concentration (mg/l), the response for native BSA is 12 times higher than for angiotensin. Aspartam was used as negative test and no response was obtained with the proteinase K biosensor. The conductometric sensor permitted also to detect difference on enzyme activity on native and non-native BSA, a response three times higher was obtained for non-native BSA.     

On a Ginzburg-Landau Type Energy with Discontinuous Constraint for High Values of Applied Field

In the presence of applied magnetic fields H such that |lnε| 《H 《1/ε2,the author evaluates the minimal Ginzburg-Landau energy with discontinuous constraint.Its expression is analogous to the work of Sandier and Serfaty.     

Natural frequencies and mode shapes of initially curved carbon nanotube resonators under electric excitation

Estimating accurately the natural frequencies of electrically actuated carbon nanotubes (CNTs) has been an active research subject over the past few years. Despite the importance of the topic, robust knowledge is still missing in the understanding of the role of various physical parameters affecting the natural frequencies, such as the stretching of doubly clamped CNTs, the DC electrostatic force, and the initial curvature of slack CNTs. In this investigation, we use a 2D nonlinear curved beam model in the form of an arch to simulate the coupled in-plane and out-of-plane motions of a CNT with curvature. We calculate the variation of its natural frequencies and mode shapes with the level of slackness and the DC electrostatic load. Towards this end, we derive a reduced-order model using a multimode Galerkin procedure. We show various scenarios of mode crossing and mode veering as the levels of slackness and DC load are varied. Finally, we tackle the forced vibration problem of a curved CNT when actuated by small DC and AC loads. The results show the transfer of energy among the vibration modes involved in the veering phenomenon.     

A New Non-centrosymmetric Microporous Fluorinated Iron Phosphate: Structural Elucidation,Spectroscopic Study and Hirshfeld Surface Analysis

The crystal structure of a new non-centrosymmetric microporous fluorinated iron phosphate, (H₃O)₂[Fe₄(H₂O)₂F₄(PO₄)₂(HPO₄)₂](H₂O), was determined by single crystal X-ray diffraction analysis and the result reveals that it belongs to the orthorhombic system with four molecules in the unit cell(space group P2₁2₁2₁). Thus, the complex was characterized by powder X-ray diffraction, spectroscopic techniques(Fourier transform infrared and Fourier transform Raman) and ¹⁹F MAS NMR. The elemental analysis of the sample was also carried out. The chiral inorganic sheets, which stacked along[100] showed the presence of FeF₂O₄ as well as FeF₂O₃H₂O octahedra, PO₄ besides HPO₄ tetrahedra, hydronium ions(H₃O⁺) and isolated water molecules. Hirshfeld surface analysis, especially d_nom surface and fingerprint plots, were used for decoding the intermolecular interactions in the crystal network and the contribution of component units for the construction of the 3D architecture. From the Hirshfeld surfaces and 2D fingerprint analysis, it was found that the subtle interactions, such as H…H associating the third intense interaction of all intercontacts, provide extra stabilization in addition to the presence of the strong hydrogen bonds mentioned above.     

Vortex analysis of the periodic Ginzburg–Landau model

We study the vortices of energy minimizers in the London limit for the Ginzburg–Landau model with periodic boundary conditions. For applied fields well below the second critical field we are able to describe the location and number of vortices. Many of the results presented appeared in [H. Aydi, Doctoral Dissertation, Université Paris-XII, 2004], others are new.     

Synthesis of Highly Fluorinated Aryl N-Acylsulfamates and Evaluation of Their Surfactant Properties

Abstract

Reaction of highly fluorinated carboxylic acids with aroxysulfonylisocyanates in the presence of triethylamine allowed the preparation of the corresponding highly fluorinated aroxy-N-sulfonylsulfamates. The reaction proceeds with good yield in toluene at room temperature or more rapidly in the same solvent at 60 °C. Surface tension measurement at the air/water interface showed that these compounds constitute new excellent nonionic surfactants exhibiting high surface activity in the range of the best nonionic fluoro surfactants, already described in the literature. The critical micelle concentration (CMC) has been calculated from the surface tension measurements on surface aqueous solutions.     

A straightforward approach to N-substituted-2H-indazol-2-amines through reductive cyclization

A versatile two-step, one-pot reaction to access N-substituted-2H-indazol-2-amine derivatives has been elaborated. A diverse set of analogues was obtained by a sequential hydrazone formation and reductive cyclization in moderate to good yields from readily available starting materials. The strategy tolerates a broad range of substitutions pattern and functional groups allowing further derivatizations.     

Polymorphism in 3‐acetyl‐4‐hydroxy‐2H‐chromen‐2‐one

A new polymorph (denoted polymorph II) of 3‐acetyl‐4‐hydroxy‐2H‐chromen‐2‐one, C₁₁H₈O₄, was obtained unexpectedly during an attempt to recrystallize the compound from salt–melted ice, and the structure is compared with that of the original polymorph (denoted polymorph I) [Lyssenko & Antipin (2001). Russ. Chem. Bull. 50 , 418–431]. Strong intramolecular O—H...O hydrogen bonds are observed equally in the two polymorphs [O...O = 2.4263 (13) Å in polymorph II and 2.442 (1) Å in polymorph I], with a slight delocalization of the hydroxy H atom towards the ketonic O atom in polymorph II [H...O = 1.32 (2) Å in polymorph II and 1.45 (3) Å in polymorph I]. In both crystal structures, the packing of the molecules is dominated and stabilized by weak intermolecular C—H...O hydrogen bonds. Additional π–π stacking interactions between the keto–enol hydrogen‐bonded rings stabilize polymorph I [the centres are separated by 3.28 (1) Å], while polymorph II is stabilized by interactions between α‐pyrone rings, which are parallel to one another and separated by 3.670 (5) Å.     

Two‐Step Synthesis of Multifunctional γ‐Lactams from γ‐Lactone

We present herein an efficient and rapid method for the synthesis of N,1‐dialkyl‐4‐(2‐hydroxyethyl)‐5‐oxopyrrolidine‐3‐carboxamides based on the conversion of γ‐lactone to γ‐lactam via the conjugate addition of primary amines to an ethyl α‐functionalized acrylate followed by intramolecular cyclization.