Infinitesimal bendings of high orders for homogeneous surfaces with positive curvature and a flat point

For any given n∈Z⁺ and k∈Z⁺, infinitesimal bendings of order n and of class Ck are constructed for a class of surfaces in R³. These surfaces are given as graphs of homogeneous polynomials P(x,y) and they have positive curvature except at the origin.     

A Random Multivalued Uniform Boundedness Principle

We present a generalization of the Uniform Boundedness Principle valid for random multivalued linear operators, i.e., multivalued linear operators taking values in the space L₀(,Y) of random variables defined on a probability space with values in the Banach space Y. Namely, for a family of such operators that are continuous with positive probability, if the family is pointwise bounded with probability at least >0, then the operators are uniformly bounded with a probability that in each case can be estimated in terms of and the index of continuity of the operator. To achieve this result, we develop the fundamental theory of multivalued linear operators on general topological vector spaces. In particular, we exhibit versions of the Closed Graph Theorem, the Open Mapping Theorem, and the Uniform Boundedness Principle for multivalued operators between F-spaces.Mathematics Subject Classifications (2000) 46A16, 46A30, 47A06, 47B80, 60H25.     

Reassignment of the structures of condensation products of α-keto α′-formylarylhydrazones with ethyl cyanoacetate: a novel route to ethyl 5-arylazo-2-hydroxynicotinates

The condensation of α-keto α′-formylarylhydrazones with ethyl cyanoacetate afforded ethyl 5-arylazo-2-hydroxy-6-aryl (or alkyl) nicotinates. The structures of the reaction products could be established based on X-ray crystal structure determination.     

Textural,structural and catalytic properties of zirconia doped by heteropolytungstic acid: a comparative study between aerogel and xerogel catalysts

Zirconia doped by heteropolytungstic acid HPW have been synthesized by sol–gel method using two drying techniques of the solvent evacuation. Samples were analyzed with adsorption–desorption of N₂ at 77 K, and the aerogel catalyst was found to exhibit a higher surface area and a higher average pore diameter compared to xerogel. XRD results show that aerogel develops ZrO₂ tetragonal phase, whereas xerogel is amorphous. The thermal analysis studies show that the aerogel’s thermal stability is better than the xerogel one. The catalytic behavior of the aerogel and xerogel toward the nature of the isomerization products probably depends on the acidity and the presence of carbide species. This has been explained by XPS and isopropanol dehydration reaction. In fact, the deconvolution aerogel’s Cls bands reveals the presence of four carbon species assigned to C–C, C=O, C–O and carbide species.     

Unleashing a Microcomputer in the Laboratory,Part III

Experimental Techniques -     

GRPIA: a new algorithm for computing interpolation polynomials

Numerical Algorithms - Let x0,x1, ? , xn, be a set of n + 1 distinct real numbers (i.e., xm ≠ xj, for m ≠ j) and let ym,k, for m = 0, 1, ? , n, and k = 0, 1, ? , rm,...     

The Use of Voltammetry for Sorption Studies of Arsenic (III) Ions by Magnetic Beads Functionalized with Nucleobase Hydrazide Derivatives

In this work the interaction characteristics of nucleobases with As(III) are studied. Novel materials consisting of magnetic nanoparticles (MNPs) functionalized with adenine hydrazide (AH), guanine hydrazide (GH) and uracil hydrazide (UH) were elaborated. The adsorption isotherms were investigated electrochemically and it was shown that the adsorption capacity of the nanoparticles towards arsenic (III) increased in the following order: AH<UH<GH. The electrochemical detection of As(III) using the GH functionalized MNPs offered better results compared with the other functionalizations, with a sensitivity of 1.92 μA μg⁻¹ L and a limit of detection of 1.6 μg/L (21 nM).     

Bis(aldehydes): Versatile precursors for novel bis(14H-dibenzo[a,j]xanthenes), bis(pyrano[3,2-c:5,6-c']dichromenedione), and bis(dihydrobenzo[a]xanthenones) via multicomponent reactions

A synthesis of novel bis(4-(14H-dibenzo[a,j]xanthenes) and bis(dihydro-8H-benzo[a]xanthenones) was performed in good yields via pseudo-multicomponent, or multicomponent reactions, of bis-aldehydes with four equivalents of β-naphthol or with a mixture of two equivalents of each β-naphthol and dimedone in the presence of a catalytic amount of p-toluenesulfonic acid. Bis(pyrano[3,2-c:5,6-c′]dichromenediones) or tetrakis(4-hydroxy-2H-chromen-2-ones) could also be obtained in good yields through pseudo-multicomponent reactions of bis(aldehydes) with four molar ratio of 4-hydroxycoumarin.     

Crystal structure,Hirshfeld surface analysis,vibrational properties,and electrical and dielectric studies of the bis (4-benzylpyridinium) tetrachlorocuprate (II)

The present paper undertakes the study of (C₁₂H₁₂N)₂CuCl₄, which is a new hybrid compound. It is synthesized and characterized by single-crystal X-ray diffraction, Hirshfeld surface analysis, and FT-IR, FT-Raman, and impedance spectroscopies. It is crystallized in the monoclinic system with C2/c space group. Its crystal structure was determined and refined down to an R value of 0.05 and a wR value of 0.14. The structure can be described by the alternation of two different, cationic–anionic layers parallel to (110) plan. This complex is assembled into 3D supramolecular architecture by hydrogen bonds (N–H…Cl, C–H…Cl) and π–π interactions. Hirshfeld surface analyses and fingerprint plots are used for decoding intermolecular interactions in the crystal network and contribution of component units for the construction of the 3D architecture. The presence of different functional groups and the nature of their vibrations were identified by FT-IR and FT-Raman spectroscopies. The material is characterized by impedance spectroscopy technique measured in 209–500 MHz frequency and 296–390 K temperature ranges. In addition, the Cole–Cole (Z? versus Z?) plots were well fitted to an equivalent circuit built up by a parallel combination of resistance (R) and constant phase elements (CPEs). The close values of activation energies obtained from the analysis of equivalent circuit data confirm that the transport is through ion hopping mechanism in the bis (4-benzylpyridinium) tetrachlorocuprate.