Targeted borate complex formation as followed with electrospray ionization Fourier transform ion cyclotron mass spectrometry: monomolecular model system and polyborate formation

Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) was applied to identify boric acid(B degrees)/borate(B-) complexes in a monomolecular model system, composed of aqueous caffeic acid and boric acid/borate solutions in various concentration ratios at pH 9.2. Using negative mode electrospray ionization as a 'soft' ionization technique, clusters of polyborate were detected beside the well-known BL degrees , BL- and BL2- complexes. An algorithm for the detection of boron complexes, based on their accurate mass and isotope patterns, is proposed which enabled the assignment of elemental compositions/structural formulae of boron/ligand complexes. We present experimental evidence of self-oligomerization of up to six borate units with caffeic acid, resulting in stable covalently bound polyborate-polyol complexes.     

Jacobi polynomials from compatibility conditions

We revisit the ladder operators for orthogonal polynomials and re-interpret two supplementary conditions as compatibility conditions of two linear over-determined systems; one involves the variation of the polynomials with respect to the variable (spectral parameter) and the other a recurrence relation in (the lattice variable). For the Jacobi weight

we show how to use the compatibility conditions to explicitly determine the recurrence coefficients of the monic Jacobi polynomials.

     

Synthesis,antibacterial activity,and fluorescence properties of a novel series from [2,4-dioxochromen-3(4<Emphasis Type="Italic">H</Emphasis>)methyl]amino acid

A new solvent-free method for synthesis of starting compounds 2,4-dioxochromen-3(4H)methyl amino acetic acid derivatives 1a–e via a green approach is reported. Also, the behavior of compound 1a towards various nitrogen nucleophiles such as primary amines, hydrazine hydrate, and hydroxylamine hydrochloride to give corresponding compounds 2–4 was studied. Furthermore, chlorination of compound 1a using a mixture of PCl₅/POCl₃ to yield acid chloride derivative 5 and the reaction of the latter compound 5 with various amino acids to obtain dipeptide compounds 6a–e are described. Moreover, cyclization of compound 1a in alkaline medium to afford dihydrochromeno[3,4-c]pyrrole-1-carboxylic acid 7 and cyclization of 6b in acidic medium, namely Ac₂O, to yield piperazine derivative 8 are reported. Also, reaction of compound 1a with maleic anhydride in dioxane to afford Diels–Alder adduct 9, which posteriorly reacted with hydrazine hydrate to give 10, was investigated. Most of the newly synthesized compounds were screened against Gram-positive and Gram-negative bacteria, with compound 5 exhibiting the maximum inhibition zone towards all four types of bacteria. In addition, the absorption and fluorescence emission of some of the substituted coumarins were studied in dioxane, revealing that the substituents altered both the absorption and fluorescence emission maxima.     

Baire Typical Results for Mixed Hölder Spectra on Product of Continuous Besov or Oscillation Spaces

In this paper, we show that the mixed Hölder spectra of finitely many functions can be recovered from a Legendre transform of a concave scaling function based on simultaneous wavelet leaders. We first prove that this Legendre transform yields an upper bound valid for uniform Hölder functions. We then study the typical optimality (in the sense of Baire’s category) of this upper bound in a product of continuous Besov or oscillation spaces.     

Uniqueness and stability in determining the heat radiative coefficient,the initial temperature and a boundary coefficient in a parabolic equation

We consider an inverse parabolic problem. We prove that the heat radiative coefficient, the initial temperature and a boundary coefficient can be simultaneously determined from the final overdetermination, provided that the heat radiative coefficient is a priori known in a small subdomain. Moreover we establish a stability estimate for this inverse problem.     

Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle

We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and q-difference equations for these polynomials. A general functional equation is found which allows one to relate the zeros of the orthogonal polynomials to the stationary values of an explicit quasi-energy and implies recurrences on the orthogonal polynomial coefficients. We also evaluate the discriminants and quantized discriminants of polynomials orthogonal on the unit circle.     

Some Orthogonal Polynomials Related to Elliptic Functions

We characterize the orthogonal polynomials in a class of polynomials defined through their generating functions. This led to three new systems of orthogonal polynomials whose generating functions and orthogonality relations involve elliptic functions. The Hamburger moment problems associated with these polynomials are indeterminate. We give infinite families of weight functions in each case. The different polynomials treated in this work are also polynomials in a parameter and as functions of this parameter they are orthogonal with respect to unique measures, which we find explicitly. Through a quadratic transformation we find a new exactly solvable birth and death process with quartic birth and death rates.     

A Mild and Versatile Friedel–Crafts Methodology for the Diversity-Oriented Synthesis of Redox-Active 3-Benzoylmenadiones with Tunable Redox Potentials

A series of highly diversified 3-aroylmenadiones was prepared by a new Friedel–Crafts acylation variant/oxidative demethylation strategy. A mild and versatile acylation was performed between 1,4-dimethoxy-2-methylnaphthalene and various activated/deactivated benzoic and heteroaromatic carboxylic acids, in the presence of mixed trifluoroacetic anhydride and triflic acid, at room temperature and in air. The 1,4-dimethoxy-2-methylnaphthalene-derived benzophenones were isolated in high yield, and submitted to oxidative demethylation with cerium ammonium nitrate to produce 3-benzoylmenadiones. All 1,4-naphthoquinone derivatives were investigated as redox-active electrophores by cyclic voltammetry. The electrochemical data recorded for 3-acylated menadiones are characterized by a second redox process, the potentials of which cover a wide range of values (500 mV). These data emphasize the ability of the generated structural diversity at the 3-aroyl chain of these electrophores to fine-tune their corresponding redox potentials. These properties are of significance in the context of antimalarial drug development and understanding of the mechanism of bioactivation/action.