Functions with derivatives given by polynomials in the function itself or a related function

We construct the set of holomorphic functions S ₁ = {f: Ω_f ? ? → ?} whose members have n-th order derivatives which are given by a polynomial of degree n+1 in the function itself. We also construct the set of holomorphic functions S ₂ = {g: Ω_g ? ? → ?} whose members have n-th order derivatives which are given by the product of the function itself with a polynomial of degree n in an element of S ₁. The union S ₁ ∪ S ₂ contains all the hyperbolic and trigonometric functions. We study the properties of the polynomials involved and derive explicit expressions for them. As particular results, we obtain explicit and elegant formulas for the n-th order derivatives of the hyperbolic functions tanh, sech, coth and csch and the trigonometric functions tan, sec, cot and csc.     

Chemical Constituents of Macaranga occidentalis,Antimicrobial and Chemophenetic Studies

Medicinal plants are known as sources of potential antimicrobial compounds belonging to different classes. The aim of the present work was to evaluate the antimicrobial potential of the crude extract, fractions, and some isolated secondary metabolites from the leaves of Macaranga occidentalis, a Cameroonian medicinal plant traditionally used for the treatment of microbial infections. Repeated column chromatography of the ethyl acetate and n-butanol fractions led to the isolation of seventeen previously known compounds (1−17), among which three steroids (1−3), one triterpene (4), four flavonoids (5−8), two stilbenoids (9 and 10) four ellagic acid derivatives (11−14), one geraniinic acid derivative (15), one coumarine (16), and one glyceride (17). Their structures were elucidated mainly by means of extensive spectroscopic and spectrometric (1D and 2D NMR and, MS) analysis and comparison with the published data. The crude extract, fractions, and isolated compounds were all screened for their antimicrobial activity. None of the natural compounds was active against Candida strains. However, the crude extract, fractions, and compounds showed varying levels of antibacterial properties against at least one of the tested bacterial strains, with minimal inhibitory concentrations (MICs) ranging from 250 to 1000 μg/mL. The n-butanol (n-BuOH) fraction was the most active against Escherichia coli ATCC 25922, with an MIC value of 250 μg/mL. Among the isolated compounds, schweinfurthin B (10) exhibited the best activity against Staphylococcus aureus NR 46003 with a MIC value of 62.5 μg/mL. In addition, schweinfurthin O (9) and isomacarangin (6) also exhibited moderate activity against the same strain with a MIC value of 125 μg/mL. Therefore, pharmacomodulation was performed on compound 6 and three new semisynthetic derivatives (6a–c) were prepared by allylation and acetylation reactions and screened for their in vitro antimicrobial activity. None of the semisynthetic derivatives showed antimicrobial activity against the same tested strains. The chemophenetic significance of the isolated compounds is also discussed in this paper.     

Epunctanone,a New Benzophenone,and Further Secondary Metabolites from Garcinia epunctata Stapf (Guttiferae)

A new polyprenylated benzophenone, named epunctanone ( 1 ), was isolated from the stem bark of Garcinia epunctata Stapf , together with eight known compounds, 7‐epiisogarcinol ( 2 ), 2,6‐dimethoxy‐p‐benzoquinone ( 3 ), friedelin ( 4 ), lupeol ( 5 ), 16β‐hydroxylupeol ( 6 ), betulin ( 7 ), stigmasterol ( 8 ), and rheediaxanthone A ( 9 ). The structure of epunctanone ( 1 ) was established by detailed analysis of its spectroscopic data, especially 1D‐ and 2D‐NMR, and HR‐MS data. All these compounds were evaluated for their antimicrobial and anti‐protozoan activities. They were also assayed to determine if any of the compounds were nonpeptide agonist ligands for nematodal G‐protein‐coupled receptors, which would be an indication of potential antinematodal activity. Among the isolated compounds, 7‐epiisogarcinol ( 2 ) was the most active against Candida albicans.     

Modification of the thermoresistance to spray-drying of a cold-adapted subtilisin by genetic engineering

The thermoresistance of a cold-adapted subtilisin dried by spray-drying was studied. Proteolytic activity of this enzyme was measured before and after spray-drying. Without chemical additives, spray-drying yields ranged from 2–13%. The use of arabic gum and lactose in the composition of the enzyme solutions allowed the strengthening of the enzyme structures and increased water mobility in the product. Increase of water mobility led to a shorter residence time of the product in the spray-drier and a net yield increase was obtained (yield higher than 50%). The effect of two selective mutations on the thermoresistance to spray-drying of the cold-adapted subtilisin was also investigated. Mutation T85D (introduction of an additional link with an ion Ca²⁺ necessary for enzyme activity, by substitution of Asp for Thr 85) had no effect on the thermoresistance of the subtilisin to spray-drying. Mutation H121W (introduction of an additional aromatic link by substitution of Trp for His 121) reduced the drying yield from 66% (not modified subtilisin) to 52%. This higher thermosensitivity could be explained by an increase of the hygroscopic character of the modified subtilisin (mutation H121W).     

Absolute line intensities determination in the nu7 band of C2H4

Absolute intensities have been measured for 26 lines of C2H4 in the nu7 fundamental transition, using a tunable diode-laser spectrometer. These lines with 3< or = J"< or = 21, 2< or = Ka< or = 4, 2< or = Kc< or = 20 are located in the spectral range 920-980 cm(-1). The intensities have been measured by using two methods: the equivalent width method (EWM) and the line profile fit method (FPM). For the last one, three models have been tested: Voigt, Rautian and Galatry profiles.     

Purification and characterization of a microbial dehydrogenase

Pseudomonas fluorescens (strain BTP9) was found to have at least two NAD(P)-dependent vanillin dehydrogenases: one is induced by vanillin, and the other is constitutive. The constitutive enzyme was purified by ammonium sulfate fractionation, gel-filtration, and Q-Sepharose chromatography. The subunit Mr value was 55,000, determined by sodium dodecyl sulfate polyacrylamide gel electrophoresis. The native M _r value estimated by gelfiltration chromatography gave a value of 210,000. The enzyme made use of NAD⁺ less effectively than NADP⁺. Benzaldehyde, 4-hydroxybenzaldehyde, hexanal, and acetaldehyde were not oxidized at detectable rates in the presence of NAD⁺ or NADP⁺. The ultraviolet absorption spectrum indicated that there is no cofactor or prosthetic group bound. The vanillin oxidation reaction was essentially irreversible. The pH optimum was 9.5 and the pI of the enzyme was 4.9. Enzyme activity was not affected when assayed in the presence of salts, except FeCl₂. The enzyme was inhibited by the thiol-blocking reagents 4-chloromercuribenzoate and N-ethylmaleimide. NAD⁺ and NADP⁺ protected the enzyme against such a type of inhibition along with vanillin to a lesser extent. The enzyme exhibited esterase activity with 4-nitrophenyl acetate as substrate and was activated by low concentrations of NAD⁺ or NADP⁺. We compared the properties of the enzyme with those of some well-characterized microbial benzaldehyde dehydrogenases.     

An Effective Fluorescent Sensor for Choline-Containing Phospholipids

A set of weak CH⋅⋅⋅O interactions is responsible for the recognition of tetraalkylammonium ions (ball-and-stick structure) by the tripodal receptors depicted in the diagram, in which the binding pocket is lined with squaramide units. The association constants of the fluorescent receptors are remarkably high at about 10⁵ M ⁻¹ and can be used for signaling the presence of selected choline phospholipids. Z=RNH, where R=alkyl, arylamino; X⁻=BH₄⁻, Cl⁻, Br⁻, I⁻.     

A new non‐polynomial univariate interpolation formula of Hermite type

A new C ^∞ interpolant is presented for the univariate Hermite interpolation problem. It differs from the classical solution in that the interpolant is of non‐polynomial nature. Its basis functions are a set of simple, compact support, transcendental functions. The interpolant can be regarded as a truncated Multipoint Taylor series. It has essential singularities at the sample points, but is well behaved over the real axis and satisfies the given functional data. The interpolant converges to the underlying real‐analytic function when (i) the number of derivatives at each point tends to infinity and the number of sample points remains finite, and when (ii) the spacing between sample points tends to zero and the number of specified derivatives at each sample point remains finite. A comparison is made between the numerical results achieved with the new method and those obtained with polynomial Hermite interpolation. In contrast with the classical polynomial solution, the new interpolant does not suffer from any ill conditioning, so it is always numerically stable. In addition, it is a much more computationally efficient method than the polynomial approach. This revised version was published online in June 2006 with corrections to the Cover Date.     

Starch‐graft‐copolymer latexes initiated and stabilized by ozonolyzed amylopectin

A method is presented for synthesizing surfactant‐free latexes comprising a starch‐graft‐vinyl polymer, (1) starting with a suspension of the highly branched starch amylopectin, either native or degraded, (2) then using ozonolysis to create free‐radical initiation sites on this amylopectin scaffold, and (3) finally adding the monomer and inducing polymerization. The ozone simultaneously thins the starch and creates initiating/grafting sites on the starch, from which starch‐graft‐copolymer latexes can be grown. The encapsulation of starch inside the hydrophobic polymer particles created by a heterogeneous free‐radical polymerization process is demonstrated with energy‐dispersive spectroscopy; this is the first time that the particle morphology of such a latex has been so characterized. The data unambiguously prove that low‐molar‐mass degraded starch can be encapsulated within a latex particle. The underlying mechanisms have been explored, and data quantifying the rates of production of hydroperoxides by ozone, the thermal decomposition of the starch hydroperoxides so formed, and the degradation of amylopectin by ozone are reported. The activation energy for the thermal decomposition of the starch macroinitiator, determined in this work to be 125 ± 8 kJ mol⁻¹, is consistent with the proposition that the initiating species are mainly hydroperoxides. Colloidally stable poly(styrene‐co‐n‐butyl acrylate) latexes based on high‐molar‐mass amylopectin have been developed. These are stable against electrolytes (several months in 4 mol L⁻¹ NaCl), with 20% of the starch effectively grafted to the particles. Films cast from such latexes are more pliable than starch films and are readily redispersed in water. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5832–5845, 2006