A functional inequality for real-analytic functions

Summary Forf ( C ⁿ() and 0 t x letJ _n (f, t, x) = (–1)ⁿ f(–x)f ⁽ⁿ⁾(t) +f(x)f ⁽ⁿ⁾ (–t). We prove that the only real-analytic functions satisfyingJ _n (f, t, x) 0 for alln = 0, 1, 2, are the exponential functionsf(x) = c e ^x,c, . Further we present a nontrivial class of real-analytic functions satisfying the inequalitiesJ ₀ (f, x, x) 0 and ₀ ^x (x – t)^{n – 1}J_n(f, t, x)dt 0 (n 1).     

Functional inequality characterizing nonnegative concave functions in (0, ∞) k

Summary In the present note we prove that every functionf: (0, ) [0, ) satisfying the inequalityaf(s) + bf(t) f(as + bt), s, t > 0, for somea andb such that 0 <a < 1 <a + b must be of the formf(t) = f(1)t, (t > 0). This improves our recent result in [2], where the inequality is assumed to hold for alls, t 0, and gives a positive answer to the question raised there.An analogue for functions of several real variables of the above result characterizes concave functions. Conjugate functions and some relations to Hölder's and Minkowski's inequalities are mentioned.     

Capture by stabilized continuum: Classical and quantum aspects

We review here the results of our investigations concerning chaotic atomic scattering in the presence of a laser field. Particular emphasis is put on the existence of classical stable resonance structures, induced by the intense laser field, which are embedded in the field-free continuum. We show that phase space structures in the vicinity of a resonance island play an important role in the chaotic scattering behavior and form the basis for a mechanism to enhance the lifetimes of the collisional partners. Quantum calculations, based on a wave packet propagation method, show that quantum solutions are strongly influenced by the classical phase space structures. More specifically, a wave packet is found to spread differently in the regular and chaotic regions; in the latter case it spreads exponentially with time until saturation occurs, defining the saturation time. We also investigate the dependence of the spreading rates in both the regular and chaotic regimes. Calculations with an ensemble of classical trajectories are also presented to further illustrate the smoothing effects of varying.     

Zur Synthese von Human-Big-Gastrin I

The synthesis of the tetratriacontapeptide amide corresponding to the revised primary structure of human big gastrin I is described. For this purpose the fragments were designed in view of the maximum use of those utilized in our previous synthesis of human big gastrin I according to the first sequence proposal. Consequently the key tripeptide-Pro-Pro-His- (sequence 7–9) was prepared in suitably protected form to be used as amino or carboxyl component for assembly of the segments 1–9 and 1–14, respectively. Final condensation of the latter nona- and tetradecapeptide derivatives with the C-terminal segments 10–34 and 15–34 via the azide and the dicyclohexylcarbodiimide/N-hydroxysuccinimide procedure, respectively, leads to crude fully protected human big gastrin I. Upon deprotection by exposure to trifluoroacetic acid in presence of ethanedithiol-(1,2) as scavanger, ion exchange chromatography and partition chromatography, the desired tetratriacontapeptide amide was isolated in satisfactory yield with a high degree of purity. The identical immunological behaviour of the synthetic material, if compared with that of natural human big gastrin I, represents ulterior strong evidence for the correctness of the newly proposed structure for this putative prohormonal form of the gastrins.

Kurzmitteilung:Wünsch E., Wendlberger G., Mladenova-Orlinova L., Göhring W., Jaeger E., Scharf R., Gregory R. A., Dockray G. J., Hoppe-Seyler's Z. Physiol. Chem.362, 179 (1981).     

Normal coordinate treatment of actinide(IV)-hexabromides

Molecular force field studies of hexabromo-thorates(IV) and-uranates(IV) have been carried out using four different force field models. Weighted least square adjustment has been used to fit the observed frequencies. Mean amplitudes of vibration have also been calculated at 0°K and 298°K. The trends of force constants and mean amplitudes have also been discussed.

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Normal-Koordinaten Berechnungen an Actiniden(IV)-hexabromiden

Zusammenfassung Es wurden für die Rechnungen an Hexabromo-thoraten(IV) und-uranaten(IV) vier verschiedene Modelle herangezogen. Die beobachteten Frequenzen wurden mittels gewichteter Kleinster-Fehlerquadrat-Methode angepaßt. Die Trends bei den Kraftkonstanten und den mittleren Amplituden der einzelnen Verbindungen werden diskutiert.

     

Oxidative Transformations of Organic Compounds Mediated by Redox Molecular Sieves

Zeolites are viewed by some as the “philosopher's stone” of modern chemistry.^[1] They are more or less indispensable in oil refining and petrochemicals manufacture where they are widely applied as solid acid catalysts. More recently attention has been focused on their use in the manufacture of fine chemicals. The synthetic utility of zeolites and related molecular sieves (zeotypes) has been considerably extended by the incorporation of redox metals into their frameworks. The resulting redox molecular sieves catalyze a variety of selective oxidations under mild conditions in the liquid phase. Their structural diversity–including variation of the redox metal, incorporation of metal complexes, and the size and polarity of the micropores–provides the possibility of designing tailor-made solid catalysts (“mineral enzymes”) for liquid-phase oxidations with clean oxidants such as O₂, H₂O₂, and RO₂H. Hence, they have enormous potential in industrial organic synthesis as environmentally friendly alternatives to traditional oxidations employing inorganic oxidants in stoichiometric amounts. A primary aim of this review is to familiarize organic chemists with the synthetic potential of redox molecular sieves. An outline of their synthesis, structures, and chemical properties, highlighting their unique advantages, is followed by a discussion of general (mechanistic) features that influence the choice of a suitable catalyst for a particular type of oxidation. The main part of the review deals with the oxidation of various substrates of synthetic interest–such as alkanes, alkenes, (alkyl)arenes, alcohols, and amines–and emphasizes the advantages of redox molecular sieves (including selectivity and stability) over their homogeneous counterparts. New directions towards truly biomimetic solid catalysts, for example zeolite-encapsulated chiral metal complexes as heterogeneous catalysts for asymmetric oxidations, are high-lighted.     

Fractionation and purification of antioxidant peptides from Chinese sturgeon (Acipenser sinensis) protein hydrolysates prepared using papain and alcalase 2.4L

Protein hydrolysates have the potential to be natural and safer sources of bioactive peptides. In this study, two proteases were used to hydrolyze Chinese sturgeon (Acipenser sinensis) protein, and the hydrolysates were then purified to yield antioxidant peptides. The degree of hydrolysis of 23.56 % and 18.14 % was obtained using papain and alcalase 2.4L, respectivly, and hydrolysates had 96.80 % and 87.24 % total amino acid content, respectivly. The papain hydrolysate (PH) and alcalase 2.4L hydrolysate (AH) showed good antioxidant activity against DPPH^? (IC₅₀ of 3.64 and 3.15 mg/mL) and ABTS^?+ (IC₅₀ of 1.92 and 1.58 mg/mL), respectively. The low-molecular-weight (<1000 Da) fraction of both hydrolysates demonstrated the highest antiradical activity (IC₅₀ of 2.59 and 2.31 mg/mL, DPPH) and (IC₅₀ of 1.54 and 1.36 mg/mL, ABTS), respectively. Nine peptides were separated from both hydrolysates using reverse phase high performance liquid chromatography (RP-HPLC). The IC₅₀ for ABTS^?+ scavenging activity of peptide P5 with valine, glycine and asparagine (MW of 282.13 Da) from PH, and peptide P3 with histidine, glycine and alanine (MW of 302.74 Da) from AH was 0.89 and 0.72 mg/mL, respectively. The fractions and purified peptides obtained from Chinese sturgeon hydrolysates could be utilized as natural antioxidant substitutes in pharmaceuticals and food products.     

Synthesis and Some Chemical Behaviour of Certain Substituted Thiosemicarbazides

Three new thiosemicarbazides (1 a-c ) were prepared from N-[4-phenyl-5-(2-thienyl)-1,2,4-triazol-3-yl]mercaptoacetohydrazide. Reaction of (1 a-c) with the appropriate phenacyl bromide afforded thiazoline derivatives (2 a-i) whereas their reaction with chloroacetic acid or maleic anhydride gave the corresponding thiazolidine derivatives (3 a,b) and (4 a,b) . Cyclodesulfurization of (1 a-c) with DCCD in toluene yielded 5-substituted-amino-1,3,4-oxadiazoles (5 a,b) , while their dehydration with PPA gave the corresponding 5-substituted-amino-1,3,4-thiadiazoles (6 a-c) . Six representative compounds were tested for their in-vitro antimicrobial activity against some pathogenic microorganisms, some of them were proved to be active.     

A theoretical study of angiotensin-converting enzyme inhibitors

Summary INDO molecular orbital calculations are reported for 35 selected angiotensin-converting enzyme inhibitors. QSARs are developed between pI₅₀ data and molecular electronic indices. The QSARs obtained reflect the importance of both charge-charge interactions between inhibitor and receptor and of specific interactions between groups on the inhibitor with points around the molecule which are postulated to correspond to binding sites at the receptor.