The laplace transform

Book Reviews

The laplace transformR. E. Bellman and R. S. Roth: World Scientific, Singapore, 1984     

Remez-, Nikolskii-, and Markov-type inequalities for generalized nonnegative polynomials with restricted zeros

Sharp Remez-, Nikolskii-, and Markov-type inequalities are proved for functions of the form

FTIR study of CO adsorption on molybdena-alumina catalysts for surface characterization

CO adsorption at low temperature has been used to probe Lewis acid sites created upon dehydroxylation of γ-Al₂O₃ and reduction of Mo/Al₂O₃ catalysts, using Fourier Transform Infrared spectroscopy (FTIR). Carbon-monoxide adsorption on γ-Al₂O₃ and Mo/Al₂O₃ catalysts dehydroxylated and reduced at different temperatures was studied at 78 K by IR spectroscopy. However, our results indicate that there is an approximately linear correlation between the increase either of dehydroxylation or the extent of reduction of the catalysts and the increasing absorbance of CO due to CO adsorption on Lewis acid sites created upon dehydroxylation of γ-Al₂O₃ and reduction of Mo/Al₂O₃.     

Poly(N-isopropylacrylamide). I. Interactions with sodium dodecyl sulfate measured by conductivity

Conductometric titration of poly(N-isopropylacrylamide) (polyNIPAM) with sodium dodecyl sulfate (SDS) gave two apparent transitions labeled C1 and C2. The C1 transition was independent of polyNIPAM concentration in the 0.05–0.3 wt % range, whereas C2 was proportional to the polymer concentration. C1 corresponded to the onset of binding of surfactant with polymer. Arguments based on a simple mass action model for micellization are presented to show that C2, the second transition, is not due to any simple explanation such as being the point above which only free micelles are formed with surfactant addition. The cloud point of polyNIPAM increased with the amount of bound surfactant. This was attributed to electrostatic contribution of bound sulfate groups to the increased solubility of polyNIPAM. © 1993 John Wiley & Sons, Inc.     

Molecular pseudopotential calculations V

The equilibrium geometries, nuclear distances, wave functions and energies for the XY ²₊ , X₂Y⁺, Y₂H⁺ (X=Li, Na, K; Y=Rb, Cs), resp. the X₂H⁺, X₂Y⁺ (X, Y=Cu, Ag, Au) triatomic alkali ions, resp. noble metal ions, further the dissociation energies for the X₂Y⁺→X⁺+XY; XY ²₊ →Y⁺+XY and Y₂H⁺→Y⁺+YH processes are determined with the pseudopotential method. The calculations were performed using the Hellmann-type analytical potential with simple floating-type one-centre wave function.

     

On triazoles XIX: The reaction of 5-amino-1,2,4-triazoles with functionalized acetoacetic esters

Summary Different functionalized alkyl 3-oxo-butyrates (2) were reacted with 5-amino-3-Q-1H-1,2,4-triazoles (1) to yield3 and4 type 1,2,4-triazolo[1,5-a]pyrimidinones. In case of2 (R ¹=methyl,R ²=1-ethoxycarbonylethyl,R ³=ethyl) beside the corresponding derivative4 the unexpected 5,6-dihydro-6,8-dimethyl-7-ethoxycarbonyl-3-methylthio-1,2,4-triazolo[4,3-a]-1,3-diazepin-5(9H)-one (7) was isolated, representing a novel ring system.

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Über Triazole, 19. Mitt.: Die Reaktion von 5-Amino-1,2,4-triazolen mit funktionalisierten Acetoessigestern

Zusammenfassung Verschiedene funktionalisierte 3-Oxo-buttersäurealkylester (2) wurden mit 5-Amino-3-Q-1H-1,2,4-triazolen (1) umgesetzt, wobei 1,2,4-Triazolo[1,5-a]pyrimidinone der Typen3 und4 erhalten wurden. Im Fall von2 (R ¹=Methyl,R ²=1-Ethoxycarbonylethyl,R ³=Ethyl) wurde neben dem erwarteten Derivat4 das unerwartete 5,6-Dihydro-6,8-dimethyl-7-ethoxycarbonyl-3-me-thylthio-1,2,4-triazolo[4,3-a]-1,3-diazepin-5(9H)-on (7) isoliert, welches ein neues Ringsystem darstellt.

     

Near-infrared laser spectroscopy of NiI

Laser-induced fluorescence spectrum of NiI in the near infrared region of 714-770 nm has been recorded. Seven bands belonging to three electronic transition systems were observed and analyzed: the (0,0), (1,0), and (2,0) bands of [13.3] (2)Sigma(+)-A (2)Pi(3/2) system; the (1,1) and (0,1) bands of [13.9] (2)Pi(3/2)-X (2)Delta(5/2) system; and the (0,0) and (1,0) bands of [13.9] (2)Pi(3/2)-A (2)Pi(3/2) system. Spectra of isotopic molecules confirmed the vibrational quantum number assignment of the observed bands. Least-squares fit of rotationally resolved transition lines yielded accurate molecular constants for the v=0-2 levels of the [13.3] (2)Sigma(+) state, the v=0 level of the A (2)Pi(3/2), and the v=1 level of the X (2)Delta(5/2) state. The vibrational separation, DeltaG(1/2), of the ground state was measured to be 276.674 cm(-1). With the observation of the [13.9] (2)Pi(3/2)-A (2)Pi(3/2) and [13.9] (2)Pi(3/2)-X (2)Delta(5/2) transitions, we accurately determined the energy separation between the A (2)Pi(3/2) and the X (2)Delta(5/2) to be 163.847 cm(-1). This confirms that the order of the A (2)Pi(3/2) and X (2)Delta(5/2) states in NiI is reversed when compared with other nickel monohalides.     

Analysis of Protein-Protein Interactions for Intermolecular Bond Prediction

Protein-protein interactions often involve a complex system of intermolecular interactions between residues and atoms at the binding site. A comprehensive exploration of these interactions can help reveal key residues involved in protein-protein recognition that are not obvious using other protein analysis techniques. This paper presents and extends DiffBond, a novel method for identifying and classifying intermolecular bonds while applying standard definitions of bonds in chemical literature to explain protein interactions. DiffBond predicted intermolecular bonds from four protein complexes: Barnase-Barstar, Rap1a-raf, SMAD2-SMAD4, and a subset of complexes formed from three-finger toxins and nAChRs. Based on validation through manual literature search and through comparison of two protein complexes from the SKEMPI dataset, DiffBond was able to identify intermolecular ionic bonds and hydrogen bonds with high precision and recall, and identify salt bridges with high precision. DiffBond predictions on bond existence were also strongly correlated with observations of Gibbs free energy change and electrostatic complementarity in mutational experiments. DiffBond can be a powerful tool for predicting and characterizing influential residues in protein-protein interactions, and its predictions can support research in mutational experiments and drug design.     

Reduced Endocannabinoid Tone in Saliva of Chronic Orofacial Pain Patients

Background: the endocannabinoid system (ECS) participates in many physiological and pathological processes including pain generation, modulation, and sensation. Its involvement in chronic orofacial pain (OFP) in general, and the reflection of its involvement in OFP in salivary endocannabinoid (eCBs) levels in particular, has not been examined. Objectives: to evaluate the association between salivary (eCBs) levels and chronic OFP. Methods: salivary levels of 2 eCBs, anandamide (AEA), 2-arachidonoylglycerol (2-AG), 2 endocannabinoid-like compoundsN-palmitoylethanolamine (PEA), N-oleoylethanolamine (OEA), and their endogenous precursor and breakdown product, arachidonic acid (AA), were analyzed using liquid chromatography/tandem mass spectrometry in 83 chronic OFP patients and 43 pain-free controls. The chronic OFP patients were divided according to diagnosis into musculoskeletal, neurovascular/migraine, and neuropathic pain types. Results: chronic OFP patients had lower levels of OEA (p = 0.02) and 2-AG (p = 0.01). Analyzing specific pain types revealed lower levels of AEA and OEA in the neurovascular group (p = 0.04, 0.02, respectively), and 2-AG in the neuropathic group compared to controls (p = 0.05). No significant differences were found between the musculoskeletal pain group and controls. Higher pain intensity was accompanied by lower levels of AA (p = 0.028), in neuropathic group. Conclusions: lower levels of eCBs were found in the saliva of chronic OFP patients compared to controls, specifically those with neurovascular/migraine, and neuropathic pain. The detection of changes in salivary endocannabinoids levels related to OFP adds a new dimension to our understanding of OFP mechanisms, and may have diagnostic as well as therapeutic implications for pain.     

Generalizations and error analysis of the iterative operator splitting method

The properties of iterative splitting with two bounded linear operators have been analyzed by Faragó et al. For more than two operators, iterative splitting can be defined in many different ways. A large class of the possible extensions to this case is presented in this paper and the order of accuracy of these methods are examined. A separate section is devoted to the discussion of two of these methods to illustrate how this class of possible methods can be classified with respect to the order of accuracy.