β-Lactam Derivatives as Enzyme Inhibitors: Peptidic Derivatives of ( RS )-2-Oxo-4-phenylazetidine-1-alkanoic Acids

4-Phenylazetidine-2-one was transformed into 4-phenylazetidine-1-alkanoic acids, which were reacted in the presence of diphenylphosphoroazidate with amino acid esters and dipeptide esters yielding β-lactam peptides with different spacers between the lactam ring and the peptide moiety. All structures were established by elementary analyses, HPLC, optical rotation, and spectroscopic data and all new compounds were tested as inhibitors of PPE using standard procedures. Four compounds exhibited a weak activity compared with the standard inhibitor trifluoroacetyl-l-val-l-tyr-l-val.     

Applying Tikhonov regularization to process pendant droplet tensiometry data

The problem of obtaining the first and second derivatives of the profile of a pendant droplet is formulated as an integral equation of the first kind. This equation is solved by Tikhonov regularization in which the method of general cross validation is used to guide the selection of the regularization parameter. These derivatives are converted into mean curvature as a function of droplet height. Surface tension is then obtained by regression computation between the mean curvature and two possible algebraic expressions suggested by the Laplace-Young equation. This way of obtaining surface tension is demonstrated by applying it to a number of published droplet profiles. Some of the problems encountered are discussed and solutions suggested.     

Imines in the Titanium Coordination Sphere – Transformation of Imidoyl Chlorides to Nitrilium Ions

In the reaction of TiCl₄ in benzene as solvent with the imidoyl chloride p‐Tolyl(Cl)C=NPh ( 1 ) the abstraction of the chloride substituent is observed, leading to the nitrilium salt [p‐Tolyl–C≡N–Ph]⁺[Ti₂Cl₉]^– ( 2 ) in quantitative yield. The highly electrophilic salt 2 is characterized by IR‐ and NMR spectroscopy. The observed band for the C≡N stretching mode of 2 clearly indicates the formation of a nitrilium ion. Especially a characteristic line broadening of the ¹³C{¹H}‐NMR signals related to carbon atoms next to the nitrogen is observed. By ¹⁵N,¹H‐HMBC NMR experiments it is shown that the nitrogen signal of 2 is significantly shifted to high‐field in relation to nitriles and imines. The molecular structure of 2 was confirmed by single‐crystal X‐ray diffraction. The C≡N bond length and the linearity of the C–C≡N–C unit in 2 confirm the triple bond character of this bond.     

Intravascular photoacoustic imaging of human coronary atherosclerosis

We demonstrate intravascular photoacoustic imaging of human coronary atherosclerotic plaque. The data was obtained from two fresh human coronary arteries ex vivo, showing different stages of disease. A 1.25?mm diameter intravascular imaging catheter was built, comprising an angle-polished optical fiber adjacent to a 30?MHz ultrasound transducer. Specific photoacoustic imaging of lipid content, a key factor in vulnerable plaques that may lead to myocardial infarction, is achieved by spectroscopic imaging at different wavelengths between 1180 and 1230?nm. Simultaneous imaging with intravascular ultrasound was performed.     

A global slice theorem for proper Hamiltonian actions

An analogue of a theorem of Abels [A] reducing the proper action of a non-compact Lie group to a compact transformation group is proved for the Hamiltonian setting. Received: 26 June 1997 / Revised version: 12 October 1998     

Unsteady Liquid Jets

The behaviour of unsteady liquid jets in a gas atmosphere is mainly governed by the conservation of momentum and the interaction with the environment. In this article it will be shown that many of the particular effects in the propagation and desintegration of unsteady jets are simply explained by the conservation of initial momentum. Many of the distortions and peculiar shapes of the liquid elements of the jet can be explained by a time and space development of weak initial distortions of momentum in travelling waves during propagation. The first part of the paper is devoted to the droplet formation in liquid jets of moderate Weber numbers in the order of ten. In this regime and higher the surface tension is not the governing influence of instability of jet decomposition and hence of the droplet formation. If there is a high frequency distortion of the velocity which is artificially implemented in our experiments by a special device, but under usual conditions also existing by turbulence or source distortions of the nozzle flow, the concentration of mass in packets in a kind of shock formation is the main reason for droplet formation. The frequency of droplets in space and time is given by the frequency of the distortion. The amplitude and phase is also given by the initial values of the driver for these quantities. For large amplitudes and low frequencies the jets are decomposed in very peculiar shapes, which can be very simply explained by the collision of packets of concentrated mass on the axis of the jet motion. The whole range of phenomena can be understood in a theoretically elegant manner by a Lagrangian transform of the nonlinear equations of motion together with some plausible considerations about the lateral motion. Solutions for the droplet formation and the formation of liquid films in different shapes can be achieved this way. As an illustration of the whole range of beautiful and regularly reproducible details of jet decomposition some photographs will be shown which summarize the phenomena and give an idea of the importance of systematic investigation of the sometimes very confusing appearance of fluid jets.     

Directional dispersion of phonons and polaritons in SnO

Using right angle Raman scattering we measured the directional dispersion for LO- and TO-phonons in ZnO. The experimental results are in good agreement with calculated dispersion curves. We also computed the directional dispersion from the measured dispersion branches of the A1-polariton. The scattering cross section of this polariton increases with polariton character.     

Symplectic algebras and poisson algebras

Abstract

A ring R is called left P-injective if for every a ∈ R, aR = r(l(a)) where l( ? ) and r( ? ) denote left and right annihilators respectively. The ring R is called left GP-injective if for any 0 ≠ a ∈ R, there exists n > 0 such that a ⁿ  ≠ 0 and a ⁿ R = r(l(a ⁿ )). As a response to an open question on GP -injective rings, an example of a left GP-injective ring which is not left P-injective is given. It is also proved here that a ring R is left FP -injective if and only if every matrix ring 𝕄 _n (R) is left GP-injective.