An inequality between thep- and (p, 1)-summing norm of finite rank operators fromC(K)-spaces

We show, for any operatorT from aC(K)-space into a Banach space with rank (T)≤n, the inequality , whereC≤4.671 is a numerical constant. The factor (1+logn)^1−1/p is asymptotically correct. This inequality extends a result of Jameson top ≠ 2. Several applications are given — one is a positive solution of a conjecture of Rosenthal and Szarek: For 1≤p<q<2,      

Aortic elastin fluorescence afterin vivo labeling with Congo red

Congo red (CR) is an azo dye which not only preferentially binds to elastin, an extracellular matrix protein found in the media of arterial vessel walls, but also fluoresces when it binds to this protein. Protein solubilization data following laser irradiation of elastin:CR suspensions determined that the amount of elastin solubilized by laser irradiation increased with the increase in CR. The saturation point of CR to elastin was attained when 400 g CR was added to 20 mg elastin suspension. When 20 ml of a 5% CR solution in 5% dextrose was administered intravenously, the CR was absorbed in levels sufficient to produce fluorescence of the main arteries in rabbits. Layers of tissue both in the media of the vessels and at the endothelial/intimal interface were clearly differentiated. Therefore, the elastin:CR complex appears to be an ideal system in which the elastin fluorescence could aid in distinguishing between normal and diseased tissue in certain pathological conditions, such as atherosclerosis and some types of breast tumors.     

Fourier analysis of the approximation power of principal shift-invariant spaces

The approximation order provided by a directed set {S _h } _h>0 of spaces, each spanned by thehZ ^d -translates of one function, is analyzed. The nearoptimal approximants of [R2] from eachs _h to the exponential functions are used to establish upper bounds on the approximation order. These approximants are also used on the Fourier transform domain to yield approximations for other smooth functions, and thereby provide lower bounds on the approximation order. As a special case, the classical Strang-Fix conditions are extended to bounded summable generating functions.The second part of the paper consists of a detailed account of various applications of these general results to spline and radial function theory. Emphasis is given to the case when the scale {s _h } is obtained froms ₁ by means other than dilation. This includes the derivation of spectral approximation orders associated with smooth positive definite generating functions.     

Iodine photodissociation laser system Perun II

A construction and exploitation of a medium size iodine photodissociation laser system Perun II is reported. This laser produced pulses of infrared light (=1.315m) up to 50 J in energy and 300 ps in duration. The diameter of the beam is 82 mm. The beam divergence is about 4×10^–4 rad. The laser beam can be focused in a focal spot of a power density exceeding 10¹⁴ W/cm². The resuls of measurements of basic plasma parameters on an Al foil target are also presented. A recent improvement of the system includes a conversion to the second harmonic by a DKDP crystal.Presented at bilateral international seminar of High Temperature Laser Plasma and High Gain Iodine Lasers held on 4 July 1991 in the Inst. of Physics, Czechosl. Acad. Sci., in Prague (organized by Division of Optics of the Inst. of Physics, Czechosl. Acad. Sci., and Physical Section (Plasma Division) of the Union of Czech Mathematicians and Physicists.     

Synthesis and structural characterization of functionalized dimeric aluminophosphonates and a monomeric gallophosphonate anion

Reaction of t-BuP(O)(OSiMe(3))(OH) with Me(3)Al leads to the formation of [Me(2)Al(mu-O)(2)P(OSiMe(3))(t-Bu)](2) (1) whereas Me(2)AlCl reacts with Ph(2)P(O)(OH) to yield [(Cl)(Me)Al(mu-O)(2)PPh(2)](2) (2). These compounds represent the first examples of functionalized dimeric four-ring type aluminophosphonate systems. The double four-ring type gallophosphonate, namely, [t-BuPO(3)GaMe](4), reacts with n-Bu(4)NHF(2) under ambient conditions, resulting in the formation of a monomeric gallophosphonate [n-Bu(4)N][MeGa[t-BuPO(2)(OH)](3)] (3). These derivatives have been adequately characterized using various spectroscopic techniques and X-ray diffraction studies.     

A note on debye potentials for spherically gyrotropic media

The Debye potentials are generalized to the case of electromagnetic fields in spherically gyrotropic media. A medium is called spherically gyrotropic if it is locally gyrotropic with the distinguished axis having a radial direction determined by a central point. Expressions for electromagnetic fields in terms of the generalized potentials are presented and the system of differential equations for the potentials is derived. The results are summarized in the form of a theorem. Basic facts about the Debye potentials in isotropic media are recalled.     

Dynamics of protein and mixed protein/surfactant adsorption layers at the water/fluid interface

The adsorption behaviour of proteins and systems mixed with surfactants of different nature is described. In the absence of surfactants the proteins mainly adsorb in a diffusion controlled manner. Due to lack of quantitative models the experimental results are discussed partly qualitatively. There are different types of interaction between proteins and surfactant molecules. These interactions lead to protein/surfactant complexes the surface activity and conformation of which are different from those of the pure protein. Complexes formed with ionic surfactants via electrostatic interaction have usually a higher surface activity, which becomes evident from the more than additive surface pressure increase. The presence of only small amounts of ionic surfactants can significantly modify the structure of adsorbed proteins. With increasing amounts of ionic surfactants, however, an opposite effect is reached as due to hydrophobic interaction and the complexes become less surface active and can be displaced from the interface due to competitive adsorption. In the presence of non-ionic surfactants the adsorption layer is mainly formed by competitive adsorption between the compounds and the only interaction is of hydrophobic nature. Such complexes are typically less surface active than the pure protein. From a certain surfactant concentration of the interface is covered almost exclusively by the non-ionic surfactant. Mixed layers of proteins and lipids formed by penetration at the water/air or by competitive adsorption at the water/chloroform interface are formed such that at a certain pressure the components start to separate. Using Brewster angle microscopy in penetration experiments of proteins into lipid monolayers this interfacial separation can be visualised. A brief comparison of the protein adsorption at the water/air and water/n-tetradecane shows that the adsorbed amount at the water/oil interface is much stronger and the change in interfacial tension much larger than at the water/air interface. Also some experimental data on the dilational elasticity of proteins at both interfaces measured by a transient relaxation technique are discussed on the basis of the derived thermodynamic model. As a fast developing field of application the use of surface tensiometry and rheometry of mixed protein/surfactant mixed layers is demonstrated as a new tool in the diagnostics of various diseases and for monitoring the progress of therapies.     

Missing-link macrocycles: hybrid heterocalixarene analogues formed from several different building blocks

The synthesis and structural characterization of hybrid heterocalix[4]arene analogues containing pyrrole, benzene, methoxy-substituted benzene, and pyridine subunits is described. Macrocycles 1 and 2, examples of calix[2]benzene[2]pyrrole and calix[1]benzene[3]pyrrole systems, respectively, are synthesized by the condensation of pyrrole and an appropriate phenylbis(carbinol). Macrocycles 3 and 7, examples of calix[2]benzene[1]pyridine[1]pyrrole and calix[1]pyridine[3]pyrrole, respectively, are synthesized by the use of a carbene-based pyrrole-to-pyridine ring-expansion procedure. Single-crystal X-ray analysis reveals that compounds 1a, 1b, and 2b adopt 1,3-alternate conformations in the solid state, whereas compounds 3 and 7 display structures that are best described as "flattened partial cones" in terms of their conformation. (Series a refers to pure benzene-derived systems, whereas series b indicates macrocycles containing 5-methoxyphenyl subunits). In the solid state, the methoxy-functionalized macrocycles 1b and 2b, and the chloropyridine-containing macrocycle 7 exist as dimers. In the case of 1a and 7, these compounds interact with neutral solvent in the solid state. The conformations of the macrocycles in solution were explored by temperature-dependent proton NMR and NOESY spectral analysis. At 188 K, macrocycles 1a and 2a adopt flattened 1,3-alternate conformations, whereas macrocycles 3 and 7 exist in the form of flattened partial-cone conformations. Standard proton NMR titration analyses were carried out in the case of macrocycles 1a and 2a, and reveal that at least the second of these systems is capable of binding fluoride and chloride anions in CD(2)Cl(2) solution at room temperature (K(a)=571 and 17M(-1) in the case of 2a and F(-) and Cl(-), respectively).