On generalized Toeplitz and little Hankel operators on Bergman spaces

We find a concrete integral formula for the class of generalized Toeplitz operators \(T_a\) in Bergman spaces \(A^p\), \(1<p<\infty \), studied in an earlier work by the authors. The result is extended to little Hankel operators. We give an example of an \(L^2\)-symbol a such that \(T_{|a|} \) fails to be bounded in \(A^2\), although \(T_a : A^2 \rightarrow A^2\) is seen to be bounded by using the generalized definition. We also confirm that the generalized definition coincides with the classical one whenever the latter makes sense.     

Solid-phase synthesis of pyrazolopyridines from polymer-bound alkyne and azomethine imines

Study was made of the 1,3-dipolar cycloaddition of polymer-bound alkynes to azomethine imines generated in situ from N-aminopyridine iodides. Aromatization of the cycloadducts gives polymer-bound pyrazolopyridines that can be released from the resin as carboxylic acids with trifluoroacetic acid or as methyl esters with sodium methoxide.     

Polymer-supported 1,3-oxazolium-5-olates: synthesis of 1,2,4-triazoles

A traceless synthesis of 3,5-disubstituted 1,2,4-triazoles has been developed on polymeric supports. The synthetic process utilizes immobilized mesoionic 1,3-oxazolium-5-olates (munchnones) as key intermediates in the 1,3-dipolar cycloaddition reaction. The initial step in the synthesis involves reductive alkylation of phenylglycine methyl esters with Ameba resin. The resulting immobilized amino acid esters were subsequently acylated with a variety of carboxylic acid chlorides and subjected to hydrolysis with 15% KOH to yield the polymer-bound carboxylic acids. Finally, the cycloaddition between diethyl diazocarboxylate or 4-phenyl-4H-1,2,4-triazoline-3,5-dione and the polymer-bound munchnones generated from the corresponding carboxylic acids afforded the polymer-bound 3,5-disubstituted 1,2,4-triazoles. Cleavage from the polymeric support using trifluoroacetic acid gave the desired 3,5-disubstituted 1,2,4-triazoles with excellent yield and high purity.     

Synthesis of azamacrocycles via a Mitsunobu reaction

Reaction of pernosylated diethylenetriamine and 2-substituted propane-1,3-diols in dry THF in the presence of triphenylphosphine and diisopropyl azodicarboxylate gives the corresponding protected 9-substituted 1,4,7-triazacyclodecanes. The Mitsunobu reaction was also used in the preparation of 3-substituted 1,5,9-triazacyclododecanes and macrocyclic pyridine derivatives.     

Cathodic protection of ships in brackish water

The operation of ice-going vessels depends on the condition of the hull surface. Corrosion increases the roughness of ship hull, which increases drag and fuel consumption. The hull surface smoothness is maintained by using coatings and cathodic protection. The cold brackish water is different from ocean water as it has lower salt content, lower conductivity, and higher concentration of dissolved oxygen. These factors mean that the design of the cathodic protection system for ship hulls requires different design values, such as protection current density and protected length, than those given in cathodic protection standards. In this paper, we have estimated the protection current density with polarization curves and the protected length by using Wagner number and dimension and conductivity scaling. In brackish water the protection current density was two times that in ocean water. The protected length in brackish water varied between 10 and 15% of that in ocean water. In poorly conducting brackish water, the current capacity of a cathodic protection system is used mostly for overcoming the solution resistance, not for delivering protection current.     

Application of high temperature high resolution gas chromatography to paraffinic deposits in petroleum production pipelines

HTHRGC was found essential for optimizing representative preparation of high molecular weight samples and enabling fingerprinting of heavy fractions of crude oils and associated paraffinic deposits in production pipelines. Laboratory experiments aimed at simulating the process of paraffin deposition could also be easily evaluated. A comparative investigation of the performance of cold on-column and SPI (PTV type) injectors, in conjunction with high temperature capillary columns, for analysis of high molecular weight fractions, was also conducted during the course of this work.     

On Unsheared Tetrads

Assuming the existence of genuine unsheared triads, we examine the possibility of having unsheared tetrads, particularly unsheared genuine tetrads.     

Giant optical activity in quasi-two-dimensional planar nanostructures

We examine the spectral dependence in the visible frequency range of the polarization rotation of two-dimensional gratings consisting of chiral gold nanostructures with subwavelength features. The gratings, which do not diffract, are shown to exhibit giant specific rotation (approximately 10(4) degrees/mm) of polarization in direct transmission at normal incidence. The rotation is the same for light incident on the front and back sides of the sample. Such reciprocity indicates three dimensionality of the structure arising from the asymmetry of light-plasmon coupling at the air-metal and substrate-metal interfaces. The structures thus enable polarization control with quasi-two-dimensional planar objects. However, in contradiction with recently suggested interpretation of experiments on larger scale but otherwise similar structures, the observed polarization phenomena violate neither reciprocity nor time-reversal symmetry.