On Calderón-Toeplitz operators

We discuss boundedness and Schatten ideal criteria for a class of Toeplitz style operators based on the Calderón reproducing formula. These operators are a variation on Calderón-Zygmund operators but our results also apply to classical Toeplitz operators acting on the weighted Bergman space of the upper half plane.     

Improvement in the synthesis of metallophthalocyanines using microwave irradiation

A successful application of microwave irradiation, in which phthalocyanines were synthesized under solventless conditions from 1,2-phthalonitrile or phthalic anhydride and urea in the presence of metal templates is described. It was found that in comparison with conventional heating, the microwave process is a very useful alternative for cyclotetramerization processes because of reduction of the reaction time, better yield, and easy-to-perform procedure.     

Highly stereoselective synthesis, structure, and application of (E)-9-[2-(silyl)ethenyl]-9H-carbazoles

(E)-N-(Silyl)vinylcarbazole has been easily prepared via a new catalytic route, silylative coupling (SC) of vinylcarbazole with vinyltrisubstituted silanes catalyzed by [RuH(Cl)(CO)(PCy3)2]. X-ray structures of two silylvinylcarbazoles as first N-vinylcarbazole derivatives have been resolved. The Pd-catalyzed Hiyama coupling reaction (also as the tandem reaction with SC) of synthesized (E)-N-(triethoxysilyl)vinylcarbazole with iodobenzene has been performed to afford (E)-N-(phenylvinyl)carbazole with high yield and stereoselectivity.     

An analogue to a conjecture of S. Chowla and H. Walum

It is proved that (for every ε > 0)

$\text{∑}\text{n?T}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{∑n<}\text{T}\text{n}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{n}{}^{\mathrm{a}}\text{m}{}^{\mathrm{b}}\text{B}{}_{\mathrm{k}}\text{({}\text{T}\text{nm}\text{}) = O(T}{}^{\mathrm{<mtext>(a+b+1)</mtext><mtext>3?</mtext>}}\text{)}$

(where {·} denotes the fractional part and B_k the Bernoulli polynomial of order k) under the suppositions that k ≥ 2 and 2a ? 1 ≥ b ≥ 1. If (1) were true for k = 1, a = b = 0, then Piltz' divisor problem (for n = 3) would be readily solved. This is an analog to a conjecture formulated by S. Chowla and H. Walum in 1963 and settled in the affirmative (under suitable suppositions) quite recently by S. Kanemitsu and R. Sita Rama Chandra Rao.     

A biosensor for monitoring formaldehyde using a new lipophilic tetrathiafulvalene-tetracyanoquinodimethane salt and a polyurethane membrane

The fabrication and application of an end-column amperometric detection (AD) system with a carbon electrode for capillary-column liquid chromatography (CLC) were described. This new amperometric detector showed good sensitivity and stability in detecting the thiocompounds and other analytes with CLC. In order to obtain the better separation and detection performance for analytes, several operational parameters had been investigated: the working potentials, pH and flow rate. Under the optimum conditions, the method could effectively separate and determine cysteine (Cys), glutathione (GSH), dopamine (DA) and 6-thiopurine (6-TP). Good repeatability for retention time was obtained with a relative standard deviation (R.S.D.) value of 0.5%. The linear range covered over three orders of magnitude and the limits of detection were 8 fmol for cysteine, 20 fmol for glutathione, 8 fmol for dopamine and 20 fmol for 6-thiopurine. This method was successfully applied in determination of urinary sample with characteristics of simplicity, high sensitivity and good repeatability.     

Unimolecular photochemistry of 4-thiouracils

Unimolecular phototautomeric reactions in 4-thiouracil, 1-methyl-4-thiouracil and 6-aza-4-thiouracil were studied using the matrix-isolation technique combined with infrared absorption spectroscopy. For monomers of these compounds, isolated in solid argon at 10 K, an intramolecular proton-transfer photoreaction was observed. Upon UV (lambda > 345 nm) irradiation, the initial oxo-thione forms of 4-thiouracils were converted into the corresponding oxo-thiol tautomers. The photogenerated oxo-thiol isomers were identified by comparing their experimental IR spectra with the spectra theoretically calculated at the DFT(B3LYP)/6-311++G(2d,p) level. Good agreement between the observed and predicted pattern of spectral bands allowed a reliable identification. This is the first report on experimental observation of isomeric forms of 4-thiouracils other than the canonical oxo-thione tautomers.     

New symmetry properties of a class of Hubbard models

In the Hubbard model for crystals of the AB-type all information on the system is already contained in the set of eigenstates where the number of sites equals the number of electrons or exceeds it by one. We prove this by deriving relations among the eigenstates with different numbers of particles which do not rely on the well-known transformation of electrons to holes. In this context a new good quantum number is identified. We report on results for the one-dimensional case.     

Proton transfer reactions from N-H acid [5,10,15,20-tetrakis(pentafluorophenyl)-21-H, 23-H-porphyrin] to strong bases in acetonitrile

Deprotonation of 5,10,15,20-tetrakis(pentafluorophenyl)-21-H, 23-H-porphyrin (PhF₅PorH₂) by various bases has been studied by ¹H NMR and kinetic methods. The kinetic parameters in acetonitrile were defined for proton transfer reactions yielding [NH]⁺ protonated bases and [NHN]⁻ anions with intramolecular hydrogen-bonded chains.     

Diastereoselective formation of glycoluril dimers: isomerization mechanism and implications for cucurbit[n]uril synthesis

Cucurbit[6]uril (CB[6]) is a macrocyclic compound, prepared in one pot from glycoluril and formaldehyde, whose molecular recognition properties have made it the object of intense study. Studies of the mechanism of CB[n] formation, which might provide insights that allow the tailor-made synthesis of CB[n] homologues and derivatives, have been hampered by the complex structure of CB[n]. By reducing the complexity of the reaction to the formation of S-shaped (12S-18S) and C-shaped (12C-18C) methylene bridged glycoluril dimers, we have been able to probe the fundamental steps of the mechanism of CB[n] synthesis to a level that has not been possible previously. For example, we present strong evidence that the mechanism of CB[n] synthesis proceeds via the intermediacy of both S-shaped and C-shaped dimers. The first experimental determination of the relative free energies of the S-shaped and C-shaped dimers indicates a thermodynamic preference (1.55-3.25 kcal mol(-)(1)) for the C-shaped diastereomer. This thermodynamic preference is not because of self-association, solvation, or template effects. Furthermore, labeling experiments have allowed us to elucidate the mechanism of this acid-catalyzed equilibrium between the S-shaped and C-shaped diastereomers. The equilibration is an intramolecular process that proceeds with high diastereoselectivity and retention of configuration. On the basis of the broad implications of these results for CB[n] synthesis, we suggest new synthetic strategies that may allow for the improved preparation of CB[n] (n > 8) and CB[n] derivatives from functionalized glycolurils.     

The psuedo‐michael reaction of 2‐aminoimidazolines 2. Part 1. Synthesis and structure assignment of isomeric 5(1H)‐Oxo and 7(1H)‐Oxo‐2,3‐dihydroimidazo[1,2‐a]pyrimidine‐6‐carboxylates

The pseudo‐Michael reaction of 1‐aryl‐2‐aminoimidazolines‐2 with diethyl ethoxymethylenemalonate (DEEM) was investigated. Extensive structural studies were performed to confirm the reaction course. For derivatives with N1 aromatic substituents, it was found that the reaction course was temperature dependent. When the reaction temperature was held at ?10 °C only the formation of 1‐aryl‐7(1H)‐oxo‐2,3‐dihydroimi‐dazo[1,2‐a]pyrimidine‐6‐carboxylates ( 4 ) was observed in contrast to earlier suggestions. Under the room temperature conditions, the same reaction yielded mixtures, with varying ratio, of isomeric 1‐aryl‐7(1H)‐oxo‐ ( 4a‐4f ) and 1‐aryl‐5(1H)‐oxo‐2,3‐dihydroimidazo[1,2‐a]pyrimidine‐6‐carboxylates ( 5a‐5f ). The molecular structure of selected isomers, 4b and 5c , was confirmed by X‐ray crystallography. Frontal chro‐matography with delivery from the edge was applied for the separation of the isomeric esters. The isomer ratio of the reaction products depended on the character of the substituents on the phenyl ring. The 1‐aryl‐7(1H)‐oxo‐carboxylates ( 4a‐4f ) were preferably when the phenyl ring contained H, 4‐CH₃, 4‐OCH₃ and 3,4‐Cl₂ substituents. Chloro substitution at either position 3 or 4 in the phenyl ring favored the formation of isomers 5a‐5f . The isomer ratios were confirmed both by ¹H NMR and chromatography. The reaction of the respective hydrobromides of 1‐aryl‐2‐aminoimidazoline‐2 with DEEM, in the presence of triethylamine, gave selectively 5(1H)‐oxo‐esters ( 5a‐5f ).