Atomic Hardy spaces

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This paper is a part of the author's Ph.D. thesis written under the supervision of Prof. F. Schipp, Eötvös L. University, Budapest.     

The asymptotic behaviour of local times and occupation integrals of theN-parameter Wiener process in R d

Summary LetL(x, T),xR ^d ,TR ₊ ^N , be the local time of theN-parameter Wiener processW taking values inR ^d . Even in the distribution valued casedd2N,L can be described in a series representation by means of multiple Wiener-Ito integrals. This setting proves to be a good starting point for the investigation of the asymptotic behaviour ofL(x, T) as |x|0 and/orT and of related occupation integrals asT. We obtain the rates of explosion in laws of the first order, i.e. normalized convergence laws forL(x, T) resp.X _T (f), and of the second order, i.e. normalized convergence laws forL(x, T)–E(L(x, T)) resp.X _T (f)–E(X _T (f)).This research was made during a stay at the LMU in München supported by DAAD     

Synthesis and Characterization of 1,10-Phenanthroline-mono-N-oxides

N-oxides of N-heteroaromatic compounds find widespread applications in various fields of chemistry. Although the strictly planar aromatic structure of 1,10-phenanthroline (phen) is expected to induce unique features of the corresponding N-oxides, so far the potential of these compounds has not been explored. In fact, appropriate procedure has not been reported for synthesizing these derivatives of phen. Now, we provide a straightforward method for the synthesis of a series of mono-N-oxides of 1,10-phenanthrolines. The parent compounds were oxidized by a green oxidant, peroxomonosulfate ion in acidic aqueous solution. The products were obtained in high quality and at good to excellent yields. A systematic study reveals a clear-cut correlation between the basicity of the compounds and the electronic effects of the substituents on the aromatic ring. The UV spectra of these compounds were predicted by DFT calculations at the TD-DFT/TPSSh/def2-TZVP level of theory.     

Preparative separation of isomeric and stereoisomeric dicarboxylic acids by pH-zone-refining counter-current chromatography

This work involves the preparative separation of some isomeric dicarboxylic acids using pH-zone-refining counter-current chromatography (CCC), a relatively new preparative technique for the separation of ionizable compounds. The paper concentrates especially on the separation of a synthetic mixture of closely related cis and trans pairs of 1-methyl- and 1,3-dimethyl-1,3-cyclohexanedicarboxylic acids. The elution sequence of the isomers is discussed in terms of their relative acidities (pK(a) values) in solution and gas phase, hydrophobicities, and steric configuration. Two possible explanations are suggested for the mechanism of separation. They both involve the amount of retainer acid used, as it affects the separation and plays a role in the chemohydrodynamic equilibrium of the dicarboxylic acids in the column.     

Potentiometric and relaxometric properties of a gadolinium-based MRI contrast agent for sensing tissue pH

The pH-sensitive contrast agent, GdDOTA-4AmP (Gd1) has been successfully used to map tissue pH by MRI. Further studies now demonstrate that two distinct chemical forms of the complex can be prepared depending upon the pH at which Gd(3+) is mixed with ligand 1. The desired pH-sensitive form of this complex, referred to here as a Type II complex, is obtained as the exclusive product only when the complexation reaction is performed above pH 8. At lower pH values, a second complex is formed that, by analogy with an intermediate formed during the preparation of GdDOTA, we tentatively assign to a Type I complex where the Gd(3+) is coordinated only by the appended side-chain arms of 1. The proportion of Type I complex formed is largely determined by the pH of the complexation reaction. The magnitude of the pH-dependent change in the relaxivity of Gd1 was found to be less than earlier reported (Zhang, S.; Wu, K.; Sherry, A. D. Angew. Chem., Int. Ed. 1999, 38, 3192), likely due to contamination of the earlier sample by an unknown amount of Type I complex. Examination of the nuclear magnetic relaxation dispersion and relaxivity temperature profiles, coupled with information from potentiometric titrations, shows that the amphoteric character of the phosphonate side chains enables rapid prototropic exchange between the single bound water of the complex with the bulk water thereby giving Gd1 a unique pH-dependent relaxivity that is quite useful for the pH mapping of tissues by MRI.     

Modeling of bovine type-I collagen fibrils: interaction with pickling and retanning agents

Bovine Type I collagen was investigated, building on a large scale computer model of a collagen fibril in water, and focusing on two stages of the leather manufacturing process. The effects of different salts (NaCl, CaCl(2), and Na(2)SO(4)) on the swelling behavior of collagen at low pH (the pickling process) were studied. The salts suppress the swelling of the fibrils at low pH and we find specific stabilizing influences for CaCl(2) and Na(2)SO(4), due to weak Ca(2+)/Cl(-) and strong SO(4) (2-)/lysine/arginine interactions, respectively. Using state-of-the-art sampling techniques, such as the metadynamics algorithm, to allow an efficient exploration of configuration space, we were able to investigate the effect of polyacrylate and poly(methyl acrylate) - two polymeric retanning agents - on the fibril. Both polymers interact with the ammonium groups on the surface, but polyacrylate shows significantly stronger interactions. We suggest that it is this stronger interaction that contributes to the reduced suitability of PAA as a tanning agent.     

Diastereochemical differentiation of β-amino acids using host-guest complexes studied by fourier transform ion cyclotron resonance mass spectrometry

Host-guest complexes where tetraethyl resorcarene was the host molecule were used to study the stereoselectivity of diasteromeric pairs of di-endo- and di-exo-2,3-disubstituted norbornane and norbornene amino acids by ion-molecule reactions and collision-induced dissociation with electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI FT-ICR MS). Both methods showed stereoselectivity for the diastereomeric pairs. Particularly high selectivity was achieved for di-endo- and di-exo-2,3-disubstituted norbornane amino acids with ion-molecule reactions. Also, ab initio and hybrid density functional theory calculations were performed to study the different structures of the host-guest complexes. Hydrogen bonding was crucial for the calculated lowest energy structures, and sterical considerations satisfactorily explained the ion-molecule reaction results.     

Hybrid multinary modulation using a phase modulating spatial light modulator and a low-pass spatial filter

We propose a method for performing binary intensity and continuous phase modulation of beams with a spatial light modulator (SLM) and a low-pass spatial filtering 4-f system. With our method it is possible to avoid the use of phase masks in holographic data storage systems or to enhance the phase encoding of the SLM by making it capable of binary amplitude modulation. The data storage capabilities and the limitations of the method are studied.     

Dispersion management for a sub-10-fs, 10 TW optical parametric chirped-pulse amplifier

We report the amplification of three-cycle, 8.5 fs optical pulses in a near-infrared noncollinear optical parametric chirped-pulse amplifier (OPCPA) up to energies of 80 mJ. Improved dispersion management in the amplifier by means of a combination of reflection grisms and a chirped-mirror stretcher allowed us to recompress the amplified pulses to within 6% of their Fourier limit. The novel ultrabroad, ultraprecise dispersion control technology presented in this work opens the way to scaling multiterawatt technology to even shorter pulses by optimizing the OPCPA bandwidth.