Ground state phase diagram of the infinite dimensional Hubbard model: A variational study

We use the Gutzwiller variational method to study the ground state phase diagram of the infinite dimensional Hubbard model, paying special attention to features associated with the Gaussian form of the tight binding band density of states. We only consider trial states for which the validity of the Gutzwiller approximation has been proven, i.e., the paramagnetic, ferromagnetic, and two-sublattice antiferromagnetic states. We map out the phase diagram numerically, and give approximate analytic arguments to explain the behaviour in the small-U, and large-U limits. We give two versions of the phase diagram: one restricted to homogeneous phases, and another when phase separation is allowed. In the latter case, a homogeneous antiferromagnetic state is found only at exact half-filling, where the state is also insulating. Off half-filling, four different regions are found: pure paramagnetic, and ferromagnetic states, as well as antiferromagnetic-paramagnetic, and antiferromagnetic-ferromagnetic mixed phases.Dedicated to Professor W. Brenig on the occasion of his 60th birthdayResearch performed within the program of the Sonderforschungsbereich 341 supported by the Deutsche Forschungsgemeinschaft     

Asymptotic Normality of Kernel Type Density Estimators for Random Fields

Kernel type density estimators are studied for random fields. It is proved that the estimators are asymptotically normal if the set of locations of observations become more and more dense in an increasing sequence of domains. It turns out that in our setting the covariance structure of the limiting normal distribution can be a combination of those of the continuous parameter and the discrete parameter cases. The proof is based on a new central limit theorem for α-mixing random fields. Simulation results support our theorems. Final version 29 October 2004     

The regional distribution of copper and other trace elements in the human brain with special reference to Wilson's disease

The regional distribution of copper and other trace elements was determined in the brain of a patient deceased in Wilson's disease against a control brain. The heterogeneous distribution of copper was checked by scanning electron microscope equipped with an X-ray microanalyzer.     

Perturbation theory for the triangular Heisenberg antiferromagnet with Ising-like anisotropy

It has been argued that the case of strong uniaxial anisotropy is especially favourable for the formation of a spin-liquid state in theS=1/2 triangular Heisenberg antiferromagnet [77]. We reconsider the old arguments using up-to-date numerical techniques, and extend the study to general values ofS. Recent progress in the understanding of this frustrated quantum spin system sheds light on the question why the original arguments in favour of an RVB state can not be conclusive. Our present results indicate that the tendency towards three-sublattice ordering is much stronger than it had been thought. However, the caseS=1/2 is still seen to be set apart from the casesS>1/2, and forS=1/2 the existence of true longrange order in the ground state remains debatable.     

5,10-A2B2-type meso-substituted porphyrins--a unique class of porphyrins with a realigned dipole moment

Current applications in porphyrin chemistry require the use of unsymmetrically substituted porphyrins. Many current industrial interests in optics and biomedicine require systems with either push-pull (electron-donating and -withdrawing groups) or amphiphilic systems (hydrophobic and hydrophilic groups). In this context we present the class of 5,10-A(2)B(2)-type porphyrins for which two different substituents are positioned in diagonally opposite meso positions. Thus, the intramolecular dipole moment in these tetrapyrroles is positioned along a β-β vector passing through two pyrrole rings. This is opposite to the situation of the frequently used 5,15-A(2)BC porphyrins for which the dipole moment is oriented along a meso-meso axis. We have elaborated syntheses of the 5,10-A(2)B(2) porphyrins by using transition-metal-catalyzed transformations of 5,10-A(2) porphyrins or direct substitutions reactions thereof; this gives the target molecules in 22-77% overall yields. The compounds exhibit interesting structural, spectroscopic, and optical features and can serve as building blocks for new porphyrin arrays and applications.     

Formation of octacalcium phosphate by heterogeneous nucleation on a titania surface

Biocompatibility of the surfaces of titanium dental implants can be improved by covering them with calcium phosphate crystals, which makes the surface bioreactive. Possibly the most effective bioreactive foreign material that improves osteointegration and adsorption/binding of extracellular proteins and structural proteins is crystalline octacalcium phosphate {2×[Ca₄H(PO₄)₃·2.5H₂O] or Ca₈(HPO₄)₂(PO₄)₄·5H₂O, OCP}. In this work the building up of OCP crystals on the surface of TiO₂ anatase is examined in the process of heterogeneous nucleation from constant-composition solutions of CaCl₂ and KH₂PO₄ at constant pH (pH 6.8) and ionic strength (I=0.05 M), in dense titania suspensions. Constant relative supersaturation with regard to the calcium phosphate formation was maintained by the controlled addition of the reagent solutions, according to the desired speed of crystallization. The surface saturation value of calcium ion adsorption was measured by detecting the pH decrease during CaCl₂ addition in a separate experiment. The OCP crystallization was also conducted on the surface of an evaporated titanium layer, and on titanium metal disks. The surface of the disks was modified by the laser ablation method in order to increase the oxide layer thickness. Calcium phosphate crystals formed on the surface of the modified titanium disks, but not in an appreciable amount on the surface of the evaporated titanium layer.     

Determination of zearalenone content in cereals and feedstuffs by immunoaffinity column coupled with liquid chromatography

The zearalenone content of maize, wheat, barley, swine feed, and poultry feed samples was determined by immunoaffinity column cleanup followed by liquid chromatography (IAC-LC). Samples were extracted in methanol-water (8 + 2, v/v) solution. The filtered extract was diluted with distilled water and applied to immunoaffinity columns. Zearalenone was eluted with methanol, dried by evaporation, and dissolved in acetonitrile-water (3 + 7, v/v). Zearalenone was separated by isocratic elution of acetonitrile-water (50 + 50, v/v) on reversed-phase C18 column. The quantitative analysis was performed by fluorescence detector and confirmation was based on the UV spectrum obtained by a diode array detector. The mean recovery rate of zearalenone was 82-97% (RSD, 1.4-4.1%) on the original (single-use) immunoaffinity columns. The limit of detection of zearalenone by fluorescence was 10 ng/g at a signal-to-noise ratio of 10:1 and 30 ng/g by spectral confirmation in UV. A good correlation was found (R2 = 0.89) between the results obtained by IAC-LC and by the official AOAC-LC method. The specificity of the method was increased by using fluorescence detection in parallel with UV detection. This method was applicable to the determination of zearalenone content in cereals and other kinds of feedstuffs. Reusability of immunoaffinity columns was examined by washing with water after sample elution and allowing columns to stand for 24 h at room temperature. The zearalenone recovery rate of the regenerated columns varied between 79 and 95% (RSD, 3.2-6.3%). Columns can be regenerated at least 3 times without altering their performance and without affecting the results of repeated determinations.     

Convergence of random step lines to Ornstein-Uhlenbeck-type processes

The paper deals with random step-line processes defined by sums of independent identically distributed random variables multiplied by independent indicators. These processes describe some models in which random variables are replaced with other ones. We prove the convergence in distribution of such processes to the weighted Ornstein-Uhlenbeck process. Supported by the Hungarian Foundation for Scientific Research (grant No. OTKA-T016933-1996) and by the Hungarian Ministry of Culture and Education (grant No. 179-1995). Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part I.     

Almost sure central limit theorems for random fields

A general almost sure limit theorem is presented for random fields. It is applied to obtain almost sure versions of some (functional) central limit theorems. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)