Spin and relativistic motion of bound states

The wave functions of moving bound states may be expected to contract in the direction of motion, in analogy to a rigid rod in classical special relativity, when the constituents are at equal (ordinary) time. Indeed, the Lorentz contraction of wave functions is often appealed to in qualitative discussions. However, only few field theory studies exist of equal-time wave functions in motion. In this thesis I use the Bethe-Salpeter formalism to study the wave function of a weakly bound state such as a hydrogen atom or positronium in a general frame. The wave function of the e^-e^+ component of positronium indeed turns out to Lorentz contract both in 1+1 and in 3+1 dimensional quantum electrodynamics, whereas the next-to-leading e^-e^+\gamma Fock component of the 3+1 dimensional theory deviates from classical contraction. The second topic of this thesis concerns single spin asymmetries measured in scattering on polarized bound states. Such spin asymmetries have so far mainly been analyzed using the twist expansion of perturbative QCD. I note that QCD vacuum effects may give rise to a helicity flip in the soft rescattering of the struck quark, and that this would cause a nonvanishing spin asymmetry in \ell p^\uparrow -> \ell' + \pi + X in the Bjorken limit. An analogous asymmetry may arise in p p^\uparrow -> \pi + X from Pomeron-Odderon interference, if the Odderon has a helicity-flip coupling. Finally, I study the possibility that the large single spin asymmetry observed in p p^\uparrow -> \pi(x_F,k_\perp) + X when the pion carries a high momentum fraction x_F of the polarized proton momentum arises from coherent effects involving the entire polarized bound state.

Interactions of natural products with β-lactoglobulins, members of the lipocalin family

Natural products constitute an important source of new drugs. The bioavailability of the drugs depends on their absorption, distribution, metabolism and elimination. To achieve good bioavailability, the drug must be soluble in water, stable in the gastrointestinal tract and palatable. Binding proteins may improve the solubility of drug compounds, masking unwanted properties, such as bad taste, bitterness or toxicity, transporting or protecting these compounds during processing and storage. The focus of this thesis was to study the interactions, including ligand binding and the effect of pH and temperature, of bovine and reindeer β-lactoglobulin (βLG) with such compounds as retinoids, phenolic compounds as well as with compounds from plant extracts, and to investigate the transport properties of the βLG-ligand complex. To examine the binding interactions of different ligands to βLG, new methods were developed. The fluorescence binding method for the evaluation of ligand binding to βLG was miniaturized from a quartz cell to a 96-well plate. A method of ultrafiltration sampling combined with high-performance liquid chromatography was developed to assess the binding of compounds from extracts. The interactions of phenolic compounds or retinoids and βLG were investigated using the 96-well plate method. The majority of flavones, flavonols, flavanones and isoflavones and all of the retinoids included were shown to bind to bovine and reindeer βLG. Phenolic compounds, contrary to retinol, were not released at acidic pH. Those results suggest that βLG may have more binding sites, probably also on the surface of βLG. An extract from Camellia sinensis (L.) O. Kunze (black tea), Urtica dioica L. (nettle) and Piper nigrum (black pepper) were used to evaluate whether βLG could bind compounds from plant extracts. Piperine from P. nigrum was found to bind tightly and rutin from U. dioica weakly to βLG. No components from C. sinensis bound to βLG in our experiment. The uptake and membrane permeation of bovine and reindeer βLG, free and bound with retinol, palmitic acid and cholesterol, were investigated using Caco-2 cell monolayers. Both bovine and reindeer βLG were able to cross the Caco-2 cell membrane. Free and βLG-bound retinol and palmitic acid were transported equally, whereas cholesterol could not cross the Caco-2 cell monolayer free or bound to βLG. Our results showed that βLG can bind different natural product compounds, but cannot enhance transport of retinol, palmitic acid or cholesterol through Caco-2 cells. Despite this, βLG, as a water-soluble binding protein, may improve the solubility of natural compounds, possibly protecting them from early degradation and transporting some of them through the stomach. Furthermore, it may decrease their bad or bitter taste during oral administration of drugs or in food preparations. βLG can also enhance or decrease the health benefits of herbal teas and food preparations by binding compounds from extracts.

Boundedness of weakly singular integral operators on domains

The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.