On Hermitian block Hankel matrices,matrix polynomials,the Hamburger moment problem,interpolation and maximum entropy

Reproducing kernel space methods are used to study the truncated matrix Hamburger moment problem on the line, an associated interpolation problem and the maximum entropy solution. Enroute a number of formulas are developed for orthogonal matrix polynomials associated with a block Hankel matrix (based on the specified matrix moments for the Hamburger problem) under less restrictive conditions than positive definiteness. An analogue of a recent formula of Alpay-Gohberg and Gohberg-Lerer for the number of roots of certain associated matrix polynomials is also established.The author would like to acknowledge with thanks Renee and Jay Weiss for endowing the chair which supported this research.     

The mechanism of proton transfer between adjacent sites exposed to water

The surface of a protein, or a membrane, is spotted with a multitude of proton-binding sites, some of which are only a few angstroms apart. When a proton is released from one site, it propagates through the water by a random walk under the bias of the local electrostatic potential determined by the distribution of the charges on the protein. Some of the released protons disperse into the bulk, but during the first few nanoseconds, the released protons can be trapped by encounter with nearby acceptor sites. This process resembles a scenario which corresponds with the time-dependent Debye-Smoluchowski equation. In the present study, we investigated the mechanism of proton transfer between sites that are only a few angstroms apart, using as a model the proton exchange between sites on a small molecule, fluorescein, having two, spectrally distinguishable, proton-binding sites. The first site is the oxyanion on the chromophore ring structure. The second site is the carboxylate moiety on the benzene ring of the molecule. Through our experiments, we were able to reconstruct the state of protonation at each site and the velocity of proton transfer between them. The fluorescein was protonated by a few nanosecond long proton pulse under specific conditions that ensured that the dye molecules would be protonated only by a single proton. The dynamics of the protonation of the chromophore were measured under varying initial conditions (temperature, ionic strength, and different solvents (H(2)O or D(2)O)), and the velocity of the proton transfer between the two sites was extracted from the overall global analysis of the signals. The dynamics of the proton transfer between the two proton-binding sites of the fluorescein indicated that the efficiency of the site-to-site proton transfer is very sensitive to the presence of the screening electrolyte and has a very high kinetic isotope effect (KIE = 55). These two parameters clearly distinguish the mechanism from proton diffusion in bulk water. The activation energy of the reaction (E(a) = 11 kcal mol(-1)) is also significantly higher than the activation energy for proton dissociation in bulk water (E(a) approximately 2.5 kcal mol(-1)). These observations are discussed with respect to the effect of the solute on the water molecules located within the solvation layer.     

Thermo-XRD-analysis of montmorillonite treated with 1,4-diaminoanthraquinone

Charcoals formed during the thermo-XRD-analysis of montmorillonite (MONT) complexes with the dye 1,4-diaminoanthraquinone (DAAQ) were investigated by using curve-fitting calculations. Five saturated dye solutions were prepared (i) in distilled water and (ii–v) in 0.1, 0.5, 1.0, and 2.0 molar HCl. Two series of dye-clay complexes were prepared by using clay suspensions of 0.6 %and of 0.006 % labeled first and second series, respectively. Five dye-clay complexes were prepared of each series by adding 25 mL of dye solution to 25 mL of clay suspension. There is no free dye in complexes of the first series, but those of the second series, which were synthesized with a high ratio between dye and clay, contain non-adsorbed dye even after five washings. Complexes of the first series are loaded with very small amounts of molecular and protonated DAAQ (5–24 mmol DAAQ per 100 g clay), and their spacings are 1.25–1.54 nm suggesting the presence of tactoids with protonated or molecular DAAQ lying parallel to the clay layers. No carbon analyses were performed to the second series complexes. In addition to tactoids with spacing of 1.32 nm, they contain tactoids with spacings of 1.81–1.96 nm, suggesting that intercalated DAAQ are lying perpendicular to the clay layers. Three types of intercalated charcoal are identified in both series during the thermal analysis, one type with a low thermal stability and two types with high thermal stabilities. Charcoals of the second series complexes preserve the geometry of the original complexes up to high temperatures.     

Fine Tuning of Chlorophyll Spectra by Protein‐Induced Ring Deformation

The ability to tune the light‐absorption properties of chlorophylls by their protein environment is the key to the robustness and high efficiency of photosynthetic light‐harvesting proteins. Unfortunately, the intricacy of the natural complexes makes it very difficult to identify and isolate specific protein–pigment interactions that underlie the spectral‐tuning mechanisms. Herein we identify and demonstrate the tuning mechanism of chlorophyll spectra in type II water‐soluble chlorophyll binding proteins from Brassicaceae (WSCPs). By comparing the molecular structures of two natural WSCPs we correlate a shift in the chlorophyll red absorption band with deformation of its tetrapyrrole macrocycle that is induced by changing the position of a nearby tryptophan residue. We show by a set of reciprocal point mutations that this change accounts for up to 2/3 of the observed spectral shift between the two natural variants.     

The bitangential inverse spectral problem for canonical systems

The theory of the direct and bitangential inverse input impedance problem is used to solve the direct and bitangential inverse spectral problem. The analysis of the direct spectral problem uses and extends a number of results that appear in the literature. Special attention is paid to the class of canonical integral systems with matrizants that are strongly regular J-inner matrix valued functions in the sense introduced in [7]. The bitangential inverse spectral problem is solved in this class. In our considerations, the data for this inverse problem is a given nondecreasing p×p matrix valued function σ(μ) on and a normalized monotonic continuous chain of pairs , of entire inner p×p matrix valued functions. Each such chain defines a class of canonical integral systems in which we find a solution of the inverse problem for the given spectral function σ(μ). A detailed comparison of our investigations of inverse problems with those of Sakhnovich is presented.     

Trace formulas for a class of Toeplitz-like operators

LetP _T denote projection onto the space of entire functions of exponential type ≦T which are square summable on the line relative to a measuredΔ and letG denote multiplication by a suitably restricted complex valued function,g. For a reasonably large class of measuresdΔ, which includes Lebesgue measuredγ, it is shown that trace {(P _TGP_T)ⁿ−P_TGⁿP_T} tends boundedly to a limit asT↑∞ and that the limit isindependent of the choice ofdΔ within the permitted class. This extends the range of validity of a formula due to Mark Kac who evaluated this limit in the special casedΔ=dγ using a different formalism.