A general approach to approximation problems of the Bernstein type

The Bernstein approximation problem is treated in a general setting of Banach function spaces. An abstract theory is developed which includes as special cases the solutions of the Bernstein problem given by Mergelyan and Pollard. It also provides a unified setting for related results from polynomial and trigonometric approximation theory and yields as corollaries a number of new results.     

Apparent molal heat capacities and volumes of pyridine and methyl-substituted pyridines in aqueous solution at 25°C

We have made calorimetric measurements leading to apparent molal heat capacities of pyridine and four methyl-substituted pyridines in aqueous solution at 25.0°C. Measurements of densities of the same solutions have led to apparent molal volumes. The results are as follows: pyridine, _C ^° = 305.7 J–°K^–1-mole^–1 and _V ^° = 77.5 cm³-mole^–1; 2-methylpyridine, _C ^° = 370.0 J–°K^–1-mole^–1 and _V ^° = 94.3 cm³-mole^–1; 3-methylpyridine, _C ^° = 380.2 J–°K^–1-mole^–1 and _V ^° = 93.7 cm³-mole^–1; 4-methylpyridine, _C ^° = 378.9 J–°K^–1-mole^–1 and _V ^° = 94.3 cm³-mole^–1; 2,6-dimethylpyridine, _C ^° = 441.8 J–°K^–1-mole^–1 and _V ^° = 109.9 cm³-mole^–1. These _C ^° and _V ^° values are discussed in terms of effects of substitution of CH₃-for H– in the various solute molecules.The research reported here was carried out in the Department of Chemistry, University of Lethbridge, Lethbridge, Alberta, Canada T1K 3M4.     

A third mode of DNA binding: Phosphate clamps by a polynuclear platinum complex

We describe a 1.2 A X-ray structure of a double-stranded B-DNA dodecamer (the Dickerson Dodecamer, DDD, [d(CGCGAATTCGCG)]2) associated with a cytotoxic platinum(II) complex, [{trans-Pt(NH3)2(NH2(CH2)6(NH3+)}2-mu-{trans-Pt(NH3)2(NH2(CH2)6NH2)2}] (TriplatinNC). TriplatinNC is a multifunctional DNA ligand, with three cationic Pt(II) centers, and directional hydrogen bonding functionalities, linked by flexible hydrophobic segments, but without the potential for covalent interaction. TriplatinNC does not intercalate nor does it bind in either groove. Instead, it binds to phosphate oxygen atoms and thus associates with the backbone. The three square-planar tetra-am(m)ine Pt(II) coordination units form bidentate N...O...N complexes with OP atoms, in a motif we call the Phosphate Clamp. The geometry is conserved among the 8 observed phosphate clamps in this structure. The interaction appears to prefer O2P over O1P atoms (frequency of interaction is O2P > O1P, base and sugar oxygens > N). The high repetition and geometric regularity of the motif suggests that this type of Pt(II) center can be developed as a modular nucleic acid binding device with general utility. TriplatinNC extends along the phosphate backbone, in a mode of binding we call "Backbone Tracking" and spans the minor groove in a mode of binding we call "Groove Spanning". Electrostatic forces appear to induce modest DNA bending into the major groove. This bending may be related to the direct coordination of a sodium cation by a DNA base, with unprecedented inner-shell (direct) coordination of penta-hydrated sodium at the O6 atom of a guanine.     

Products of Markovian semi-groups of operators

Summary Let A and B denote the generators of two contraction semi-groups of operators (P ^t) and (Q ^t) acting on some Banach space. If the operator A + B has a closure generating a third semi-group (R ^t), then it is known (Trotter) that . The existence and identification of this limit is of interest even when the closure of A + B is not a generator. A probabilistic version of this problem is given here in the case of Markovian transition semi-groups when the corresponding processes have identical hitting distributions. Sufficient conditions for the existence of (R ^t) are given, and in special cases its generator is identified.This paper is part of a Ph. D. thesis written at Princeton University. The research was done with the partial support of the Office of Army Research. The author also wishes to thank his thesis supervisor Professor W. Feller for his advice and interest in this work.     

Scaling limits of Gaussian vector fields

For Gaussian vector fields {X(t) ∈ Rⁿ:t ∈ R^d} we describe the covariance functions of all scaling limits Y(t) = $\text{L}$lim_α↓0 B^?1(α) X(αt) which can occur when B(α) is a d × d matrix function with B(α) → 0. These matrix covariance functions $\text{r(t, s) = EY(t) Y}{}^1\text{(s)}$ are found to be homogeneous in the sense that for some matrix L and each α > 0, $\text{(}{}^1\text{) r(αt, αs) = α}{}^{\mathrm{L1}}\text{r(t, s) α}{}^{\mathrm{L}}$. Processes with stationary increments satisfying (¹) are further analysed and are found to be natural generalizations of Lévy's multiparameter Brownian motion.     

Particle-hole symmetric Luttinger liquids in a quantum Hall circuit

We report current transmission data through a split-gate constriction fabricated onto a two-dimensional electron system in the integer quantum Hall (QH) regime. Split-gate biasing drives interedge backscattering and is shown to lead to suppressed or enhanced transmission, in marked contrast to the expected linear Fermi-liquid behavior. This evolution is described in terms of particle-hole symmetry and allows us to conclude that an unexpected class of gate-controlled particle-hole-symmetric chiral Luttinger liquids (CLLs) can exist at the edges of our QH circuit. These results highlight the role of particle-hole symmetry on the properties of CLL edge states.     

The performance of matched-field track-before-detect methods using shallow-water Pacific data

Matched-field track-before-detect processing, which extends the concept of matched-field processing to include modeling of the source dynamics, has recently emerged as a promising approach for maintaining the track of a moving source. In this paper, optimal Bayesian and minimum variance beamforming track-before-detect algorithms which incorporate a priori knowledge of the source dynamics in addition to the underlying uncertainties in the ocean environment are presented. A Markov model is utilized for the source motion as a means of capturing the stochastic nature of the source dynamics without assuming uniform motion. In addition, the relationship between optimal Bayesian track-before-detect processing and minimum variance track-before-detect beamforming is examined, revealing how an optimal tracking philosophy may be used to guide the modification of existing beamforming techniques to incorporate track-before-detect capabilities. Further, the benefits of implementing an optimal approach over conventional methods are illustrated through application of these methods to shallow-water Pacific data collected as part of the SWellEX-1 experiment. The results show that incorporating Markovian dynamics for the source motion provides marked improvement in the ability to maintain target track without the use of a uniform velocity hypothesis.     

Two-dimensional metal in a parallel magnetic field

We have investigated the effect of an in-plane parallel magnetic field (B(axially) on two high mobility metallic-like dilute two-dimensional hole gas systems in GaAs quantum wells. The experiments reveal that, while suppressing the magnitude of the low temperature resistance drop, B(axially) does not affect E(a), the characteristic energy scale of the metallic resistance drop. The field B(c) at which the metallic-like resistance drop vanishes is dependent on both the width of the quantum well and the orientation of B(axially). It is unexpected that E(a) is unaffected by B(axially) up to B(c) despite the fact that the Zeeman energy at B(c) is roughly equal to E(a).