Free sets for nowhere-dense set mappings

We give some consistency results on the existence of uncountable free sets for nowhere-dense set mappings. For example, we prove that it is relatively consistent with ZFC and Martin’s Axiom that any nowhere-dense set mapping defined on the reals has an uncountable free set.     

Interpolation by splines satisfying mixed boundary conditions

We consider interpolation of Hermite data by splines of degreen withk given knots, satisfying boundary conditions which may involve derivatives at both end points (e.g., a periodicity condition). It is shown that, for a certain class of boundary conditions, a necessary and sufficient condition for the existence of a unique solution is that the data points and knots interlace properly and that there does not exist a polynomial solution of degreen?k. The method of proof is to show that any spline interpolating zero data vanishes identically, rather than the usual determinantal approach.     

Stretching of homopolymeric RNA reveals single-stranded helices and base-stacking

We have found strong supporting evidence for the helical structures of single-stranded nucleic acids by stretching individual molecules of polyadenylic acid [poly(A)] and polycytidylic acid [poly(C)]. Analyzing the force versus extension data using a two-state elastic model in which random-coil domains alternate with rigid helical domains allows one to extract the thermodynamic and structural properties. In addition, it also yields moderate to low cooperativity of the helix-coil transition for poly(A) and poly(C), respectively.     

Few-Body Approaches and Problems in Hypernuclei

It takes two nucleons to bind a Λ hyperon, and perhaps as many as three nucleons to bind two Λ hyperons. Here I review few-body calculations which consider the onset of binding in multi-strange hypernuclei, including ${\Xi}$ hyperons once the free-space strong-interaction conversion ${\Xi N \to \Lambda \Lambda}$ becomes Pauli forbidden in Λ-abundant matter. Quasibound states of ${\overline {K}}$ mesons in few-nucleon systems are also briefly discussed.     

Dimension-dependent stimulated radiative interaction of a single electron quantum wavepacket

In the foundation of quantum mechanics, the spatial dimensions of electron wavepacket are understood only in terms of an expectation value – the probability distribution of the particle location. One can still inquire how the quantum electron wavepacket size affects a physical process. Here we address the fundamental physics problem of particle–wave duality and the measurability of a free electron quantum wavepacket. Our analysis of stimulated radiative interaction of an electron wavepacket, accompanied by numerical computations, reveals two limits. In the quantum regime of long wavepacket size relative to radiation wavelength, one obtains only quantum-recoil multiphoton sidebands in the electron energy spectrum. In the opposite regime, the wavepacket interaction approaches the limit of classical point-particle acceleration. The wavepacket features can be revealed in experiments carried out in the intermediate regime of wavepacket size commensurate with the radiation wavelength.     

The equivalent nonlinearity for a nonlinear system with dither

Given a single loop nonlinear control system. The problem of constructing a dither signal in order to obtain a desired equivalent nonlinearity is considered. It is assumed that the nonlinearity may be described by a kth order polynomial. For this case it is shown that in general k different levels for the dither signal are necessary.     

Parametric interaction and backward wave oscillation in stimulated compton scattering

Stimulated Compton-Raman scattering and free electron lasers are formulated as parametric (four-photon) or three-wave interaction processes. Manley-Rowe relations and depletable pump equations are derived for both free electron lasers and optical klystron schemes. A process of backward wave oscillation is predicted when a pump radiation field is back scattered off a codirectionally propagating e beam with frequency down conversion. A practicable experiment in the optical regime is proposed to demonstrate this effect.     

Light-dependent Oxygen Consumption in Bacteriochlorophyll-Serine-treated Melanoma Tumors: On-line Determination Using a Tissue-inserted Oxygen Microsensor

Successful application of anticancer therapy, and especially photodynamic therapy (PDT) mediated by type II (PDTII) processes, depends on the oxygen content within the tumor before, during and after treatment. The high consumption of oxygen during type II PDT imposes constraints on therapy strategies. Although rates of oxygen consumption and repletion during PDTII were suggested by theoretical studies, direct measurements have not been reported. Application of a novel oxygen sensor allowed continuous and direct in situ measurements (up to a depth of 8–9 mm from the tumor surface and for several hours) of temporal variations in the oxygen partial pressure (pO₂) during PDT. Highly pigmented M2R mouse melanoma tumors implanted in CD1 nude mice were treated with bacteriochlorophyll-serine (Bchl-Ser; a new photodynamic reagent) and were subjected to fractionated illumination (700 < λ. < 900 nm) at a fluence rate of 12 mW cm^-2. This illumination led to total oxygen depletion with an average consumption rate of 7.2 uAf(O₂) s^-1. Spontaneous reoxygenation (at an average rate of 2.5 µM(O₂)/s) was observed during the following dark period. These rates are in good agreement with theoretical considerations (Foster et al., Radiat. Res. 126, 296,1991 and Henning et al, Radiat. Res. 142, 221, 1995). The observed patterns of oxygen consumption and recovery during prolonged periods of light/dark cycles were interpreted in terms of vasculature damage and sensitizer clearance. The presented data support the previously suggested advantages of fractionated illumination for type II photodynamic processes.     

Interfacial characterization of chemical solution‐deposited thin films of PbSe on GaAs(100)

The microstructure and composition of the interfacial layer between chemically deposited PbSe and GaAs substrates were studied using high‐resolution transmission electron microscopy (HRTEM), Auger electron spectroscopy (AES), x‐ray photoelectron spectroscopy (XPS) and energy‐filtered TEM. The thickness of the interfacial layer varied significantly from direct contact of the film with the substrate to 5 nm in the thickest regions. The results established the presence of a discontinuous, amorphous intermediate layer of Ga₂O₃ at the PbSe/GaAs interface. Copyright © 2008 John Wiley & Sons, Ltd.     

Model for cost estimation in a finite-capacity stochastic environment based on shop floor optimization combined with simulation

In recent years several researchers suggested cost estimation models that consider limited capacity. These researchers ignored the stochastic nature of the shop floor. This paper presents a cost estimation model that takes into account the stochastic environment. It is based on marginal analysis – the difference between the total cost without the new order and the total cost with the new order. The proposed model is based on the integration of simulation and optimization. Data generated by the simulation is inserted into the optimization procedure that finds good feasible solutions quickly. A significant advantage of the proposed stochastic cost estimation over an existing deterministic approach is shown. A computational study is performed to test different factors affecting the proposed model.