OptiDose: Computing the Individualized Optimal Drug Dosing Regimen Using Optimal Control

Journal of Optimization Theory and Applications - Providing the optimal dosing strategy of a drug for an individual patient is an important task in pharmaceutical sciences and daily clinical...     

Approximations and solution estimates in optimization

Approximation is central to many optimization problems and the supporting theory provides insight as well as foundation for algorithms. In this paper, we lay out a broad framework for quantifying approximations by viewing finite- and infinite-dimensional constrained minimization problems as instances of extended real-valued lower semicontinuous functions defined on a general metric space. Since the Attouch-Wets distance between such functions quantifies epi-convergence, we are able to obtain estimates of optimal solutions and optimal values through bounds of that distance. In particular, we show that near-optimal and near-feasible solutions are effectively Lipschitz continuous with modulus one in this distance. Under additional assumptions on the underlying metric space, we construct approximating functions involving only a finite number of parameters that still are close to an arbitrary extended real-valued lower semicontinuous functions.     

Random walks on Baumslag–Solitar groups

We consider random walks on non-amenable Baumslag–Solitar groups BS(p, q) and describe their Poisson–Furstenberg boundary. The latter is a probabilistic model for the long-time behaviour of the random walk. In our situation, we identify it in terms of the space of ends of the Bass–Serre tree and the real line using Kaimanovich’s strip criterion.     

Spreadable Nilpotent Nonassociative Rings and K-Algebras

A nilpotent, not necessarily associative, ring that possesses a spread of subrings is a zero ring. Especially, a nilpotent, not necessarily associative, K-algebra that possesses a spread of subalgebras has always trivial multiplication. This is true for every field K.     

Digital Expansions with Respect to Different Bases

We consider the g-ary expansion N=∑ _k b _k (N, g)g ^k of non-negative integers N and prove various results on the distribution and the mean value of the k-th digit b _k (N, g) if g varies in an interval of the form 2≤g≤N ^η. As an application we also consider the average value of the sum-of-digits function s(N, g)=∑ _k b _k (N, g). Received 5 November 2001 RID="a" ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday     

Enhancement of the superconducting transition temperature of MgB2 by a strain-induced bond-stretching mode softening

We report a systematic increase of the superconducting transition temperature T(c) with a biaxial tensile strain in MgB2 films to well beyond the bulk value. The tensile strain increases with the MgB2 film thickness, caused primarily by the coalescence of initially nucleated discrete islands (the Volmer-Weber growth mode.) The T(c) increase was observed in epitaxial films on SiC and sapphire substrates, although the T(c) values were different for the two substrates due to different lattice parameters and thermal expansion coefficients. We identified, by first-principles calculations, the underlying mechanism for the T(c) increase to be the softening of the bond-stretching E(2g) phonon mode, and we confirmed this conclusion by Raman scattering measurements. The result suggests that the E(2g) phonon softening is a possible avenue to achieve even higher T(c) in MgB2-related material systems.     

Composition tunable cobalt-nickel and cobalt-iron alloy nanoparticles below 10?nm synthesized using acetonated cobalt carbonyl

A general organometallic route has been developed to synthesize Co(x)Ni(1-x) and Co(x)Fe(1-x) alloy nanoparticles with a fully tunable composition and a size of 4-10?nm with high yield. In contrast to previously reported synthesis methods using dicobalt octacarbonyl (Co(2)(CO)(8)), here the cobalt-cobalt bond in the carbonyl complex is first broken with anhydrous acetone. The acetonated compound, in the presence of iron carbonyl or nickel acetylacetonate, is necessary to obtain small composition tunable alloys. This new route and insights will provide guidelines for the wet-chemical synthesis of yet unmade bimetallic alloy nanoparticles. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s11051-012-0991-5) contains supplementary material, which is available to authorized users.     

Neutron bound beta-decay: BOB

Frozen solution samples were made from gold chloride and KAu(CN)₂ solvated with TBP/xylene. The ¹⁹⁷Au M?ssbauer parameters were similar to those same species as frozen solutions or adsorbed onto activated carbon. Solvated samples from EuO dissolved in HCl or H₂SO₄ and frozen gave characteristic Eu(III) spectra. All the spectra were consistent with bonding to the TBP being through hydronium ions or water molecules.     

The near infrared cavity-enhanced absorption spectrum of methyl cyanide

The absorption spectrum of methyl cyanide (CH₃CN) has been measured in the near IR between 6000 and 8000 cm^?1 with a resolution of 0.12 cm^?1 using Fourier transform incoherent broadband cavity-enhanced absorption spectroscopy. The spectrum contains several weakly perturbed spectral regions; potential vibrational combination bands contributing to the spectrum are outlined. Line positions and cross-sections of CH₃CN between 6814 and 7067 cm^?1 have been measured at high-resolution of 0.001 cm^?1 using diode laser based off-axis cavity-enhanced absorption spectroscopy. A total of 4630 new absorption lines of CH₃CN are identified in this region. A value for the self-broadening coefficient has determined to be (3.3±0.2)×10^?3 cm^?1 mbar^?1 for one isolated line at 7034.171 cm^?1. Several line series have been identified in these regions and an autocorrelation analysis performed with a view to aiding future assignments of the rotational-vibrational transitions.