Formulae and growth rates of high-dimensional polycubes

A d-dimensional polycube is a facet-connected set of cubes in d dimensions. Fixed polycubes are considered distinct if they differ in their shape or orientation. A proper d-dimensional polycube spans all the d dimensions, that is, the convex hull of the centers of its cubes is d-dimensional. In this paper we prove rigorously some (previously conjectured) closed formulae for fixed (proper and improper) polycubes, and show that the growth-rate limit of the number of polycubes in d dimensions is 2ed−o(d). We conjecture that it is asymptotically equal to (2d−3)e+O(1/d).     

One-pot synthesis of 4,8-dibromobenzo[1,2-d;4,5-d']bistriazole and synthesis of its derivatives as new units for conjugated materials

The one-pot synthesis of 4,8-dibromobenzo[1,2-d;4,5-d']bistriazole, followed by alkylation and Stille coupling to yield three different isomeric derivatives with markedly different optoelectronic properties, is reported. These derivatives show potential as new units in organic oligomers and polymers for electronics applications.     

Quantum absorption refrigerator

A quantum absorption refrigerator driven by noise is studied with the purpose of determining the limitations of cooling to absolute zero. The model consists of a working medium coupled simultaneously to hot, cold, and noise baths. Explicit expressions for the cooling power are obtained for Gaussian and Poisson white noise. The quantum model is consistent with the first and second laws of thermodynamics. The third law is quantified; the cooling power J(c) vanishes as J(c) ∝ T(c)(α), when T(c)→0, where α=d+1 for dissipation by emission and absorption of quanta described by a linear coupling to a thermal bosonic field, where d is the dimension of the bath.     

Assessment of spatial BOLD sensitivity variations in fMRI using gradient-echo field maps

Clinical blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI) is becoming increasingly valuable in, e.g., presurgical planning, but the commonly used gradient-echo echo-planar imaging (GE-EPI) technique is sometimes hampered by macroscopic field inhomogeneities. This can affect the degree of signal change that will occur in the GE-EPI images as a response to neural activation and the subsequent blood oxygenation changes, i.e., the BOLD sensitivity (BS). In this study, quantitative BS maps were calculated directly from gradient-echo field maps obtainable on most clinical scanners. In order to validate the accuracy of the calculated BS-maps, known shim gradients were applied and field maps and GE-EPI images of a phantom were acquired. Measured GE-EPI image intensity was then compared with the calculated (predicted) image intensity (pII) which was obtained from the field maps using theoretical expressions for image-intensity loss. The validated expressions for pII were used to calculate the corresponding predicted BOLD sensitivity (pBS) maps in healthy volunteers. Since the field map is assumed to be valid throughout an entire fMRI experiment, the influence of subject motion on the pBS maps was also assessed. To demonstrate the usefulness of such maps, pBS was investigated for clinically important functional areas including hippocampus, Broca's area and primary motor cortex. A systematic left/right pBS difference was observed in Broca's area and in the hippocampus, most likely due to magnetic field inhomogeneity of the particular MRI-system used in this study. For all subjects, the hippocampus showed pBS values above unity with a clear anterior–posterior gradient and with an abrupt drop to zero pBS in the anterior parts of hippocampus. It is concluded that GE field maps can be used to accurately predict BOLD sensitivity and that this parameter is useful to assess spatial variations which will influence fMRI experiments.     

Exploring informal mathematical products of low achievers at the secondary school level

This article examines the notion of informal mathematical products, in the specific context of teaching mathematics to low achieving students at the secondary school level. The complex and relative nature of this notion is illustrated and some of its characteristics are suggested. These include the use of ad-hoc strategies, mental calculations, idiosyncratic ideas, everyday rather than mathematical language, non-symbolic explanations, visual justifications and common-sense based reasoning. The main argument raised in the article concerns the challenge of valuing informal mathematical products, created by low achievers, and using them within the mathematics classroom as means for advancing such students. The data draws from several research and design projects conducted in Israel since 1991. Selected examples of students’ products, gathered from low-track mathematics classrooms involved in these projects, are presented and analyzed. The analyses highlight various features of such products, and portray the possible gains of teaching approaches that legitimize, and build onwards from, informal products of low achievers.     

Propagation of a reaction front accompanied by island formation: CO/Au/Ni(1 1 1)

Recent high-pressure scanning tunneling microscopy studies, performed at room temperature, have explicitly demonstrated the specifics of the CO-mediated removal of Ni atoms from the topmost layer of an Au/Ni(1 1 1) surface alloy. After an incubation period, the reaction is found to start at step edges. On each edge, a large fraction of Ni atoms is removed from the terrace in certain areas, whereas other areas are nearly intact after a given time. With increasing time, the former areas begin to overlap and the reaction front becomes somewhat more homogeneous. The Au atoms remaining behind the front form nm-sized islands. Here, we present Monte Carlo simulations reproducing all these observations.     

Application of quantum coherence and decoherence

Coherent phenomena in molecular chromophores interacting with a dissipative environment is addressed. We defined coherence by the phenomena of decoherence which collapses the system to pointer states. Coherent irreducible phenomena takes place in a time window before the system collapses. We describe a computational model: The Stochastic Surrogate Hamiltonian that can deal with such complex quantum systems. The conditions for coherent control are analyzed. A prerequisite for coherent phenomena is the ability to perform coherent control using shaped light sources. We show that weak field coherent control is enabled by interaction with the environment.     

PIV measurements of slow flow of a viscoelastic fluid within a porous medium

Particle image velocimetry (PIV) and pressure loss measurements were used to investigate slow flow through a square array of cylinders having a solid fraction of 10%. The test fluids were a Newtonian fluid and a Boger fluid, both of high viscosity such that the Reynolds number did not exceed 0.1. The pressure loss data reveal that the onset of elastic effects occurred at a Deborah number around 0.5 and that flow resistance was up to several times Newtonian values at Deborah numbers up to 3. PIV showed that the transverse velocity profiles for the Newtonian and non-Newtonian fluid were the same at Deborah numbers below onset. Above onset, the profiles became skewed, increasingly so as the Deborah number increased. In the wake regions between cylinders in a column, periodic flow structures formed in the spanwise direction. The structures were staggered from column to column, consistent with the skewing and were offset. These flow patterns are the result of an apparent elastic instability.     

Characterization of β‐cyclodextrin modified SiO2

Silica particles containing a layer of β‐cyclodextrins were synthesized using a modified method of Armstrong (1985). The modified silica particles were extensively characterized to both the presence and amount of β‐cyclodextrin introduced onto the surface. Raman confirmed that β‐cyclodextrin was introduced onto the particle. The combination of thermogravmetric analysis (TGA) and direct pyrolysis mass spectroscopy were used to determine the amount and the chemical composition of organic material present on the silica, respectively. The two methods confirmed that β‐cyclodextrin was successfully introduced in amounts comparable to earlier literature values. The values obtained by TGA were compared to amounts found by elemental analysis and XPS. The elemental analysis and TGA found the same amount of β‐cyclodextrin, while the XPS values were in the region of 1.5 times higher. This suggests a heterogeneous distribution of the β‐cyclodextrin on the silica particles. Copyright © 2010 John Wiley & Sons, Ltd.     

NMR Studies of Drugs. Applications of Achiral and Chiral Wthanide Shift Reagents to Bupropion

Abstract

The ¹H NMR spectra of racemic samples of the antidepressant drug, bupropion, 1, have been studied in CDCl₃ solution at 60 and 200 MHz with the achiral lanthanide shift reagent (LSR), tris(6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-3,5-octanedionato)europium (III), 2, and the chiral reagent, tris[3-(heptafluoropropylhydroxymethylene)-d-camphorato]europium(III), 3. Both LSR produced substantial lanthanide induced shifts consistent with ¹H assignments, but the bound complexes of 1 with 2 versus 3 may not be isostructural. With 3, substantial enantiomeric shift differences were observed for the t-butyl, CH ₃CH, NCH, and the aryl H-2 and H-6 signals, which should permit potential direct determination of enantiomeric excess.