Fully asynchronous stochastic coordinate descent: a tight lower bound on the parallelism achieving linear speedup

Mathematical Programming - We seek tight bounds on the viable parallelism in asynchronous implementations of coordinate descent that achieves linear speedup. We focus on asynchronous coordinate...     

Preliminary studies on a variable energy positron annihilation lifetime spectroscopy system

There are many advantages in being able to perform positron annihilation lifetime spectroscopy (PALS) using a variable energy positron beam, the most obvious being the easy identification of different defect types at different depths. The difficulty in conducting variable energy (VE) PALS studies lies in the fact that a “start” signal is required to signal the entry of the positron into the target. Two methods have been used to overcome this problem, namely the bunching technique, which employs radio frequency (RF) cavities and choppers, and secondly the use of secondary electrons emitted from the target. The latter technique is in terms of experimental complexity much simpler, but has in the past suffered from poor time resolution (typically ∼500 ps). In this work, we present a series of computer simulations of a design based on the secondary electron emission from thin C-foils in transmission mode which shows that significant improvements in time resolution can be made with resolutions ∼200 ps being in principle possible.     

Probabilistic Analysis of Condition Numbers for Linear Programming

In this paper, we provide bounds for the expected value of the log of the condition number C(A) of a linear feasibility problem given by a n × m matrix A (Ref. 1). We show that this expected value is O(min{n, m log n}) if n > m and is O(log n) otherwise. A similar bound applies for the log of the condition number C _R(A) introduced by Renegar (Ref. 2).     

Fixed-sign solutions for a system of singular focal boundary value problems

We consider a system of focal boundary value problems where the nonlinearities may be singular in the independent variable and may also be singular in the dependent arguments. Using Schauder fixed point theorem, we establish criteria such that the system of boundary value problems has at least one fixed-sign solution.     

Some new nonlinear inequalities and applications to boundary value problems

In this paper, we establish some new nonlinear integral inequalities of the Gronwall–Bellman–Ou-Iang-type in two variables. These on the one hand generalizes and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of differential equations. We illustrate this by applying our new results to certain boundary value problem.     

O− and OH− chemical ionization of some fatty acid methyl esters and triacylglycerols

O^? and OH^? react with fatty acid methyl esters (FAMES) under chemical ionization conditions both as Bronsted bases to form [M - H]^? and as nucleophiles to form the carboxylate ion RCOO^?. O^? shows a much greater tendency to react as a nucleophile than does OH^?. The [M - H]^? ions fragment by elimination of CH³OH, with unsaturation in certain positions in the fatty acid hydrocarbon chain promoting this elimination for unknown reasons. The reaction of O^? and OH^? with triacylglycerols leads to [M - H]^?, characteristic of the molecular mass, and to carboxylate ions characteristic of the fatty acid(s) present in the lipid. The presence of the three ester functions in the lipids greatly enhances the formation of carboxylate ions compared to the FAMES.     

Covalent crosslinking of 1-D photonic crystals of microporous Si by hydrosilylation and ring-opening metathesis polymerization

Free-standing porous Si multilayer dielectric mirrors, prepared by electrochemical etching of crystalline Si, are treated with a ruthenium ring-opening metathesis polymerization (ROMP) catalyst followed by norbornene to produce flexible, stable composite materials in which poly(norbornene) is covalently attached to the porous Si matrix.     

PDMS-based microfluidic device with multi-height structures fabricated by single-step photolithography using printed circuit board as masters

We have developed a method for fabricating microfluidic devices with multi-height structures using single step photolithography. The whole fabrication process is executed by conventional printed circuit board (PCB) technology without the need of having access to clean room facilities. Specifically designed "windows" and "rims" architectures were printed on films that were used as photomasks. Different levels of protruding features on the PCB master were produced by exposing a photomask followed by chemical wet etching. Poly(dimethylsiloxane) (PDMS) was then moulded against the positive relief master to generate microfluidic structures. In this report, we described the fabrication of a microfluidic device featured with a multi-height "sandbag" structure for particle entrapment and peripheral microchannels. Controlled immobilization of biological cells and immunocytochemcial staining assays were performed to demonstrate the applicability of the microfluidic device for cellular analysis. The integrity of the microdevice remained stable under applied pressure, indicating the robustness of the elastic PDMS structures for analytical operation. The simple microfabrication process requires only low-cost materials and minimal specialized equipment and can reproducibly produce mask lines of about 20 microm in width, which is sufficient for most microfluidic applications.     

Direct functionalization of the cyclometalated 2-(2′-pyridyl)phenyl ligand bound to iridium(III)

Treatment of [Ir(ppy)₂(μ-Cl)]₂ and [Ir(ppy)₂(dtbpy)][OTf] (ppy = 2-(2′-pyridyl)phenyl; dtbpy = 4,4′-di-tert-butyl-2,2′-bipyridine; OTf = triflate) with pyridinium tribromide in the presence of Fe powder led to isolation of [Ir(4-Br-ppy)(μ-Br)]₂ (1) and [Ir(4-Br-ppy)₂(dtbpy)][OTf] (2), respectively. Pd-catalyzed cross-coupling of 2 with RB(OH)₂ afforded [Ir(4-R-ppy)₂(dtbpy)][OTf] (R = 4′-FC₆H₄ (3)), 4′-PhC₆H₄ (4), 2′-thienyl (5), 4′-C₆H₄CH₂OH (6). Treatment of 4 with B₂(pin)₂ (pin = pinacolate) afforded [Ir{4-(pin)B-ppy}₂(dtbpy)][OTf] (7). The alkynyl complexes [Ir(4-PhCC-ppy)₂(dtbpy)][OTf] (8) and [Ir{4-Me₂(OH)CC-ppy}(4-Br-ppy)(dtbpy)][OTf] (9) were prepared by cross-coupling of 2 with PhCCSnMe₃ and Me₂C(OH)CCH, respectively. Ethynylation of [Ir(fppy)₂(dtbpy)][OTf] (fppy = 5-formyl-2-(2′-pyridyl)phenyl) with Ohira’s reagent MeCOC(N₂)P(O)(OEt)₂ afforded [Ir{5-HCC-ppy}₂(dtbpy)][OTf] (10). The solid-state structures of 2, 5, 7, and 10 have been determined.     

Synthesis and structural characterization of mono- and bisfunctional o-carboranes

Functionalized o-carboranes are interesting ligands for transition metals. Reaction of LiC2B10H11 with Me2NCH2CH2Cl in toluene afforded 1-Me2NCH2CH2-1,2-C2B10H11 (1). Treatment of 1 with 1 equiv. of n-BuLi gave [(Me2NCH2CH2)C2B10H10]Li ([1]Li), which was a very useful synthon for the production of bisfunctional o-carboranes. Reaction of [1]Li with RCH2CH2Cl afforded 1-Me2NCH2CH2-2-RCH2CH2-1,2-C2B10H10 (R = Me2N (2), MeO (3)). 1 and 2 were also prepared from the reaction of Li2C2B10H10 with excess Me2NCH2CH2Cl. Treatment of [1]Li with excess MeI or allyl bromide gave the ionic salts, [1-Me3NCH2CH2-2-Me-1,2-C2B10H10][I] (4) and [1-Me2N(CH2=CHCH2)CH2CH2-2-(CH2=CHCH2)-1,2-C2B10H10][Br] (6), respectively. Interaction of [1]Li with 1 equiv. of allyl bromide afforded 1-Me2NCH2CH2-2-(CH2=CHCH2)-1,2-C2B10H10 (5). Treatment of [1]Li with excess dimethylfulvene afforded 1-Me2NCH2CH2-2-C5H5CMe2-1,2-C2B10H10 (7). Interaction of [1]Li with excess ethylene oxide afforded an unexpected product 1-HOCH2CH2-2-(CH2=CH)-1,2-C2B10H10 (8). 1 and 3 were conveniently converted into the corresponding deborated compounds, 7-Me2NHCH2CH2-7,8-C2B9H11 (9) and 7-Me2NHCH2CH2-8-MeOCH2CH2-7,8-C2B9H10 (10), respectively, in MeOH-MeOK solution. All of these compounds were characterized by various spectroscopic techniques and elemental analyses. The solid-state structures of 4 and 6-10 were confirmed by single-crystal X-ray analyses.