The asymmetric sandwich theorem

We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations of the Fenchel duality theorem. Most of the results are about affine functions defined on convex subsets of vector spaces, rather than linear functions defined on vector spaces. We consider both results that use a simple boundedness hypothesis (as in Rockafellar's version of the Fenchel duality theorem) and also results that use Baire's theorem (as in the Robinson-Attouch-Brezis version of the Fenchel duality theorem). This paper also contains some new results about metrizable topological vector spaces that are not necessarily locally convex.Comment: 17 page

User’s Guide to For2R: A Module of Fortran 95 Output Routines Compatible with the R Statistics Language

For2R is a collection of Fortran routines for saving complex data structures into a file that can be read in the R statistics environment with a single command.1 For2R provides both the means to transfer data structures significantly more complex than simple tables, and an archive mechanism to store data for future reference. We developed this software because we write and run computationally intensive numerical models in Fortran, C++, and AD Model Builder. We then analyse results with R. We desired to automate data transfer to speed diagnostics during working-group meetings. We thus developed the For2R interface to write an R data object (of type list) to a plain-text file. The master list can contain any number of matrices, values, dataframes, vectors or lists, all of which can be read into R with a single call to the dget function. This allows easy transfer of structured data from compiled models to R. Having the capacity to transfer model data, metadata, and results has sharply reduced the time spent on diagnostics, and at the same time, our diagnostic capabilities have improved tremendously. The simplicity of this interface and the capabilities of R have enabled us to automate graph and table creation for formal reports. Finally, the persistent storage in files makes it easier to treat model results in analyses or meta-analyses devised months—or even years—later. We offer For2R to others in the hope that they will find it useful. (PDF contains 31 pages

Effect of the C-bridge length on the ultraviolet-resistance of oxycarbosilane low-k films

The ultra-violet (UV) and vacuum ultra-violet (VUV) resistance of bridging alkylene groups in organosilica films has been investigated. Similar to the Si-CH3 (methyl) bonds, the Si-CH2-Si (methylene) bonds are not affected by 5.6 eV irradiation. On the other hand, the concentration of the Si-CH2-CH2-Si (ethylene) groups decreases during such UV exposure. More significant difference in alkylene reduction is observed when the films are exposed to VUV (7.2 eV). The ethylene groups are depleted by more than 75% while only about 40% methylene and methyl groups loss is observed. The different sensitivity of bridging groups to VUV light should be taken into account during the development of curing and plasma etch processes of low-k materials based on periodic mesoporous organosilicas and oxycarbosilanes. The experimental results are qualitatively supported by ab-initio quantum-chemical calculations

User’s Guide to C2R: A Set of C Language Output Routines Compatible with the R Statistics Language

C2R is a collection of C routines for saving complex data structures into a file that can be read in the R statistics environment with a single command.1 C2R provides both the means to transfer data structures significantly more complex than simple tables, and an archive mechanism to store data for future reference. We developed this software because we write and run computationally intensive numerical models in Fortran, C++, and AD Model Builder. We then analyse results with R. We desired to automate data transfer to speed diagnostics during working-group meetings. We thus developed the C2R interface to write an R data object (of type list) to a plain-text file. The master list can contain any number of matrices, values, dataframes, vectors or lists, all of which can be read into R with a single call to the dget function. This allows easy transfer of structured data from compiled models to R. Having the capacity to transfer model data, metadata, and results has sharply reduced the time spent on diagnostics, and at the same time, our diagnostic capabilities have improved tremendously. The simplicity of this interface and the capabilities of R have enabled us to automate graph and table creation for formal reports. Finally, the persistent storage in files makes it easier to treat model results in analyses or meta-analyses devised months—or even years—later. We offer C2R to others in the hope that they will find it useful. (PDF contains 27 pages

Impact of UV wavelength and curing time on the properties of spin-coated low-k films

Advanced spin-on k 2.3 films with similar to 40% porosity were enabled by liquid phase self-assembly (LPSA) mechanism on Si substrates. UV-assisted thermal template removal is investigated as a faster alternative to the conventional thermal process. The as-deposited films were exposed to narrow-band UV light of 172 nm, 222 nm, 254 nm or 185/254 nm at 400 degrees C for different time. The optical, mechanical, chemical and electrical properties of the resulting films are discussed in this work. Photons with wavelength of about 172 nm from one side are detrimental to the electrical and chemical properties of the low-k films hut from the other side notably improve the porous low-k mechanical properties. Exposure to 222 nm light as short as 3 min, is more efficient in terms of template removal when compared to 2h thermal cure, while in both cases similar mechanical and electrical properties are reported. UV-cure using 254 nm or dual band 254/185 nm photons seem to have a minor contribution to the template removal efficiency for the applied doses. Higher doses are necessary in order to better understand the effective contribution of these photon energies. Finally, the HF etching mechanism is discussed

SiGe quantum dots for fast hole spin Rabi oscillations

We report on hole g-factor measurements in three terminal SiGe self-assembled quantum dot devices with a top gate electrode positioned very close to the nanostructure. Measurements of both the perpendicular as well as the parallel g-factor reveal significant changes for a small modulation of the top gate voltage. From the observed modulations we estimate that, for realistic experimental conditions, hole spins can be electrically manipulated with Rabi frequencies in the order of 100MHz. This work emphasises the potential of hole-based nano-devices for efficient spin manipulation by means of the g-tensor modulation technique

Improved timed-mating, non-invasive method using fewer unproven female rats with pregnancy validation via early body mass increases

For studies requiring accurate conception-timing, reliable, efficient methods of detecting oestrus reduce time and costs, whilst improving welfare. Standard methods use vaginal cytology to stage cycle, and breeders are paired–up using approximately five proven females with proven males to achieve at least one conception on a specific day. We describe an alternative, fast, consistent, non-invasive method of timed-mating using detection of lordosis behaviour in Wistar and Lister-Hooded rats that used unproven females with high success rates. Rats under reverse-lighting had body masses recorded pre-mating, day (d) 3-4, d8, d10 and d18 of pregnancy. Using only the presence of the oestrus dance to time-mate females for 24-hrs, 89% Wistar and 88% Lister-Hooded rats successfully conceived. We did not observe behavioural oestrus in Sprague-Dawleys without males present. Significant body mass increases following mating distinguished pregnant from non-pregnant rats, as early as d4 of pregnancy (10% ± 1.0 increase cf 3% ± 1.2). The pattern of increases throughout gestation was similar for all pregnant rats until late pregnancy, when there were smaller increases for primi- and multiparous rats (32% ± 2.5; 25% ± 2.4), whereas nulliparous rats had highest gains (38% ± 1.5). This method demonstrated a distinct refinement of the previous timed-mating common practice used, as disturbance of females was minimised. Only the number required of nulli-, primi- or multiparous rats were mated, and body mass increases validated pregnancy status. This new breeding-management method is now established practice for two strains of rat and resulted in a reduction in animal use

Band Formation during Gaseous Diffusion in Aerogels

We study experimentally how gaseous HCl and NH_3 diffuse from opposite sides of and react in silica aerogel rods with porosity of 92 % and average pore size of about 50 nm. The reaction leads to solid NH_4Cl, which is deposited in thin sheet-like structures. We present a numerical study of the phenomenon. Due to the difference in boundary conditions between this system and those usually studied, we find the sheet-like structures in the aerogel to differ significantly from older studies. The influence of random nucleation centers and inhomogeneities in the aerogel is studied numerically.Comment: 7 pages RevTex and 8 figures. Figs. 4-8 in Postscript, Figs. 1-3 on request from author

Liesegang patterns: Effect of dissociation of the invading electrolyte

The effect of dissociation of the invading electrolyte on the formation of Liesegang bands is investigated. We find, using organic compounds with known dissociation constants, that the spacing coefficient, 1+p, that characterizes the position of the n-th band as x_n ~ (1+p)^n, decreases with increasing dissociation constant, K_d. Theoretical arguments are developed to explain these experimental findings and to calculate explicitly the K_d dependence of 1+p.Comment: RevTex, 8 pages, 3 eps figure