Natural Density of Rectangular Unimodular Integer Matrices

In this paper, we compute the natural density of the set of k x n integer matrices that can be extended to an invertible n x n matrix over the integers. As a corollary, we find the density of rectangular matrices with Hermite normal form [O Id]. Connections with Cesaro's Theorem on the density of coprime integers and Quillen-Suslin's Theorem are also presented.Comment: 8 page

Radical and ion molecule mechanisms in the polymerization of hydrocarbons and chlorosilanes in RF plasmas at low pressures ( 1.0 torr)

The ion-molecule and the radical-molecule mechanisms are responsible for the dissociation of hydrocarbons, and chlorosilane monomers and the formation of polymerized species, respectively, in the plasma state of a RF discharge. In the plasma, of a mixture of monomer with Ar, the rate determining step for both dissociation and polymerization is governed by an ion-molecular type interaction. Additions of H2 or NH3 to the monomer Ar(+) mixture transforms the rate determining step from an ion-molecular interaction to a radical-molecule type interaction for both monomer dissociation and polymerization processes

Homogeneous reactions of hydrocarbons, silane, and chlorosilanes in radiofrequency plasmas at low pressures

The ion-molecule and radical-molecule mechanisms are responsible for the dissociation of hydrocarbon, silane, and chlorosilane monomers and the formation of polymerized species, respectively, in an RF plasma discharge. In a plasma containing a mixture of monomer and argon the rate-determining step for both dissociation and polymerization is governed by an ion-molecule type of interaction. Adding hydrogen or ammonia to the monomer-argon mixture transforms the rate-determining step from an ion-molecule interaction to a radical-molecule interaction for both monomer dissociation and polymerization

A chemical method for the assessment of grapes according to their seed content

Polyphenolic compounds, which are unevenly distributed between seed, pulp and skin, are the basis of a chemical method for the assessment of seedlessness in grapes. Known seedless and seeded grapes were evaluated using this method and a statistic test showed a significant difference between them. The color of the grapes did not interfere with this method. Frozen storage of samples at -20 °C for 3 months did not alter the results of the test. Hybrids of known progenies which were evaluated gave results which generally agree with those of the taste test. This chemical method, compared to assessment by taste, is more reliable, quantitative and relatively easy to perform.Une méthode chimique pour la détermination des raisins selon leur teneur en pépinsUne analyse chimique pour la détermination de l'absence de grains de raisins est décrite. La méthode est basée sur la détermination colorimétrique de composés phénoliques dans les raisins

Exocytosis from permeabilized bovine adrenal chromaffin cells is differently modulated by guanosine 5'-[gamma-thio]triphosphate and guanosine 5'-[beta gamma-imido]triphosphate

1. In bovine adrenal chromaffin cells made permeable either to molecules less than or equal to 3 kDa with alphatoxin or to proteins less than or equal to 150 kDa with streptolysin O, the GTP analogues guanosine 5'-[beta gamma-imido]triphosphate (p[NH]ppG) and guanosine 5'-[gamma-thio]triphosphate (GTP[S]) differently modulated Ca(2+)-stimulated exocytosis. 2. In alphatoxin-permeabilized cells, p[NH]ppG up to 20 microM activated Ca(2+)-stimulated exocytosis. Higher concentrations had little or no effect. At a free Ca2+ concentration of 5 microM, 7 microM-p[NH]ppG stimulated exocytosis 6-fold. Increasing the free Ca2+ concentration reduced the effect of p[NH]ppG. Pretreatment of the cells with pertussis toxin prevented the activation of the Ca(2+)-stimulated exocytosis by p[NH]ppG. 3. In streptolysin O-permeabilized cells, p[NH]ppG did not activate, but rather inhibited Ca(2+)-dependent catecholamine release under all conditions studied. In the soluble cytoplasmic material that escaped during permeabilization with streptolysin O, different G-protein alpha-subunits were detected using an appropriate antibody. Around 15% of the cellular alpha-subunits were detected in the supernatant of permeabilized control cells. p[NH]ppG or GTP[S] stimulated the release of alpha-subunits 2-fold, causing a loss of about 30% of the cellular G-protein alpha-subunits under these conditions. Two of the alpha-subunits in the supernatant belonged to the G(o) type, as revealed by an antibody specific for G(o) alpha. 4. GTP[S], when present alone during stimulation with Ca2+, activated exocytosis in a similar manner to p[NH]ppG. Upon prolonged incubation, GTP[S], in contrast to p[NH]ppG, inhibited Ca(2+)-induced exocytosis from cells permeabilized by either of the pore-forming toxins. This effect was resistant to pertussin toxin. 5. The p[NH]ppG-induced activation of Ca(2+)-stimulated release from alphatoxin-permeabilized chromaffin cells may be attributed to one of the heterotrimeric G-proteins lost during permeabilization with streptolysin O. The inhibitory effect of GTP[S] on exocytosis is apparently not mediated by G-protein alpha-subunits, but by another GTP-dependent process still occurring after permeabilization with streptolysin O

Output feedback invariants

The paper is concerned with the problem of determining a complete set of invariants for output feedback. Using tools from geometric invariant theory it is shown that there exists a quasi-projective variety whose points parameterize the output feedback orbits in a unique way. If the McMillan degree n ≥ mp, the product of the number of inputs and number of outputs, then it is shown that in the closure of every feedback orbit there is exactly one nondegenerate system

Crystal structure of η5-1-(tris(pentafluorophenyl) boranylmethyl)-2,3,4,5-tetramethylcyclopentadienyl-η5, η1-3,6-di-tert-butyl-9,10,11-trimethyl-bicyclo(6.3.0) undeca-3-en-8,10-dienyl)titanium(IV),Ti(C50H48BF 15)

C50H48BF15Ti, monoclinic, P12 1/c1 (no. 14), a = 12.007(2) Å, b = 19.511(4) Å, c = 20.010(4) Å, β = 98.90(3)°, V= 4631.3 Å3, Z = 4, Rgt(F) = 0.052, wRref(F2) = 0.120, T = 200 K. © by Oldenbourg Wissenchaftsverlag

Crystal structure of bis(pentamethylcyclopentadienyl)(1-tert- butylisocyanido)-2-trimethylsilyl-3-[(trimethylsilyl)ethynyl]-hafnacyclopropene, (C10H15)2(C5H9N) Hf(C10H18Si2)

C35H57HfNSi2, monoclinic, P121/c1 (no. 14), a = 10.7410(3) Å, b = 16.2302(5) Å, c = 21.6945(7) Å, β = 104.512(2)°, V = 3661.3 Å3, Z = 4, R gt(F) = 0.049, wRref(F2) = 0.138, T = 200 K. © 2014 Oldenbourg Wissenschaftsverlag, München