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A permutoid is a set of partial permutations that contains the identity and is such that partial compositions, when defined, have at most one extension in the set. In 2004 Peter Cameron conjectured that there can exist no algorithm that determines whether or not a permutoid based on a finite set can be completed to a finite permutation group. In this note we prove Cameron’s conjecture by relating it to our recent work on the profinite triviality problem for finitely presented groups. We also prove that the existence problem for finite developments of rigid pseudogroups is unsolvable. In an appendix, Steinberg recasts these results in terms of inverse semigroups.
We show results from a positive degree-day (PDD) model of Greenland ice sheet (GrIS) surface mass balance (SMB), 1870–2012, forced with reanalysis data. The model includes an improved daily temperature parameterization as compared with a previous version and is run at 1 km rather than 5 km resolution. The improvements lead overall to higher SMB with the same forcing data. We also compare our model with results from two regional climate models (RCMs). While there is good qualitative agreement between our PDD model and the RCMs, it usually results in lower precipitation and lower runoff but approximately equivalent SMB: mean 1979–2012 SMB (± standard deviation), in Gt a−1, is 382 ± 78 in the PDD model, compared with 379 ± 101 and 425 ± 90 for the RCMs. Comparison with in situ SMB observations suggests that the RCMs may be more accurate than PDD at local level, in some areas, although the latter generally compares well. Dividing the GrIS into seven drainage basins we show that SMB has decreased sharply in all regions since 2000. Finally we show correlation between runoff close to two calving glaciers and either calving front retreat or calving flux, this being most noticeable from the mid-1990s.
In this work, a very efficient mixed-potential integral-equation formulation is implemented for the rigorous analysis of multilayered structures with arbitrarily shaped two-dimensional periodic metallic and/or dielectric inclusions. Original acceleration techniques have been developed for the computation of the components of the scalar and dyadic Green's functions, based on different types of asymptotic extractions according to the potential considered. The theoretical approach and its computational convenience have been validated through different full-wave analyses concerning both scattering problems and complex-mode dispersive behaviors in various frequency-selective structures for microwave applications.
By definition, an $\omega$-residually free tower is positive-genus if all surfaces used in its construction are of positive-genus. We prove that every limit group is virtually a subgroup of a positive-genus, $\omega$-residually free tower. By combining this construction with results of Gaboriau, we prove that elementarily free groups are measure-equivalent to free groups.
Cotton is the single most economically important natural textile fiber in the world. It is a seed hair and has historically composed a large portion of the world's textiles. The plant is grown in most tropical and subtropical regions of the world. The demand for cotton, especially as a garment fiber, it due to properties such as its soft hand, water absorption, spinnability, and dyeability, and to its ease of home laundering. Perhaps cotton's most important textile property is its comfort. These properties are due to the unique, multilayered construction of the fiber subunits. The nature of this construction has been studied microscopically for more than 100 years, first using light microscopes, then electron microscopes as they became available. Because they are natural biological materials, no two cotton fibers are exactly alike. Yet they do have certain structural features in common. Structure in cotton can refer to several levels of construction.
Foliated to massive hornblende and biotite-bearing tonalite, trondhjemite and granodiorite comprise a terrane of batholithic dimensions in southwestern to central Newfoundland. These rocks intrude and include Ordovician ophiolite fragments and metasedimentary rocks of Fleur de Lys type, and are cut by a suite of Silurian gabbro-diorite and norite and Siluro-Devonian (?) granite intrusions.
A U/Pb (zircon, sphene) age of 456 ± 3 Ma (2σ) and a K/Ar (hornblende) age of 455 ± 14 Ma (previously reported) for a representative least-deformed tonalite of the Southwest Brook Complex indicate that it crystallised and cooled in Caradoc time. A less precise U/Pb (zircon) age of 428 ± 41 Ma (2σ) is measured for tonalitic Cape Ray Granite in southern Newfoundland. On discrimination diagrams which use Rb, Nb and Y contents to infer tectonic setting, these rocks fall in the field of volcanic arc granites. The occurrence of zircon cores with average ages of 1430 + 18/–17 and 1541 ± 173 Ma (2σ) also indicate that the magmas formed in part by partial melting of Proterozoic crust, or sediments derived from such crust. It is suggested that the tonalitic magmas were generated during the Taconic Orogeny in an arc: continent collision zone at the ancient margin of eastern North America.
Tonalitic rocks in western Newfoundland broadly correlative in age and chemistry with the batholith include the Burlington Granodiorite and Hungry Mountain Complex, as well as allochthonous slices of foliated tonalite emplaced over Ordovician platform carbonates W of Grand Lake.
Dusts produced in the processing of cotton fibers are believed to be causative factors of the chronic respiratory ailment byssinosis (1). Although these multicomponent dusts have been studied extensively, neither the identity of the causative agent(s) nor its exact origin have been determined. Differences in the physiological activity of dusts generated at different stages of cotton processing have been reported, indicating some variation in components. Sources are not known for all components of these dusts but they are probably composed largely of the various crushed parts of the cotton plant, along with a possible complex mixture of soil dusts, pollens, and fungal materials. Cotton plant parts, especially the bract (2), may be the responsible factor in production of byssinotic symptoms. However, it has been difficult to identify specific sources of respirable particles in the dusts because the various components have been mascerated beyond recognition by anatomical or morphological structure.
Radiation induced graft polymerization of the cellulose of cotton fibers with various other polymers produces textile fibers with new properties. Chemical analysis and physical tests are used to determine changes in such properties as breaking strength, wrinkle recovery angle, and resistance to abrasion. While such tests give reliable evaluations of the overall nature of any improvement, they give little information on what changes actually occurred in the fiber itself. One means of obtaining this information is through microscopical observations.
Penetration and reaction of the polymer within yarns and fibers can be tested by cutting Hardy cross sections of the fibers after they have been dyed with a stain specific for the reacted polymer. More detailed information can be obtained from ultrathin sections, using the transmission electron microscope. Structural changes often occur which are obvious from comparison of cross sections of untreated and treated fibers. Use of the scanning electron microscope permits evaluation of changes in surface features of fabrics and individual fibers.
The reaction of cellulose with certain cross-linking agents has produced cotton fabrics with outstanding durable press characteristics. However, many of these reactions decrease the natural abrasion resistance of the fiber. Wet abrasion and dry abrasion are known to produce different types of damage in the cotton fiber. It was of interest to determine whether such differences occur in the machine washing and drying of cotton fabrics. To study this problem, both untreated and cross-linked cotton fabrics were made into trouser cuffs, washed repeatedly and line dried, or machine dried until extensive damage had occurred. The two reacted fabrics studied had been treated with dimethyloldihydroxyethyleneurea and tris(l-aziridinyl) phosphine oxide. Cuene solubility tests on ultrathin sections of fibers from th ese fabrics observed with the transmission electron microscope indicated that the fibers were uniformly cross-linked throughout.
High energy irradiation produces unique reactions in cellulose. Radiation induced reactions between vinyl polymers and cellulose fibers produce vinyl-cellulose copolymers which retain a fibrous nature and exhibit desirable properties acquired from the grafted polymer. These include increased elongation, toughness, and thermoplasticity, improved abrasion, and not resistance, and decreased permanent set. The nature and extent of such improvements are dependent not only on the amount of graft polymer formed, but also on its location within the fiber. Electron microscopy has been used to investigate the location and distribution of the graft polymer. Polyacrylonitrile, polystyrene, (poly)methyl methacrylate, and polyvinyl acetate were used for grafting. It was found that distribution of the grafted polymer was dependent on such factors as type of polymer solvent used, cellulose-polymer ratio, functional groups present in the fibers, irradiation dosage used, and whether post irradiation polymerization or simultaneous polymerization was employed. Location of the graft polymer is determined microscopically by applying solvents for cellulose and for the graft polymer to the grafted fibers or their ultrathin cross sections. That portion of the section which is insoluble in either solvent is accepted to be grafted copolymer.
In the July number of the Gazette Mr. E. G. Phillips says: “Frequently it happens that students whose early training has been on the lines of many of the existing elementary text-books on the Differential Calculus come up to the University never even having heard of a differential! It would be of the greatest possible assistance to those responsible for the later teaching of the Calculus if the schoolmasters taught the subject from the differential standpoint right from the start”. I have the very greatest hesitation in subscribing to this latter statement.
1. The subject-matter of this communication I believe to be new, but after Lemma 1 the method is classical; Lemma 1 is itself a particular case of a theorem which I have given elsewhere, and is a straightforward extension of a well-known result.
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