Ambiskew Hopf algebras

Necessary and sufficient conditions are obtained for an ambiskew polynomial algebra A over a Hopf k-algebra R to possess the structure of a Hopf algebra extending that of R, in which the added variables X+ and X- are skew primitive. The coradical filtration is calculated, many examples are described, and properties determined

Azumaya loci and discriminant ideals of PI algebras

We prove that, under mild assumptions, for all positive integers ℓ, the zero set of the discriminant ideal D ℓ (R/Z(R), tr)of a prime affine polynomial identity (PI) algebra R coincides with the zero set of the modified discriminant ideal MD ℓ (R/Z(R), tr) of R, and give an explicit description of this set in terms of the dimensions of the irreducible representations of R. Furthermore, we prove that, when ℓ is the square of the PI-degree of R, this zero set is precisely the complement of the Azumaya locus of R. This description is used to classify the Azumaya loci of the multiparameter quantized Weyl algebras at roots of unity. As another application, we prove that the zero set of the top discriminant ideal of a prime affine PI algebra R coincides with the singular locus of the center of R, provided that the discriminant ideal has height at least 2, R has finite global dimension and R is a Cohen–Macaulay module over its center

Coarse woody debris: Managing benefits and fire hazard in the recovering forest

Management of coarse woody debris following fire requires consideration of its positive and negative values. The ecological benefits of coarse woody debris and fire hazard considerations are summarized. This paper presents recommendations for desired ranges of coarse woody debris. Example simulations illustrate changes in debris over time and with varying management

Connected (graded) Hopf algebras

We study algebraic and homological properties of two classes of infinite dimensional Hopf algebras over an algebraically closed field k of characteristic zero. The first class consists of those Hopf k-algebras that are connected graded as algebras, and the second class are those Hopf k-algebras that are connected as coalgebras. For many but not all of the results presented here, the Hopf algebras are assumed to have finite Gel'fand-Kirillov dimension. It is shown that if the Hopf algebra H is a connected graded Hopf algebra of finite Gel'fand-Kirillov dimension n, then H is a noetherian domain which is Cohen-Macaulay, Artin-Schelter regular and Auslander regular of global dimension n. It has S2 = IdH, and is Calabi-Yau. Detailed information is also provided about the Hilbert series of H. Our results leave open the possibility that the first class of algebras is (properly) contained in the second. For this second class, the Hopf k-algebras of finite Gel'fand-Kirillov dimension n with connected coalgebra, the underlying coalgebra is shown to be Artin-Schelter regular of global dimension n. Both these classes of Hopf algebra share many features in common with enveloping algebras of finite dimensional Lie algebras. For example, an algebra in either of these classes satisfies a polynomial identity only if it is a commutative polynomial algebra. Nevertheless, we construct, as one of our main results, an example of a Hopf k-algebra H of Gel'fand-Kirillov dimension 5, which is connected graded as an algebra and connected as a coalgebra, but is not isomorphic as an algebra to U(g) for any Lie algebra g

A Comparison Of Dietary Intakes Of Title Iii-C Participants On Home-Delivered Meal And Non-Meal Days

U okviru robotom potpomognutog protokola za dijagnozu autizma razvijen je modul za detekciju i praćenje proizvoljnog broja predmeta čije su boje poznate te prepoznavanje gesta u pokretima koje se tim predmetima izvode. Modul je prilagođen za izvođenje na humanoidnom robotu NAO u realnom vremenu. Praćenje predmeta se izvodi na robusan način koji dopušta snažnu interakciju između predmeta slične boje bez da se time gubi identitet pojedinog predmeta, te se pokazalo pouzdanim u realnim uvjetima izvođenja zadatka i u testovima praćenja. Prepoznavanje geste s korisničke je strane intuitivno i kvalitetno prepoznaje pokrete koji se koriste pri izvođenju protokola za dijagnozu.As part of a robot-assisted autism diagnostic protocol, a module has been developed for the detection and tracking of an arbitrary number of objects of known color, as well as recognition of gestures based on the movements made by the objects. The module is built for real-time execution on the NAO humanoid robot. Object tracking is done using a robust method allowing for strong interaction between objects of a similar color without disrupting the tracking of any interacting object, and is shown to be reliable both in real-world conditions as well as in tracking tests. The module's gesture recognition capabilities are intuitive to use and provide quality recognition of all movements used in the diagnostic protocol

DIFFERENT WEIGHT TRANSFER PATTERNS IN GOLF

The aim of this study was to determine if weight transfer swing styles exist in the golf swing. 40 golfers performed swings using a driver while standing on two force plates. Centre of pressure, used to indicate weight transfer, was normalized to foot position and quantified at eight swing events. Cluster analysis indicated that two major swing styles existed; a Front Foot style and a Reverse style. Both styles were similar from Takeaway to Early Downswing. Then, while the Front Foot group moved weight towards the front foot during the downswing, the Reverse group moved weight back towards the back foot. In the heel to toe direction, the Front Foot group hit from a mid-foot position, while the Reverse group hit with weight near the toes at ball contact. Cluster analysis is a useful tool for identifying different styles

Revisiting the Hugenholtz-Van Hove theorem in nuclear matter

An assessment of the magnitude of the rearrangement contribution to the Fermi energy and to the binding energy per particle is carried out in symmetric nuclear matter by extending the G-matrix framework. The restoration of the thermodynamic consistency or, equivalently, the fulfillment of the Hugenholtz-Van Hove theorem, is discussed.Comment: 14 pages, 3 figure

Poisson structures on affine spaces and flag varieties. I. Matrix affine Poisson space

The standard Poisson structure on the rectangular matrix variety Mm,n(C) is investigated, via the orbits of symplectic leaves under the action of the maximal torus T ⊂ GLm+n(C). These orbits, finite in number, are shown to be smooth irreducible locally closed subvarieties of Mm,n(C), isomorphic to intersections of dual Schubert cells in the full flag variety of GLm+n(C). Three different presentations of the T-orbits of symplectic leaves in Mm,n(C) are obtained – (a) as pullbacks of Bruhat cells in GLm+n(C) under a particular map; (b) in terms of rank conditions on rectangular submatrices; and (c) as matrix products of sets similar to double Bruhat cells in GLm(C) and GLn(C). In presentation (a), the orbits of leaves are parametrized by a subset of the Weyl group Sm+n, such that inclusions of Zariski closures correspond to the Bruhat order. Presentation (b) allows explicit calculations of orbits. From presentation (c) it follows that, up to Zariski closure, each orbit of leaves is a matrix product of one orbit with a fixed column-echelon form and one with a fixed rowechelon form. Finally, decompositions of generalized double Bruhat cells in Mm,n(C) (with respect to pairs of partial permutation matrices) into unions of T-orbits of symplectic leaves are obtained

Formal Quantum Efficiencies for the Photocatalytic Reduction of CO2 in a Gas Phase Batch Reactor

The photocatalytic reduction of CO2 to fuels, or useful products, is an area of active research. In this work, nanoengineering and surface modification of titania were investigated as approaches for improving the CO2 reduction efficiency in a fixed-bed gas phase batch photoreactor under UV–vis irradiation. Titania nanotubes were prepared by a hydrothermal method, and TiO2 (P25) was surface modified with copper clusters. Unmodified TiO2 (P25) was used as the bench-mark comparison. The titania nanotubes and Cu-TiO2 materials showed higher efficiency for the photocatalytic reduction of CO2 to yield CH4 as compared to P25. Carbon monoxide yields were similar for all photocatalysts tested. The photocatalytic reduction of CO2 was observed on all photocatalyst tested, with the nanotubes proving to be the most efficient for the production of CH4. The product yields per mass of catalyst observed in this work are similar to those reported in the literature (with similar reactor parameters) but the calculated formal quantum efficiencies for CO2 reduction are very low (4.41 × 10−5 to 5.95 × 10-4)