A NOTE ON FREE GROUPS IN THE RING OF FRACTIONS OF SKEW POLYNOMIAL RINGS

Let L be a function field over the rationals and let D denote the skew field of fractions of L[t; sigma], the skew polynomial ring in t, over L, with automorphism sigma. We prove that the multiplicative group D(x) of D contains a free noncyclic subgroup.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

On E-functions of semisimple Lie groups

We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group G as their expansions into series of special functions that are invariant under the action of the even subgroup of the Weyl group of G. We distinguish two cases of even Weyl groups-one is the direct product of even Weyl groups of simple components of G and the second is the full even Weyl group of G. The problem is rather simple in two dimensions. It is much richer in dimensions greater than two-we describe in detail E-transforms of semisimple Lie groups of rank 3.

INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS

Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let * be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (u(k,m)(x*), u(k,m)(x*)) or (u(k,m)(x), u(k,m)(y)), formed respectively by Bass cyclic and *-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ZG.

CENTRAL UNITS IN METACYCLIC INTEGRAL GROUP RINGS

In this article, we give a method to compute the rank of the subgroup of central units of ZG, for a finite metacyclic group, G, by means of Q-classes and R-classes. Then we construct a multiplicatively independent set u subset of Z(U(ZC(p,q))) and by applying our results, we prove that u generates a subgroup of finite index.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

Locally nilpotent groups of units in tiled rings

We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.

NATURAL TOPOLOGIES ON COLOMBEAU ALGEBRAS

We define intrinsic, natural and metrizable topologies T(Omega), T, T(s,Omega) and T(s) in G(Omega), (K) over bar, G(s)(Omega) and (K) over bar (s) respectively. The topology T(Omega) induces T, T(s,Omega) and T(s). The topologies T(s,Omega) and T(s) coincide with the Scarpalezos sharp topologies.

Behaviour of TiO(2)-SiMgO(x) hybrid composites on the solar photocatalytic degradation of polluted air

The photocatalytic performance of TiO(2)-SiMgO(x) ceramic plates for trichloroethylene abatement in gas phase has been evaluated under sun irradiance conditions. A continuous flow Pyrex glass reactor fixed on the focus of a compound parabolic collector has been used. The performance of the hybrid photocatalyst has been evaluated as the variation of TCE conversion and reaction products formation with the solar irradiance at different total gas flow, TCE concentration, and water vapour content. SiMgO(x) not only provides adsorbent properties to the photocatalyst, but it also allows the effective use of the material during low solar irradiance conditions. The adsorption-desorption phenomena play a pivotal role in the behaviour of the system. Thus, TCE conversion curves present two different branches when the sun irradiance increases (sunrise) or decreases (sunset). CO(2), COCl(2) and DCAC were the most relevant products detected. Meanwhile CO(2) concentration was insensitive to the branch analysed, COCl(2) or DCAC were not indicating the ability of these compounds to be adsorbed on the composite. An increase of the UV irradiation at total TCE conversion promotes the CO(2) selectivity. The excess of energy arriving to the reactor favours the direct reaction pathway to produce CO(2). The photonic efficiency, calculated as a function of the rate of CO(2) formation, decreases linearly with the solar irradiance up to around 2 mW cm(-2), where it becomes constant. For decontamination systems high TCE conversion is pursuit and then high solar irradiance values are required, in spite of lower photonic efficiency values. The present photocatalyst configuration, with only 17% of the reactor volume filled with the photoactive material, allows total TCE conversion for 150 ppm and 1 L min(-1) in a wide sun irradiance window from 2 to 4 mW cm(-2). The incorporation of water vapour leads to an increase of the CO(2) selectivity keeping the TCE conversion around 90%, although significant amounts of COCl(2) were observed. (c) 2010 Elsevier B.V. All rights reserved.

LASER-TESTING RIG : Measurement System for evaluation of Shape of concentrating reflector for solar collector Absolicon X10

This Thesis project is a part of the all-round automation of production of concentrating solar PV/T systems Absolicon X10. ABSOLICON Solar Concentrator AB has been invented and started production of the prospective solar concentrated system Absolicon X10. The aims of this Thesis project are designing, assembling, calibrating and putting in operation the automatic measurement system intended to evaluate the shape of concentrating parabolic reflectors.On the basis of the requirements of the company administration and needs of real production process the operation conditions for the Laser testing rig were formulated. The basic concept to use laser radiation was defined.At the first step, the complex design of the whole system was made and division on the parts was defined. After the preliminary conducted simulations the function and operation conditions of the all parts were formulated.At the next steps, the detailed design of all the parts was conducted. Most components were ordered from respective companies. Some of the mechanical components were made in the workshop of the company. All parts of the Laser-testing rig were assembled and tested. Software part, which controls the Laser-testing rig work, was created on the LabVIEW basis. To tune and test software part the special simulator was designed and assembled.When all parts were assembled in the complete system, the Laser-testing rig was tested, calibrated and tuned.In the workshop of Absolicon AB, the trial measurements were conducted and Laser-testing rig was installed in the production line at the plant in Soleftea.

Universal Experimental Measurement System «Sun-Walker» : Automotive measurement system for the evaluation of the solar irradiation distribution for the tests of the solar concentrated systems.

This Thesis project is a part of the research conducted in Solar industry. ABSOLICON Solar Concentrator AB has invented and started production of the prospective solar concentrated system Absolicon X10. The aims of this Thesis project are designing, assembling, calibrating and putting in operation the automatic measurement system intended to evaluate distribution of density of solar radiation in the focal line of the concentrated parabolic reflectors and to measure radiation from the artificial source of light being a calibration-testing tool.On the basis of the requirements of the company’s administration and needs of designing the concentrated reflectors the operation conditions for the Sun-Walker were formulated. As the first step, the complex design of the whole system was made and division on the parts was specified. After the preliminary conducted simulation of the functions and operation conditions of the all parts were formulated.As the next steps, the detailed design of all the parts was made. Most components were ordered from respective companies. Some of the mechanical components were made in the workshop of the company. All parts of the Sun-Walker were assembled and tested. The software part, which controls the Sun-Walker work and conducts measurements of solar irradiation, was created on the LabVIEW basis. To tune and test the software part, the special simulator was designed and assembled.When all parts were assembled in the complete system, the Sun-Walker was tested, calibrated and tuned.

Experimental performance of a string module in a CPC reflector cavity

The purpose of the work is to develop a cost effective semistationary CPC concentrator for a string PV-module. A novel method of using annual irradiation distribution diagram projected in a north-south vertical plane is developed. This method allows us easily to determine the optimum acceptance angle of the concentrator and the required number of annual tilts. Concentration ranges of 2-5x are investigated with corresponding acceptance angles between 5 and 15°. The concentrator should be tilted 2-6 times per year. Experiments has been performed on a string module of 10 cells connected in a series and equipped with a compound parabolic concentrator with C = 3.3X. Measurement show that the output will increase with a factor of 2-2.5 for the concentrator module, compared to a reference module without concentrator. If very cheap aluminium reflectors are used the costs for the PV-module can be decreased nearly by a factor of two.

Techno-economic Appraisal of Concentrating Solar Power Systems (CSP)

The diffusion of Concentrating Solar Power Systems (CSP) systems is currently taking place at a much slower pace than photovoltaic (PV) power systems. This is mainly because of the higher present cost of the solar thermal power plants, but also for the time that is needed in order to build them. Though economic attractiveness of different Concentrating technologies varies, still PV power dominates the market. The price of CSP is expected to drop significantly in the near future and wide spread installation of them will follow. The main aim of this project is the creation of different relevant case studies on solar thermal power generation and a comparison betwwen them. The purpose of this detailed comparison is the techno-economic appraisal of a number of CSP systems and the understanding of their behaviour under various boundary conditions. The CSP technologies which will be examined are the Parabolic Trough, the Molten Salt Power Tower, the Linear Fresnel Mirrors and the Dish Stirling. These systems will be appropriatly sized and simulated. All of the simulations aim in the optimization of the particular system. This includes two main issues. The first is the achievement of the lowest possible levelized cost of electricity and the second is the maximization of the annual energy output (kWh). The project also aims in the specification of these factors which affect more the results and more specifically, in what they contribute to the cost reduction or the power generation. Also, photovoltaic systems will be simulated under same boundary conditions to facolitate a comparison between the PV and the CSP systems. Last but not leats, there will be a determination of the system which performs better in each case study.

Defining Relevant Product Markets for Pharmaceuticals

To identify the relevant product markets for Swedish pharmaceuticals, a spatial econometrics approach is employed. First, we calculate Moran’s Is for different market definitions and then we use a spatial Durbin model to determine the effect of price changes on quantity sold off own and competing products. As expected, the results show that competition is strongest between close substitutes; however, the relevant product markets for Swedish pharmaceuticals extend beyond close substitutes down to products included in the same class on the four-digit level of the Anatomic Therapeutic Chemical system as defined by the World Health Organization. The spatial regression model further indicates that increases in the price of a product significantly lower the quantity sold of that product and in the same time increase the quantity sold of competing products. For close substitutes (products belonging to the same class on the seven-digit level of the Anatomic Therapeutic Chemical system), as well as for products that, without being close substitutes, belong to the same therapeutic/pharmacological/chemical subgroup (the same class on the five-digit level of the Anatomic Therapeutic Chemical system), a significant change towards increased competition is also visible after 1 July 2009 when the latest policy changes with regards to pharmaceuticals have been implemented in Sweden.