A Proof of Tarski’s Fixed Point Theorem by Application of Galois Connections

Two examples of Galois connections and their dual forms are considered. One of them is applied to formulate a criterion when a given subset of a complete lattice forms a complete lattice. The second, closely related to the first, is used to prove in a short way the Knaster-Tarski’s fixed point theore

An Integrated Tracker for STAR

The STAR experiment at the Relativistic Heavy Ion Collider RHIC studies the new state of matter produced in relativistic heavy ion collisions and the spin structure of the nucleon in collisions of polarized protons. In order to improve the capabilities for heavy flavor measurements and the reconstruction of charged vector bosons an upgrade of the tracking system both in the central and the forward region is pursued. The integrated system providing high resolution tracking and secondary vertex reconstruction capabilities will use silicon pixel, strip and GEM technology.Comment: 4 pages, 2 figures, to be published in the Proceedings of the 9th Conference on the Intersections of Particle and Nuclear Physics (CIPANP 2006), Rio Grande, Puerto Rico, May 30 - June 3, 200

Inclusive Hadron Production in p+p Collisions at STAR

The STAR experiment at RHIC has measured a variety of inclusive hadron cross sections in $p+p$ collisions at Sqrt(s) = 200 GeV. Measurements of the differential cross section for inclusive charged pion production at mid rapidity and for inclusive neutral pion production at forward rapidity (3.0 < eta < 4.2) as well as the first preliminary result from STAR for the differential cross section for inclusive neutral pion production near mid rapidity are presented. These cross sections are compared to next-to-leading order perturbative QCD calculations and can provide constraints on the pion fragmentation functions. Good agreement between data and pQCD has been found for all three cross sections.Comment: 4 pages, 1 figure, to be published in the Proceedings of the 9th Conference on the Intersections of Particle and Nuclear Physics (CIPANP 2006), Rio Grande, Puerto Rico, May 30 - June 3, 2006, v2 with updated reference

Towards a generalisation of formal concept analysis for data mining purposes

In this paper we justify the need for a generalisation of Formal Concept Analysis for the purpose of data mining and begin the synthesis of such theory. For that purpose, we first review semirings and semimodules over semirings as the appropriate objects to use in abstracting the Boolean algebra and the notion of extents and intents, respectively. We later bring to bear powerful theorems developed in the field of linear algebra over idempotent semimodules to try to build a Fundamental Theorem for K-Formal Concept Analysis, where K is a type of idempotent semiring. Finally, we try to put Formal Concept Analysis in new perspective by considering it as a concrete instance of the theory developed

A reduced actuation mecanum wheel platform for pipe inspection

This paper focuses on the design, development and assessment of a novel, 2 degrees-of-freedom magnetic pipe inspection robot. It consists of 4 mecanum wheels, with the diagonals functionally coupled and the system rotation constrained by the surface geometry, maintaining full translational mobility with reduced control and actuation requirements. The system uses positional encoding that is decoupled from the transmission system to overcome the main sources of positional/positioning errors when using mecanum wheels. The kinematic and dynamic models of the system are derived and integrated within the controller. The prototype robot is then tested and shown to follow a scan path at 20mm/s within ±1.5mm whilst correcting for gravitational drift and slip events

Some studies on the formation and interconversion of iron-sulfur nitrosyl complexes

Studies on the effect of substituting iron(III) for iron(II) or nitrate for nitrite in the reaction of cysteine with iron(II) salts and nitrite with and without sodium ascorbate present demonstrated the formation of the tetranuclear Na[Fe₄S₃(NO)₇] complex when iron(III) is substituted for iron(II), albeit in smaller yield; but no iron-sulfur-nitrosyl clusters were detected when nitrite was replaced with nitrate. Similarly in the case of reaction of methionine with iron(II) salts and nitrite in the presence of sodium ascorbate, the dinuclear complex Fe₂(SMe)₂(NO)₄ is formed in reduced yield when iron(III) is substituted for iron(II) and no iron-sulfur-nitrosyl complexes are detected when nitrite is replaced with nitrate. The effect of pH on the reactions of cysteine and methionine with iron(II) salts and nitrate, with and without sodium ascorbate present in the case of cysteine, were studied. The cysteine reactions showed that in the presence of sodium ascorbate, the yield of Na[Fe₄S₃(NO)₇] fell slightly as pH was decreased due to formation of the less soluble ascorbic acid from acidification of sodium ascorbate. At very low pH both cysteine reactions with and without sodium ascorbate present did not yield Na[Fe₄S₃(NO)₇] due to the formation of nitric oxide from nitrite, which would rapidly oxidise to give nitrogen dioxide, and to the instability of the Na[Fe₄S₃(NO)₇] complex itself at very low pH. The dinuclear complex Fe₂(SMe)₂(NO)₄ is very stable to conditions of low pH but its formation at very acidic conditions was hindered, again due to the formation of nitric oxide from nitrite. A range of iron-sulfur containing amino acid complexes of the general type [Fe₃o(amino acid)₆(H₂0)₃]X₇, were synthesised and their reactions with nitrite studied. In the presence of sodium ascorbate, when the amino acid is methylcysteine, both [Fe₄S₃(NO)₇]' and Fe₂(SMe)₂(NO)₄ were isolated after reaction with nitrite. However no identified iron-sulfur-nitrosyl complexes could be detected when the amino acid was methionine. In the absence of sodium ascorbate both the methylcysteine and methionine complexes yielded a range of unidentified complexes which infra-red spectroscopy demonstrated absorbed strongly in the nitrosyl stretching region and it was postulated that the species observed were inorganic nitrosyl complexes. FTIR analysis of Fe₄S₄(NO)₄ in the polar coordinating solvents THF, DMF and DMSO demonstrated conversion to [Fe₄S₃(NO)₇]⁻. No such conversion was observed using the solvents diethyl ether or dichloromethane. An intermediate species was observed in THF and DMSO using FTIR spectroscopy which was postulated to be a [Fe(solvent)₆][Fe₄S₄(NO)₄]₂ complex. Another peak observed in the latter stages of the conversion was believed to be that of a dinuclear Fe(SR)₂(NO)₄ type complex. ESR analysis of Fe₄S₄(NO)₄ in THF and DMSO however demonstrated formation of a mononuclear species of type [Fe(NO)₂(X)₂]ⁿ⁺. Thus in the dilute solutions required for ESR analysis, mononuclear species of the type [Fe₂(NO)₂(X)₂]ⁿ⁺ are favoured but in the more concentrated solutions needed for FTIR analysis polynuclear species of the type [Fe₄S₄(NO)₄] are predominant

An exactly solvable coarse-grained model for species diversity

We present novel analytical results about ecosystem species diversity that stem from a proposed coarse grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing both theoretical results of ecological neutral theory and empirical evidence on species diversity preservation. Neutral model of biodiversity deals with ecosystems in the same trophic level where per-capita vital rates are assumed to be species-independent. Close-form analytical solutions for neutral theory are obtained within a coarse-grained model, where the only input is the species persistence time distribution. Our results pertain: the probability distribution function of the number of species in the ecosystem both in transient and stationary states; the n-points connected time correlation function; and the survival probability, definned as the distribution of time-spans to local extinction for a species randomly sampled from the community. Analytical predictions are also tested on empirical data from a estuarine fish ecosystem. We find that emerging properties of the ecosystem are very robust and do not depend on specific details of the model, with implications on biodiversity and conservation biology.Comment: 20 pages, 4 figures. To appear in Journal of Statistichal Mechanic

Oscillatory oblique stagnation-point flow toward a plane wall

Two-dimensional oscillatory oblique stagnation-point flow toward a plane wall is investigated. The problem is a eneralisation of the steady oblique stagnation-point flow examined by previous workers. Far from the wall, the flow is composed of an irrotational orthogonal stagnation-point flow with a time-periodic strength, a simple shear flow of constant vorticity, and a time-periodic uniform stream. An exact solution of the Navier-Stokes equations is sought for which the flow streamfunction depends linearly on the coordinate parallel to the wall. The problem formulation reduces to a coupled pair of partial differential equations in time and one spatial variable. The first equation describes the oscillatory orthogonal stagnation-point flow discussed by previous workers. The second equation, which couples to the first, describes the oblique component of the flow. A description of the flow velocity field, the instantaneous streamlines, and the particle paths is sought through numerical solutions of the governing equations and via asymptotic analysis