Random walks on finite lattice tubes

Exact results are obtained for random walks on finite lattice tubes with a single source and absorbing lattice sites at the ends. Explicit formulae are derived for the absorption probabilities at the ends and for the expectations that a random walk will visit a particular lattice site before being absorbed. Results are obtained for lattice tubes of arbitrary size and each of the regular lattice types; square, triangular and honeycomb. The results include an adjustable parameter to model the effects of strain, such as surface curvature, on the surface diffusion. Results for the triangular lattice tubes and the honeycomb lattice tubes model diffusion of adatoms on single walled zig-zag carbon nano-tubes with open ends.Comment: 22 pages, 4 figure

Comment on ``the Klein-Gordon Oscillator''

The different ways of description of the $S=0$ particle with oscillator-like interaction are considered. The results are in conformity with the previous paper of S. Bruce and P. Minning.Comment: LaTeX file, 5p

Maxwell - Chern - Simons topologically massive gauge fields in the first-order formalism

We find the canonical and Belinfante energy-momentum tensors and their nonzero traces. We note that the dilatation symmetry is broken and the divergence of the dilatation current is proportional to the topological mass of the gauge field. It was demonstrated that the gauge field possesses the `scale dimensionality' d=1/2. Maxwell - Chern - Simons topologically massive gauge field theory in 2+1 dimensions is formulated in the first-order formalism. It is shown that 6x6-matrices of the relativistic wave equation obey the Duffin - Kemmer - Petiau algebra. The Hermitianizing matrix of the relativistic wave equation is given. The projection operators extracting solutions of field equations for states with definite energy-momentum and spin are obtained. The 5x5-matrix Schrodinger form of the equation is derived after the exclusion of non-dynamical components, and the quantum-mechanical Hamiltonian is obtained. Projection operators extracting physical states in the Schrodinger picture are found.Comment: 18 pages, correction in Ref. [5

On Equivalence of Duffin-Kemmer-Petiau and Klein-Gordon Equations

A strict proof of equivalence between Duffin-Kemmer-Petiau (DKP) and Klein-Gordon (KG) theories is presented for physical S-matrix elements in the case of charged scalar particles interacting in minimal way with an external or quantized electromagnetic field. First, Hamiltonian canonical approach to DKP theory is developed in both component and matrix form. The theory is then quantized through the construction of the generating functional for Green functions (GF) and the physical matrix elements of S-matrix are proved to be relativistic invariants. The equivalence between both theories is then proved using the connection between GF and the elements of S-matrix, including the case of only many photons states, and for more general conditions - so called reduction formulas of Lehmann, Symanzik, Zimmermann.Comment: 23 pages, no figures, requires macro tcilate

PolyEDA: Combining Estimation of Distribution Algorithms and Linear Inequality Constraints

Algorithmus , Linearität , Ungleichhei

Teaching mathematics for search using a tutorial style of delivery

Understanding of mathematics is needed to underpin the process of search, either explicitly with Exact Match (Boolean logic, adjacency) or implicitly with Best match natural language search. In this paper we outline some pedagogical challenges in teaching mathematics for information retrieval (IR) to postgraduate information science students. The aim is to take these challenges either found by experience or in the literature, to identify both theoretical and practical ideas in order to improve the delivery of the material and positively affect the learning of the target audience by using a tutorial style of teaching. Results show that there is evidence to support the notion that a more pro-active style of teaching using tutorials yield benefits both in terms of assessment results and student satisfaction

Spin 1 fields in Riemann-Cartan space-times "via" Duffin-Kemmer-Petiau theory

We consider massive spin 1 fields, in Riemann-Cartan space-times, described by Duffin-Kemmer-Petiau theory. We show that this approach induces a coupling between the spin 1 field and the space-time torsion which breaks the usual equivalence with the Proca theory, but that such equivalence is preserved in the context of the Teleparallel Equivalent of General Relativity.Comment: 8 pages, no figures, revtex. Dedicated to Professor Gerhard Wilhelm Bund on the occasion of his 70th birthday. To appear in Gen. Rel. Grav. Equations numbering corrected. References update

Kochen-Specker Vectors

We give a constructive and exhaustive definition of Kochen-Specker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in n-dim Hilbert space, H^n, n>3 to which it is impossible to assign 1s and 0s in such a way that no two mutually orthogonal vectors from the set are both assigned 1 and that not all mutually orthogonal vectors are assigned 0. Our constructive definition of such KS vectors is based on algorithms that generate MMP diagrams corresponding to blocks of orthogonal vectors in R^n, on algorithms that single out those diagrams on which algebraic 0-1 states cannot be defined, and on algorithms that solve nonlinear equations describing the orthogonalities of the vectors by means of statistically polynomially complex interval analysis and self-teaching programs. The algorithms are limited neither by the number of dimensions nor by the number of vectors. To demonstrate the power of the algorithms, all 4-dim KS vector systems containing up to 24 vectors were generated and described, all 3-dim vector systems containing up to 30 vectors were scanned, and several general properties of KS vectors were found.Comment: 19 pages, 6 figures, title changed, introduction thoroughly rewritten, n-dim rotation of KS vectors defined, original Kochen-Specker 192 (117) vector system translated into MMP diagram notation with a new graphical representation, results on Tkadlec's dual diagrams added, several other new results added, journal version: to be published in J. Phys. A, 38 (2005). Web page: http://m3k.grad.hr/pavici

Downregulation of Mcl-1 has anti-inflammatory pro-resolution effects and enhances bacterial clearance from the lung

Phagocytes not only coordinate acute inflammation and host defense at mucosal sites, but also contribute to tissue damage. Respiratory infection causes a globally significant disease burden and frequently progresses to acute respiratory distress syndrome, a devastating inflammatory condition characterized by neutrophil recruitment and accumulation of protein-rich edema fluid causing impaired lung function. We hypothesized that targeting the intracellular protein myeloid cell leukemia 1 (Mcl-1) by a cyclin-dependent kinase inhibitor (AT7519) or a flavone (wogonin) would accelerate neutrophil apoptosis and resolution of established inflammation, but without detriment to bacterial clearance. Mcl-1 loss induced human neutrophil apoptosis, but did not induce macrophage apoptosis nor impair phagocytosis of apoptotic neutrophils. Neutrophil-dominant inflammation was modelled in mice by either endotoxin or bacteria (Escherichia coli). Downregulating inflammatory cell Mcl-1 had anti-inflammatory, pro-resolution effects, shortening the resolution interval (R(i)) from 19 to 7 h and improved organ dysfunction with enhanced alveolar–capillary barrier integrity. Conversely, attenuating drug-induced Mcl-1 downregulation inhibited neutrophil apoptosis and delayed resolution of endotoxin-mediated lung inflammation. Importantly, manipulating lung inflammatory cell Mcl-1 also accelerated resolution of bacterial infection (R(i); 50 to 16 h) concurrent with enhanced bacterial clearance. Therefore, manipulating inflammatory cell Mcl-1 accelerates inflammation resolution without detriment to host defense against bacteria, and represents a target for treating infection-associated inflammation