Local homology and dimensional full-valuedness

A natural criterion for dimensional full-valuedness of locally compact spaces with finitely generated local homology is given.     

The π-π-theorem for manifold pairs with boundaries

The surgery obstruction of a normal map to a simple Poincaré pair (X, Y) lies in the relative surgery obstruction group L _*(π ₁(Y) → π ₁(X)). A well-known result of Wall, the so-called π-π-theorem, states that in higher dimensions a normal map of a manifold with boundary to a simple Poincaré pair with π ₁(X) ? π ₁(Y) is normally bordant to a simple homotopy equivalence of pairs. In order to study normal maps to a manifold with a submanifold, Wall introduced the surgery obstruction groups LP _* for manifold pairs and splitting obstruction groups LS _*. In the present paper, we formulate and prove for manifold pairs with boundary results similar to the π-π-theorem. We give direct geometric proofs, which are based on the original statements of Wall’s results and apply obtained results to investigate surgery on filtered manifolds.     

On the distribution of the number of retrials

We consider queuing systems where customers are not allowed to queue, instead of that they make repeated attempts, or retrials, in order to enter service after some time. We obtain the distribution of the number of retrials produced by a tagged customer, until he finds an available server.     

Synthesis of high-purity α- and β-PbO and possible applications to synthesis and processing of other lead oxide materials

Litharge, the red tetragonal form of lead oxide α-PbO and massicot, the yellow orthorhombic form β-PbO, are synthesized from lead(II) salts in aqueous media at elevated temperatures. Scanning electron microscopy (SEM) and X-ray diffraction (XRD) were used to characterize the size, morphology, and crystallographic structural forms of the products. The role of impurities in the experimental synthesis of the materials and microstructural variations in the final products are described. The implications of these observations regarding the synthesis of different conducting lead oxides and other related materials are discussed. PACS 71.20.Ps; 72.80.Jc; 74.62.Bf; 74.62.Dh; 75.50.Tt     

Existence Results for Semilinear Neutral Functional Differential Inclusions via Analytic Semigroups

In this paper we prove existence results for semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families.      

Stored energy release behaviour of disordered carbon

The use of graphite as a moderator in a low temperature thermal nuclear reactor is restricted due to accumulation of energy caused by displacement of atoms by neutrons and high energetic particles. Thermal transients may lead to a release of stored energy that may raise the temperature of the fuel clad above the design limit. Disordered carbon is thought to be an alternative choice for this purpose. Two types of disordered carbon composites, namely, CB (made up of 15 wt. % carbon black dispersed in carbonized phenolic resin) and PAN (made up of 20 vol. % chopped polyacrylonitrile carbon fibre dispersed in carbonized phenolic resin matrix) have been irradiated with 145 MeV Ne⁶⁺ ions at three fluence levels of 1.0×10¹³, 5.0×10¹³ and 1.5×10¹⁴ Ne⁶⁺/cm², respectively. The XRD patterns revealed that both the samples remained disordered even after irradiation. The maximum release of stored energy for CB was 212 J/g and that of PAN was 906 J/g. For CB, the release of stored energy was a first order reaction with activation energy of 2.79 eV and a frequency factor of 3.72×10²⁸ per second. 13% of the defects got annealed by heating up to 700 °C. PAN showed a third-order release rate with activation energy of 1.69 eV and a frequency factor of 1.77×10¹⁴ per second. 56% of the total defects got annealed by heating it up to 700 °C. CB seems to be the better choice than PAN as it showed less energy release with a slower rate. PACS 61.80.Jh; 61.80.-x; 61.43Er; 61.43.-j; 68.43.Vx     

Dynamic programming in cricket: optimizing batting order for a sticky wicket

In cricket, a rain-affected pitch can make batting more difficult than normal. Several other conditions such as poor light or an initially lively pitch, may also result in difficulties for the batsmen. In this note, we refer to all of them as ‘sticky wickets’. On sticky wickets, lower order batsmen are often sent into ‘hold the fort’ until conditions improve. In this paper, a stochastic dynamic programming model is used to examine the appropriateness of this policy. The model suggests that the tactic is often optimal when the sticky wicket persists until the end of the day's play, but not often when the sticky wicket is transitory. In some circumstances, it is worthwhile, on a normal wicket near the end of the day, to send in a lower order batsman to hold the fort (a night watchman): when the wicket is sticky, this tactic is even more worthwhile.