Generalized green operator for an impulsive boundary-value problem with switchings

We establish constructive existence conditions and construct a generalized Green operator for the construction of solutions of a Noetherian linear boundary-value problem for a system of ordinary differential equations with switchings and pulse action in critical and noncritical cases. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 1, pp. 51–65, January–March, 2007.     

Products of residue currents of Cauchy–Fantappiè–Leray type

With a given holomorphic section of a Hermitian vector bundle, one can associate a residue current by means of Cauchy–Fantappiè–Leray type formulas. In this paper we define products of such residue currents. We prove that, in the case of a complete intersection, the product of the residue currents of a tuple of sections coincides with the residue current of the direct sum of the sections.     

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.     

An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings

In this paper,we will establish several strong convergence theorems for the approximation ofcommon fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banachspaces using the modiied implicit iteration sequence with errors,and prove the necessary and sufficient conditionsfor the convergence of the sequence.Our results generalize,extend and improve the recent work,in thistopic.     

A Penrose-like inequality for maximal asymptotically flat spin initial data sets

We prove a Penrose-like inequality for the mass of a large class of constant mean curvature (CMC) asymptotically flat n-dimensional spin manifolds which satisfy the dominant energy condition and have a future converging, or past converging compact and connected boundary of non-positive mean curvature and of positive Yamabe invariant. We prove that for every n ≥ 3 the mass is bounded from below by an expression involving the norm of the linear momentum, the volume of the boundary, dimensionless geometric constants and some normalized Sobolev ratio.     

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     

Artificial time integration

Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be “close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought. In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency. AMS subject classification (2000)  65L05, 65M32, 65N21, 65N22, 65D18     

Estimation of the convergence rate in a transfer theorem for centered random sums

Estimates of the convergence rate in a transfer theorem for random sums centered by constants are presented. The estimates are obtained as a consequence of the estimates of the stability of the distributions of the sums represented in the form of special mixtures to small variations in the mixing and miscible distributions.     

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