Plancherel–Rotach Asymptotic Expansion for Some Polynomials from Indeterminate Moment Problems

We study the Plancherel–Rotach asymptotics of four families of orthogonal polynomials: the Chen–Ismail polynomials, the Berg–Letessier–Valent polynomials, and the Conrad–Flajolet polynomials I and II. All these polynomials arise in indeterminate moment problems, and three of them are birth and death process polynomials with cubic or quartic rates. We employ a difference equation asymptotic technique due to Z. Wang and R. Wong. Our analysis leads to a conjecture about large degree behavior of polynomials orthogonal with respect to solutions of indeterminate moment problems.     

An Explicit Solution with Correctors for the Green–Naghdi Equations

In this paper, the water waves problem for uneven bottoms in a highly nonlinear regime is studied. It is well known that, for such regimes, a generalization of the Boussinesq equations called the Green–Naghdi equations can be derived and justified when the bottom is variable (Lannes and Bonneton in Phys Fluids 21, 2009). Moreover, the Green–Naghdi and Boussinesq equations are fully nonlinear and dispersive systems. We derive here new linear asymptotic models of the Green–Naghdi and Boussinesq equations so that they have the same accuracy as the standard equations. We solve explicitly the new linear models and numerically validate the results.     

A one-dimensional plume plasma expansion: Self-similar approach

The expansion of a plasma induced by laser ablation is investigated using a single-fluid model combined with Saha?s equation. The space coordinates x and time t are combined to a one self-similar variable ξ=x/(ct). To obtain ordinary differential equations, two different transformations for the density are used. The density profiles during the expansion are found to be completely different, one corresponds to the common results i.e., the density decreases monotonically with ξ, while with the second transformation, the profile shows a density increasing for certain interval of the self-similar variable. This effect is enhanced with higher initial ionization fraction. The role of the initial velocity which corresponds to the start of the expansion from an unperturbed plasma or from an expansion already going on is pointed out.     

DSC study of the kinetic parameters of the metastable phases formation during non-isothermal annealing of an Al–Si–Mg alloy

Kinetics of β″ and β′ precipitations in an AlSiMg have been studied under non-isothermal conditions using differential scanning calorimetry (DSC) technique. The variation of the activation energy as a function of transformed fraction is determined using two isoconversional methods of Kissinger–Akahira–Sunose (KAS) and Friedman. The results obtained using the two methods show a change in the activation energy for both metastable phases precipitations as a function of transformed fraction. The results obtained from KAS method as compared with those obtained from Friedman method, show some major disagreements between the two methods. The growth exponent, determined by Ozawa method, decreases as a function of temperature for both phases.     

Dynamic Scheduling on a Single Batch Processing Machine with Split Compatibility Graphs

We consider the problem of minimizing the makespan on a batch processing machine, in which jobs are not all compatible. Only compatible jobs can be included into the same batch. This relation of compatibility is represented by a split graph. Jobs have release dates. The capacity of the batch processing machine is finite or infinite. The processing time of a batch is given by the processing time of the longest job in the batch. We establish the NP-hardness of the general problem and present polynomial algorithms for several special cases. Relating scheduling theory and graph theory appears to be an interesting and important concept.     

Performance of Low Earth Orbit Satellite Systems with Coding

The effect of block, convolutional and Turbo coding on the probability of error and the capacity are investigated for CDMA Low Earth Orbit (LEO) Satellite systems. The model employed assumes a contaminated Gaussian traffic model to be more compatible with different population areas. The conventional Gaussian distribution can be considered as a special case.     

Forced convection from a microstructure on a flat plate

In this work, a cooling of a flat microelectronic structure with single-phase forced convection is investigated. The axial conduction, usually neglected in boundary layer theory, is considered here since the length of the heated element is in the same order of magnitude as the thickness of the boundary layer. The microstructure represents a package of chips mounted flush with the surface of the plate, and uniformly heated with a constant heat flux. The differential method is used to reduce the governing partial differential equations to ordinary differential ones, which are solved numerically by the use of a computational code developed by the authors. This code is based on Keller–Box method. The temperature profiles and Nusselt numbers are plotted at several locations on the heated element and are given as functions of the Reynolds number at the beginning of heated microstructure and of the ratio of unheated to heated length. Furthermore, the average Nusselt numbers on the heated length are computed for Prandtl numbers in the range 0.7≤Pr≤7,000. The results are compared to the boundary layer solution of unheated starting length problem. The results will be used as a baseline for successively more complex situations of cooling in electronics.     

On formulas of Ramanujan and Evans

We give short elementary proofs of a formula of Ramanujan as interpreted by Bradley, and a companion formula originally proved by W. Chu. We also give an elementary proof of a generalization of an identity originally proved using modular functions and used to study a generating function for the number of partitions with specified crank. Research partially supported by NSF grant DMS 99-70865. 2000 Mathematics Subject Classification Primary—39A70, 11P83; Secondary—33C20     

Additive preservers of Drazin invertible operators with bounded index

Let B(X) be the algebra of all bounded linear operators on an infinite-dimensional complex or real Banach space X. Given an integer n ≥ 1, we show that an additive surjective map Φ on B(X)preserves Drazin invertible operators of index non-greater than n in both directions if and only if Φ is either of the form Φ(T) = αATA~(-1) or of the form Φ(T) = αBT~*B~(-1) where α is a non-zero scalar,A:X → X and B:X~*→ X are two bounded invertible linear or conjugate linear operators.