Expansions for the distribution and the maximum from distributions with an asymptotically gamma tail when a trend is present

We give expansions about the Gumbel distribution in inverse powers of n and log n for Mn, the maximum of a sample size n or n + 1 when the j-th observation is μ(j/n) + ej, μ is any smooth trend function and the residuals {ej } are independent and identically distributed with P(e r) ≈ exp(-δx)xd0∑∞k=1ckx-kβ as x →∞. We illustrate practical value of the expansions using simulated data sets.     

Generalized Cornish-Fisher expansions

Cornish-Fisher expansions about the normal distribution provide accurate approximations for distributions of estimates and also for the level in the nominal error of confidence intervals. However, there is an advantage is expanding about a skew distribution like the chi-square, since the first order approximations become second order if the skewness is matched. Higher order approximations are also simplified. We demonstrate the method by approximating the distribution of standardized and Studentized linear combinations of means.     

Recent Developments in Solid-Propellant Binders

Abstract

The complex and important role of the propellant binder in solid-propellant rockets is described. The severe weight problems of space exploratrion cause high propellant performance to be of major concern in a highly competitive field. Binders contribute to performance, not only in terms of fuel value, but by being compatible with energetic components and by providing good mechanical properties. Both sterilization required for planetary landings and compatibility problems of new energetic oxidizers generate new requirements too stringent for existing binders; only binders composed essentially of saturated aliphatic hydrocarbon are predicted to be suitable. Several saturated-binder developments are in progress. The achievements of one of these programs, based on free-radical synthesis, are evaluated against the goals of the new binder.     

Compact High-Order Finite Differences for Interface Problems in One Dimension

This paper is concerned with the construction and analysis ofcompact finite difference approximations to the model linearsource problem –(pu')' + qu = f where the functions p,q, and f can have jump discontinuities at a finite number ofpoints. Explicit formulae that give O(h²) O(h³) and O(h⁴) accuracyare derived, and a procedure for computing three-point schemesof any prescribed order of accuracy is presented. A rigoroustruncation and discretization error analysis is offered. Numericalresults are also given.     

Mechanistic insights into the 1,3-xylanases: useful enzymes for manipulation of algal biomass

Xylanases capable of degrading the crystalline microfibrils of 1,3-xylan that reinforce the cell walls of some red and siphonous green algae have not been well studied, yet they could prove to be of great utility in algaculture for the production of food and renewable chemical feedstocks. To gain a better mechanistic understanding of these enzymes, a suite of reagents was synthesized and evaluated as substrates and inhibitors of an endo-1,3-xylanase. With these reagents, a retaining mechanism was confirmed for the xylanase, its catalytic nucleophile identified, and the existence of -3 to +2 substrate-binding subsites demonstrated. Protein crystal X-ray diffraction methods provided a high resolution structure of a trapped covalent glycosyl-enzyme intermediate, indicating that the 1,3-xylanases likely utilize the (1)S(3) → (4)H(3) → (4)C(1) conformational itinerary to effect catalysis.     

Expansions about the Gamma for the Distribution and Quantiles of a Standard Estimate

We give expansions for the distribution, density, and quantiles of an estimate, building on results of Cornish, Fisher, Hill, Davis and the authors. The estimate is assumed to be non-lattice with the standard expansions for its cumulants. By expanding about a skew variable with matched skewness, one can drastically reduce the number of terms needed for a given level of accuracy. The building blocks generalize the Hermite polynomials. We demonstrate with expansions about the gamma.     

An anisotropic enhanced thermal conductivity approach for modelling laser melt pools for Ni-base super alloys

Ni-base super alloys are extensively used in high temperature gas turbine engines and energy industries. Due to the high replacement costs of these components, there are huge economic benefits of repairing these components. Laser direct metal deposition processes (LDMD) based on laser cladding, laser fusion welding, and laser surface melting are some of the processes which are used to repair these high value components. Precise control of these processes is important to achieve the desired microstructure, stress distribution, distortions due to thermal stresses and other important output variables. Modelling of these processes is therefore an extremely important activity for achieving any degree of control/optimisation. However, modelling of these processes is not straight-forward due to melt pool flows dominated by Marangoni and buoyancy driven convection. Detailed CFD models are required for accurate prediction of melt pool geometry. But these models are computationally expensive and require greater expertise. To simplify and speed up the modelling process, many researchers have used the isotropic enhanced thermal conductivity approach to account for melt pool convection. A recent study on mild steel has highlighted that isotropic enhanced thermal conductivity approach is not able to accurately predict the melt pool geometry. Based on these findings a new approach namely anisotropic enhanced thermal conductivity approach has been developed. This paper presents an analysis on the effectiveness of the isotropic and anisotropic enhanced thermal conductivity approaches for laser melting of Inconel 718 using numerical technique. Experimental melt pool geometry has been compared with modelling results. It has been found that the isotropic enhanced thermal conductivity approach is not able to accurately predict the melt pool geometry, whereas anisotropic enhanced thermal conductivity approach gives good agreement with the experimental results.