ON THE SUM OF THE FIRST n PRIMES

In this note, we show that the set of n such that the arithmeticmean of the first n primes is an integer is of asymptotic densityzero. We use the same method to show that the set of n suchthat the sum of the first n primes is a square is also of asymptoticdensity zero. We also prove that both the arithmetic mean ofthe first n primes as well as the square root of the sum ofthe first n primes are well distributed modulo 1.     

An approximation result for free discontinuity functionals by means of non‐local energies

We approximate, in the sense of Γ‐convergence, free discontinuity functionals with linear growth by a sequence of non‐local integral functionals depending on the average of the gradient on small balls. The result extends to a higher dimension what is already proved in (Ann. Mat. Pura Appl. 2007; 186 (4): 722–744), where there is the proof of the general one‐dimensional case, and in (ESAIM Control Optim. Calc. Var. 2007; 13 (1):135–162), where the n‐dimensional case with ?=Id is treated. Moreover, we investigate whether it is possible to approximate a given free discontinuity functional by means of non‐local energies. Copyright © 2008 John Wiley & Sons, Ltd.     

The Comparative and Concurrent Simulation of discrete-event experiments

Discrete-Event Simulation is a powerful, but underexploited alternative for many kinds of physical experimentation. It permits what is physically impossible or unaffordable, to conduct and run related experiments in parallel, against each other. Comparative and Concurrent Simulation (CCS) is a parallel experimentation method that adds a comparative dimension to discrete-event simulation. As a methodology or style, CCS resembles a many-pronged rake; its effectiveness is proportional to the number of prongs—the number of parallel experiments. It yields information in parallel and in time order, rather than in the arbitrary order of one-pronged serial simulations. CCS takes advantage of the similarities between parallel experiments via the one-for-many simulation of their identical parts; if many experiments are simulated, then it is normally hundreds to thousands times faster than serial simulation. While CCS is a one-dimensional method, a more general, multi-dimensional or multidomain version is MDCCS. MDCCS permits parent experiments to interact and produce offspring experiments, i.e., to produce more, but smaller experiments, and many zero-size/zero-cost experiments. MDCCS is more general, informative, and faster (usually over 100:1) than CCS for most applications. It handles more complex applications and experiments, such as multiple faults, variant executions of a software program, animation, and others.From a forthcoming book by E. Ulrich, V. Agrawal, and J. Arabian, and a Ph.D. thesis on MDCCS by K.P. Lentz, Northeastern University.     

Dense fluid displacement in wet porous media by spin relaxation selective contrast

Low field Magnetic Resonance Imaging is used to study oil diffusion in a wet soil model. A complete discrimination between oil and water has been obtained by using Inversion-Recovery pulse sequence. The time evolution of the oil image gives the parameters which describe the dense fluid diffusion rate in the whole space directions.     

Inter-cycle variation in whole-body vibration exposures of operators driving track-type loader machines

Whole-body vibration (WBV) measurements are an important aspect of performing risk assessments for those exposed to vibration. A large array of variables affect the outcome of a vibration measurement and its extrapolation to a daily dose measure: e.g. variability in driving style, road surface roughness, loading. The variability in vibration emission is an inherent property for most vibrating environments and there is a risk that a vibration measurement might not be representative of the long-term exposures. It is important to acknowledge the variation inherent to WBV exposure to help understand how this variation will affect health risk assessments. A field investigation was conducted in order to characterise the variation of WBV magnitudes between work cycles of track-type loaders. Six different track-type loaders were measured at four different work sites. The vibrations were measured at the operators seat in three translational axes (x-, y-, and z-axis) in accordance with ISO 2631-1 (1997). The findings indicate the worst axis of vibration for the track-type loaders was predominantly the fore-and-aft (x-axis), for most operations. The most severe emission values were measured for machine C at site 2 (1.12 ms⁻² rms) and machine D at site 2 (1.03 ms⁻² rms). These machines would exceed the action value of the Physical Agents (Vibration) Directive within 2 h of exposure. All of the machines measured would exceed the exposure action value of the Directive within an 8 h working period. The lateral (y-axis) produced the greatest amount of variability between work cycles (coefficient of variation up to 20%). It is concluded that the inherent variability between work cycles and tasks reinforces the requirement to perform a full task analysis prior to measuring WBV exposures to ensure that all tasks are measured and that adequate cycles are measured to obtain a reliable indication of the vibration emission.     

Do the molecules which form discotic liquid crystals have disc-like structures? The conformation of a simple model compound, 1,2-dihydroxydiacetylbenzene, determined from the NMR spectra of samples dissolved in liquid crystalline solvents

Many discotic mesogens are molecules with a central aromatic ring with adjacent alkylcarboxylate substituents. The simplest such molecule, 1,2-dihydroxydiacetylbenzene, which is not mesogenic, is studied by NMR spectroscopy as a solute in a nematic solvent. The spectra are analysed to give sets of residual dipolar couplings, D_ij , which are then used to test models for the conformation adopted by the acetate side groups. The conformations and geometry of an isolated molecule are calculated by the ab initio MP2/6-311G method and also by the DFT approach using the B3LYP functional with the 6-311++G** basis set. The quantum chemical calculations find that the minimum energy conformer has the acetate groups rotated in opposite directions out of the ring plane, and this kind of structure is also consistent with the NMR data.     

Neville elimination for rank-structured matrices

In this paper it is shown that Neville elimination is suited to exploit the rank structure of an order-r quasiseparable matrix A∈C^n×n by providing a condensed decomposition of A as product of unit bidiagonal matrices, all together specified by O(nr) parameters, at the cost of O(nr³) flops. An application of this result for eigenvalue computation of totally positive rank-structured matrices is also presented.