On computing rational Gauss-Chebyshev quadrature formulas

We provide an algorithm to compute the nodes and weights for Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary real poles outside . Contrary to existing rational quadrature formulas, the computational effort is very low, even for extremely high degrees, and under certain conditions on the poles it can be shown that the complexity is of order . This method is based on the derivation of explicit expressions for Chebyshev orthogonal rational functions, which are (thus far) the only examples of explicitly known orthogonal rational functions on with arbitrary real poles outside this interval.

     

A curved no-slip boundary condition for the lattice Boltzmann method

We present a generalization of the no-slip boundary condition by Lätt et al. [J. Lätt, B. Chopard, O. Malaspinas, M. Deville, A. Michler, Straight velocity boundaries in the lattice Boltzmann method, Physical Review E 77 (5) (2008) 056703] from straight to curved geometries for the lattice Boltzmann Bhatnager–Gross–Krook method (LBGK). The boundary condition is based on a reconstruction of the populations from the density, velocity and rate of strain. For curved boundaries, the reconstruction reduces the question of accuracy to a technical issue of interpolation. We present a method of interpolation allowing a very accurate representation of the curved boundary. The resulting boundary condition is verified for three different test cases: Taylor–Couette flow in-between rotating cylinders, laminar flow around a cylinder and flow past an impulsively started cylinder, demonstrating its second order accuracy and low error constant. The present boundary is stable for relaxation frequencies close to two.     

Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service

Whereas the buffer content of batch-service queueing systems has been studied extensively, the customer delay has only occasionally been studied. The few papers concerning the customer delay share the common feature that only the moments are calculated explicitly. In addition, none of these surveys consider models including the combination of batch arrivals and a server operating under the full-batch service policy (the server waits to initiate service until he can serve at full capacity). In this paper, we aim for a complete characterisation—i.e., moments and tail probabilities - of the customer delay in a discrete-time queueing system with batch arrivals and a batch server adopting the full-batch service policy. In addition, we demonstrate that the distribution of the number of customer arrivals in an arbitrary slot has a significant impact on the moments and the tail probabilities of the customer delay.     

Delay analysis of two batch-service queueing models with batch arrivals: Geo X /Geo c /1

In this paper, we compute the probability generating functions (PGF’s) of the customer delay for two batch-service queueing models with batch arrivals. In the first model, the available server starts a new service whenever the system is not empty (without waiting to fill the capacity), while the server waits until he can serve at full capacity in the second model. Moments can then be obtained from these PGF’s, through which we study and compare both systems. We pay special attention to the influence of the distribution of the arrival batch sizes. The main observation is that the difference between the two policies depends highly on this distribution. Another conclusion is that the results are considerably different as compared to Bernoulli (single) arrivals, which are frequently considered in the literature. This demonstrates the necessity of modeling the arrivals as batches.     

A semi-preemptive priority scheduling discipline: Performance analysis

In this paper, we present an in-depth analytical study of a semi-preemptive priority scheduling discipline. This discipline eliminates the deficits of both the full- and non-preemptive versions. Under the non-preemptive category, in particular, higher-priority customers may have to wait even when the service of a lower-priority customer has just started, while under the full-preemptive discipline, the almost completed service of a lower-priority customer may be interrupted due to the arrival of higher-priority customers, possibly causing a large extra delay. For fixed low-priority service times, the semi-preemptive priority scheduling discipline shows a performance gain of up to 6% compared to the full- and non-preemptive versions.     

Bacillus licheniformis peptidoglycan characterization by CZE–MS: Assessment with the benchmark RP‐HPLC‐MS method

Peptidoglycan or murein is an essential polymer found in bacterial cell wall. It is a dynamic structure that is continuously remodeled or modified during bacterial cell growth or in presence of cell wall stresses. These modifications are still poorly understood mainly due to the peptidoglycan, which is rather non‐soluble, and the difficulties to separate the hydrophilic glycopeptides (muropeptides) by reversed phase liquid chromatography, generated by the enzymatic digestion using mutanolysin, an N‐acetyl‐muramidase, cleaving the β_1→4 bound between N‐acetylglucosamine and N‐acetylmuramic acid. Here, we report the use of CZE–MS for an easy and fast screening of muropeptides generated by the action of muramidase on the Bacillus licheniformis cell wall. Electron transfer and CID–MS were also used to unambiguously identify and localize the presence or the absence of amidation and acetylation moieties on muropeptide variants. The reference method to analyse muropeptides by reversed phase chromatography was also tested and the advantages and disadvantages of both methods were evaluated.     

Strong Exchange Couplings Drastically Slow Down Magnetization Relaxation in an Air‐Stable Cobalt(II)‐Radical Single‐Molecule Magnet (SMM)

The energy barrier leading to magnetic bistability in molecular clusters is determined by the magnetic anisotropy of the cluster constituents. By incorporating a highly anisotropic four‐coordinate cobalt(II) building block into a strongly coupled fully air‐ and moisture‐stable three‐spin system, it proved possible to suppress under‐barrier Raman processes leading to 350‐fold increase of magnetization relaxation time and pronounced hysteresis. Relaxation times of up to 9 hours at low temperatures were found.     

Reducing spatial data using an optimized regressive discrete Fourier series

With the development of optical measurement techniques it is possible to obtain vast amounts of data. In vibrometry applications in particular operational deflection shapes are often obtained with very high spatial resolution. Fortunately, many techniques exist to reduce (approximate) the measurement data. One of the most common techniques for evaluating optical measurement data is by means of a Fourier analysis. However, this technique suffers from what is known as leakage when a non-integer number of periods is considered. This gives rise to non-negligible errors, which will obviously hamper the accuracy of the synthesized shape. Another technique such as a discrete cosine transform, used in the widely spread -jpeg standard does not suffer these anomalies but can still prove erroneous at times. One of the more recent approaches is via a so-called regressive discrete Fourier series (introduced by Arruda) which suffers one disadvantage. The problem statement is nonlinear in the parameters and needs a priori information about the deflection shape. This can be resolved by using the optimized regressive discrete fourier series (ORDFS), introduced in this article, which uses a nonlinear least squares approach. In this article the method will be applied in particular to the reduction of data for laser vibrometer measurements performed on an inorganic phosphate cement (IPC) beam (1D), as well as on a car door (2D). The proposed technique will also be validated on simulations to illustrate the properties concerning compression ratio and synthesized mode shape error. The introduced method will be bench marked for compression ratio and synthesized deflection shape error with all prior mentioned techniques.