Analytic approximations of queues with lightly- and heavily-correlated autoregressive service times

We consider a single-server queueing system. The arrival process is modelled as a Poisson process while the service times of the consecutive customers constitute a sequence of autoregressive random variables. Our interest into autoregressive service times comes from the need to capture temporal correlation of the channel conditions on wireless network links. If these fluctuations are slow in comparison with the transmission times of the packets, transmission times of consecutive packets are correlated. Such correlation needs to be taken into account for an accurate performance assessment. By means of a transform approach, we obtain a functional equation for the joint transform of the queue content and the current service time at departure epochs in steady state. To the best of our knowledge, this functional equation cannot be solved by exact mathematical techniques, despite its simplicity. However, by means of a Taylor series expansion in the parameter of the autoregressive process, a “light-correlation” approximation is obtained for performance measures such as moments of the queue content and packet delay. We illustrate our approach by some numerical examples, thereby assessing the accuracy of our approximations by simulation. For the heavy correlation case, we give differential equation approximations based on the time-scale separation technique, and present numerical examples in support of this approximation.     

What makes mathematical word problem solving challenging? Exploring the roles of word problem characteristics,text comprehension,and arithmetic skills

ZDM – Mathematics Education - In this study we investigated word-problem (WP) item characteristics, individual differences in text comprehension and arithmetic skills, and their relations to...     

Interpreting technical evidence from spectral imaging of paintings by Édouard Manet in the Courtauld Gallery

The paintings by Édouard Manet in The Courtauld Gallery Déjeuner sur l'herbe (1863–68), Marguerite de Conflans en Toilette de Bal (1870–1880), Banks of the Seine at Argenteuil (1874), and A Bar at the Folies–Bergère (1882) were investigated for the first time using a range of non-invasive in situ analyses. The aims of the study were to investigate the painting techniques and materials used for this group of works and to critically evaluate the technical evidence derived from the integrated use of imaging techniques and portable spectroscopic methods in this context. The paintings were investigated by means of macro X-ray fluorescence (MA-XRF), reflection spectral imaging, portable UV–Vis–NIR spectroscopy, portable Raman spectroscopy, and reflection FTIR. MA-XRF and reflection spectral imaging allowed visualising elements in the compositions that were not visible using traditional methods of technical study. For example, MA-XRF analysis of Déjeuner sur l'herbe revealed elements of the development of the composition that provided new evidence to consider its relationship to other versions of the composition. The study also highlighted questions about the interpretation of elemental distribution maps and spectral images that did not correspond to the reworking visible in X-radiographs. For example, in A Bar at the Folies–Bergère Manet made numerous changes during painting, which were not clearly visualised with any of the techniques used. The research has wider implications for the study of Impressionist paintings, as the results will support technical studies of works by other artists of the period who used similar materials and painting methods.     

Metabolism of methylstenbolone studied with human liver microsomes and the uPA+/+‐SCID chimeric mouse model

Anti‐doping laboratories need to be aware of evolutions on the steroid market and elucidate steroid metabolism to identify markers of misuse. Owing to ethical considerations, in vivo and in vitro models are preferred to human excretion for nonpharmaceutical grade substances. In this study the chimeric mouse model and human liver microsomes (HLM) were used to elucidate the phase I metabolism of a new steroid product containing, according to the label, methylstenbolone. Analysis revealed the presence of both methylstenbolone and methasterone, a structurally closely related steroid. Via HPLC fraction collection, methylstenbolone was isolated and studied with both models. Using HLM, 10 mono‐hydroxylated derivatives (U1–U10) and a still unidentified derivative of methylstenbolone (U13) were detected. In chimeric mouse urine only di‐hydroxylated metabolites (U11–U12) were identified. Although closely related, neither methasterone nor its metabolites were detected after administration of isolated methylstenbolone. Administration of the steroid product resulted mainly in the detection of methasterone metabolites, which were similar to those already described in the literature. Methylstenbolone metabolites previously described were not detected. A GC‐MS/MS multiple reaction monitoring method was developed to detect methylstenbolone misuse. In one out of three samples, previously tested positive for methasterone, methylstenbolone and U13 were additionally detected, indicating the applicability of the method. Copyright © 2014 John Wiley & Sons, Ltd.     

Pitfalls in the experimental recording of ultrasonic (backscatter) polar scans for material characterization

The ultrasonic polar scan (UPS), either in transmission, reflection or backscatter mode, is a promising non-destructive testing technique for the characterization of composites, providing information about the mechanical anisotropy, the viscoelastic damping, the surface roughness, and more. At present, the technique is merely being used for qualitative purposes. The limited quantitative exploration and use of the technique can be primarily ascribed to limitations of current theoretical models as well as the difficulty to perform accurate, and more importantly, reproducible UPS experiments. Over the last years, we have identified several potential pitfalls in the experimental implementation of the technique which severely deteriorate the accurateness and reproducibility of a UPS. In this paper, we make an inventory of the most important difficulties, illustrate each of them by a real experiment and present a feasible mediation, either numerical or experimental in nature. Once the experimental set-up is fine-tuned to overcome these pitfalls, it is expected that the recording of high-level UPS experiments, in combination with numerical computations, will facilitate the technique to become a fully quantitative non-destructive characterization method.     

A Minimal Framework for Non-Commutative Quantum Mechanics

Deformation quantisation is applied to ordinary Quantum Mechanics by introducing the star product in a configuration space combining a Riemannian structure with a Poisson one. A Hilbert space compatible with such a configuration space is designed. The dynamics is expressed by a Hermitian Hamiltonian containing a scalar potential and a one-form potential. As a simple illustration, it is shown how a particular type of non-commutativity of the star product is interpretable as generating the Zeeman effect of ordinary Quantum Mechanics.     

Facile synthesis of novel indolo[3,2-b]carbazole derivatives and a chromogenic-sensing 5,12-dihydroindolo[3,2-b]carbazole

Novel indolo[3,2-b]carbazole derivatives and a chromogenic-sensing 5,12-dihydroindolo[3,2-b]carbazole have been synthesized starting from tetra-tert-butylated 6,12-diaryl-5,11-dihydroindolo[3,2-b]carbazoles, which were prepared via an efficient tert-butylation of 6,12-diaryl-5,11-dihydroindolo[3,2-b]carbazoles.     

Stop-and-return DSC method to study fat crystallization

Differential scanning calorimeters have frequently been used to study the isothermal crystallization kinetics of fats and oils. In some circumstances (e.g. start of crystallization during cooling to the crystallization temperature, crystallization in emulsion) this straightforward approach is not applicable. This paper describes an indirect DSC method for determination of the crystallization kinetics under these ‘difficult’ circumstances. The principle is to stop the crystallization at different moments during the isothermal crystallization and raise the sample temperature. The amount of heat released is then used as a measure for the amount of crystallization and plotted as function of time. Combination of the stop-and-return method with the direct method may sometimes be used to save on measurement time. Stop-and-return experiments can furthermore be used to gain more insight in the crystallization mechanism based on the fact that different polymorphic forms and fractions have different melting temperatures.