Variable sampling interval Shewhart control charts for monitoring the multivariate coefficient of variation

In many industrial manufacturing processes, the ratio of the variance to the mean of a quantity of interest is an important characteristic to ensure the quality of the processes. This ratio is called the coefficient of variation (CV). A lot of control charts have been designed for monitoring the CV of univariate quantity in the literature. However, the CV control charts for multivariate quantity have not received much attention yet. In this paper, we investigate a variable sampling interval (VSI) Shewhart control chart for monitoring multivariate CV. The time between two consecutive samples is allowed to vary according to the previous value of the multivariate CV, which will help the chart to detect the process shifts faster. The comparison with the fixed sampling interval Shewhart chart is implemented to highlight the advantage of the VSI method. Finally, an illustrative example is demonstrated on real data.     

Planar Hall effect in biosensor with a tilted angle of the cross-junction

A typical planar Hall effect (PHE) sensor junction consists of two Hall bars that the bars appear normal to each other and the junction can have the required four terminals for current and voltage measurements. We are now introducing a tilted angle of the cross-junction and studying the role of the PHE therein. The results show that although there is a tilted angle of the cross-junction, the PHE voltage is remained constant. The result is interpreted by assuming the sensor material with the behavior of a basic single domain structure under the external magnetic field reversals. The calculations of the model are found to be in good concurrence with the experimental results.     

On an Anisotropic Equation with Critical Exponent and Non-Standard Growth Condition

Using variational methods, we prove the existence of a nontrivial weak solution for the problem
{-∑i=1^Nδxi（｜δxiu｜pi-2δxiu）=λα（x）｜u｜q（x）-2u＋｜u｜p＊-2u,in Ω,
u=0 inδΩ,
where Ω R^N（N≥3） is a bounded domain with smooth boundary δΩ,2≤pi〈N,i=1,N,q：Ω→（1,p＊）is a continuous function, p＊ =N/∑i=1^N 1/pi-1 is the critical exponent for this class of problem, and λ is a parameter.     

Analysis of the mean squared derivative cost function

In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by‐product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory. Copyright © 2017 John Wiley & Sons, Ltd.     

Fixed point approach for weakly asymptotic stability of fractional differential inclusions involving impulsive effects

We prove the global solvability and weakly asymptotic stability for a semilinear fractional differential inclusion subject to impulsive effects by analyzing behavior of its solutions on the half-line. Our analysis is based on a fixed point principle for condensing multi-valued maps, which is employed for solution operator acting on the space of piecewise continuous functions. The obtained results will be applied to a lattice fractional differential system.     

Variational Bayes With Intractable Likelihood

Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes their use in many interesting situations such as in state--space models and in approximate Bayesian computation (ABC), where application of VB methods was previously impossible. This article extends the scope of application of VB to cases where the likelihood is intractable, but can be estimated unbiasedly. The proposed VB method therefore makes it possible to carry out Bayesian inference in many statistical applications, including state--space models and ABC. The method is generic in the sense that it can be applied to almost all statistical models without requiring too much model-based derivation, which is a drawback of many existing VB algorithms. We also show how the proposed method can be used to obtain highly accurate VB approximations of marginal posterior distributions. Supplementary material for this article is available online.     

Fast Li-Ion Conduction in Spinel-Structured Solids

Spinel-structured solids were studied to understand if fast Li⁺ ion conduction can be achieved with Li occupying multiple crystallographic sites of the structure to form a “Li-stuffed” spinel, and if the concept is applicable to prepare a high mixed electronic-ionic conductive, electrochemically active solid solution of the Li⁺ stuffed spinel with spinel-structured Li-ion battery electrodes. This could enable a single-phase fully solid electrode eliminating multi-phase interface incompatibility and impedance commonly observed in multi-phase solid electrolyte–cathode composites. Materials of composition Li_1.25M(III)_0.25TiO₄, M(III) = Cr or Al were prepared through solid-state methods. The room-temperature bulk Li⁺-ion conductivity is 1.63 × 10⁻⁴ S cm⁻¹ for the composition Li_1.25Cr_0.25Ti_1.5O₄. Addition of Li₃BO₃ (LBO) increases ionic and electronic conductivity reaching a bulk Li⁺ ion conductivity averaging 6.8 × 10⁻⁴ S cm⁻¹, a total Li-ion conductivity averaging 4.2 × 10⁻⁴ S cm⁻¹, and electronic conductivity averaging 3.8 × 10⁻⁴ S cm⁻¹ for the composition Li_1.25Cr_0.25Ti_1.5O₄ with 1 wt. % LBO. An electrochemically active solid solution of Li_1.25Cr_0.25Mn_1.5O₄ and LiNi_0.5Mn_1.5O₄ was prepared. This work proves that Li-stuffed spinels can achieve fast Li-ion conduction and that the concept is potentially useful to enable a single-phase fully solid electrode without interphase impedance.     

The Influence of Dopant Concentration on Optical-Electrical Features of Quantum Dot-Sensitized Solar Cell

In this study, TiO₂/CdS/Cd_xCu_1−xSe, TiO₂/CdS/Cd_xMn_1−xSe, and TiO₂/CdS/Cd_xAg_2−2xSe thin films were synthesized by chemical bath deposition for the fabrication of photoanode in quantum-dot-sensitized solar cells. As a result, the structural properties of the thin films have been studied by X-ray diffraction, which confirmed the zinc Blende structure in the samples. The optical films were researched by their experimental absorption spectra with different doping concentrations. Those results were combined with the Tauc correlation to estimate the absorption density, the band gap energy, valence band and conduction band positions, steepness parameter, and electron–phonon interaction. Furthermore, the electrical features, electrochemical impedance spectrum and photocurrent density curves were carried out. The result was used to explain the enhancing performance efficiency.     

Synthesis and properties of an ω,ω′-appended eighteen carbon chains hypericin derivative

Summary An ,-appended eighteen carbon chains hypercin derivative (2) was synthesized starting from emodin. The overall yield of the seven step synthesis was 12%. The¹H and¹³C NMR, absorption, and emission spectroscopic properties were measured;2 can be dissolved even in apolar solvents and polyethylene.

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Synthese und Eigenschaften eines mit C₁₈-Ketten ,-substituierten Hypericinderivats

Zusammenfassung Ein in den Positionen , mit zwei C₁₈-Ketten substituiertes Derivat des Hypericins (2) wurde ausgehend von Emodin synthetisiert. Die Gesamtausbeute der siebenstufigen Synthese betrug 12%. Die¹H- und¹³C-NMR, absorptions- und emissionsspektroskopischen Eigenschaften wurden gemessen;2 kann sogar in apolaren Lösungsmitteln und Polyethylen gelöst werden.