On A Simpler and Faster Derivation of Single Use Reliability Mean and Variance for Model-Based Statistical Testing

Markov chain usage-based statistical testing has proved sound and effective in providing audit trails of evidence in certifying software-intensive systems. The system end-toend reliability is derived analytically in closed form, following an arc-based Bayesian model. System reliability is represented by an important statistic called single use reliability, and defined as the probability of a randomly selected use being successful. This paper continues our earlier work on a simpler and faster derivation of the single use reliability mean, and proposes a new derivation of the single use reliability variance by applying a well-known theorem and eliminating the need to compute the second moments of arc failure probabilities. Our new results complete a new analysis that could be shown to be simpler, faster, and more direct while also rendering a more intuitive explanation. Our new theory is illustrated with three simple Markov chain usage models with manual derivations and experimental results

A Life Prediction Model of Multilayered PTH Based on Fatigue Mechanism.

Plated through hole (PTH) plays a critical role in printed circuit board (PCB) reliability. Thermal fatigue deformation of the PTH material is regarded as the primary factor affecting the lifetime of electrical devices. Numerous research efforts have focused on the failure mechanism model of PTH. However, most of the existing models were based on the one-dimensional structure hypothesis without taking the multilayered structure and external pad into consideration. In this paper, the constitutive relation of multilayered PTH is developed to establish the stress equation, and finite element analysis (FEA) is performed to locate the maximum stress and simulate the influence of the material properties. Finally, thermal cycle tests are conducted to verify the accuracy of the life prediction results. This model could be used in fatigue failure portable diagnosis and for life prediction of multilayered PCB

Descriptions of strongly multiplicity free representations for simple Lie algebras

Let $\mathfrak{g}$ be a simple Lie algebra over the complex numbers $\mathbb{C}$. Let $Z(\mathfrak{g})$ be the center of the universal enveloping algebra $U(\mathfrak{g})$. Denote by $V_\lambda$ the finite-dimensional simple $\mathfrak{g}$-module with highest weight $\lambda$. Lehrer and Zhang defined the notion of strongly multiplicity free representations for simple Lie algebras motivited by studying the structure of the endomorphism algebras $End _{ U(\mathfrak{g})}(V_\lambda^{\otimes r})$in terms of the quotients of Kohno's infinitesimal braid algebra. Kostant introduced the $\mathfrak{g}$ -invariant endomorphism algebras $R_\lambda= (End V_\lambda\otimes U(\mathfrak{g}))^\mathfrak{g}$ and $R_{\lambda,\pi}=(End V_\lambda\otimes \pi[U(\mathfrak{g})])^\mathfrak{g}.$ In this paper, we give some other criterion for a multiplicity free representation to be a strongly multiplicity free representation for simple Lie algebras by classifing the pairs $(\mathfrak{g}, V_\lambda)$, which are multiplicity free irreducible modules and for such pairs, $R_\lambda$ and $R_{\lambda,\pi}$ are generated by generalizations of the quadratic Casimimir elements of $Z(\mathfrak{g})$

Strongly Commuting Ring and The Prounet-Tarry-Escott Problem

In 1935, Wright conjectured that ideal solutions to the PTE problem in Diophantine number theory should exist. In this paper, we prove Wright's conjecture holds true based on the the representation theory of the minuscule strongly commuting ring introduced by Kostant in 1975 and the complex coefficient cohomology ring structures of the Grassmannian variey

Mesoporous SnO2 sensor prepared by carbon nanotubes as template and its sensing properties to indoor air pollutants

AbstractAn effort has been made to develop a kind of mesoporous SnO2 gas sensor for detecting indoor air pollutants such as ethanol, benzene, meta-xylene. Mesoporous SnO2 material has been prepared by sol-gel method joined into multiwall carbon nanotubes as template. The field emission scanning electron microscope (FSEM) was used to characterize the samples, by which the mesoporous structure of SnO2 was obviously observed. The investigation results suggest that the as-prepared mesoporous SnO2 has a good response and reversibility to indoor environmental air pollutants. At last, the selectivity of the mesoporous sensor was investigated