The school bus routing problem: A review

This paper aims to provide a comprehensive review of the school bus routing problem (SBRP). SBRP seeks to plan an efficient schedule for a fleet of school buses where each bus picks up students from various bus stops and delivers them to their designated schools while satisfying various constraints such as the maximum capacity of a bus, the maximum riding time of a student in a bus, and the time window of a school. This class of problem consists of different sub-problems involving data preparation, bus stop selection, bus route generation, school bell time adjustment, and bus scheduling. In this paper, the various assumptions, constraints, and solution methods used in the literature on SBRP are summarized. A list of issues requiring further research is also presented.     

The KKM principle in abstract convex spaces: Equivalent formulations and applications

The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. A KKM space is an abstract convex space satisfying the partial KKM principle and its “open” version. In this paper, we clearly derive a sequence of a dozen statements which characterize the KKM spaces and equivalent formulations of the partial KKM principle. As their applications, we add more than a dozen statements including generalized formulations of von Neumann minimax theorem, von Neumann intersection lemma, the Nash equilibrium theorem, and the Fan type minimax inequalities for any KKM spaces. Consequently, this paper unifies and enlarges previously known several proper examples of such statements for particular types of KKM spaces.     

Rhombohedral epitaxy of cubic SiGe on trigonal c-plane sapphire

Highly [1 1 1]-oriented rhombohedral hetero-structure epitaxy of cubic SiGe semiconductor on trigonal c-plane sapphire was achieved and characterized with two new advanced X-ray diffraction methods to control the formation of primary-twin crystals. The formation of twin crystals on (1 1 1) plane was controlled with growth parameters such that the volume percentage of primary-twin crystal was reduced from 40% to 0.3% compared to the majority single crystal. The control of stacking faults can yield single-crystalline semiconductors without defects or improved thermoelectric materials with twinned crystals for phonon scattering while maintaining electrical integrity. In this study, about 94% of all epitaxial layers were fabricated in a single-crystalline phase. We propose the temperature-dependent alignment model of energetically favored majority single-crystalline SiGe layer on c-plane sapphire. This study shows that nearly single-crystalline cubic semiconductors can be grown in the [1 1 1] orientation on the basal (0 0 0 1) planes of selected trigonal crystal substrates.     

The effect of thermal annealing on the structural and mechanical properties of a-C:H thin films prepared by the CFUBM magnetron sputtering method

a-C:H films were prepared by closed-field unbalanced magnetron (CFUBM) sputtering on silicon substrates using argon (Ar) and acetylene (C₂H₂) gases, and the effects of post-annealing temperature on structural and mechanical properties were investigated. Films were annealed at temperatures ranging from 300 °C to 700 °C in increments of 200 °C using rapid thermal annealing equipment in vacuum ambient. Variations in microstructure were examined using Raman spectroscopy and X-ray photoelectron spectroscopy (XPS). Surface and mechanical properties were investigated by atomic force microscopy (AFM), nano-indentation, residual stress tester, and nano-scratch tester. We found that the mechanical properties of a-C:H films deteriorated with increased annealing temperature.     

SnO<Subscript>2</Subscript> nanowires bridged across trenched electrodes and their gas-sensing characteristics

By using a thermal chemical vapor deposition and Au-catalyzed in situ alignment and growth process, SnO₂ nanowires could be bridged across trenched electrodes. In this process, a complicated and individual alignment process could be avoided and a number of devices can be fabricated in one step in a wafer scale. The gas-sensing characteristics of the developed sensor were significantly better when compared to those of other types of NO₂ sensors reported in the literature. When the concentration of NO₂ was 5 ppm, the sensitivity was higher than 150. Especially, the reaction time of 8–14 s was noticeably fast, which is attributed to the microtrench structure beneath the nanowires. PACS 61.46.Fg; 85.35.Kt; 81.15.Gh     

Synthesis of Crosslinked Sulfonated Poly(phenylene sulfide sulfone nitrile) for Direct Methanol Fuel Cell Applications

With a view towards direct methanol fuel cell applications, novel sulfonated poly(phenylene sulfide sulfone nitrile) (sPPSSfN) has been prepared and subsequently crosslinked by a Friedel‐Craft reaction using 4,4′‐oxybis(benzoic acid) as a crosslinker to achieve lower water swelling and lower methanol permeability. The dimensional change of SPPSSfN40 is 43.7% in 90 °C liquid water but that of the crosslinked membrane, XsPPSSfN40, is 23.3% while maintaining proton conductivity at 0.22 S · cm⁻¹. These results show that the Friedel‐Craft crosslinking of the novel sPPSSfN membrane effectively reduces water uptake and the degree of swelling while improving the dimensional stability and maintaining high proton conductivity.

     

Transparent and Conductive Polyethylene Oxide Film by the Introduction of Individualized Single‐Walled Carbon Nanotubes

It is demonstrated that an optically transparent and electrically conductive polyethylene oxide (PEO) film is fabricated by the introduction of individualized single‐walled carbon nanotubes (SWNTs). The incorporated SWNTs in the PEO film sustain their intrinsic electronic and optical properties and, in addition, the intrinsic properties of the polymer matrix are retained. The individualized SWNTs with smaller diameter provide high transmittance as well as good electrical conductivity in PEO films.

     

An Edgeworth expansion for functionals of Gaussian fields and its applications

This paper is concerned with the rate of convergence in the normal approximation of the sequence $\left\{F_n\right\}$, where each $F_n$ is a functional of an infinite-dimensional Gaussian field. We develop new and powerful techniques for computing the exact rate of convergence in distribution with respect to the Kolmogorov distance. As a tool for our works, the Edgeworth expansion of general orders, with an explicitly expressed remainder, will be obtained, and this remainder term will be controlled to find upper and lower bounds of the Kolmogorov distance in the case of an arbitrary sequence $\left\{F_n\right\}$. As applications, we provide the optimal fourth moment theorem of the sequence $\left\{F_n\right\}$ in the case when $\left\{F_n\right\}$ is a sequence of random variables living in a fixed Wiener chaos or a finite sum of Wiener chaoses. In the former case, our results show that the conditions given in this paper seem more natural and minimal than ones appeared in the previous works.     

Quasi-Baer module hulls and applications

Let V be a module with $S=\mathrm{End}(V)$. V is called a quasi-Baer module if for each ideal J of S, $r_V(J)=eV$ for some $e^2=e\in S$. On the other hand, V is called a Rickart module if for each $?\in S$, $\mathrm{Ker}(?)=eV$ for some $e^2=e\in S$. For a module N, the quasi-Baer module hull $\mathbf{qB}(N)$ (resp., the Rickart module hull $\mathbf{Ric}(N)$) of N, if it exists, is the smallest quasi-Baer (resp., Rickart) overmodule, in a fixed injective hull $E(N)$ of N. In this paper, we initiate the study of quasi-Baer and Rickart module hulls. When a ring R is semiprime and ideal intrinsic over its center, it is shown that every finitely generated projective R-module has a quasi-Baer hull. Let R be a Dedekind domain with F its field of fractions and let $\{K_i|i\in \mathrm{\Lambda }\}$ be any set of R-submodules of $F_R$. For an R-module $M_R$ with ${\mathrm{Ann}}_R(M)\ne 0$, we show that $M_R\oplus {({?}_{i\in \mathrm{\Lambda }}{K}_i)}_R$ has a quasi-Baer module hull if and only if $M_R$ is semisimple. This quasi-Baer hull is explicitly described. An example such that $M_R\oplus {({?}_{i\in \mathrm{\Lambda }}{K}_i)}_R$ has no Rickart module hull is constructed. If N is a module over a Dedekind domain for which $N/t(N)$ is projective and ${\mathrm{Ann}}_R(t(N))\ne 0$, where $t(N)$ is the torsion submodule of N, we show that the quasi-Baer hull $\mathbf{qB}(N)$ of N exists if and only if $t(N)$ is semisimple. We prove that the Rickart module hull also exists for such modules N. Furthermore, we provide explicit constructions of $\mathbf{qB}(N)$ and $\mathbf{Ric}(N)$ and show that in this situation these two hulls coincide. Among applications, it is shown that if N is a finitely generated module over a Dedekind domain, then N is quasi-Baer if and only if N is Rickart if and only if N is Baer if and only if N is semisimple or torsion-free. For a direct sum $N_R$ of finitely generated modules, where R is a Dedekind domain, we show that N is quasi-Baer if and only if N is Rickart if and only if N is semisimple or torsion-free. Examples exhibiting differences between the notions of a Baer hull, a quasi-Baer hull, and a Rickart hull of a module are presented. Various explicit examples illustrating our results are constructed.     

A strip-shield improves the efficiency of a solenoid coil in probes for high-field solid-state NMR of lossy biological samples

A strip-shield inserted between a high inductance double-tuned solenoid coil and the glass tube containing the sample improves the efficiency of probes used for high-field solid-state NMR experiments on lossy aqueous samples of proteins and other biopolymers. A strip-shield is a coil liner consisting of thin copper strips layered on a PTFE (polytetrafluoroethylene) insulator. With lossy samples, the shift in tuning frequency is smaller, the reduction in Q, and RF-induced heating are all significantly reduced when the strip-shield is present. The performance of 800 MHz ¹H/¹⁵N and ¹H/¹³C double-resonance probes is demonstrated on aqueous samples of membrane proteins in phospholipid bilayers.