Vector cross product in n-dimensional vector space

The definition of vector cross product (VCP) introduced by Eckmann only exists in thethree- and the seven- dimensional vector space. In this paper, according to the orthogonal completeness, magnitude of basis vector cross product and all kinds of combinations of basis vector $\hat{e}_i$, the generalized definition of VCP in the odd n-dimensional vector space is given by introducing a cross term $X_{AB}$. In addition, the definition is validated by reducing the generalization definition to the fundamental three- and seven-dimensional vector space.Comment: 9 pages, 1 figure, comments are welcom

The Network Structure of Posttraumatic Stress Disorder Among Filipina Migrant Domestic Workers: Comorbidity With Depression

Background Labour migrants are exposed to potentially traumatic events throughout the migration cycle, making them susceptible to developing mental disorders. Posttraumatic stress disorder (PTSD) is often comorbid with depression. Comorbidity worsens the course of illness, prognosis, treatment response, and increases suicidal risk. Using network analysis, this study examined the structure of PTSD and depression in a sample of migrant domestic workers, an especially vulnerable community of labour migrants. This study sought to derive the central or most important symptoms, strongest edges or relationships among symptoms, and bridge symptoms between PTSD and depression. Methods Data were obtained from 1,375 Filipina domestic workers in Macao SAR, China. Data from a subsample of 1,258 trauma-exposed participants were analysed using R software. Results Most of the strongest edges were within the same disorder and, for PTSD, within the same symptom cluster. Highest node centrality were PCL-5’s ‘avoid thoughts’, ‘lose interest’, ‘negative emotions’, and ‘not concentrate’, and PHQ-9’s ‘sleep difficulties’. The bridge symptoms were PHQ-9’s ‘sleep difficulties,’ ‘psychomotor agitation/retardation,’ and ‘fatigue,’ PCL-5’s ‘not concentrate’, and PHQ-9’s ‘worthlessness’ and ‘anhedonia’. Limitations Results may not generalize to Filipino migrant workers in other occupations and to male migrant workers. Potentially relevant symptoms like somatic symptoms and fear of somatic and mental symptoms were not included. Conclusions Central and bridge symptoms are the most important nodes in the network. Developing interventions targeting these symptoms, particularly depression symptoms, is a promising alternative to PTSD treatment given substantial barriers to specialist care for this population

A Fully Nonmetallic Gas Turbine Engine Enabled by Additive Manufacturing, Part II: Additive Manufacturing and Characterization of Polymer Composites

This publication is the second part of the three part report of the project entitled "A Fully Nonmetallic Gas Turbine Engine Enabled by Additive Manufacturing" funded by NASA Aeronautics Research Institute (NARI). The objective of this project was to conduct additive manufacturing to produce aircraft engine components by Fused Deposition Modeling (FDM), using commercially available polyetherimides-Ultem 9085 and experimental Ultem 1000 mixed with 10% chopped carbon fiber. A property comparison between FDM-printed and injection molded coupons for Ultem 9085, Ultem 1000 resin and the fiber-filled composite Ultem 1000 was carried out. Furthermore, an acoustic liner was printed from Ultem 9085 simulating conventional honeycomb structured liners and tested in a wind tunnel. Composite compressor inlet guide vanes were also printed using fiber-filled Ultem 1000 filaments and tested in a cascade rig. The fiber-filled Ultem 1000 filaments and composite vanes were characterized by scanning electron microscope (SEM) and acid digestion to determine the porosity of FDM-printed articles which ranged from 25 to 31%. Coupons of Ultem 9085, experimental Ultem 1000 composites and XH6050 resin were tested at room temperature and 400F to evaluate their corresponding mechanical properties. A preliminary modeling was also initiated to predict the mechanical properties of FDM-printed Ultem 9085 coupons in relation to varied raster angles and void contents, using the GRC-developed MAC/GMC program

Constructal blade shape in nanofluids

Blade configuration of nanofluids has been proven to perform much better than dispersed configuration for some heat conduction systems. The analytical analysis and numerical calculation are made for the cylinder--shaped and regular-rectangular-prism--shaped building blocks of the blade-configured heat conduction systems (using nanofluids as the heat conduction media) to find the optimal cross-sectional shape for the nanoparticle blade under the same composing materials, composition ratio, volumetric heat generation rate, and total building block volume. The regular-triangular-prism--shaped blade has been proven to perform better than all the other three kinds of blades, namely, the regular-rectangular-prism--shaped blade, the regular-hexagonal-prism--shaped blade, and the cylinder--shaped blade. Thus, the regular-triangular-prism--shaped blade is selected as the optimally shaped blade for the two kinds of building blocks that are considered in this study. It is also proven that the constructal cylinder--regular-triangular-prism building block performs better than the constructal regular-rectangular-prism--regular-triangular-prism building block

Advances in Molecular Quantum Chemistry Contained in the Q-Chem 4 Program Package

A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube

Urban, semi-urban and rural difference in the prevalence of metabolic syndrome in Shaanxi province, northwestern China : a population-based survey

Background The ongoing rapid urbanization in China offers rural population opportunities not only for economic improvement but also for substantial health risks. Albeit some researches related to rural-urban difference of metabolic syndrome (MS), there lacks studies focusing on this point in undeveloped provinces in China. Methods The survey, as part of China National Diabetes and Metabolic disorders Study, was conducted in Shaanxi province from June 2007 to May 2008. A total of 3,297 adults aged 20 years or older were included, of which 1,467 individuals were from urban areas, 839 from semi-urban areas, and 890 from rural areas. The MS was defined according to the 2009 Joint Interim Statement. Results The age-standardized prevalence of MS was significant higher in rural residents than in urban counterparts (29.0% vs. 25.9%, P = 0.017), in particular among females (30.2% vs. 24.4%, P = 0.003). After adjusted for the listed risk factors, rural residents had a 27.6% increased risk of having MS than urban residents. With respect to MS components, the crude prevalence of raised fasting glucose and raised blood pressure was significantly greater in rural than in urban participants. However, no significant difference in the prevalence of MS was observed between semi-urban and urban participants. Conclusions Rural residents in Shaanxi province, northwest China, were at increased risk of MS, which could be partly explained by sociodemographic and lifestyle differences. In addition, the gap between urban and semi-urban areas seemed to be minimized in related to MS prevalence. Much more attention should be paid to and intervention strategies were needed to address the rural-urban disparities in China

Software for the frontiers of quantum chemistry:An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange–correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear–electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an “open teamware” model and an increasingly modular design