ON THE DIVISOR PRODUCTS AND PROPER DIVISOR PRODUCTS SEQUENCES

Let n be a positive integer, Pd(n) denotes the product of all positive divisors of n, qd(n) denotes the product of all proper divisors of n

A NUMBER THEORETIC FUNCTION AND ITS MEAN VALUE PROPERTY

Let p be a prime, n be any positive integer, a(n,p) denotes the power of p in the factorization of n!

A NUMBER THEORETIC FUNCTION AND ITS MEAN VALUE PROPERTY

Studying the asymptotic properties of a mean value, and giving an interesting asymptotic formula for it

Analytical solution of axi-symmetrical lattice Boltzmann model for cylindrical Couette flows

Analytical solution for the axi-symmetrical lattice Boltzmann model is obtained for the low-Mach number cylindrical Couette flows. In the hydrodynamic limit, the present solution is in excellent agreement with the result of the Navier-Stokes equation. Since the kinetic boundary condition is used, the present analytical solution using nine discrete velocities can describe flows with the Knudsen number up to 0.1. Meanwhile, the comparison with the simulation data obtained by the direct simulation Monte Carlo method shows that higher-order lattice Boltzmann models with more discrete velocities are needed for highly rarefied flows

Knowledge Integrated Business Process Management for Third Party Logistics Companies

The growing importance of logistics as well as the increasing dynamic complexity of markets, technologies, and customer needs has brought great challenges to logistics. In order to focus on their core competency in such a competitive environment, more and more companies have outsourced a part or the entirety of the logistics process to third party logistics (3PL) service providers. 3PL has played a crucial role in managing logistics processes within supply chain management. Logistics processes require and supply various types of knowledge for planning, developing, operating, controlling and improving business processes. Therefore, in the current knowledge era, knowledge integrated business process management (KIBPM) is of significant importance for 3PL. This work applies KIBPM in 3PL from both a theoretical and practical perspective. The methodology for this study is a combination of literature and primary source research. From the theoretical perspective, it reviews the related literature on knowledge, KM, KIBPM and 3PL. It next analyzes application potentials as well as basic theories of KIBPM in 3PL, and proposes a framework for application. Furthermore, it studies the issues, knowledge sources and content, as well as KM approaches from the strategic and operational perspectives. In particular, it discusses the dynamics, logistics networks, business process networks and tacit knowledge sharing in 3PL. From the practical perspective, a case study of a leading 3PL provider demonstrates the drivers, practices and approaches of KIBPM application. The case study is based on in-depth interviews and extensive access to the secondary data of the firm. It analyzes the core business processes, the process knowledge and key activities of KM in the formulation of business strategy and the operation of business processes in contract logistics. In addition, it applies the proposed framework in this case. Furthermore, it discusses the findings from the literature and case study that relate to the research questions, compares the differences and similarities of KM in 3PL between theory and practice, and puts forward some research and managerial implications. This study has come to the conclusion that it is more effective and efficient to integrate KM in business processes. Knowledge of market, customer requirements, partners, and competitors and collaborative KM in the logistics networks are essential when choosing competitive strategies, process designs and development strategies for business. 3PL needs dynamic capabilities to sustain competitive advantage through KM. In operation, knowledge related business procedures and domains, as well as the results in project management of warehousing, intermodal transport and cooperation between geographic networks, have considerable value for business process execution, evaluation and improvement. 3PL motivates tacit knowledge sharing and effective knowledge acquisition, production, warehousing, distribution and application with a trusting organizational culture, process oriented structure, appropriate technology, and incentive measures. However, while KM is a tool for improving the competency and performance for the organization, learning capability is more important to keeping sustainable competitive advantage in the long term for 3PL. The application of KIBPM in 3PL supports business process management at both the strategic and operational levels. It especially contributes to business development, collaborative projects, intermodal transport, and logistics service improvement

Sketch-based subspace clustering of hyperspectral images

Sparse subspace clustering (SSC) techniques provide the state-of-the-art in clustering of hyperspectral images (HSIs). However, their computational complexity hinders their applicability to large-scale HSIs. In this paper, we propose a large-scale SSC-based method, which can effectively process large HSIs while also achieving improved clustering accuracy compared to the current SSC methods. We build our approach based on an emerging concept of sketched subspace clustering, which was to our knowledge not explored at all in hyperspectral imaging yet. Moreover, there are only scarce results on any large-scale SSC approaches for HSI. We show that a direct application of sketched SSC does not provide a satisfactory performance on HSIs but it does provide an excellent basis for an effective and elegant method that we build by extending this approach with a spatial prior and deriving the corresponding solver. In particular, a random matrix constructed by the Johnson-Lindenstrauss transform is first used to sketch the self-representation dictionary as a compact dictionary, which significantly reduces the number of sparse coefficients to be solved, thereby reducing the overall complexity. In order to alleviate the effect of noise and within-class spectral variations of HSIs, we employ a total variation constraint on the coefficient matrix, which accounts for the spatial dependencies among the neighbouring pixels. We derive an efficient solver for the resulting optimization problem, and we theoretically prove its convergence property under mild conditions. The experimental results on real HSIs show a notable improvement in comparison with the traditional SSC-based methods and the state-of-the-art methods for clustering of large-scale images

Outflow and hot dust emission in high redshift quasars

Correlations of hot dust emission with outflow properties are investigated, based on a large z~2 non-broad absorption lines quasar sample built from the Wide-field Infrared Survey and the Sloan Digital Sky Survey data releases. We use the near infrared slope and the infrared to UV luminosity ratio to indicate the hot dust emission relative to the emission from the accretion disk. In our luminous quasars, these hot dust emission indicators are almost independent of the fundamental parameters, such as luminosity, Eddington ratio and black hole mass, but moderately dependent on the blueshift and asymmetry index (BAI) and full width at half-maximum (FWHM) of CIV lines. Interestingly, the latter two correlations dramatically strengthen with increasing Eddington ratio. We suggest that, in high Eddington ratio quasars, CIV regions are dominated by outflows so the BAI and FWHM(CIV) can reliably reflect the general properties and velocity of outflows, respectively. While in low Eddington ratio quasars, CIV lines are primarily emitted by virialized gas so the BAI and FWHM(CIV) become less sensitive to outflows. Therefore, the correlations for the highest Eddington ratio quasars are more likely to represent the true dependence of hot dust emission on outflows and the correlations for the entire sample are significantly diluted by the low Eddington ratio quasars. Our results show that an outflow with a large BAI or velocity can double the hot dust emission on average. We suggest that outflows either contain hot dust in themselves or interact with the dusty interstellar medium or torus.Comment: 14 page, 4 figures, accepted for publication in ApJ

Obscured Binary Quasar Cores in SDSS J104807.74+005543.5?

We report the discovery of a possible close binary system of quasars in SDSS J1048+0055. The [OIII]4959,5007 emission lines are clearly double-peaked, and two discrete radio sources with a projected physical separation of ~20 pc are found in the VLBA milliarcsec resolution image at 8.4 GHz. Each of the [O III]4959,5007 doublets and Hbeta can be well modelled by two Gaussians and the line ratio, [O III]5007/Hbeta ~7, is typical of Seyfert 2 galaxies. No broad component of Hbeta was detected and its [O III]5007 luminosity, L_[OIII] ~ 9.2 times 10^42 erg s^-1, is comparable to luminous quasars and is a few ten times more luminous than typical Seyfert galaxies. One natural interpretation is that SDSS J1048+0055 contains two close quasar-like nuclei and the BLR around them are obscured. Other possible models are also discussed. We suggest that double-peaked narrow emission line profile may be an effective way of selecting candidates of binary black holes with intermediate separation