Pochhammer Symbol with Negative Indices. A New Rule for the Method of Brackets

The method of brackets is a method of integration based upon a small number of heuristic rules. Some of these have been made rigorous. An example of an integral involving the Bessel function is used to motivate a new evaluation rule

Monitoring Costs and the Mode of International Investment

contract, vertical integration, opportunism, international investment, China

Qualitative analysis of academic group and discussion forum on Facebook

In the present study, data was triangulated and two methods of data analysis were used. Qualitative analysis was undertaken of free-text data from students’ reflective essaysto extract socially-related themes. Heuristic evaluation was conducted by expert evaluators, who investigated forum contributions and discourse in line with contemporary learning theory and considered the social\ud culture of participation. Findings of the qualitative analysis of students’ perceptions and results of the\ud heuristic evaluation of forum participation confirmed each other, indicating a warm social climate and a conducive, well-facilitated environment that supported individual styles of participation. It fostered interpersonal relationships between distance learners, as well as study-related benefits enhanced by peer teaching and insights acquired in a culture of social negotiation. The environment was effectively moderated, while supporting student-initiative.\u

Monitoring Costs and the Mode of International Investment

Our central proposition is that monitoring costs increase with physical distance, and hence, direct investments located further from the foreign investor’s home base should be more likely formed as joint ventures. Tests on a data set of Taiwanese direct investments in Mainland China provide robust support to the hypothesis. A project that was located 1000 kilometers further away was 13-17% more likely to be formed as a joint venture.contract, vertical integration, opportunism, international investment, China

Packet equalisation in PONs using adjustable gain-clamped semiconductor optical amplifiers (AGC-SOA)

The past ten years have witnessed a dramatic growth in the delivery of high bandwidth services through Passive Optical Networks (PONs), directly to the home or to the kerb. The bursty nature of upstream traffic in a PON (from the user to Optical Network Unit, ONU) combined with a wide dynamic range of signal strength (-15dB to -28dB the difference between a very close Optical Network Terminal (ONT) with a small split ratio and a distant ONT with a high split ratio), places severe demands on the burst mode receiver at the ONU. We report here on an adjustable gain-clamped semiconductor optical amplifier (AGC-SOA) designed to maximize the output saturated power while adjusting gain to regulate the power differences between packets without loss of linearity. This device is shown to be able to modulate gain at rates that are compatible with packet to packet equalisation. Through theoretical analysis coupled with experimental verification, this paper demonstrates for the first time that this is entirely feasible

An Extension of the Method of Brackets. Part 1

The method of brackets is an efficient method for the evaluation of a large class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the concepts of null and divergent series. These are formal representations of functions, whose coefficients $a_{n}$ have meromorphic representations for $n \in \mathbb{C}$, but might vanish or blow up when $n \in \mathbb{N}$. These ideas are illustrated with the evaluation of a variety of entries from the classical table of integrals by Gradshteyn and Ryzhik

Harnessing machine learning for fiber-induced nonlinearity mitigation in long-haul coherent optical OFDM

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).Coherent optical orthogonal frequency division multiplexing (CO-OFDM) has attracted a lot of interest in optical fiber communications due to its simplified digital signal processing (DSP) units, high spectral-efficiency, flexibility, and tolerance to linear impairments. However, CO-OFDM’s high peak-to-average power ratio imposes high vulnerability to fiber-induced non-linearities. DSP-based machine learning has been considered as a promising approach for fiber non-linearity compensation without sacrificing computational complexity. In this paper, we review the existing machine learning approaches for CO-OFDM in a common framework and review the progress in this area with a focus on practical aspects and comparison with benchmark DSP solutions.Peer reviewe