Solitary-wave solutions of the Degasperis-Procesi equation by means of the homotopy analysis method

The homotopy analysis method is applied to the Degasperis-Procesi equation in order to find analytic approximations to the known exact solitary-wave solutions for the solitary peakon wave and the family of solitary smooth-hump waves. It is demonstrated that the approximate solutions agree well with the exact solutions. This provides further evidence that the homotopy analysis method is a powerful tool for finding excellent approximations to nonlinear solitary waves

Generalizing Boolean Satisfiability I: Background and Survey of Existing Work

This is the first of three planned papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high-performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal is to define a representation in which this structure is apparent and can easily be exploited to improve computational performance. This paper is a survey of the work underlying ZAP, and discusses previous attempts to improve the performance of the Davis-Putnam-Logemann-Loveland algorithm by exploiting the structure of the problem being solved. We examine existing ideas including extensions of the Boolean language to allow cardinality constraints, pseudo-Boolean representations, symmetry, and a limited form of quantification. While this paper is intended as a survey, our research results are contained in the two subsequent articles, with the theoretical structure of ZAP described in the second paper in this series, and ZAP's implementation described in the third

Generalizing Boolean Satisfiability II: Theory

This is the second of three planned papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal is to define a representation in which this structure is apparent and can easily be exploited to improve computational performance. This paper presents the theoretical basis for the ideas underlying ZAP, arguing that existing ideas in this area exploit a single, recurring structure in that multiple database axioms can be obtained by operating on a single axiom using a subgroup of the group of permutations on the literals in the problem. We argue that the group structure precisely captures the general structure at which earlier approaches hinted, and give numerous examples of its use. We go on to extend the Davis-Putnam-Logemann-Loveland inference procedure to this broader setting, and show that earlier computational improvements are either subsumed or left intact by the new method. The third paper in this series discusses ZAPs implementation and presents experimental performance results

Generalizing Boolean Satisfiability III: Implementation

This is the third of three papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high-performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal has been to define a representation in which this structure is apparent and can be exploited to improve computational performance. The first paper surveyed existing work that (knowingly or not) exploited problem structure to improve the performance of satisfiability engines, and the second paper showed that this structure could be understood in terms of groups of permutations acting on individual clauses in any particular Boolean theory. We conclude the series by discussing the techniques needed to implement our ideas, and by reporting on their performance on a variety of problem instances

Multimegawatt MPD thruster design considerations

Performance and lifetime requirements for multimegawatt magnetoplasmadynamic (MPD) thrusters were used to establish a baseline 2.5 MW thruster design. The chamber surface power deposition resulting from current conduction, plasma and surface radiation, and conduction from the hot plasma was then evaluated to establish the feasibility of thruster operation. It was determined that state of the art lithium heat pipes were adequate to cool the anode electrode, and that the liquid hydrogen propellant could be used to cool the applied field magnet, cathode, and backplate. Unresolved issues having an impact of thruster design are discussed to help focus future research

Application of near infrared reflectance spectroscopy in screening of fresh cassava (Manihot esculenta crantz) storage roots for provitamin A carotenoids

A developed Near Infrared Reflectance Spectroscopy (NIRS) calibration equation was used for determining provitamin A carotenoids contents of different trials of fresh yellow root cassava genotypes using a total of 50 cassava genotypes scanned twice by NIRS from 400 nm to 2498 nm. The NIRS calibration equations were used to predict the β-cryptoxanthin, 13-cis β-carotene, trans β-carotene, 9-cis β -carotene, total β-carotene and total carotenoid concentrations of the samples. The predicted values for total carotenoids (TC-pred) ranged from 3.93 μg g–1 to 10.51 μg g–1 with mean of 7.07 ± 2.55 μg g–1 for International Collaborative Trials (ICT), 7.97–11.03 μg g–1 fresh weight with mean of 9.40 ± 0.76 μg g–1 for yellow root trial 8 (Multi-location Uniform Yield Trial) and 6.38–10.44 μg g–1 with mean of 8.74 ± 1.07 μg g–1 for yellow root trial 9 (Multilocation Advanced Yield Trial). Total carotenoids results using reference spectrophotometric method (TC-spec) ranged from 2.57 μg g–1 to 9.97 μg g–1 with mean of 5.66 ± 2.99 μg g–1 for ICT, 6.55–8.74 μg g–1 with mean of 7.74 ± 0.64 μg g–1 for yellow root trial 8 and 4.22–11.00 μg g–1 with mean of 7.57 ± 1.54 μg g–1 for yellow root trail 9. There is significant (P ≤ 0.001) positive correlation (r = 0.55) between TC-pred by NIRS and TC-spec. Also, significant (P ≤ 0.001) positive correlation (r = 0.52) exist between trans β-carotene predicted by NIRS and high-performance liquid chromatography reference. The developed NIRS calibration equations could be used to predict total carotenoids and trans β-carotene content of yellow root cassava and serve as rapid and cost-effective screening method for large cassava sample sets

Genetic variability, stability and heritability for quality and yield characteristics in provitamin A cassava varieties

Open Access Article; Published online: 25 Jan 2020Cassava is widely consumed in many areas of Africa, including Ghana, and is a major part of most household diets. These areas are characterized by rampant malnutrition, because the tuberous roots are low in nutritional value. Provitamin A biofortified cassava varieties have been developed by the International Institute for Tropical Agriculture, but adoption of these varieties in Ghana will largely depend on their agronomic performance, including fresh root yield, dry matter content, resistance to major pests and diseases, mealiness, starch content and the stability of these traits. Eight provitamin A varieties with two white checks were planted in three environments for two seasons to determine stability and variability among the varieties for important traits. There were significant variations in performance between varieties and between environments for cassava mosaic disease, root number, fresh root yield and starch content. High broad-sense heritability and genetic advance were observed in all traits, except for storage root number, and could be exploited through improvement programs. This study identified the best performing enhanced provitamin A varieties for traits that are key drivers of variety adoption in Ghana. In view of this, some varieties can be recommended for varietal release after on-farm testing. The study also showed the possibility of tapping heterosis after careful selection of parents

Approach in theory of nonlinear evolution equations : the Vakhnenko-Parkes equation

A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE) as an example. It is shown how the equation arises in modelling the propagation of high-frequency waves in a relaxing medium. The VE is related to a particular form of the Whitham equation. Periodic and solitary traveling wave solutions are found by direct integration. Some of these solutions are loop-like in nature. The VE can be written in an alternative form, now known as the Vakhnenko-Parkes equation (VPE), by a change of independent variables. The VPE can be written in Hirota bilinear form. It is then possible to show that the VPE satisfies the ‘N-soliton condition’, in other words that the equation has an N-soliton solution. This solution is found by using a blend of the Hirota method and ideas originally proposed by Moloney & Hodnett. This solution is discussed in detail, including the derivation of phase shifts due to interaction between solitons. Individual solitons are hump-like in nature. However, when transformed back into the original variables, the corresponding solution to the VE comprises N loop-like solitons. It is shown how aspects of the inverse scattering transform (IST) method, as applied originally to the KdV equation, can be used to find one and two-soliton solutions to the VPE even though, in contrast to the KdV equation, the VPE’s spectral equation is not second-order (the isospectral Schr¨odinger equation). A B¨acklund transformation is found for the VPE and this is used to construct conservation laws. It is shown that the specral equation for the VPE is actually third-order. Then, based on ideas of Kaup and Caudrey, the standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads to N-soliton solutions andM-mode periodic solutions respectively. Interactions between these types of solutions are investigated

Preparing Aston Business School students for placement

Aston Business School (ABS) has offered four-year sandwich degrees (including a year long placement) for over 30 years, and ABS has often been ranked top for graduate employability. This report outlines the activities ABS uses to meet its ever increasing placement targets. ABS builds relationships in students’ thinking between theory and practice, and this has implications for their study, the placement period and beyond. Developing the links has certainly been a factor in the enhanced employabilility of ABS graduates, resulting in ABS having been ranked top for graduate employability for many years. The eight employability skills used as the basis for the placement preparation objectives originate from Smith at al’s (2002) work on employability. We were encouraged to find that these employability skills overlap with the benchmark of the ‘Profile summary for Business and Management’ outlined by Hawkridge (2005). In this case study we provide a rationale and then the objectives of the placement preparation period, followed by specific details of the preparation process. The evaluation highlights key achievements and areas for development, and the discussion is future-focused. Readers should note that the ABS Undergraduate curriculum is aimed at preparing students for employment but this case study focuses on the role of the Placements Team