The date and authorship of Culhwch ac Olwen: a reassessment

Rodway, S. (2005). The date and authorship of Culhwch ac Olwen: a reassessment. Cambrian Medieval Celtic Studies. 49, pp.21-44. RAE2008

Letter to nephew, no date.

Handwritten letter from Daniel D. Whedon to nephew, Daniel Avery Whedon. Not dated.

Earliness penalties on a single machine subject to precedence constraints: SLK due date assignment

The paper considers the single machine due date assignment and scheduling problems with n jobs in which the due dates are to be obtained from the processing times by adding a positive slack q. A schedule is feasible if there are no tardy jobs and the job sequence respects given precedence constraints. The value of q is chosen so as to minimize a function ϕ(F,q) which is non-decreasing in each of its arguments, where F is a certain non-decreasing earliness penalty function. Once q is chosen or fixed, the corresponding scheduling problem is to find a feasible schedule with the minimum value of function F. In the case of arbitrary precedence constraints the problems under consideration are shown to be NP-hard in the strong sense even for F being total earliness. If the precedence constraints are defined by a series-parallel graph, both scheduling and due date assignment problems are proved solvable in time, provided that F is either the sum of linear functions or the sum of exponential functions. The running time of the algorithms can be reduced to if the jobs are independent. Scope and purpose We consider the single machine due date assignment and scheduling problems and design fast algorithms for their solution under a wide range of assumptions. The problems under consideration arise in production planning when the management is faced with a problem of setting the realistic due dates for a number of orders. The due dates of the orders are determined by increasing the time needed for their fulfillment by a common positive slack. If the slack is set to be large enough, the due dates can be easily maintained, thereby producing a good image of the firm. This, however, may result in the substantial holding cost of the finished products before they are brought to the customer. The objective is to explore the trade-off between the size of the slack and the arising holding costs for the early orders.

Single machine scheduling and due date assignment under series-parallel precedence constraints

We consider a single machine due date assignment and scheduling problem of minimizing holding costs with no tardy jobs tinder series parallel and somewhat wider class of precedence constraints as well as the properties of series-parallel graphs.

A fully polynomial approximation scheme for the single machine weighted total tardiness problem with a common due date

We develop a fully polynomial-time approximation scheme (FPTAS) for minimizing the weighted total tardiness on a single machine, provided that all due dates are equal. The FPTAS is obtained by converting an especially designed pseudopolynomial dynamic programming algorithm.

Schedules with due-date assignment and position-dependent processing times

Single machine scheduling problems are considered, in which the processing of jobs depend on positions of the jobs in a schedule and the due-dates are assigned either according to the CON rule (a due-date common to all jobs is chosen) or according to the SLK rule (the due-dates are computed by increasing the actual processing times of each job by a slack, common to all jobs). Polynomial-time dynamic programming algorithms are proposed for the problems with the objective functions that include the cost of assigning the due-dates, the total cost of disgarded jobs (which are not scheduled) and, possibly, the total earliness of the scheduled jobs.

Single machine scheduling and due date assignment with positionally dependent processing times

We consider single machine scheduling and due date assignment problems in which the processing time of a job depends on its position in a processing sequence. The objective functions include the cost of changing the due dates, the total cost of discarded jobs that cannot be completed by their due dates and, possibly, the total earliness of the scheduled jobs. We present polynomial-time dynamic programming algorithms in the case of two popular due date assignment methods: CON and SLK. The considered problems are related to mathematical models of cooperation between the manufacturer and the customer in supply chain scheduling.

Is there a role for n-3 long-chain polyunsaturated fatty acids in the regulation of mood and behaviour? A review of the evidence to date from epidemiological studies, clinical studies and intervention trials

Selected biochemical evidence suggests a potential role for n-3 long-chain PUFA (n-3PUFA) in the regulation of mood and behaviour. The present paper reviews the relevant evidence, to date, from epidemiological studies, clinical studies and intervention trials. Most evidence is available investigating a role for n-3PUFA in depression, depressive illness and suicidal behaviour, but work is also available on anxiety and anxiety-related disorders, fatigue and fatigue-related disorders, aggression, hostility and anti-social behaviour, inattention, impulsivity and attention deficit hyperactivity disorder and schizophrenic disorders. For all these aspects of mood and behaviour, the evidence available is currently limited and highly inconsistent, both in terms of study methodology and study findings. There is a clear need for further work in this area.

Adsorption mechanisms of removing heavy metals and dyes from aqueous solution using date pits solid adsorbent

A potential usefulness of raw date pits as an inexpensive solid adsorbent for methylene blue (MB), copper ion (Cu2+), and cadmium ion (Cd2+) has been demonstrated in this work. This work was conducted to provide fundamental information from the study of equilibrium adsorption isotherms and to investigate the adsorption mechanisms in the adsorption of MB, Cu2+, and Cd2+ onto raw date pits. The fit of two models, namely Langmuir and Freundlich models, to experimental data obtained from the adsorption isotherms was checked. The adsorption capacities of the raw date pits towards MB and both Cu2+ and Cd2+ ions obtained from Langmuir and Freundlich models were found to be 277.8, 35.9, and 39.5 mg g(-1), respectively. Surface functional groups on the raw date pits surface substantially influence the adsorption characteristics of MB, Cu2+, and Cd2+ onto the raw date pits. The Fourier transform infrared spectroscopy (FTIR) studies show clear differences in both absorbances and shapes of the bands and in their locations before and after solute adsorption. Two mechanisms were observed for MB adsorption, hydrogen bonding and electrostatic attraction, while other mechanisms were observed for Cu2+ and Cd2+. For Cu2+, binding two cellulose/lignin units together is the predominant mechanism. For Cd2+. the predominant mechanism is by binding itself using two hydroxyl groups in the cellulose/lignin unit. (C) 2009 Elsevier B.V. All rights reserved.