S-Restricted Compositions Revisited

An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years. This paper is an attempt at finding a closed- form formula for the number of S-restricted compositions of n. To do so, we reduce the problem to finding solutions to corresponding so-called interpreters which are linear homogeneous recurrence relations with constant coefficients. Then, we reduce interpreters to Diophantine equations. Such equations are not in general solvable. Thus, we restrict our attention to those S-restricted composition problems whose interpreters have a small number of coefficients, thereby leading to solvable Diophantine equations. The formalism developed is then used to study the integer sequences related to some well-known cases of the S-restricted composition problem

Comparing Firm Performance Using Transitive Productivity Index Numbers in a Meta-frontier Framework

The meta-frontier framework has been used extensively for evaluating the technical efficiency of heterogeneous production units that can be classified into different groups. This paper shows how the framework can also be used to make total factor productivity (TFP) comparisons within and across groups. The paper develops a new measure of the distance between a group frontier and the meta-frontier (the so-called ‘technology gap’). It then shows how a spatially- and temporally-transitive TFP index can be decomposed into measures of global technical change (measuring movements in the metafrontier), local technical change (measuring movements in the group frontiers) and efficiency change (measuring movements towards or around the group frontiers). To illustrate the methodology, the paper examines the productive performance of road authorities responsible for maintaining interstate highways in the US state of Virginia.

Polystyrene-supported 1-methylimidazolium tetrachloro ferrate: Synthesis, characterization, and application as an efficient and reusable heterogeneous catalyst for one-pot synthesis of 4h-chromene derivatives in aqueous media

Polystyrene-supported 1-methylimidazolium tetrachloroferrate (PS[mim][FeCl4]) was prepared and characterized by Fourier transform infrared spectroscopy (FT-IR), scanning electron microscopy (SEM) and energy dispersive X-ray analysis (EDX). The catalytic activity of the heterogeneous catalyst was evaluated through one-pot synthesis of 2-amino-4H-chromene-3-carbonitriles via the three-component condensation reaction of aromatic aldehydes, malononitrile and dimedone or 2-naphthol in water. The heterogeneous catalyst could be recovered easily and reused five times without significant loss of its catalytic activity.               KEY WORDS: Green chemistry, Heterogeneous catalyst, 4H-chromene derivatives, Multi-component reactions, One-pot synthesis Bull. Chem. Soc. Ethiop. 2018, 32(3), 531-540.DOI: https://dx.doi.org/10.4314/bcse.v32i3.1

Efficacy and Safety of Lamotrigine in Lennox - Gastaut Syndrome

ObjectiveThe Lennox-Gastaut syndrome (LGS), one of the most difficult epilepsy syndromes to treat, is characterized by a triad of intractable seizures of various types, a slow (< 2.5-hertz) spike-wave pattern in EEG and mental retardation. The aim of this study was to evaluate the efficacy and safety of lamotrigine as add-on therapy in intractable epilepsy of children with LGS.Materials & MethodsIn a quasi- experimental study, 40 children with LGS referred to the pediatric neurology clinic of Shaheed Sadoughi Hospital in Yazd, between August 2007 and to November 2008, were evaluated.ResultsTwenty-two boys and 18 girls with a mean age of 4.12 ±1.8 years were evaluated. At the end of three months of treatment with lamotrigine, 12 % were seizure free, 52% had> 50% reduction in seizure frequency and 12% had increase in seizures. Means of seizure frequency/per week, before and after treatment were 70 (range 1-180) and 18.6 (range 0-60) respectively, indicating effectiveness of the drug in seizure reduction (P value = 0.003). The drug was effective in 72 % of mixed type seizures, 40 % of generalized tonic-clonic and 33% of drop attack and tonic seizures. Transient side effects were seen in 12.5 % (drowsiness in 3 and ataxia in 2 children). No serious side effects were seen.ConclusionLamotrigine should be considered as an add-on therapy in management of intractable epilepsy in LGS

A new method for critical path method with fuzzy processing time

Critical path method plays an important role on managing medium to large-scale problems. It is often difficult to determine the critical path for different reasons such as the existing uncertainties in processing tasks. One alternative to handle the uncertainty associated with the processing time is to use fuzzy techniques. We present a new method to calculate the critical path method when the processing times follow trapezoidal fuzzy numbers. The proposed model of this paper does not use any defuzzification technique to find the final processing time. The implementation of the proposed model is compared with other techniques using a well-known example from the literature