Factorization in Formal Languages

We consider several novel aspects of unique factorization in formal languages. We reprove the familiar fact that the set uf(L) of words having unique factorization into elements of L is regular if L is regular, and from this deduce an quadratic upper and lower bound on the length of the shortest word not in uf(L). We observe that uf(L) need not be context-free if L is context-free. Next, we consider variations on unique factorization. We define a notion of "semi-unique" factorization, where every factorization has the same number of terms, and show that, if L is regular or even finite, the set of words having such a factorization need not be context-free. Finally, we consider additional variations, such as unique factorization "up to permutation" and "up to subset"

Exploring the Use of the Internet and Online Social Networks in Entrepreneurship within Developing Economies

Entrepreneurship has recently received a lot of attention from policy-makers and academics. They see it as a way to boost slowing economies and build developing ones. This paper seeks to explore the instance of being entrepreneurial within a developing economic climate. Concepts of entrepreneurship as it relates to economic change and how this applies to developing environments were explored. Key supporting factor for new entrepreneurs were then pick out and examined to determine their suitability for being shared via the internet. These insights were then combined with data gathered from subjects through interviews. The overall objective was to determine if the internet and online social networks could be used to bypass limiting factors to entrepreneurial activities within unsuitable environments using current behaviours exhibited by entrepreneurs in this area

Mejoramiento de los procesos en el quirófano mediante la aplicación de la metodología Lean de Toyota

ResumenEl sector de la atención en salud está necesitando un cambio fundamental a fin de mejorar significativamente los resultados y limitar al mismo tiempo los costos. Los métodos Lean desarrollados inicialmente en la industria manufacturera han demostrado mejorar realmente la calidad, la productividad y la seguridad, a la vez que permiten utilizar menos recursos en la gestión de la salud. Estas herramientas, prácticas gerenciales y filosofías se han adaptado con éxito en los servicios de cirugía del SC. Pueden transformar el sistema y la cultura mediante el compromiso del personal de asistencia para el desarrollo de un servicio que mejora continuamente y permite obtener mejores resultados clínicos duraderos.AbstractHealthcare is in need of fundamental change if we are going to make significant improvements in outcomes while limiting costs. Lean methods, initially developed in the manufacturing industry, have been shown to deliver real improvements in quality, productivity, and safety while using fewer resources in healthcare service settings. These tools, management practices and philosophies have been successfully adapted in operative services at SC. They can transform your system and culture through engagement of frontline staff into a continuously improving service with real and sustainable enhancements in clinical outcomes

Fife's Theorem for 7/3-powers

We prove a Fife-like characterization of the infinite binary 7/3-power-free words, by giving a finite automaton of 15 states that encodes all such words. As a consequence, we characterize all such words that are 2-automatic. © 2011 N. Rampersad

Repetitions in infinite palindrome-rich words

Rich words are characterized by containing the maximum possible number of distinct palindromes. Several characteristic properties of rich words have been studied; yet the analysis of repetitions in rich words still involves some interesting open problems. We address lower bounds on the repetition threshold of infinite rich words over 2 and 3-letter alphabets, and construct a candidate infinite rich word over the alphabet $\Sigma_2=\{0,1\}$ with a small critical exponent of $2+\sqrt{2}/2$. This represents the first progress on an open problem of Vesti from 2017.Comment: 12 page

Finite Automata for the Sub- and Superword Closure of CFLs: Descriptional and Computational Complexity

We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing sub- or superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of $2^{\mathcal{O}(n)}$ on the size of nondeterministic finite automata (NFAs) representing the subword closure of a CFG of size $n$. (2) We present a family of CFGs for which the minimal deterministic finite automata representing their subword closure matches the upper-bound of $2^{2^{\mathcal{O}(n)}}$ following from (1). Furthermore, we prove that the inequivalence problem for NFAs representing sub- or superword-closed languages is only NP-complete as opposed to PSPACE-complete for general NFAs. Finally, we extend our results into an approximation method to attack inequivalence problems for CFGs

Perceptions and opinions of graduating South African optometry students on the proposed community service

Community service (CS) was introduced inSouth Africa in an attempt to address the shortageand maldistribution of health care professionalswithin the public sector. The Professional Board forOptometry and Dispensing Opticians (PBODO)has approved legislation for the introductionof CS for graduating optometry students. This study examined the perceptions and opinionsof graduating optometry students regarding the proposed CS. A mixed-method design(questionnaires and interviews) was used. Bothapproaches yielded similar results. The quantitativecomponent included 119 participants, aged between 20 and 35 years (mean age and standard deviation;22.8 ± 2.3 years). There were 43.2% Blacks, 28.5%Whites, 19.1% Indians and 9.2% Coloureds. The qualitative part included fourteen participantsfrom the Optometry Department of the University of KwaZulu-Natal. The major themes emergingfrom the questions concerning the participants’ perceived advantages and benefits of CS were (i) it would improve the eye care service delivery to disadvantaged communities; (ii) it would improve the technical and clinical skills of the graduating optometrists and (iii) it would enhance their confidence, personal and social skills. Some of the perceived drawbacks cited by the participants about such service included poor remuneration and concerns about personal safety, transport and accommodation. The findings of this study suggest that graduating optometry students acknowledge the importance of CS in improving access of many South Africans to quality eye care. In order to maximise the full benefits of CS, all stakeholders need to address the highlighted concerns of the participants. (S Afr Optom 2013 72(1) 11-18

A validated measure of adherence to antibiotic prophylaxis in children with sickle cell disease

BACKGROUND: Antibiotic prophylaxis is a mainstay in sickle cell disease management. However, adherence is estimated at only 66%. This study aimed to develop and validate a Sickle Cell Antibiotic Adherence Level Evaluation (SCAALE) to promote systematic and detailed adherence evaluation. METHODS: A 28-item questionnaire was created, covering seven adherence areas. General Adherence Ratings from the parent and one health care provider and medication possession ratios were obtained as validation measures. RESULTS: Internal consistency was very good to excellent for the total SCAALE (α=0.89) and four of the seven subscales. Correlations between SCAALE scores and validation measures were strong for the total SCAALE and five of the seven subscales. CONCLUSION: The SCAALE provides a detailed, quantitative, multidimensional, and global measurement of adherence and can promote clinical care and research

African American Review' Special Issue - Introduction

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