Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

Thermal characterization of copolymers obtained by radiation grafting of styrene onto poly(tetrafluoroethyleneperfluoropropylvinylether) substrates: thermal decomposition, melting behavior and low-temperature transitions

Differential scanning calorimetric (DSC) and thermogravimetric analysis (TGA) have been used to study the thermal decomposition, the melting behavior and low-temperature transitions of copolymers obtained by radiation-induced grafting of styrene onto poly (tetrafluoroethylene- perfluoropropylvinylether) (PFA) substrates. PFA with different contents of perfluoropropylvinylether (PPVE) as a comonomer have been investigated. A two step degradation pattern was observed from TGA thermograms of all the grafted copolymers, which was attributed to degradation of PSTY followed by the degradation of the PFA backbone at higher temperature. One broad melting peak can be identified for all copolymers, which has two components in the samples with higher PPVE content. The melting peak, crystal-crystal transition and the degree of crystallinity of the grafted copolymers increases with radiation grafting up to 50 kGy, followed by a decrease at higher doses. No such decrease was observed in the ungrafted PFA samples after irradiation. This indicated that the changes in the heats of transitions and crystallinity at low doses are due to the radiation effects on the microstructure of PFA (chain scission), whereas at higher doses the grafted PSTY is the driving force behind these changes. (C) 2001 Elsevier Science Ltd. All rights reserved.

Capacity utilisation and profitability: A decomposition of short-run profit efficiency

The principal aim of this paper is to measure the amount by which the profit of a multi-input, multi-output firm deviates from maximum short-run profit, and then to decompose this profit gap into components that are of practical use to managers. In particular, our interest is in the measurement of the contribution of unused capacity, along with measures of technical inefficiency, and allocative inefficiency, in this profit gap. We survey existing definitions of capacity and, after discussing their shortcomings, we propose a new ray economic capacity measure that involves short-run profit maximisation, with the output mix held constant. We go on to describe how the gap between observed profit and maximum profit can be calculated and decomposed using linear programming methods. The paper concludes with an empirical illustration, involving data on 28 international airline companies. The empirical results indicate that these airline companies achieve profit levels which are on average US$815m below potential levels, and that 70% of the gap may be attributed to unused capacity. (C) 2002 Elsevier Science B.V. All rights reserved.

Further decompositions of complete tripartite graphs into 5-cycles

Let K(r,s,t) denote the complete tripartite graph with partite sets of sizes r, s and t, where r less than or equal to s less than or equal to t. Necessary and sufficient conditions are given for decomposability of K(r, s, t) into 5-cycles whenever r, s and t are all even. This extends work done by Mahmoodian and Mirza-khani (Decomposition of complete tripartite graphs into 5-cycles, in: Combinatorics Advances, Kluwer Academic Publishers, Netherlands, 1995, pp. 235-241) and Cavenagh and Billington. (C) 2002 Elsevier Science B.V. All rights reserved.

Conditional simulation of random fields by successive residuals

This paper presents a new approach to the LU decomposition method for the simulation of stationary and ergodic random fields. The approach overcomes the size limitations of LU and is suitable for any size simulation. The proposed approach can facilitate fast updating of generated realizations with new data, when appropriate, without repeating the full simulation process. Based on a novel column partitioning of the L matrix, expressed in terms of successive conditional covariance matrices, the approach presented here demonstrates that LU simulation is equivalent to the successive solution of kriging residual estimates plus random terms. Consequently, it can be used for the LU decomposition of matrices of any size. The simulation approach is termed conditional simulation by successive residuals as at each step, a small set (group) of random variables is simulated with a LU decomposition of a matrix of updated conditional covariance of residuals. The simulated group is then used to estimate residuals without the need to solve large systems of equations.

Leaf litter decomposition of Piper aduncum, Gliricidia sepium and Imperata cylindrica in the humid lowlands of Papua New Guinea

No information is available on the decomposition and nutrient release pattern of Piper aduncum and Imperata cylindrica despite their importance in shifting cultivation systems of Papua New Guinea and other tropical regions. We conducted a litter bag study (24 weeks) on a Typic Eutropepts in the humid lowlands to assess the rate of decomposition of Piper aduncum, Imperata cylindrica and Gliricidia sepium leaves under sweet potato (Ipomoea batatas). Decomposition rates of piper leaf litter were fastest followed closely by gliricidia, and both lost 50% of the leaf biomass within 10 weeks. Imperata leaf litter decomposed much slower and half-life values exceeded the period of observation. The decomposition patterns were best explained by the lignin plus polyphenol over N ratio which was lowest for piper (4.3) and highest for imperata (24.7). Gliricidia leaf litter released 79 kg N ha(-1), whereas 18 kg N ha(-1) was immobilised in the imperata litter. The mineralization of P was similar for the three species, but piper litter released large amounts of K. The decomposition and nutrient release patterns had significant effects on the soil. The soil contained significantly more water in the previous imperata plots at 13 weeks due to the relative slow decomposition of the leaves. Soil N levels were significantly reduced in the previous imperata plots due to immobilisation of N. Levels of exchangeable K were significantly increased in the previous piper plots due to the large addition of K. It can be concluded that piper leaf litter is a significant and easily decomposable source of K which is an important nutrient for sweet potato. Gliricidia leaf litter contained much N, whereas imperata leaf litter releases relatively little nutrients and keeps the soil more moist. Gliricidia fallow is more attractive than an imperata fallow for it improves the soil fertility and produces fuelwood as additional saleable products.

Decomposition of ground biomass of secondary forest and yield of annual crops in no tillage

ABSTRACT The objective of this work was to evaluate the dynamics of decomposition process of chopped secondary forest system, previously enriched with legumes Inga velutina Willd. and Stryphnodendron pulcherrimum (Willd.) Hochr. and the contribution of this process to the nutrient input to the cultivation of corn and bean under no-tillage. The experimental design was a randomized block, split plot with four replications. The plots were two species (I. velutina and S. pulcherrimum) and the subplots were seven times of evaluation (0, 7, 28, 63, 189, 252, 294 days after experiment installation). There was no difference (p ≥ 0.05) between the secondary forest systems enriched and no interaction with times for biomass waste, decomposition constant and half-life time. The waste of S. pulcherrimum trees had higher (p < 0.05) C/N ratio than that I. velutina. However, this one was higher (p < 0.05) in lignin content. Nevertheless, the dynamics of residue decomposition was similar. The corn yield was higher (p < 0.05) in cultivation under I.velutina waste. Meanwhile, the beans planted after corn, shows similar (p > 0.05) yield in both areas, regardless of the waste origin.

Teaching and learning mathematics using moodle

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the student understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. We also use the Excel and the mathematical open source software wxMaxima. To supplement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study giving them more confidence. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

Developing multiple - choice questions in mathematics

In this paper we wish to illustrate different perspectives used to create Multiple-Choice questions and we will show how we can improve these in the construction of math tests. As it is known, web technologies have a great influence on student’s behaviour. Based on an on-line project beginning at 2007 which has been contributing to help students on their individual work, we would like to share our experience and thoughts with colleagues who have a common concern when they have the task of constructing Multiple-Choice tests. We feel that Multiple-Choice tests play an important and a very useful supporting role in selfevaluation or self-examination of our students. Nonetheless, good Multiple–Choice Test Items are generally more complex and time-consuming to create than other types of tests. It requires a certain amount of skill. However, this skill maybe increases through study, practice and experience. This paper discusses a number of issues related to the use of Multiple-Choice questions, lists the advantages and disadvantages of this question format contrasting it with open questions. Some examples are given in this context.

How to teach mathematics with MOODLE

The aim of this article is to present a Project in the Oporto’s Institute of Accounting and Administration, which pretends to contribute for a change in the way of teaching and learning Mathematics. One of the main objectives of this project is to innovate the teaching and learning processes, exploring technologies as a pedagogical resource and to induce higher motivation to students, improve the rate of success and make available to students a set of materials adapted to their needs. This concern is justified due to the fact that students have a weak preparation, without consolidated basis. Since the year 2007/2008 the courses were adjusted to the Bologna process, which requires several changes in teacher’s and student’s roles, methodologies and assessment. The number of weekly classes has been reduced, so it was necessary to develop new strategies and methodologies to support the student. With the implementation of the Bologna Process in the Accounting degree, we felt a great need to provide other types of activities to students. To complement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio On-Line (Online Support Project). Moodle allows us to use the language TEX to create materials that use mathematical symbols. Using this functionality, we created a set of easy to use interactive resources. In MatActiva project, the students have access to a variety of different materials. We have followed a strategy that makes the project compatible with the theoretical and practical subjects/classes, complementing them. To do so, we created some resources, for instance multiple-choice tests, which are the most accessed by the students. These tests can be realized and corrected on-line and for each wrong answer there is a feedback with the resolution. We can find other types of resources: diagnostic tests, theoretical notes. There are not only the pre-requirements for subjects mathematics, but also materials to help students follow up the programs. We also developed several lessons. This activity consists of a number of pages, where each page has contents and leads to other pages, based on the student's progress. The teacher creates the choices and determines the next page that the student will see, based upon their knowledge. There is also an area of doubts, where the students can place all the mathematical doubts they have, and a teacher gives the answers or clues to help them in their work. MatActiva also offers an area where we can find some humour, curiosities, contests and games including mathematical contents to test the math skills, as well as links to pages about mathematical contents that could be useful for the study. Since ISCAP receives ERASMUS students and some of them attend mathematics, we developed some materials in English, so they can also use MatActiva. The main objectives of our project are not only to bring success in the subjects of mathematics, but also to motivate the students, encourage them to overcome theirs difficulties through an auto-study giving them more confidence and improve their relationship with the mathematics as well as the communication between students and teachers and among students.

The active mathematics project at ISCAP

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the students understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. To supplement our theoretical and practical classes we have developed an active mathematics project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). In the last versions of Moodle, it is possible use the TeX language to create math questions. Using this tool we created a set of interactive materials. With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study, giving them more confidence and the opportunity to seeing others perspectives of the mathematics subjects. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

New challenges in mathematics for the european higher education

In this paper we will talk about a math project submitted to the Lifelong Learning Programme. European higher education needs a reform in order to play its full role in the Europe of Knowledge. Modernisation of higher education is necessary in the areas of curricula (Bologna process), funding and governance so that higher education institutions can face the challenges posed by globalisation and contribute more effectively to the training and retraining of the European workforce. On the other hand Mathematics is an essential component of all educational systems. Mathematical literacy is being scrutinized in assessment efforts such as the OCDE Programme for International Student Assessment (PISA). This showed a low level in Europe. Due to the Bologna Process, which brought several didactical implications for Higher Education (HE) institutions, there is the need of lifelong learning. This evolution is in conflict with the earlier mentioned lack of competencies on basic sciences, such as Mathematics. Forced by this duality, efforts are combined to share expertise in the Math field and the integration of pedagogical methodologies becomes a necessity. Thus, several European countries have proposed an International Project to the Lifelong Learning Programme, Action ERASMUS Modernisation of Higher Education, to make institutions more attractive and more responsive to the needs of the labour market, citizens and society at large. One of the main goals of the project is to attract students to math through high-quality instructional units in an understandable, exciting and attractive way.