Generalized Nets Model of an E-Learning System Software Architecture

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshko ff and Lubomir Tschakaloff , Sofi a, July, 2006.

Algorithms for Finding Unitals and Maximal Arcs in Projective Planes of Order 16

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakalo ff , Sofia, July, 2006.

On the Arithmetic of Errors

An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from familiar properties of real numbers. We focus on certain operations of errors which seem not to have been sufficiently studied algebraically. In this work we restrict ourselves to arithmetic operations for errors related to addition and multiplication by scalars. We pay special attention to subtractability-like properties of errors and the induced “distance-like” operation. This operation is implicitly used under different names in several contemporary fields of applied mathematics (inner subtraction and inner addition in interval analysis, generalized Hukuhara difference in fuzzy set theory, etc.) Here we present some new results related to algebraic properties of this operation.

Financial Education Through Mathematics and IT Curricula: Pocket Money Management

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

Financial Decisions via Methods of Guaranteed Control Theory

AMS subject classification: 93C95, 90A09.

Recent Developments in Digital Mathematics Libraries

The paper presents recent developments in the domain of digital mathematics libraries towards the envisioned 21st Century Global Library for Mathematics. The Bulgarian Digital Mathematical Library BulDML and the Czech Digital Mathematical Library DML-CZ are founding partners of the EuDML Initiative and through it contribute to the sustainable development of the European Digital Mathematics Library EuDML and to the global advancements in this area.

A New Characterization of Weighted Peetre K-Functionals (II)

2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.

Structure of the Unit Group of FD10

2000 Mathematics Subject Classification: 16U60, 20C05.

Does the balanced scorecard make a difference to the strategy development process

A great number of strategy tools are being taught in strategic management modules. These tools are available to managers for use in facilitating strategic decision making and enhancing the strategy development process in their organisations. A number of studies have been published examining which are the most popular tools; however there is little empirical evidence on how their utilisation influences the strategy process. This paper is based on a large scale international survey on the strategy development process, and seeks to examine the impact of a particular strategy tool, the Balanced Scorecard (BSC), upon the strategy process. Recently, it has been suggested that as a strategy tool, the BSC can influence all elements of the strategy process. The results of this study indicate that although there are significant differences in some elements of the strategy process between the organisations that have implemented the BSC and those that have not, the impact is not comprehensive. © 2011 Operational Research Society Ltd. All rights reserved.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric and axisymmetric backward heat conduction problem (BHCP) in a solid or hollow cylinder. In the BHCP, the initial temperature is to be determined from the temperature measurements at a later time. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach [B.T. Johansson and D. Lesnic, A method of fundamental solutions for transient heat conduction, Eng. Anal. Boundary Elements 32 (2008), pp. 697–703] for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.

Előszó egy pénzügyi matematika tankönyvhöz = Preface to a textbook on financial mathematics

A szerző a pénzügyi válság kapcsán a pénzügyi matematikát ért kritikai észrevételekre próbál válaszolni. Megítélése szerint a pénzügyi matematika negatív hatása a magyarországi pénzügyi problémák esetében nem mutatható ki, ugyanis Magyarországon a pénzügyi döntések mindenfajta kvantitatív megalapozás nélkül, nagyrészt politikai alapon történtek, így a felelősséget is a politikát körülvevő gazdaságpolitikusoknak kell viselniük. A matematikai modellek legfőbb felhasználási területe nem a konkrét pénzügyi döntések megalapozásában, hanem sokkal inkább az oktatásban található. _____ The author discusses some critical observations about financial mathematics in connection with the financial crisis. In his view no negative effect of financial mathematics on Hungary's financial problems can be observed, since the financial decisions in Hungary were made without any kind of serious quantitative basis. The decisions were made mainly on political ground, so that the blame must go to economic politicians involved in that policy. The main area of application of mathematical models is not its application in specific financial decisions, but far more in the field of education.

An analysis of the on-time graduation rate in the two-year program at National Taipei Institute of Technology in Taiwan

Taiwan's technical vocational educational system includes three levels: (1) institutes of technology (two and four year programs), (2) junior colleges (two, three and five year programs), and (3) senior vocational schools. Two-year junior colleges enroll their students through two channels: (1) based on results of the Particular Screening Entrance Examination (PSEE), (2) based on the Joint College Entrance Examination (JCEE). The PSEE has two categories: Category I includes on-time graduates with excellent performance, which means that they are within the top ten of their classes; Category II students include award-winning students in talent contests who have achieved a minimum grade point average of 75%. The JCEE is a regular entrance examination given to any senior vocation school graduate.^ Basic courses have a great impact on the students' academic performance. The purpose of the study was to focus on the effectiveness of teaching mathematics in two-year junior colleges and to analyze and correlate the results of two-year junior college students' performance in calculus and on-time graduation. The target group consisted of 521 students enrolled at National Taipei Institute of Technology in 1993.^ Calculus is a very important course for engineering majors in two-year junior colleges and has a great impact on the students' academic performance. This retrospective study showed that there was a correlation between students' performance in calculus and on-time graduation after two years of study.^ The conclusions of the study urge the Ministry of Education to reform two-year junior college curriculum standards to emphasize basic rudimentary courses. It is recommended that engineering majors receive three hours of calculus per week as the current requirement of only two hours per week is inadequate. The future job market will require a technologically advanced labor force that can be trained in a higher education system. More channels of higher education for two-year junior college graduates should be made available for those wishing to pursue bachelor degrees. Additional work in calculus will not only enhance the opportunities for two-year junior college graduates to continue their pursuit of an advanced academic degree, but also serve them well as they seek career advancement. ^

The effect of an enriched learning community on success and retention in chemistry courses

Since the mid-1990s, the United States has experienced a shortage of scientists and engineers, declining numbers of students choosing these fields as majors, and low student success and retention rates in these disciplines. Learning theorists, educational researchers, and practitioners believe that learning environments can be created so that an improvement in the numbers of students who complete courses successfully could be attained (Astin, 1993; Magolda & Terenzini, n.d.; O'Banion, 1997). Learning communities do this by providing high expectations, academic and social support, feedback during the entire educational process, and involvement with faculty, other students, and the institution (Ketcheson & Levine, 1999). ^ A program evaluation of an existing learning community of science, mathematics, and engineering majors was conducted to determine the extent to which the program met its goals and was effective from faculty and student perspectives. The program provided laptop computers, peer tutors, supplemental instruction with and without computer software, small class size, opportunities for contact with specialists in selected career fields, a resource library, and Peer-Led Team Learning. During the two years the project has existed, success, retention, and next-course continuation rates were higher than in traditional courses. Faculty and student interviews indicated there were many affective accomplishments as well. ^ Success and retention rates for one learning community class ( n = 27) and one traditional class (n = 61) in chemistry were collected and compared using Pearson chi square procedures ( p = .05). No statistically significant difference was found between the two groups. Data from an open-ended student survey about how specific elements of their course experiences contributed to success and persistence were analyzed by coding the responses and comparing the learning community and traditional classes. Substantial differences were found in their perceptions about the lecture, the lab, other supports used for the course, contact with other students, helping them reach their potential, and their recommendation about the course to others. Because of the limitation of small sample size, these differences are reported in descriptive terms. ^

Effect of the Florida A+ Plan on curriculum and instruction in Title I public elementary schools

The purpose of this research was to study the effect of the Florida A+ Plan accountability program on curriculum and instruction in four Title I public elementary schools in the Miami-Dade County Public Schools system. It focused on the experiences of the school principals and the classroom teachers of the four schools as they related to curriculum and instruction. The study included an analysis of the school improvement plans in curriculum and instruction for each school during the school years 1998-2004. ^ The study was conducted in the format of interviews with the school principals and principal selected classroom teachers who taught third, fourth, or fifth grade during the first six years of the Florida A+ Plan. The analysis of the school improvement plans focused on the implementation of curriculum and instruction for each of the four schools. It focused on the goals and measurable objectives selected by each school to improve its instructional program in the academic subjects of reading, mathematics, writing, and science. ^ The findings indicated that under the pressure to improve their school grade on the Florida A+ Plan, each of the target schools, based on individual needs assessments, and restructured their instructional program each school year as documented in their school improvement plans. They altered their programs by analyzing student performance data to realign curriculum and instruction. The analysis of the interviews with the principals and the teachers showed that each school year they restructured their program to align it with the FCAT content. This realigning was a collaborative effort on the part of the administration and the instructional staff. ^