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A Software Platform for Educational Board Games
http://hdl.handle.net/10525/1470
Title: A Software Platform for Educational Board Games<br/><br/>Authors: Bontchev, Boyan<br/><br/>Abstract: Educational games such as quizzes, quests, puzzles, mazes and logicalproblems may be modeled as multimedia board games. In the scope of theADOPTA project1 being under development at the Faculty of Mathematics andInformatics at Sofia University, a formal model for presentation of sucheducational board games was invented and elaborated. Educational games can bemodeled as special board mini-games, with a board of any form and any types ofpositions. Over defined positions, figures (objects) with certain properties areplaced and, next, there are to be defined formal rules for manipulation of thesefigures and resulted effects.The model has been found to be general enough in order to allow descriptionand execution control of more complex logical problems to be solved by severalactions delivered to/by the player according some formal rules and contextconditions and, in general, of any learning activities and their workflow. It is usedas a base for creation of a software platform providing facilities for easyconstruction of multimedia board games and their execution. The platform consistsof game designer (i.e., a game authoring tool) and game run-time controllercommunicating each other through game repository. There are created andmodeled many examples of educational board games appropriate for didacticpurposes, self evaluations, etc., which are supposed to be designed easily byauthors with no IT skills and experience. By means of game metadata descriptions,these games are going be included into narrative storyboards and, next, delivered tolearners with appropriate profile according their learning style, preferences, etc.Moreover, usage of artificial intelligence agents is planned as well – once asplaying virtual opponents of the player or, otherwise, being virtual advisers of thegamer helping him/her in finding the right problem solution within given domainsuch as discovering a treasure using a location map, finding best tour in a virtualmuseum, guessing an unknown word in a hangman game, and many others.Automatic Discovery of Word Semantic Relations
http://hdl.handle.net/10525/1469
Title: Automatic Discovery of Word Semantic Relations<br/><br/>Authors: Dias, Gael; Moraliyski, Rumen; Cordeiro, Joao; Doucet, Antoine; Ahonen-Myka, Helena<br/><br/>Abstract: In this paper, we propose an unsupervised methodology to automatically discover pairs of semantically related words by highlighting theirlocal environment and evaluating their semantic similarity in local and globalsemantic spaces. This proposal di®ers from previous research as it tries to takethe best of two different methodologies i.e. semantic space models and information extraction models. It can be applied to extract close semantic relations,it limits the search space and it is unsupervised.Mathematical Modeling and Simulation of Radial Temperature Profile of Strontium Bromide Lasers
http://hdl.handle.net/10525/1468
Title: Mathematical Modeling and Simulation of Radial Temperature Profile of Strontium Bromide Lasers<br/><br/>Authors: Gocheva-Ilieva, Snezhana<br/><br/>Abstract: For metal and metal halide vapor lasers excited by high frequencypulsed discharge, the thermal effect mainly caused by the radial temperaturedistribution is of considerable importance for stable laser operation andimprovement of laser output characteristics. A short survey of the obtainedanalytical and numerical-analytical mathematical models of the temperatureprofile in a high-powered He-SrBr2 laser is presented. The models are describedby the steady-state heat conduction equation with mixed type nonlinear boundaryconditions for the arbitrary form of the volume power density. A complete model ofradial heat flow between the two tubes is established for precise calculating theinner wall temperature. The models are applied for simulating temperature profilesfor newly designed laser. The author’s software prototype LasSim is used forcarrying out the mathematical models and simulations.A New Charging and Billing Model and Architecture for the Ubiquitous Consumer Wireless World
http://hdl.handle.net/10525/1467
Title: A New Charging and Billing Model and Architecture for the Ubiquitous Consumer Wireless World<br/><br/>Authors: Jakab, Jeno; Ganchev, Ivan; O'Droma, Máirtín<br/><br/>Abstract: In a Ubiquitous Consumer Wireless World (UCWW) environmentthe provision, administration and management of the authentication, authorizationand accounting (AAA) policies and business services are provided by third-partyAAA service providers (3P-AAA-SPs) who are independent of the wireless accessnetwork providers (ANPs). In this environment the consumer can freely choose anysuitable ANP, based on his/her own preferences. This new AAA infrastructuralarrangement necessitates assessing the impact and re-thinking the design,structure and location of ‘charging and billing’ (C&B) functions and services. Thispaper addresses C&B issues in UCWW, proposing potential architectural solutionsfor C&B realization. Implementation approaches of these novel solutions togetherwith a software testbed for validation and performance evaluation are addressed.On The Critical Points of some Iteration Methods for Solving Algebraic Equations. Global Convergence Properties
http://hdl.handle.net/10525/1466
Title: On The Critical Points of some Iteration Methods for Solving Algebraic Equations. Global Convergence Properties<br/><br/>Authors: Kyurkchiev, Nikolay; Iliev, Anton<br/><br/>Abstract: In this work we give su±cient conditions for k-th approximations of the polynomial roots of f(x) when the Maehly{Aberth{Ehrlich,Werner-Borsch-Supan, Tanabe, Improved Borsch-Supan iteration methodsfail on the next step. For these methods all non-attractive sets are found. Thisis a subsequent improvement of previously developed techniques and knownfacts. The users of these methods can use the results presented here forsoftware implementation in Distributed Applications and Simulation Environ-ments. Numerical examples with graphics are shown.Natural Connections with Totally Skew-Symmetric Torsion on Manifolds with Norden-Type Metrics
http://hdl.handle.net/10525/1465
Title: Natural Connections with Totally Skew-Symmetric Torsion on Manifolds with Norden-Type Metrics<br/><br/>Authors: Manev, Mancho; Mekerov, Dimitar; Gribachev, Kostadin<br/><br/>Abstract: This paper is a survey of results obtained by the authors on the geometry of connections with totally skew-symmetric torsion on the following manifolds: almost complex manifolds with Norden metric, almost contact manifolds with B-metric and almost hypercomplex manifolds with Hermitianand anti-Hermitian metric.Group Rings – A Brief History and some their Generalizations
http://hdl.handle.net/10525/1464
Title: Group Rings – A Brief History and some their Generalizations<br/><br/>Authors: Mihovski, Stoil<br/><br/>Abstract: We give a brief exposition of the history of the group rings and some their generalizations. Also we indicate some information of certain problems andresults.Nonlinear Waves: An Introduction
http://hdl.handle.net/10525/1463
Title: Nonlinear Waves: An Introduction<br/><br/>Authors: Popivanov, Petar; Slavova, Angela<br/><br/>Abstract: This book deals with equations of mathematical physics as the differentmodifications of the KdV equation, the Camassa-Holm type equations, severalmodifications of Burger's equation, the Hunter-Saxton equation, conservation lawsequations and others. The equations originate from physics but are proposed herefor their investigation via purely mathematical methods in the frames of universitycourses. More precisely, we propose classification theorems for the traveling wavesolutions for a sufficiently large class of third order nonlinear PDE when thecorresponding profiles develop different kind of singularities (cusps, peaks),existence and uniqueness results, etc. The orbital stability of the periodic solutionsof traveling type for mKdV equations are also studied. Of great interest too is theinteraction of peakon type solutions of the Camassa-Holm equation and thesolvability of the classical and generalized Cauchy problem for the Hunter-Saxtonequation. The Riemann problem for special systems of conservation laws and thecorresponding -shocks are also considered. As it concerns numerical methods weapply the CNN approach.The book is addressed to a broader audience including graduate students,Ph.D. students, mathematicians, physicist, engineers and specialists in the domainof PDE.Percent in a Nutshell …
http://hdl.handle.net/10525/1462
Title: Percent in a Nutshell …<br/><br/>Authors: Rozov, Nikolai<br/><br/>Abstract: Ironically, the “learning of percent” is one of the most problematic aspects ofschool mathematics.In our view, these difficulties are not associated with the arithmetic aspects ofthe “percent problems”, but mostly with two methodological issues: firstly,providing students with a simple and accurate understanding of the rationalebehind the use of percent, and secondly - overcoming the psychologicalcomplexities of the fluent and comprehensive understanding by the students of thesometimes specific wordings of “percent problems”.Before we talk about percent, it is necessary to acquaint students with a muchmore fundamental and important (regrettably, not covered by the school syllabus)classical concepts of quantitative and qualitative comparison of values, to givestudents the opportunity to learn the relevant standard terminology and becomeaccustomed to conventional turns of speech.Further, it makes sense to briefly touch on the issue (important in its ownright) of different representations of numbers.Percent is just one of the technical, but common forms of data representation:p% = p × % = p × 0.01 = p × 1/100 = p/100 = p × 10-2"Percent problems” are involved in just two cases:I. The ratio of a variation m to the standard MII. The relative deviation of a variation m from the standard MThe hardest and most essential in each specific "percent problem” is not theroutine arithmetic actions involved, but the ability to figure out, to clearlyunderstand which of the variables involved in the problem instructions is thestandard and which is the variation. And in the first place, this is what teachersneed to patiently and persistently teach their students.As a matter of fact, most primary school pupils are not yet quite ready for thelexical specificity of “percent problems”. ....Math teachers should closely, hand in hand with their students, carry out a linguistic analysis of the wording of eachproblem ...Schoolchildren must firmly understand that a comparison of objects is onlymeaningful when we speak about properties which can be objectively expressed interms of actual numerical characteristics.In our opinion, an adequate acquisition of the teaching unit on percent cannotbe achieved in primary school due to objective psychological specificities relatedto this age and because of the level of general training of students. Yet, if we wantto make this topic truly accessible and practically useful, it should be taught in highschool.A final question to the reader (quickly, please): What is greater: % of e ore% of PiRolle's Theorem for Complex Polynomials with Real Coefficients
http://hdl.handle.net/10525/1461
Title: Rolle's Theorem for Complex Polynomials with Real Coefficients<br/><br/>Authors: Sendov, Blagovest<br/><br/>Abstract: Let p(z) be an algebraic polynomial of degree n ¸ 2 with real coefficientsand p(i) = p(¡i). According to Grace-Heawood Theorem, at least one zero ofthe derivative p0(z) is on the disk with center in the origin and radius cot(¼=n).In this paper is found the smallest domain containing at leas one zero of thederivative p0(z).Online Education: What Works in Mathematics
http://hdl.handle.net/10525/1460
Title: Online Education: What Works in Mathematics<br/><br/>Authors: Seppälä, Mika<br/><br/>Abstract: Florida State University and University of Helsinki Informationtechnology has the potential to deliver education to everybody by high qualityonline courses and associated services, and to enhance traditional face-to-faceinstruction by, e.g., web services offering virtually unlimited practice and step-bystepsolutions to practice problems. Regardless of this, tools of informationtechnology have not yet penetrated mathematics education in any meaningful way.This is mostly due to the inertia of academia: instructors are slow to change theirworking habits. This paper reports on an experiment where all the instructors(seven instructors and six teaching assistants) of a large calculus course wererequired to base their instruction on online content. The paper will analyze theeffectiveness of various solutions used, and finishes with recommendationsregarding best practices.Context-Aware and Adaptable Architecture CA
http://hdl.handle.net/10525/1459
Title: Context-Aware and Adaptable Architecture CA<br/><br/>Authors: Stoyanov, Stanimir<br/><br/>Abstract: In the paper some important notions and features of context-awareand adaptable service provision have been discussed. An approach has beendescribed which can be used to develop architectures with the mentioned features.The abstract architecture AC3 and its application for implementing an eLearningenvironment have been described as well.Motzkin Decomposable Sets
http://hdl.handle.net/10525/1458
Title: Motzkin Decomposable Sets<br/><br/>Authors: Todorov, Maxim<br/><br/>Abstract: Theodore Motzkin proved, in 1936, that any polyhedral convex set can beexpressed as the (Minkowski) sum of a polytope and a polyhedral convex cone. Wehave provided several characterizations of the larger class of closed convex sets,Motzkin decomposable, in finite dimensional Euclidean spaces which are the sumof a compact convex set with a closed convex cone. These characterizationsinvolve different types of representations of closed convex sets as the supportfunctions, dual cones and linear systems whose relationships are also analyzed. Theobtaining of information about a given closed convex set F and the parametriclinear optimization problem with feasible set F from each of its differentrepresentations, including the Motzkin decomposition, is also discussed. Anotherresult establishes that a closed convex set is Motzkin decomposable if and only ifthe set of extreme points of its intersection with the linear subspace orthogonal toits lineality is bounded. We characterize the class of the extended functions whoseepigraphs are Motzkin decomposable sets showing, in particular, that thesefunctions attain their global minima when they are bounded from below. Calculusof Motzkin decomposable sets and functions is provided.Distance Learning Education of Software Engineering: Principles and Experiences
http://hdl.handle.net/10525/1457
Title: Distance Learning Education of Software Engineering: Principles and Experiences<br/><br/>Authors: Zedan, Hussein<br/><br/>Abstract: Whether distance learning spells the end of traditional campuses, as somemaintain, or whether distance learning instead represents a powerful additionto a growing array of delivery options for higher education, its impact onhigher education is great and growing.Distance learning is creating alternative models of teaching and learning,new job descriptions for faculty, and new types of higher education providers.The advent of Distance and Distributed Learning has raised numerousquestions about quality and quality assurance:² How do established distance learning institutions ensure quality?² What more needs to be done?² How do quality assurance agencies view the distinction between on-and off-campus teaching and learning?This talk discusses these issues from the viewpoints of funding organisa-tion, quality assurance agencies and the learners.On Compositions in Equiaffine Space
http://hdl.handle.net/10525/1456
Title: On Compositions in Equiaffine Space<br/><br/>Authors: Badev, Ivan<br/><br/>Abstract: In an equiaffine space q N E using the connection define withprojective tensors naand mathe connections 1 , 2 and 3 . For thespaces N N 1A ,2A and N 3A , with coefficient of connection 1 , 2 and 3 respectively, we proved that the affinor of composition and the projective affinorshave equal covariant derivatives. It follows that the connection 3 is equaffineas well, and the connections and 3 are projective to each other. In thecase where q N E and N 3A have equal Ricci tensors, we find the fundamental nvector .In [4] compositions with structural affinor a are studied. Space containingcompositions with symmetric connection and Weyl connection are studied in [6]and [7] respectively.Application of an Acceleration Scheme for an Age-Structured Diffusion Model
http://hdl.handle.net/10525/1455
Title: Application of an Acceleration Scheme for an Age-Structured Diffusion Model<br/><br/>Authors: Boyadzhiev, Doychin<br/><br/>Abstract: In this paper we propose an optimized algorithm, which isfaster compared to previously described finite difference acceleration scheme,namely the Modified Super-Time-Stepping (Modified STS) scheme for age-structured population models with diffusion.