Table of contents

This volume of Journal of Physics: Conference Series is devoted to the selected papers presented in the 2015 International Conference on Mathematics, its Applications, and Mathematics Education (ICMAME 2015). ICMAME 2015 was held by Sanata Dharma University in Yogyakarta, Indonesia, on 14-15 September 2015. This Conference was conducted to bring together mathematicians and other scientists working on new trends of mathematics, physics, its applications and also on mathematics education.

More than 100 submissions were received by the committee for oral presentations. Peer-review was conducted after the Conference. Each full paper was reviewed by two or three referees. After review, 44 papers were accepted for publication. However, based on referees' recommendations, the editors decided that 20 papers would be selected for publication in this volume of Journal of Physics: Conference Series. The rest (24 other papers which are not selected to be in this Journal but still publishable) are included in the Proceedings Book of ICMAME 2015.

At least 200 people participated in this Conference. They were from, based on alphabetical order, Australia, Brazil, Cambodia, Germany, Indonesia, Malaysia, The Philippines, Timor-Leste, and Vietnam. Among them, we had seven keynote/plenary speakers:

Prof. Dr. Stephen Roberts (The Australian National University, Australia),

Prof. Dr. Lutz Gross (The University of Queensland, Australia),

Prof. em. Dr. Elmar Cohors-Fresenborg (The University of Osnabrueck, Germany),

Dr. Eka Budiarto (Swiss German University, Indonesia),

Dr. Yansen Marpaung (Sanata Dharma University, Indonesia),

Dr. Herry Pribawanto Suryawan (Sanata Dharma University, Indonesia), and

Dr. Hongki Julie (Sanata Dharma University, Indonesia).

We thank all of the speakers, participants and organising committee members for their contribution. In particular, we also thank our generous sponsor for the financial support to ICMAME 2015:

Australia Awards Indonesia Alumni Grant Scheme 2015 under project title "International Conference on Science and Education: ANUGA Software for Flood Mitigation in Indonesia".

Details of the conference committee can be found in the PDF

Photos from the conference can be viewed in the PDF

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

In this paper we propose the wavelet operational method based on shifted Legendre polynomial to obtain the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. The operational matrices of fractional derivative and collocation method turn the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques.

In this paper, we first define generalized shifted Jacobi polynomial on interval and then use it to define Jacobi wavelet. Then, the operational matrix of fractional integration for Jacobi wavelet is being derived to solve fractional differential equation and fractional integro-differential equation. This method can be seen as a generalization of other orthogonal wavelet operational methods, e.g. Legendre wavelets, Chebyshev wavelets of 1st kind, Chebyshev wavelets of 2nd kind, etc. which are special cases of the Jacobi wavelets. We apply our method to a special type of fractional integro-differential equation of Fredholm type.

We performed an investigation of the stability of fixed points in the complex Swift- Hohenberg equation using a variational formulation. The analysis is based on fixed points Euler-Lagrange equations and analytically showed that the Jacobian eigenvalues touched the imaginary axis and in general, Hopf bifurcation arises. The eigenvalues undergo a stability criterion in order to have Hopf's stability. Trial functions and linear loss dispersion parameter ε are responsible for the existence of stable pulse solutions in this system. We study behavior of the stable soliton-like solutions as we vary a bifurcation ε.

In this paper controllability and observability analysis are performed for the heat flow on the state-space of one dimension. The process is described by a semilinear parabolic partial differential equation. We report that the associated linear infinite-dimensional operator is a Riesz-spectral operator and generates a C₀-semigroup of bounded linear operators. Then we construct a sufficient and necessary condition for the approximate controllability and observability of the system. In particular, a finite number of dominant modes of the system are approximately observable when the input is measured at the heat output by an appropriate sensor.

Let be the sequence of k-Fibonacci numbers recursively defined by and m be a fixed positive integer. In this work we prove that, for almost every x (0,1), the pattern k, k,..., k (comprising of m-digits) appears in the continued fraction expansion x = [0; a₁,a₂,. ..] with frequency where where

We assume that all graphs in this paper are finite, undirected and no loop and multiple edges. Given a graph G of order p and size q. Let H',H be subgraphs of G. By H'-covering, we mean every edge in E(G) belongs to at least one subgraph of G isomorphic to a given graph H. A graph G is said to be an (a,d)-H-antimagic total labeling if there exist a bijective function f : V(G) ∪︀E(G) → {1, 2,...,p + q} such that for all subgraphs H' isomorphicto H,the total H-weights ω(H) = form an arithmetic sequence {a, a+d, a+2d,..., a+(s-1)d}, where a and d are positive integers and s is the number of all subgraphs H' isomorphic to H. Such a labeling is called super if f : V(G) → {1, 2,. .., | V(G)|}. In this paper, we will discuss a cycle-super (a,d)-atimagicness of a connected and disjoint union of semi jahangir graphs. The results show that those graphs admit a cycle-super (a,d)-atimagic total labeling for some feasible d ∈ {0,1, 2, 4, 6, 7,10,13,14}.

A fuzzy goal programming (FGP) model for biodiesel production in the Philippines was formulated with Coconut (Cocos nucifera) and Jatropha (Jatropha curcas) as sources of biodiesel. Objectives were maximization of feedstock production and overall revenue and, minimization of energy used in production and working capital for farming subject to biodiesel and non-biodiesel requirements, and availability of land, labor, water and machine time. All these objectives and constraints were assumed to be fuzzy. Model was tested for different sets of weights. Results for all sets of weights showed the same optimal allocation. Coconut alone can satisfy the biodiesel requirement of 2% per volume.

This paper presents an integrated single-vendor two-buyer production-inventory model with stochastic demand and service level constraints. Shortage is permitted in the model, and partial backordered partial lost sale. The lead time demand is assumed follows a normal distribution and the lead time can be reduced by adding crashing cost. The lead time and ordering cost reductions are interdependent with logaritmic function relationship. A service level constraint policy corresponding to each buyer is considered in the model in order to limit the level of inventory shortages. The purpose of this research is to minimize joint total cost inventory model by finding the optimal order quantity, safety stock, lead time, and the number of lots delivered in one production run. The optimal production-inventory policy gained by the Lagrange method is shaped to account for the service level restrictions. Finally, a numerical example and effects of the key parameters are performed to illustrate the results of the proposed model.

All Quality control of the bullet is usually done manually. Manual inspection process has some disadvantages for instance human error factor and the time inspection are relatively longer. In this study, defect detection and classification of bullets by using Support Vector Machine (SVM)has been done. The stages of classification of scheme bullets in this study include pre-processing, feature extraction with Principal Component Analysis (PCA) and classification of bullets by using SVM normalized. Performance of the proposed classification of scheme was tested using 80 images of bullets in which 40 images free of defects and 40 images with defect. The results show that the scheme can classify images of bullets with a 90% accuracy rate with test data in the form of 10 images free-defect and 10 image defects.

This study aims to explain stability of the spread of AIDS through treatment and vertical transmission model. Human with HIV need a time to positively suffer AIDS. The existence of a time, human with HIV until positively suffer AIDS can be delayed for a time so that the model acquired is the model with time delay. The model form is a nonlinear differential equation with time delay, SIPTA (susceptible-infected-pre AIDS-treatment-AIDS). Based on SIPTA model analysis results the disease free equilibrium point and the endemic equilibrium point. The disease free equilibrium point with and without time delay are local asymptotically stable if the basic reproduction number is less than one. The endemic equilibrium point will be local asymptotically stable if the time delay is less than the critical value of delay, unstable if the time delay is more than the critical value of delay, and bifurcation occurs if the time delay is equal to the critical value of delay.

The Ripa model is the system of shallow water equations taking the water temperature fluctuations into account. For one-dimensional case, the Ripa model consists of three partial differential equations relating to three primitive variables, namely water depth, velocity, and temperature. The Ripa model is hyperbolic, and its solution can be discontinuous. When the Ripa model is solved using a conservative numerical method, the solution is usually diffusive around discontinuities. The diffusion at rough regions (around discontinuities, such as contact and shock discontinuities) makes the solution inaccurate. In practice, we want to know the places where the solution is accurate, and where it is inaccurate. That is, we want to know where the solution is smooth, and where it is rough. In this paper we propose the numerical entropy production to detect the smoothness of numerical solutions to the Ripa model. Numerical results show that the numerical entropy production is a robust smoothness indicator for numerical solutions to the Ripa model.

A two-four finite difference scheme for Boussinesq equations was developed by Mohapatra and Chaudhry in 2004. This scheme is of course also applicable to solve the shallow water equations. However this scheme is not robust to deal with dry bed, that is, spurious oscillations appear around wet-dry areas. In this paper we propose a modified two-four finite difference scheme to solve the shallow water equations involving (almost) dry bed. The modified scheme has fewer number of divisions by zero or almost zero, and at the same time, only conserved quantities (mass and momentum) are used in the evolution of the new scheme. The modification lies on the discretisation of the momentum equation. We discretise the momentum equation using the momentum variable itself rather than using the velocity variable as done by Mohapatra and Chaudhry. Numerical results show that our proposed scheme is more robust for wetting and drying processes of the shallow water equations.

Vegetation in coastal area lead to wave mitigation has been studied by some researchers recently. The effect of vegetation forest in coastal area is minimizing the negative impact of wave propagation. In order to describe the effect of vegetation resistance into the water flow, the modified model of framework smoothed hydrodynamics particle has been constructed. In the Lagrangian framework, the Darcy, Manning, and laminar viscosity resistances are added. The effect of each resistances is given in some results of numerical simulations. Simulation of wave mitigation on sloping beach is also given.

This study aims to find out that there are differences in mathematical literacy ability in content Change and Relationship class VII Junior High School 19, Semarang by Problem Based Learning (PBL) model with an Indonesian Realistic Mathematics Education (called Pendidikan Matematika Realistik Indonesia or PMRI in Indonesia) approach assisted Elearning Edmodo, PBL with a PMRI approach, and expository; to know whether the group of students with learning PBL models with PMRI approach and assisted E-learning Edmodo can improve mathematics literacy; to know that the quality of learning PBL models with a PMRI approach assisted E-learning Edmodo has a good category; to describe the difficulties of students in working the problems of mathematical literacy ability oriented PISA. This research is a mixed methods study. The population was seventh grade students of Junior High School 19, Semarang Indonesia. Sample selection is done by random sampling so that the selected experimental class 1, class 2 and the control experiment. Data collected by the methods of documentation, tests and interviews. From the results of this study showed average mathematics literacy ability of students in the group PBL models with a PMRI approach assisted E-learning Edmodo better than average mathematics literacy ability of students in the group PBL models with a PMRI approach and better than average mathematics literacy ability of students in the expository models; Mathematics literacy ability in the class using the PBL model with a PMRI approach assisted E-learning Edmodo have increased and the improvement of mathematics literacy ability is higher than the improvement of mathematics literacy ability of class that uses the model of PBL learning with PMRI approach and is higher than the improvement of mathematics literacy ability of class that uses the expository models; The quality of learning using PBL models with a PMRI approach assisted E-learning Edmodo have very good category.

Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers' responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers' work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.

The aim of this study was to analyze the teachers' understanding on the concept of limits and derivative and the way they deliver the subjects to their students. The study was divided into two main phases during two years of research. This research was conducted in 7 high schools vary from general, Islamic and occasional schools. The participants of the study were 20 in-service mathematics teachers from 7 high schools. Questioners were given to find out how teachers' understanding on the concepts and how they organized their class. The teachers' level of complexity on the subject was analyzed by Structure of the Observed Learning Outcome (SOLO) Taxonomy, and teachers' class organizations was analyzed by assessing and classifying their responds written on the questioner sheets and discussion with the selected participants.. Based on the data, it can be figured out that the most teachers' position were on third level out of five level of SOLO Taxonomy. Data also told us that half of the teachers experienced the difficulties in teaching the concept due to their limitations on mastering subject. Data also showed that there is a relevance between teachers' level of understanding and teachers' ability in delivering subject to their students.

This study aims to explore the extent to which the use of analogy reasoning when students conduct conjecture in developing the scientific approach, so that the knowledge of the students can be used to build new knowledge. Analysis was conducted on student learning outcomes in Ciamis district. Based on these results, it was found the teacher not give an opportunity to the students to make conjecture on the students in problem solving as well as the construction of new knowledge. Moreover, teachers do not take advantage of analogical reasoning and scientific approach in constructing new knowledge.

This research aims to describe the process of implementation collaborative learning with AfL through giving feedback strategy for improving students' attention to mathematics lesson. Data which is collected in this research are students' attention towards learning and students' achievement. The result of this research showed that the learning steps by using collaborative learning with AfL through giving feedback strategy which can improve students' attention are: 1) pre activity: the teacher delivers the purpose of the learning, successful criteria, apperception, and motivation. 2) main activity: the teacher gives the background of learning activity, explains learning materials at a glance, divides students discuss, the teacher observes and guides students to the problem solving, present their discussion result, gives feedback, the students do AfL problem and the answer is collected and result will be given before next meeting. 3) post activity: the teacher with students concludes the material. Test result, the percentage of students who complete the examination in the second cycle is 77.27%. Based on those results can be concluded that the implementation of collaborative learning using AfL through giving feedback can improve students' attention towards learning and students' achievement of XI IPA Students MA Al-Islam Jamsaren Surakarta academic year 2013/2014.

This study used a model of Concurrent Embedded with the aim of: (1) determine the difference between the conceptual understanding and mathematical power of students grade fourth who take the constructivist learning using scientific approach and direct learning, (2) determine the interaction between learning approaches and initial competence on the mathematical power and conceptual of understanding, and (3) describe the mathematical power of students grade fourth. This research was conducted in the fourth grade elementary school early 2015. Data initial competence and mathematical power obtained through tests, and analyzed using statistical tests multivariate and univariate. Statistical analysis of the results showed that: (1) There are differences in the concept of understanding and mathematical power among the students who follow the scientifically-based constructivist learning than students who take the Direct Learning in terms of students initial competency (F = 5.550; p = 0.007 < 0.05), and (2) There is an interaction between the scientific-based constructivist learning approach with an initial competence (high and low) on the ability of concept of understanding and mathematical power (F = 5.259; p =0.033 < 0,05). Observations and in-depth interviews with students, shows that the construction of mathematical power of students have influenced the thinking of students in problem solving and contributes tremendous increase students' math skills. Researcher suggested that the learning of mathematics in schools using scientifically- based constructivist approach to improve the mathematical power of students and conceptual understanding.

This research was development research that aimed to develop and produce a Statistics textbook model that supported with information and communication technology (ICT) and Portfolio-Based Assessment. This book was designed for students of mathematics at the college to improve students' ability in mathematical connection and communication. There were three stages in this research i.e. define, design, and develop. The textbooks consisted of 10 chapters which each chapter contains introduction, core materials and include examples and exercises. The textbook developed phase begins with the early stages of designed the book (draft 1) which then validated by experts. Revision of draft 1 produced draft 2 which then limited test for readability test book. Furthermore, revision of draft 2 produced textbook draft 3 which simulated on a small sample to produce a valid model textbook. The data were analysed with descriptive statistics. The analysis showed that the Statistics textbook model that supported with ICT and Portfolio-Based Assessment valid and fill up the criteria of practicality.