Table of contents

Preface

The 1^st International Conference on Mathematics: Education, Theory, and Application (ICMETA) was held on December 6-7, 2016 at Universitas Sebelas Maret (UNS), Solo, Indonesia. The ICMETA is a conference that was first accomplished by Department of Mathematics, Universitas Sebelas Maret and planned to be held biennially.

The main objective of the conference is to gather world-class researchers, engineers, and educators engaged in the fields of mathematics and its applications to meet and present their latest activities. It provides a platform to disseminate research findings, and hopefully, it also sparks innovative ideas, foster research relations or partnership between the various institutions. As a scientific meeting event we invited experts from six different countries including Australia, the Netherlands, Indonesia, Japan, Malaysia, and France as keynote speakers.

We are grateful to all speakers for their presentations and all delegates who contributed for the success of this conference.

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.

The aims of this study is to detect the outliers by using coefficients of Ordinal Logistic Regression (OLR) for the case of k category responses where the score from 1 (the best) to 8 (the worst). We detect them by using the sum of moduli of the ordinal regression coefficients calculated by jackknife technique. This technique is improved by scalling the regression coefficients to their means. R language has been used on a set of ordinal data from reference distribution. Furthermore, we compare this approach by using studentised residual plots of jackknife technique for ANOVA (Analysis of Variance) and OLR. This study shows that the jackknifing technique along with the proper scaling may lead us to reveal outliers in ordinal regression reasonably well.

Given paired observation (x_i, v_1i, v_2i, ..., v_pi, t_1i, t_2i, ..., t_qi, y_i), i = 1, 2, ..., n, follow the additive semiparametric regression model y_i = μ(x_i, v_i, t_i) + _i, where

$$\begin{eqnarray*}&&\mu ({x}_{i},{{\bf{v}}}_{t},{{\bf{t}}}_{i})=f({x}_{i})+\displaystyle \sum _{j=1}^{p}{g}_{j}({\nu }_{ji})+\displaystyle \sum _{s=1}^{q}{h}_{s}({t}_{si})\end{eqnarray*}$$

${H}_{s}({t}_{si})={b}_{s}{t}_{si}+\frac{1}{2}{a}_{0s}+\displaystyle \sum _{k=1}^{N}{a}_{ks}\,\cos \,k{t}_{si}$

$\displaystyle \sum _{j=1}^{p}{g}_{j}({\nu }_{ji})$

$\displaystyle \sum _{j=1}^{p}{\hat{{\bf{g}}}}_{j{\varphi }_{j}}({\nu }_{ji})$

$\displaystyle \sum _{j=1}^{p}{\hat{{\bf{g}}}}_{j{\varphi }_{j}}({\nu }_{ji})={\bf{V}}({\boldsymbol{\Phi }}){\bf{y}}$

$$\begin{eqnarray*}&&\mathop{Min}\limits_{{\bf{c}},{\boldsymbol{\beta }}}\left\{L({\bf{c}})+L({\boldsymbol{\beta }})+\displaystyle \sum _{s=1}^{q}{\theta }_{s}S({H}_{s}({t}_{si}))\right\}\end{eqnarray*}$$

$\hat{{\bf{f}}}(x)$

$\displaystyle \sum _{s=1}^{q}{h}_{s}({t}_{si})$

$\displaystyle \sum _{s=1}^{q}{\hat{{\bf{h}}}}_{{\theta }_{s}}({t}_{si})$

$\hat{{\bf{f}}}(x)={\bf{X}}\hat{{\boldsymbol{\beta }}}$

$\displaystyle \sum _{s=1}^{q}{\hat{{\bf{h}}}}_{{\theta }_{s}}({t}_{si})={\bf{X}}\hat{{\bf{c}}}(\theta )$

$$\begin{eqnarray*}&&{\hat{{\boldsymbol{\mu }}}}_{{\boldsymbol{\Phi }},\theta, N}({{\bf{v}}}_{i},{{\bf{t}}}_{i})={\bf{Z}}({\boldsymbol{\Phi }},\theta, N){\bf{y}}\end{eqnarray*}$$

Matrix C(Φ, θ, N), V(Φ) and E(Φ, θ, N) are depended on Φ, θ and N. Optimal Φ, θ and N can be obtained by the smallest Generalized Cross Validation (GCV).

Let G = (V, E) be a simple, nontrivial, finite, connected and undirected graph. Let c be a coloring c : E(G) → {1, 2, ..., s}, s ∈ N. A path of edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph G is said to be a rainbow connected graph if there exists a rainbow u − v path for every two vertices u and v of G. The rainbow connection number of a graph G, denoted by rc(G), is the smallest number of k colors required to edge color the graph such that the graph is rainbow connected. Furthermore, for an l-connected graph G and an integer k with 1 ≤ k ≤ l, the rainbow k-connection number rc_k(G) of G is defined to be the minimum number of colors required to color the edges of G such that every two distinct vertices of G are connected by at least k internally disjoint rainbow paths. In this paper, we determine the exact values of rainbow connection number of some special graphs and obtain a sharp lower bound.

A total edge irregularity strength of G has been already widely studied in many papers. The total α-labeling is said to be a total edge irregular α-labeling of the graph G if for every two different edges e₁ and e₂, it holds w(e₁) ≠ w(e₂), where w(uv) = f(u) + f(uv) + f(v), for e = uv. The minimum α for which the graph G has a total edge irregular α-labeling is called the total edge irregularity strength of G, denoted by tes(G). A natural extension of this concept is by considering the evaluation of the weight is not only for each edge but we consider the weight on each subgraph H ⊆ G. We extend the notion of the total α-labeling into a total H-irregular α-labeling. The total α-labeling is said to be a total H-irregular α-labeling of the graph G if for H ⊆ G, the total H-weights W (H) = ∑_v∈V(H)f(v) + ∑e∈E(H) f(e) are distinct. The minimum α for which the graph G has a total H-irregular α-labeling is called the total H-irregularity strength of G, denoted by tHs(G). In this paper we initiate to study the tHs of shackle and amalgamation of any graphs and their bound.

Let G = (V, E) be a connected graphs with vertex set V (G), edge set E(G) and S ⊆ V (G). For an ordered partition Π = {S₁, S₂, S₃, ..., S_k} of V (G), the representation of a vertex v ∈ V (G) with respect to Π is the k-vectors r(v|Π) = (d(v, S₁), d(v, S₂), ..., d(v, S_k)), where d(v, S_k) represents the distance between the vertex v and the set S_k, defined by d(v, S_k) = min{d(v, x)|x ∈ S_k}. The partition Π of V (G) is a resolving partition if the k-vektors r(v|Π), v ∈ V (G) are distinct. The minimum resolving partition Π is a partition dimension of G, denoted by pd(G). The resolving partition Π = {S₁, S₂, S₃, ..., S_k} is called a star resolving partition for G if it is a resolving partition and each subgraph induced by S_i, 1 ≤ i ≤ k, is a star. The minimum k for which there exists a star resolving partition of V (G) is the star partition dimension of G, denoted by spd(G). Finding a star partition dimension of G is classified to be a NP-Hard problem. Furthermore, the comb product between G and H, denoted by G ⊲ H, is a graph obtained by taking one copy of G and |V (G)| copies of H and grafting the i-th copy of H at the vertex o to the i-th vertex of G. By definition of comb product, we can say that V (G ⊲ H) = {(a, u)|a ∈ V (G), u ∈ V (H)} and (a, u)(b, v) ∈ E(G ⊲ H) whenever a = b and uv ∈ E(H), or ab ∈ E(G) and u = v = o. In this paper, we will study the star partition dimension of comb product of cycle and complete graph, namely C_n ⊲ K_m and K_m ⊲ C_n for n ≥ 3 and m ≥ 3.

Research in education often involves a latent variable. Statistical analysis technique that has the ability to analyze the pattern of relationship among latent variables as well as between latent variables and their indicators is Structural Equation Modeling (SEM). SEM partial least square (PLS) was developed as an alternative if these conditions are met: the theory that underlying the design of the model is weak, does not assume a certain scale measurement, the sample size should not be large and the data does not have the multivariate normal distribution. The purpose of this paper is to compare the results of modeling of the educational quality in high school level (SMA/MA) in Sumenep Regency with structural equation modeling approach partial least square with three schemes estimation of score factors. This paper is a result of explanatory research using secondary data from Sumenep Education Department and Badan Pusat Statistik (BPS) Sumenep which was data of Sumenep in the Figures and the District of Sumenep in the Figures for the year 2015. The unit of observation in this study were districts in Sumenep that consists of 18 districts on the mainland and 9 districts in the islands. There were two endogenous variables and one exogenous variable. Endogenous variables are the quality of education level of SMA/MA (Y1) and school infrastructure (Y2), whereas exogenous variable is socio-economic condition (X1). In this study, There is one improved model which represented by model from path scheme because this model is a consistent, all of its indicators are valid and its the value of R-square increased which is: Y₁=0.651Y₂. In this model, the quality of education influenced only by the school infrastructure (0.651). The socio-economic condition did not affect neither the school infrastructure nor the quality of education. If the school infrastructure increased 1 point, then the quality of education increased 0.651 point. The quality of education had an R² of 0.418, which indicates that 41.8 percent of variance in the quality of education is explained by the school infrastructure, the remaining 58.2% is explained by the other factors which were not investigated in this work.

MGWR model is combination of linear regression model and geographically weighted regression (GWR) model, therefore, MGWR model could produce parameter estimation that had global parameter estimation, and other parameter that had local parameter in accordance with its observation location. The linkage between locations of the observations expressed in specific weighting that is adaptive bi-square. In this research, we applied MGWR model with weighted adaptive bi-square for case of DHF in Surakarta based on 10 factors (variables) that is supposed to influence the number of people with DHF. The observation unit in the research is 51 urban villages and the variables are number of inhabitants, number of houses, house index, many public places, number of healthy homes, number of Posyandu, area width, level population density, welfare of the family, and high-region. Based on this research, we obtained 51 MGWR models. The MGWR model were divided into 4 groups with significant variable is house index as a global variable, an area width as a local variable and the remaining variables vary in each. Global variables are variables that significantly affect all locations, while local variables are variables that significantly affect a specific location.

Ebola is a deadly infectious disease and has caused an epidemic on several countries in West Africa. Mathematical modeling to study the spread of Ebola disease has been developed, including through models susceptible infected removed (SIR) and susceptible exposed infected removed (SEIR). Furthermore, susceptible exposed infected isolated recovered (SEII_hR) model has been derived. The aims of this research are to derive SEII_hR model for Ebola disease, to determine the patterns of its spread, to determine the equilibrium point and stability of the equilibrium point using phase plane analysis, and also to apply the SEII_hR model on Ebola epidemic in Sierra Leone in 2014. The SEII_hR model is a differential equation system. Pattern of ebola disease spread with SEII_hR model is solution of the differential equation system. The equilibrium point of SEII_hR model is unique and it is a disease-free equilibrium point that stable. Application of the model is based on the data Ebola epidemic in Sierra Leone. The free-disease equilibrium point (S_e; E_e; I_e; I_he; R_e)=(5743865, 0, 0, 0, 0) is stable.

The demand of a product is linearly dependent on the retail price and quality of the product. We address a closed-loop supply chain where the manufacturer manufactures products according to the demand and sells them through a retailer in the market. A third party collects the used products from costumers and sends to the manufacturer to increase the quality. If the products can retrieve the original quality, thus the process is called remanufacturing. Not every products can retrieve the original quality, thus manufacturer refurbish this products with lower price. We construct four different scenarios – centralized and decentralized led by manufacturer, retailer, and third party. From the comparison of the result obtained in the numerical example, we conclude that the joint profit obtained under centralized, manufacturer-led, and retailer-led policies is higher than third party-led policy.

All graphs in this paper are simple, finite, and undirected graph. Let r be a edges of H. The edge comb product between L and H, denoted by L⊵H, is a graph obtained by taking one copy of L and |E(L)| copies of H and grafting the i-th copy of H at the edges r to the i-th edges of L, we call such a graph as an edge comb product of graph with subgraph as a terminal of its amalgamation, denoted by G = K⊵Amal(H, L ⊂ H, n). The graph G is said to admits an (a, d)-H-antimagic total labeling if there exist a bijection f : V(G) ∪ E(G) → {1, 2, ..., |V (G)| + |E(G)|} such that for all subgraphs isomorphic to H, the total H-weights W (H) = ∑_v∈V(H)f(v) + ∑e∈E(H) f(e) form an arithmetic sequence {a, a + d, a + 2d, ..., a + (t − 1)d}, where a and d are positive integers and t is the number of all subgraphs isomorphic to H. An (a, d)-H-antimagic total labeling f is called super if the smallest labels appear in the vertices. In this paper, we will study the super H−antimagicness of disjoint union of edge comb product of graphs with subgraph as a terminal of its amalgamation.

Let G be a simple, connected and undirected graph. Let r, k be natural numbers. By a proper k-coloring of a graph G, we mean a map c : V (G) → S, where |S| = k, such that any two adjacent vertices receive different colors. An r-dynamic k-coloring is a proper k-coloring c of G such that |c(N(v))| ≥ min{r, d(v)} for each vertex v in V (G), where N(v) is the neighborhood of v and c(S) = {c(v) : v ∈ S} for a vertex subset S. The r-dynamic chromatic number, written as χ_r(G), is the minimum k such that G has an r-dynamic k-coloring. By simple observation it is easy to see that χ_r(G) ≤ χ_r+1(G), however χ_r+1(G) − χ_r(G) does not always show a small difference for any r. Thus, finding an exact value of χ_r(G) is significantly useful. In this paper, we will study some of them especially when G are prism graph, three-cyclical ladder graph, joint graph and circulant graph.

Let G be a connected graph with vertex set V (G), such that V (G) can be divided into any partition set S. The set Π with S ∈ Π is a resolving partition of G if each vertex in G has a distinct representation with respect to Π, and Π is an ordered k−partition. The minimum cardinality of resolving k−partitions of V (G) is called a partition dimension of G, denoted by pd(G). The lollipop graph L_m,n is a graph obtained by joining a complete graph K_m to a path P_n with a bridge. A generalized Jahangir graph is a graph consisting of a cycle C_mn and one additional vertex which is adjacent to n vertices of C_mn at m distance to each other on C_mn. Many researchers have conducted research in determining the partition dimension for speci c graph classes. They are as references to determine some of the graph classes that haven't been studied previously.

In this paper, we determine the partition dimension of a lollipop graph L_m,n and a generalized Jahangir graph J_m,n. The research methods in this paper is a book study.

The results of this paper are as follows. We obtain the partition dimension of a lollipop graph pd(L_m,n) = m for m ≥ 3 and n ≥ 1. The partition dimension of a generalized Jahangir graph consists of two cases. We showed that pd(J_m,n) = 3 for n = 3, 4, 5 and we prove that $pd({J}_{m,n})=\lfloor \frac{n}{2}\rfloor +1\,\mathrm{for}\,n\ge 6$.

Product take-back recovery has currently became a promising effort for companies in order to create a sustainable supply chain. In addition, some restrictions including government regulations, social-ethical responsibilities, and up to economic factors have contributed to the reasons for the importance of product take-back recovery. This study aims to develop an inventory model in a system of reverse logistic management consisting of a manufacturer and a collector. Recycle dealer collects used products from the market and ships it to manufacturer. Manufacturer then recovers the used products and sell it eventually to the market. Some recovered products that can not be recovered as good as new one will be sold to the secondary market. In this study, we investigate the effects of environmental factors including GHG emissions and energy usage from transportation, regular production, and remanufacturing operations conducted by manufacturer and solve the model to get the maximum annual joint total profit for both parties. The model also considers price-dependent return rate and determine it as a decision variable as well as number of shipments from collector to manufacturer and optimal cycle period. An iterative procedure is proposed to determine the optimal solutions. We present a numerical example to illustrate the application of the model and perform a sensitivity analysis to study the effects of the changes in environmental related costs on the model's decision.

Let G = (V, E) be a simple, nontrivial, finite, connected and undirected graph. For an integer 1 ≤ k ≤ diam(G), a distance k-dominating set of a connected graph G is a set S of vertices of G such that every vertex of V (G)\S is at distance at most k from some vertex of S. The k-domination number, denoted by γ_k(G), of G is the minimum cardinality of a k-dominating set of G. In this paper, we improve the lower bound on the distance domination number of G regarding to the diameter and minimum degree as well as the upper bound regarding to the order and minimum k distance neighbourhood. In addition, we determine the bound of distance domination number of edge comb product graph.

The planning of planting period became non-optimal due to the uncertain rainfall fluctuation condition in the past few years. To anticipate food insecurity caused by such a matter, the development of rainfall prediction models in several rice production areas in Central Java, which represent the center for rice production, is required. This paper provides the application of GSTAR model on the rainfall data in Sragen Regency, Karanganyar Regency, and Klaten Regency with considering time and location conditions. The weighting applied in the model was normalized cross-correlation. By applying the least square method and stepwise procedure, GSTAR model for six, seven in Sragen, seven areas in Karanganyar, and seven areas in Klaten respectively was obtained. The validity of the model was tested by applying RMSE.

This paper presents a new method on passive copy-move forgery detection by exploiting the effectiveness and usability of Halftoning-based Block Truncation Coding (HBTC) image feature. Copy-move forgery detection precisely locates the large size or flat tampered regions of an image. On our method, the tampered input image is firstly divided into several overlapping image blocks to construct the image feature descriptors. Each image block is further divided into several non-overlapping image blocks for processing HBTC. Two image feature descriptors, namely Color Feature (CF) and Bit Pattern Feature (BF) are computed from the HBTC compressed data-stream of each image block. Lexicography sorting rearranges the image feature descriptors in ascending manner for whole image. The similarity between some tampered image regions is measured based on their CF and BF under specific shift frequency threshold. As documented in the experimental results, the proposed method yields a promising result for detecting the tampered or copy-move forgery regions. It has proved that the HBTC is not only suitable for image compression, but it can also be used in the copy-move forgery detection.

Direct observation results are often used to review the estimation model. However, actual data observation findings still need to be re-examined, because of measurement error factors (ME). In the regression modeling if X is a random variable with Measurement Error then the complicated calculation will not loose from application of Computer and Technology. As is the case for a review of the following model estimation, given data (Xi, Yi), then the regression model is

Y_i = g(X_i) + _i

where Xi is the element i from the predictor variables X and Yi is the element i of the response variable Y. The variable X is the predictor variables From the findings specific observations usually are constants, but generally found X which is a random variable variable or where Fixed value is not constant. In this case is called the regression model Regression Model with the measurement Errors. Purpose of this research are estimated nonparametric model approach with B-Spline Method to review regression with Measurement Errors are ignored and methods Iterative Conditional Mode (ICM) for review Model regression with measurement error.

Let G be a simple, connected and undirected graph with vertex set V and edge set E. A total k-labeling f : V ∪ E → {1, 2, ..., k} is defined as totally irregular total k-labeling if the weights of any two different both vertices and edges are distinct. The weight of vertex x is defined as wt(x) = f(x) + ∑_xy∈Ef(xy), while the weight of edge xy is wt(xy) = f(x) + f(xy) + f(y). A minimum k for which G has totally irregular total k-labeling is mentioned as total irregularity strength of G and denoted by ts(G). This paper contains investigation of totally irregular total k-labeling for caterpillar graphs S_n,2,m and determination of their total irregularity strengths. In addition, the total vertex and total edge irregularity strength of this graph also be determined. The results are $tvs({S}_{n,2,m})=\lceil \frac{n+m-1}{2}\rceil, \,tes({S}_{n,2,m})=\lceil \frac{n+m+2}{3}\rceil$, and $ts({S}_{n,2,m})=\lceil \frac{n+m-1}{2}\rceil$ for n, m ≥ 3.

This research is aimed to find out the effect of learning model towards learning achievement in terms of students' logical mathematics intelligences. The learning models that were compared were NHT by Concept Maps, TGT by Concept Maps, and Direct Learning model. This research was pseudo experimental by factorial design 3×3. The population of this research was all of the students of class XI Natural Sciences of Senior High School in all regency of Karanganyar in academic year 2016/2017. The conclusions of this research were: 1) the students' achievements with NHT learning model by Concept Maps were better than students' achievements with TGT model by Concept Maps and Direct Learning model. The students' achievements with TGT model by Concept Maps were better than the students' achievements with Direct Learning model. 2) The students' achievements that exposed high logical mathematics intelligences were better than students' medium and low logical mathematics intelligences. The students' achievements that exposed medium logical mathematics intelligences were better than the students' low logical mathematics intelligences. 3) Each of student logical mathematics intelligences with NHT learning model by Concept Maps has better achievement than students with TGT learning model by Concept Maps, students with NHT learning model by Concept Maps have better achievement than students with the direct learning model, and the students with TGT by Concept Maps learning model have better achievement than students with Direct Learning model. 4) Each of learning model, students who have logical mathematics intelligences have better achievement then students who have medium logical mathematics intelligences, and students who have medium logical mathematics intelligences have better achievement than students who have low logical mathematics intelligences.

Radiation isocenter is more important part of quality assurance for the linear accelerator (Linac) due to radiation isocenter is a main location in irradiation radiotherapy, isocenter can shift when the gantry and collimator rotation. In general, the radiation isocenter verification using a special film. This research was conducted radiation isocenter verification using computed radiography with digital image processing techniques. Image acquisition was done using the modalities of Linac 6 MV with star shot method is star-shaped beam due to rotation of the collimator, gantry and couch. Then do the delineation on each beam to determine the centroid and beam diameter. By the results of verification of radiation isocenter performed on collimator and the couch, it shows that the size diameter for rotational collimator is 0.632 mm and 0.458 mm for the couch. Based on AAPM report 40 about the size of the Linac radiation isocenter diameter used in this study is still in good condition and worth to be operated because the value of the radiation isocenter diameter is below 2 mm.

This research aimed to analyse students' mathematical representations on secondary school in solving trigonometric problems. This research used qualitative method. The participants were 4 students who had high competence of knowledge taken from 20 students of 12th natural-science grade SMAN-1 Kota Besi, Central Kalimantan. Data validation was carried out using time triangulation. Data analysis used Huberman and Miles stages. The results showed that their answers were not only based on the given figure, but also used the definition of trigonometric ratio on verbal representations. On the other hand, they were able to determine the object positions to be observed. However, they failed to determine the position of the angle of depression at the sketches made on visual representations. Failure in determining the position of the angle of depression to cause an error in using the mathematical equation. Finally, they were unsuccessful to use the mathematical equation properly on symbolic representations. From this research, we could recommend the importance of translations between mathematical problems and mathematical representations as well as translations among mathematical representaions (verbal, visual, and symbolic) in learning mathematics in the classroom.

In this study, we consider a stochastic integrated manufacturer-retailer inventory model with service level constraint. The model analyzed in this article considers the situation in which the vendor and the buyer establish a long-term contract and strategic partnership to jointly determine the best strategy. The lead time and setup cost are assumed can be controlled by an additional crashing cost and an investment, respectively. It is assumed that shortages are allowed and partially backlogged on the buyer's side, and that the protection interval (i.e., review period plus lead time) demand distribution is unknown but has given finite first and second moments. The objective is to apply the minmax distribution free approach to simultaneously optimize the review period, the lead time, the setup cost, the safety factor, and the number of deliveries in order to minimize the joint total expected annual cost. The service level constraint guarantees that the service level requirement can be satisfied at the worst case. By constructing Lagrange function, the analysis regarding the solution procedure is conducted, and a solution algorithm is then developed. Moreover, a numerical example and sensitivity analysis are given to illustrate the proposed model and to provide some observations and managerial implications.

In this paper, we study the identification of variables on a model reduction process and estimation of variables on reduced system. We aim to relate variables on reduced and original system, so that we can compare the estimation accuracy of the original system and reduced system. As such, the objective of this paper is to discuss identification and estimation of variables on reduced model. First, model order reduction is done by using balanced truncation method. This process begins with the construction of balanced system. After that, we identify the relationship between variables of the balanced system and the original system. Then, we eliminate variables of the balanced system that have a small influence on the system. Furthermore, we estimate state variables on the original system and reduced system using a Kalman Filter algorithm. Finally, we compare the estimation result of the identified reduced and original system.

The SIS epidemic model describes the pattern of disease spread with characteristics that recovered individuals can be infected more than once. The number of susceptible and infected individuals every time follows the discrete time Markov process. It can be represented by the discrete time Markov chains (DTMC) SIS. The DTMC SIS epidemic model can be developed for two pathogens in two patches. The aims of this paper are to reconstruct and to apply the DTMC SIS epidemic model with two pathogens in two patches. The model was presented as transition probabilities. The application of the model obtain that the number of susceptible individuals decreases while the number of infected individuals increases for each pathogen in each patch.

In this study, a statistical analysis is performed by model the variations of the disabled about 0-19 years old population among French departments. The aim is to classify the departments according to their profile determinants (socioeconomic and behavioural profiles). The analysis is focused on two types of methods: principal component analysis (PCA) and multiple correspondences factorial analysis (MCA) to review which one is the best methods for interpretation of the correlation between the determinants of disability (independent variable). The PCA is the best method for interpretation of the correlation between the determinants of disability (independent variable). The PCA reduces 14 determinants of disability to 4 axes, keeps 80% of total information, and classifies them into 7 classes. The MCA reduces the determinants to 3 axes, retains only 30% of information, and classifies them into 4 classes.

Stocks are known as the financial instruments traded in the capital market which have a high level of risk. Their risks are indicated by their uncertainty of their return which have to be accepted by investors in the future. The higher the risk to be faced, the higher the return would be gained. Therefore, the measurements need to be made against the risk. Value at Risk (VaR) as the most popular risk measurement method, is frequently ignore when the pattern of return is not uni-modal Normal. The calculation of the risks using VaR method with the Normal Mixture Autoregressive (MNAR) approach has been considered. This paper proposes VaR method couple with the Mixture Laplace Autoregressive (MLAR) that would be implemented for analysing the first three biggest capitalization Islamic stock return in JII, namely PT. Astra International Tbk (ASII), PT. Telekomunikasi Indonesia Tbk (TLMK), and PT. Unilever Indonesia Tbk (UNVR). Parameter estimation is performed by employing Bayesian Markov Chain Monte Carlo (MCMC) approaches.

Competition between the homoneous companies cause the company have to keep production quality. To cover this problem, the company controls the production with statistical quality control using control chart. Shewhart control chart is used to normal distributed data. The production data is often non-normal distribution and occured small process shift. Grand median control chart is a control chart for non-normal distributed data, while cumulative sum (cusum) control chart is a sensitive control chart to detect small process shift. The purpose of this research is to compare grand median and cusum control charts on shuttlecock weight variable in CV Marjoko Kompas dan Domas by generating data as the actual distribution. The generated data is used to simulate multiplier of standard deviation on grand median and cusum control charts. Simulation is done to get average run lenght (ARL) 370. Grand median control chart detects ten points that out of control, while cusum control chart detects a point out of control. It can be concluded that grand median control chart is better than cusum control chart.

In this paper the -integral of sequence-valued functions, the new concept of integral theory, is constructed. The concept is based on the M_α-integral. We report some of the fundamental properties of the -integral including the uniqueness, linearity, the Cauchy criterion for integrability and the Henstock Lemma.

In this paper, we discuss the reduction of unstable systems. Suppose we have a large-scale unstable system. The reduction of such systems are done in order to obtain a simpler model that has a similar behavior with the original model. In reality, a higher order model is not preferred because the computation takes more time. Thus we need a method to reduce the order of a model that is known as model reduction. Model reduction of a system is the method of approximation of a system with a lower order but the dynamic behavior is equal or almost equal to the original model. In this paper, we discuss model reduction of unstable systems. Finally this method is applied to shallow water equation that describes the flow of water in rivers: we obtain a procedure for model reduction of unstable systems and the reduced model of shallow water equations.

This study aims to describe how conjecturing process and generalization process of structural development to thirty children in middle school at grade 8 in solving problems of patterns. Processing of the data in this study uses qualitative data analysis techniques. The analyzed data is the data obtained through direct observation technique, documentation, and interviews. This study based on research studies Mulligan et al (2012) which resulted in a five - structural development stage, namely prestructural, emergent, partial, structural, and advance. From the analysis of the data in this study found there are two phenomena that is conjecturing and generalization process are related. During the conjecturing process, the childrens appropriately in making hypothesis of patterns problem through two phases, which are numerically and symbolically. Whereas during the generalization of process, the childrens able to related rule of pattern on conjecturing process to another context.

Internet enables information to be accessible anytime and anywhere. This scenario creates an environment whereby information can be easily copied. Easy access to the internet is one of the factors which contribute towards piracy in Malaysia as well as the rest of the world. According to a survey conducted by Compliance Gap BSA Global Software Survey in 2013 on software piracy, found out that 43 percent of the software installed on PCs around the world was not properly licensed, the commercial value of the unlicensed installations worldwide was reported to be $62.7 billion. Piracy can happen anywhere including universities. Malaysia as well as other countries in the world is faced with issues of piracy committed by the students in universities. Piracy in universities concern about acts of stealing intellectual property. It can be in the form of software piracy, music piracy, movies piracy and piracy of intellectual materials such as books, articles and journals. This scenario affected the owner of intellectual property as their property is in jeopardy. This study has developed a classification model for detecting software piracy. The model was developed using a swarm intelligence algorithm called the Ant Colony Optimization algorithm. The data for training was collected by a study conducted in Universiti Teknologi MARA (Perlis). Experimental results show that the model detection accuracy rate is better as compared to J48 algorithm.

Code-based Cryptography (CBC) is a powerful and promising alternative for quantum resistant cryptography. Indeed, together with lattice-based cryptography, multivariate cryptography and hash-based cryptography are the principal available techniques for post-quantum cryptography. CBC was first introduced by McEliece where he designed one of the most efficient Public-Key encryption schemes with exceptionally strong security guarantees and other desirable properties that still resist to attacks based on Quantum Fourier Transform and Amplitude Amplification.

The original proposal, which remains unbroken, was based on binary Goppa codes. Later, several families of codes have been proposed in order to reduce the key size. Some of these alternatives have already been broken.

One of the main requirements of a code-based cryptosystem is having high performance t-bounded decoding algorithms which is achieved in the case the code has a t-error-correcting pair (ECP). Indeed, those McEliece schemes that use GRS codes, BCH, Goppa and algebraic geometry codes are in fact using an error-correcting pair as a secret key. That is, the security of these Public-Key Cryptosystems is not only based on the inherent intractability of bounded distance decoding but also on the assumption that it is difficult to retrieve efficiently an error-correcting pair.

In this paper, the class of codes with a t-ECP is proposed for the McEliece cryptosystem. Moreover, we study the hardness of distinguishing arbitrary codes from those having a t-error correcting pair.

In this paper, we present a procedure for modeling earthquake based on spatial-temporal point process. The magnitude distribution is expressed as truncated exponential and the event frequency is modeled with a spatial-temporal point process that is characterized uniquely by its associated conditional intensity process. The earthquakes can be regarded as point patterns that have a temporal clustering feature so we use self-exciting point process for modeling the conditional intensity function. The choice of main shocks is conducted via window algorithm by Gardner and Knopoff and the model can be fitted by maximum likelihood method for three random variables.

Dr Yap Eye Hospital Yogyakarta is one of the most popular reference eye hospitals in Yogyakarta. There are so many patients coming from other cities and many of them are BPJS (Badan Penyelenggara Jaminan Sosial, Social Security Administrative Bodies) patients. Therefore, it causes numerous BPJS patients were in long queue at counter C of the registration section so that it needs to be analysed using queue system. Queue system analysis aims to give queue model overview and determine its effectiveness measure. The data collecting technique used in this research are by interview and observation. After getting the arrival data and the service data of BPJS patients per 5 minutes, the next steps are investigating steady-state condition, examining the Poisson distribution, determining queue models, and counting the effectiveness measure. Based on the result of data observation on Tuesday, February 16th, 2016, it shows that the queue system at counter C has (M/M/1):(GD/∞/∞) queue model. The analysis result in counter C shows that the queue system is a non-steady-state condition. Three ways to cope a non-steady-state problem on queue system are proposed in this research such as bounding the capacity of queue system, adding the servers, and doing Monte Carlo simulation. The queue system in counter C will reach steady-state if the capacity of patients is not more than 52 BPJS patients or adding one more server. By using Monte Carlo simulation, it shows that the effectiveness measure of the average waiting time for BPJS patients in counter C is 36 minutes 65 seconds. In addition, the average queue length of BPJS patients is 11 patients.

An ordered set of vertices S is called as a (local) resolving set of a connected graph G = (V_G, E_G) if for any two adjacent vertices s ≠ t ∈ V_G have distinct representation with respect to S, that is r(s | S) ≠ r(t | S). A representation of a vertex in G is a vector of distances to vertices in S. The minimum (local) resolving set for G is called as a (local) basis of G. A (local) metric dimension for G denoted by dim(G), is the cardinality of vertices in a basis for G, and its local variant by dim_l(G).

Given two graphs, G with vertices s₁, s₂, ..., s_p and edges e₁, e₂, ..., e_q, and H. An edge-corona of G and H, G◊H is defined as a graph obtained by taking a copy of G and q copies of H and for each edge e_j = s_is_h of G joining edges between the two end-vertices s_i, s_h of e_j and each vertex of j-copy of H.

In this paper, we determine and compare between the metric dimension of graphs with m-pendant points, G◊mK₁, and its local variant for any connected graph G. We give an upper bound of the dimensions.

This paper elaborates a research of the cancer patients after receiving a treatment in cencored data using Bayesian estimation under Linex Loss function for Survival Model which is assumed as an exponential distribution. By giving Gamma distribution as prior and likelihood function produces a gamma distribution as posterior distribution. The posterior distribution is used to find estimatior ${\hat{\lambda }}_{BL}$ by using Linex approximation. After getting ${\hat{\lambda }}_{BL}$, the estimators of hazard function ${\hat{h}}_{BL}$ and survival function ${\hat{S}}_{BL}$ can be found. Finally, we compare the result of Maximum Likelihood Estimation (MLE) and Linex approximation to find the best method for this observation by finding smaller MSE. The result shows that MSE of hazard and survival under MLE are 2.91728E-07 and 0.000309004 and by using Bayesian Linex worths 2.8727E-07 and 0.000304131, respectively. It concludes that the Bayesian Linex is better than MLE.

Let G(V (G), E(G)) be a finite simple graph with |V (G)| = _G and |E(G)| = e_G. Let H be a subgraph of G. The graph G is said to be (a, d)-H-antimagic covering if every edge in G belongs to at least one of the subgraphs G isomorphic to H and there is a bijective function ξ : V ∪ E → {1, 2, ...,ν_G + e_G} such that all subgraphs H^' isomorphic to H, the H^'-weights

$$\begin{eqnarray*}&&w(H^{\prime} )=\displaystyle {\sum }_{v\in V(H^{\prime} )}\xi (v)+\displaystyle {\sum }_{e\in E(H^{\prime} )}\xi (e)\end{eqnarray*}$$

Curriculum 2013 is the new national Curriculum in Indonesia that is targeted to be used in all Indonesian schools in 2019. At this time the teacher training continues but the number and locations of teachers very diffuse and time constraints to be an obstacle for the government to be able to conduct training for teachers. This research resulted in the e-tutorial which is designed for mathematics teachers in studying the process of Curriculum implementation. This product will assist the government in accelerating the preparation of teachers in implementation of Curriculum 2013. This e-tutorial contains the dynamics of Curriculum development, learning model, learning assessment, lesson plan, curriculum stages of implementation and government regulation that is relevant to the implementation of Curriculum 2013. The product development started with a needs analysis through discussions with mathematics teachers about their difficulties in the implementation of the Curriculum 2013. This e-tutorial was developed using Application of Adobe Director 11. This paper discusses the results of need analysis, process development and results of product revisions made based on input from teachers during the FGD. From the discussion, it can be concluded that this e-tutorial easily understood by teachers and help them to understand the implementation of Curriculum 2013

Hurdle negative binomial model regression is a method that can be used for discreate dependent variable, excess zero and under- and overdispersion. It uses two parts approach. The first part estimates zero elements from dependent variable is zero hurdle model and the second part estimates not zero elements (non-negative integer) from dependent variable is called truncated negative binomial models. The discrete dependent variable in such cases is censored for some values. The type of censor that will be studied in this research is right censored. This study aims to obtain the parameter estimator hurdle negative binomial regression for right censored dependent variable. In the assessment of parameter estimation methods used Maximum Likelihood Estimator (MLE). Hurdle negative binomial model regression for right censored dependent variable is applied on the number of neonatorum tetanus cases in Indonesia. The type data is count data which contains zero values in some observations and other variety value. This study also aims to obtain the parameter estimator and test statistic censored hurdle negative binomial model. Based on the regression results, the factors that influence neonatorum tetanus case in Indonesia is the percentage of baby health care coverage and neonatal visits.

Flood forecasting is widely being studied in order to reduce the effect of flood such as loss of property, loss of life and contamination of water supply. Usually flood occurs due to continuous heavy rainfall. This study used a variant of Ant Colony Optimization (ACO) algorithm named the Ant-Miner to develop the classification prediction model to predict flood. However, since Ant-Miner only accept discrete data, while rainfall data is a time series data, a pre-processing steps is needed to discretize the rainfall data initially. This study used a technique called the Symbolic Aggregate Approximation (SAX) to convert the rainfall time series data into discrete data. As an addition, Simple K-Means algorithm was used to cluster the data produced by SAX. The findings show that the predictive accuracy of the classification prediction model is more than 80%.

This study we investigate whether the emphasis in mathematics courses for engineering students would benefit from being more conceptually oriented than more procedurally oriented way of teaching. In this paper, we report in some detail from twenty-five engineering students comes from three departements ; mechanical engineering, civil engineering and industrial engineering. The aim was to explore different kinds of arguments regarding the role of mathematics in engineering courses, as well as some common across contexts. The result of interview showed that most of engineering students feel that conceptual mathematics is more important than procedural mathematics for their job the future.

A simple graph G = (V; E) admits an H-covering if every edge in E belongs to a subgraph on G that isomorphic to H. A graph G is H-magic if there is exists a total labeling f : V (G)∪E(G) → {1, 2, ..., |V|+|E|}, such that each subgraph H^' = (V^'(H^'); E^'(H^')) on G satisfies f(H^') = ∑_v∈V'f(v) + ∑_e∈E'f(e) = m(f), where m(f) is a constant magic sum. A graph G is a H-supermagic labeling if f(V ) = {1, ..., |V|} and s(f) is a constant supermagic sum. The research aims to study a H-supermagic labeling on corona product of a star graph with a path and a wheel graph with a path. We prove that the corona product of a star graph with a path S_n ⊙ P_m is a U_m,2-supermagic for m is odd or m, n are even and m ≥ 3 and the corona product of a wheel graph with a path W_n ⊙ P_m is a C₃ ⊙ P_m-supermagic for m ≥ 3.

Evaluation and assessment is an important part of learning. In evaluation process of learning, written test is still commonly used. However, the tests usually do not following-up by further evaluation. The process only up to grading stage not to evaluate the process and errors which done by students. Whereas if the student has a pattern error and process error, actions taken can be more focused on the fault and why is that happen. NEA procedure provides a way for educators to evaluate student progress more comprehensively. In this study, students' mistakes in working on some word problem about linear programming have been analyzed. As a result, mistakes are often made students exist in the modeling phase (transformation) and process skills (process skill) with the overall percentage distribution respectively 20% and 15%. According to the observations, these errors occur most commonly due to lack of precision of students in modeling and in hastiness calculation. Error analysis with students on this matter, it is expected educators can determine or use the right way to solve it in the next lesson.

The aim of rudder-roll stabilization (RSS) is controlling ship heading and reducing roll motion simultaneously using one actuator, rudder. In this paper, RSS using FGS-PID for SIGMA-e warship was performed, both in normal and disturbed sea conditions. The fuzzy system for determining PID controller are constructed from SIGMA-e linear mathematical model. The wave disturbances are generated based on the WMO. The results show that FGS-PID has superior performance compared to conventional PID controller in heading control and roll damping. It means that the proposed control method can encounter the environmental changes.

Behaviour analysis for host-vector model without control of dengue disease is based on the value of basic reproduction number obtained using next generation matrices. Furthermore, the model is further developed involving a preventive control to minimize the contact between host and vector. The purpose is to obtain an optimal preventive strategy with minimal cost. The Pontryagin Minimum Principal is used to find the optimal control analytically. The derived optimality model is then solved numerically to investigate control effort to reduce infected class.

In this paper, it is presented how to cluster inflation data of cities in Indonesia by using k-means cluster method and fuzzy c-means method. The data that are used is limited to the monthly inflation data from 15 cities across Indonesia which have highest weight of donations and is supplemented with 5 cities used in the calculation of inflation in Indonesia. When they are applied into two clusters with k = 2 for k-means cluster method and c = 2, w = 1.25 for fuzzy c-means cluster method, Ambon, Manado and Jayapura tend to become one cluster (high inflation) meanwhile other cities tend to become members of other cluster (low inflation). However, if they are applied into two clusters with c=2, w=1.5, Surabaya, Medan, Makasar, Samarinda, Makasar, Manado, Ambon dan Jayapura tend to become one cluster (high inflation) meanwhile other cities tend to become members of other cluster (low inflation). Furthermore, when we use two clusters with k=3 for k-means cluster method and c=3, w = 1.25 for fuzzy c-means cluster method, Ambon tends to become member of first cluster (high inflation), Manado and Jayapura tend to become member of second cluster (moderate inflation), other cities tend to become members of third cluster (low inflation). If it is applied c=3, w = 1.5, Ambon, Manado and Jayapura tend to become member of first cluster (high inflation), Surabaya, Bandung, Medan, Makasar, Banyuwangi, Denpasar, Samarinda dan Mataram tend to become members of second cluster (moderate inflation), meanwhile other cities tend to become members of third cluster (low inflation). Similarly, interpretation can be made to the results of applying 5 clusters.

The importance of tourism and its related sectors to support economic development and poverty reduction in many countries increase researchers' attentions to study and model tourists' arrival. This work is aimed to demonstrate time varying parameter (TVP) technique to model the arrival of Korean's tourists to Bali. The number of Korean tourists whom visiting Bali for period January 2010 to December 2015 were used to model the number of Korean's tourists to Bali (KOR) as dependent variable. The predictors are the exchange rate of Won to IDR (WON), the inflation rate in Korea (INFKR), and the inflation rate in Indonesia (INFID). Observing tourists visit to Bali tend to fluctuate by their nationality, then the model was built by applying TVP and its parameters were approximated using Kalman Filter algorithm. The results showed all of predictor variables (WON, INFKR, INFID) significantly affect KOR. For in-sample and out-of-sample forecast with ARIMA's forecasted values for the predictors, TVP model gave mean absolute percentage error (MAPE) as much as 11.24 percent and 12.86 percent, respectively.

A country is said to be a crisis when the financial system is experiencing a disruption that affects systems that can not function efficiently. The performance efficiency of macroeconomic indicators especially in imports and exports can be used to detect the financial crisis in Indonesia. Based on the import and export indicators from 1987 to 2015, the movement of these indicators can be modelled using SWARCH three states. The results showed that SWARCH (3,1) model was able to detect the crisis that occurred in Indonesia in 1997 and 2008. Using this model, it can be concluded that Indonesia is prone to financial crisis in 2016.

Semiparametric regression is a statistical analysis method that consists of parametric and nonparametric regression. There are various approach techniques in nonparametric regression. One of the approach techniques is spline. Central Java is one of the most densely populated province in Indonesia. Population density in this province can be modeled by semiparametric regression because it consists of parametric and nonparametric component. Therefore, the purpose of this paper is to determine the factors that in uence population density in Central Java using the semiparametric spline regression model. The result shows that the factors which in uence population density in Central Java is Family Planning (FP) active participants and district minimum wage.

The generalized mixed fractional Brownian motion is defined by taking linear combinations of a finite number of independent fractional Brownian motions with different Hurst parameters. It is a Gaussian process with stationary increments, posseses self-similarity property, and, in general, is neither a Markov process nor a martingale. In this paper we study the generalized mixed fractional Brownian motion within white noise analysis framework. As a main result, we prove that for any spatial dimension and for arbitrary Hurst parameter the self-intersection local times of the generalized mixed fractional Brownian motions, after a suitable renormalization, are well-defined as Hida white noise distributions. The chaos expansions of the self-intersection local times in the terms of Wick powers of white noises are also presented.

The volume of mobility flows are increasing day by day and the condition of the number of people using private transport modes contribute to traffic congestion. With the limited capacity of the road, one of the alternatives solution to reduce congestion is to optimize the use of public transport. The purposes of this study are to determine the factors that influence user's satisfaction on the quality of public bus transportation service and determine variables that became identifier on the dominant factor affecting user's satisfaction. The study was conducted for the public bus transportation between districts in the province of Bali, which is among the eight regencies and one municipality, using a questionnaire as a data collection instrument. Service variables determinant of user's satisfaction in this study, described in 25 questions, which were analyzed using factor analysis. The results showed there were six factors that explain the satisfaction of users of public transport in Bali, with a total diversity of data that can be parsed by 61.436%. These factors are: Safety and comfort, Responsiveness, Capacity, Tangible, Safety, Reliability. The dominant factor affecting public transport user satisfaction is the safety and comfort, with the most influential variable is feeling concerned about the personal safety of users when on the bus.

In this paper we focus on the abstract Cauchy problems of the time-dependent evolution equation = A(t)x(t). If the operator A(t) is time-independent, we can use the C₀-semigroups theory to solve the abstract Cauchy problem. In this case A is a infinitesimal generator of the C₀-semigroups. However, if A(t) is time-dependent, we can not apply directly the C₀-semigroups theory to solve the problem. In this situation we can use the quasi semigroups theory as development of the two parameters semigroups. This semigroups is induced by bounded evolution operators U(t, s) that satisfy some assumptions. In this paper we determine the fundamental properties of the quasi semigroups included its generator related to the time-dependent evolution equation.

The indicator of region economic success can be measured by economic growth, presented by value of Gross Regional Domestic Product (GRDP). Java island has the biggest GDP contribution toward the Indonesian government, but not all of the region gives equality contribution. The C4.5, CHAID, and CART methods can be used for classifying the status of the region with nonparametric approach. The C4.5 and CHAID methods are non-binary decision tree, meanwhile the CART methods is binary decision tree. The purposes of this paper are to know how the classification and to determine the factors that influence on classification of the region. The dependent variable is status of the region which is divided into four categories based on Klassen typology. The result shows factors that have the biggest contribution on classification of status of the region on Java island based on C4.5 method are economic growth rate, electricity, gas, and water sector, and area. The factors that have the biggest contribution based on CHAID method are growth rate, manufacturing sector, and electricity, gas, and water sector, while based on CART method are growth rate, manufacturing sector, and electricity, gas, and water sector.

Regression analysis (statistical analmodelling) are among statistical methods which are frequently needed in analyzing quantitative data, especially to model relationship between response and explanatory variables. Nowadays, statistical models have been developed into various directions to model various type and complex relationship of data. Rich varieties of advanced and recent statistical modelling are mostly available on open source software (one of them is R). However, these advanced statistical modelling, are not very friendly to novice R users, since they are based on programming script or command line interface. Our research aims to developed web interface (based on R and shiny), so that most recent and advanced statistical modelling are readily available, accessible and applicable on web. We have previously made interface in the form of e-tutorial for several modern and advanced statistical modelling on R especially for independent responses (including linear models/LM, generalized linier models/GLM, generalized additive model/GAM and generalized additive model for location scale and shape/GAMLSS). In this research we unified them in the form of data analysis, including model using Computer Intensive Statistics (Bootstrap and Markov Chain Monte Carlo/ MCMC). All are readily accessible on our online Virtual Statistics Laboratory. The web (interface) make the statistical modeling becomes easier to apply and easier to compare them in order to find the most appropriate model for the data.

A nite simple graph G admits an H-covering if every edge of E(G) belongs to a subgraph of G isomorphic to H. We said the graph G = (V, E) that admits H-covering to be H-magic if there exists a bijection function f : V(G) ∪ E(G) → {1, 2, ..., |V(G)| + |E(G)|} such that for each subgraph H' of G isomorphic to H, f(H') = ∑_υ∈V'f(υ) + ∑_e∈E'f(e) = m(f) is constant.

Furthermore, if f(V) = 1, 2, ..., |V(G)| then G is called H-supermagic. In this research we de ned S_2,2-supermagic labeling on shrub graph Š(m₁, m₂, ..., m_n) and fish-supermagic labeling on L_m ⨀ P_n for m, n ≥ 2.

Internet messenger (IM) has become an important educational technology component in college education, IM makes it possible for students to engage in learning and collaborating at smart virtual class learning (SVCL) using ubiquitous computing. However, the model of IM-based smart virtual class learning using ubiquitous computing and empirical evidence that would favor a broad application to improve engagement and behavior are still limited. In addition, the expectation that IM based SVCL using ubiquitous computing could improve engagement and behavior on smart class cannot be confirmed because the majority of the reviewed studies followed instructions paradigms. This article aims to present the model of IM-based SVCL using ubiquitous computing and showing learners' experiences in improved engagement and behavior for learner–learner and learner–lecturer interactions. The method applied in this paper includes design process and quantitative analysis techniques, with the purpose of identifying scenarios of ubiquitous computing and realize the impressions of learners and lecturers about engagement and behavior aspect and its contribution to learning

The binary puzzle is a sudoku-like puzzle with values in each cell taken from the set {0, 1}. We look at the mathematical theory behind it. A solved binary puzzle is an n × n binary array where n is even that satisfies the following conditions:

(1) No three consecutive ones and no three consecutive zeros in each row and each column,

(2) Every row and column is balanced, that is the number of ones and zeros must be equal in each row and in each column,

(3) Every two rows and every two columns must be distinct.

The binary puzzle had been proven to be an NP-complete problem [5].

Research concerning the satisfiability of formulas with respect to some background theory is called satisfiability modulo theory (SMT). An SMT solver is an extension of a satisfiability (SAT) solver. The notion of SMT can be used for solving various problem in mathematics and industries such as formula verification and operation research [1, 7].

In this paper we apply SMT to solve binary puzzles. In addition, we do an experiment in solving different sizes and different number of blanks. We also made comparison with two other approaches, namely by a SAT solver and exhaustive search.

Let G be a connected graph with V (G) = {v₁, v₂, ..., v_i} and E(G) = {e₁, e₂, ..., e_j}, where V (G) is vertex set and E(G) is edge set. If S ⊆ V (G) and v ∈ V (G), then the distance between v and S is de ned by d(v, S) = min{d(v, x)|x ∈ S}. For an ordered k-partition Π = {S₁, S₂, ..., S_k} of V (G), the representation of v with respect to Π is r(v|Π) with r(v|Π) = (d(v, S₁), d(v, S₂), ..., d(v, S_k)). If the representation of v ∈ V (G) with respect to Π are distinct, so Π is called a resolving partition of V (G). The minimum cardinality of resolving partition Π is called a partition dimension of G, denoted by pd(G). In this paper, we study the partition dimension of a C_m + P_n graph. C_m + P_n graph is a graph formed from join operation of cycle graph C_m with order m ≥ 3 and path P_n with order n ≥ 2. C_m + P_n is the union C_m ∪ P_n together with all edges u_av_b, for u_a ∈ V (C_m) and v_b ∈ V (P_n) with 1 ≤ a ≤ m and 1 ≤ b ≤ n. We obtain the partition dimension of C_m + P_n graph is pd(C₃ + P_n) = g where g is the smallest positive integer such that n ≤ 5g − 12 for g = 5 and $n\le \frac{{g}^{3}-7{g}^{2}+20g-18}{2}$ for g ≥ 6, and pd(C_q + P_n) = min{p + f, r + t, x + y} for q ≥ 4 and n ≥ 2 where p, f, r, t, x and y are some positive integers related to the number of partition classes containing vertices of C_q and P_n.

For a graph G = (V, E), a subset S of V is called a dominating set if every vertex x in V is either in S or adjacent to a vertex in S. The domination number γ(G) is the minimum cardinality of the dominating set of G. The dominating set of G with a minimum cardinality denoted by γ(G)-set. Let G₁, G₂, ..., G_t be subgraphs of the graph G. If the union of all these subgraphs is G and their intersection is {v}, then we say that G is the vertex-amalgamation of G₁, G₂, ..., G_t at vertex v. Based on the membership of the common vertex v in the γ(G_i)-set, there exist three conditions to be considered. First, if v elements of every γ(G_i)-set, second if there is no γ(G_i)-set containing v, and third if either v is element of γ(G_i)-set for 1 ≤ i ≤ p or there is no γ(G_i)-set containing v for p < i ≤ t. For these three conditions, the domination number of G as vertex-amalgamation of G₁, G₂, ..., G_t at vertex v can be determined.

GWOLR model combines geographically weighted regression (GWR) and (ordinal logistic reression) OLR models. Its parameter estimation employs maximum likelihood estimation. Such parameter estimation, however, yields difficult-to-solve system of nonlinear equations, and therefore numerical approximation approach is required. The iterative approximation approach, in general, uses Newton-Raphson (NR) method. The NR method has a disadvantage—its Hessian matrix is always the second derivatives of each iteration so it does not always produce converging results. With regard to this matter, NR model is modified by substituting its Hessian matrix into Fisher information matrix, which is termed Fisher scoring (FS). The present research seeks to determine GWOLR model parameter estimation using Fisher scoring method and apply the estimation on data of the level of vulnerability to Dengue Hemorrhagic Fever (DHF) in Semarang. The research concludes that health facilities give the greatest contribution to the probability of the number of DHF sufferers in both villages. Based on the number of the sufferers, IR category of DHF in both villages can be determined.

Hierarchical data structures are common throughout many areas of research. Beforehand, the existence of this type of data was less noticed in the analysis. The appropriate statistical analysis to handle this type of data is the hierarchical linear model (HLM). This article will focus only on random intercept model (RIM), as a subclass of HLM. This model assumes that the intercept of models in the lowest level are varied among those models, and their slopes are fixed. The differences of intercepts were suspected affected by some variables in the upper level. These intercepts, therefore, are regressed against those upper level variables as predictors. The purpose of this paper would demonstrate a proven work of the proposed two level RIM of the modeling on per capita household expenditure in Maluku Utara, which has five characteristics in the first level and three characteristics of districts/cities in the second level. The per capita household expenditure data in the first level were captured by the three parameters Gamma distribution. The model, therefore, would be more complex due to interaction of many parameters for representing the hierarchical structure and distribution pattern of the data. To simplify the estimation processes of parameters, the computational Bayesian method couple with Markov Chain Monte Carlo (MCMC) algorithm and its Gibbs Sampling are employed.

In this paper, we consider spatial operation median filter to reduce the noise in the cervical images yielded by colposcopy tool. The backpropagation neural network (BPNN) model is applied to the colposcopy images to classify cervical cancer. The classification process requires an image extraction by using a gray level co-occurrence matrix (GLCM) method to obtain image features that are used as inputs of BPNN model. The advantage of noise reduction is evaluated by comparing the performances of BPNN models with and without spatial operation median filter. The experimental result shows that the spatial operation median filter can improve the accuracy of the BPNN model for cervical cancer classification.

In this research, calculation process of the lung cancer volume of target based on computed tomography (CT) thorax images was done. Volume of the target calculation was done in purpose to treatment planning system in radiotherapy. The calculation of the target volume consists of gross tumor volume (GTV), clinical target volume (CTV), planning target volume (PTV) and organs at risk (OAR). The calculation of the target volume was done by adding the target area on each slices and then multiply the result with the slice thickness. Calculations of area using of digital image processing techniques with active contour segmentation method. This segmentation for contouring to obtain the target volume. The calculation of volume produced on each of the targets is 577.2 cm³ for GTV, 769.9 cm³ for CTV, 877.8 cm³ for PTV, 618.7 cm³ for OAR 1, 1,162 cm³ for OAR 2 right, and 1,597 cm³ for OAR 2 left. These values indicate that the image processing techniques developed can be implemented to calculate the lung cancer target volume based on CT thorax images. This research expected to help doctors and medical physicists in determining and contouring the target volume quickly and precisely.

A regression model is the representation of relationship between independent variable and dependent variable. The dependent variable has categories used in the logistic regression model to calculate odds on. The logistic regression model for dependent variable has levels in the logistics regression model is ordinal. GWOLR model is an ordinal logistic regression model influenced the geographical location of the observation site. Parameters estimation in the model needed to determine the value of a population based on sample. The purpose of this research is to parameters estimation of GWOLR model using R software. Parameter estimation uses the data amount of dengue fever patients in Semarang City. Observation units used are 144 villages in Semarang City. The results of research get GWOLR model locally for each village and to know probability of number dengue fever patient categories.