Table of contents

Dafik

Editor in Chief of International Conference on Combinatorics, Graph Theory, and Network Topology 2021

E-mail: d.dafik@unej.ac.id

We gratefully acknowledge the presence of all participants on "The Fifth International Conference on Combinatorics, Graph Theory, and Network Topology (ICCGANT)". It is the 5^th International conference was held on 21-22 August 2021 by the CGANT Research Group, University of Jember in collaboration with the Indonesian Combinatorics Society (INACOMBS). The conference welcomed participants from several countries, with a wide and variety of mathematics research of interests, in particular combinatorial research. The mission of this conference is to be an annual international forum where members of society organizations, research students, educators and researchers, writers, physicists, teachers and practitioners from all over the world can meet and exchange ideas to communicate and discuss theoretical and practical knowledge of mathematical research and its applications. The aim of the fifth conference is to present and discuss the latest research that leads to the exchange of new theoretical, analytical and scientific knowledge and to a deeper understanding of the fields of mathematics, application of mathematics, and mathematics education. The topics of this conference have been identified on the ic.cgant.unej.ac.id website.

List of The Committees, Editorial Board, Scientific Committee and Reviewers, Peer review statement are available in the pdf.

All conference organisers/editors are required to declare details about their peer review. Therefore, please provide the following information:

• Type of peer review: The type of peer review article is Double-blind review where the authors name and affiliation of the paper are hidden. The reviewer independently made some suggestion and corrections on the papers.

• Conference submission management system: All the papers were submitted online through EasyChair system

https://easychair.org/conferences/?conf=the5thiccgant2021

• Number of submissions received: 138

• Number of submissions sent for review: 95

• Number of submissions accepted:71

• Acceptance Rate (Number of Submissions Accepted / Number of Submissions Accepted X 100): 51.45%

• Average number of reviews per paper: 3

• Total number of reviewers involved: 54

• Any additional info on review process: The reviewers gave some feedback to each paper based on the referring guidelines such as the state of the art of research, methodology, a gap, a proposed novelty, originality, and language. They also review the originality of the research finding, and the bibliography cited in their paper. In general they have made refereeing on three things, namely the content, layout, and language.

• Contact person for queries:

Prof. Drs. Dafik, M.S., Ph.D.

University of Jember

d.dafik@unej.ac.id

Let G be a nontrivial connected graph and let c : V (G) → be a vertex coloring of G, where adjacent vertices may have the same color. For a vertex υ of G, the color sum σ(υ) of υ is the sum of the colors of the vertices adjacent to υ. The coloring c is said to be a sigma coloring of G if σ(u) ≠ σ(υ) whenever u and υ are adjacent vertices in G. The minimum number of colors that can be used in a sigma coloring of G is called the sigma chromatic number of G and is denoted by σ(G). In this study, we investigate sigma coloring in relation to a unary graph operation called middle graph. We will show that the sigma chromatic number of the middle graph of any path, cycle, sunlet graph, tadpole graph, ladder graph, or triangular snake graph is 2 except for some small cases. We also determine the sigma chromatic number of the middle graph of stars.

Let G be a graph with vertex set V(G), edge set E(G), and the number of edges q. An edge odd graceful labeling of G is a bijection f : E(G) → {1,3,5, ...,2q − 1} so that induced mapping f⁺ : V(G) → {0,1,2, ...,2q − 1} given by f⁺(x) = ∑_xy∈E(G)f(xy) (mod 2q) is injective. A graph which admits an edge odd graceful labeling is called edge odd graceful. An alternate triangular snake graph $A({C}_{3}^{m})$ is a graph obtained from a path u₁u₂u₃ ... u_2m by joining every u_2i−1 and u_2i to a new vertex υ_i, 1 ≤ i ≤ m. An alternate quadrilateral snake graph $A({C}_{4}^{m})$ is a graph obtained from vertices u₁, u₂,u₃,...,u_2m by joining every u_2i−1 and u_2i to two vertices υ_i and w_i,1 ≤ i ≤ m, and joining every u_2i to u_2i+1 with 1 ≤ i ≤ m − 1. In this paper, we show that alternate triangular snake and alternate quadrilateral snake graphs are edge odd graceful.

Graph theory is part of the field of mathematics that can be applied in various other fields of science to solve problems. One of them is the problem of determining the color on the map. The map that will be colored here is a map of the Deli Serdang regency which consists of 22 sub-districts. The coloring of the map is done by first modeling it in the form of a graph. One way to determine the minimum color of a graph is to use a greedy algorithm. From the map, we get a dual graph with 22 vertices and 41 edges. Based on the greedy algorithm that has been applied, the minimum number of colors is obtained as many as four colors, namely blue, green, red, and yellow with each district directly bordering having a different color. The results of map coloring by applying the greedy algorithm are also obtained with the help of the python 3.7 programming language.

Let G be a connected graph. A vertex w is said to strongly resolve a pair u, ν of vertices of G if there exists some shortest u − w path containing ν or some shortest ν − w path containing u. A set W of vertices is a local strong resolving set for G if every pair of adjacent vertices of G is strongly resolved by some vertex of W. The smallest cardinality of a local strong resolving set for G is called the local strong metric dimension of G. In this paper we studied the local strong metric dimension in the join of graphs. We use the path, cycle, complete, and star graphs in this studies.

Let k ≥ 2 be an integer and G be a connected graph of order at least 3. In this paper, we introduce a new neighbor-distinguishing coloring called twin edge mean coloring. A proper edge coloring of G that uses colors from _k = {0,1,..., k − 1} is called a twin k-edge mean coloring of G if it induces a proper vertex coloring of G such that the color of each vertex υ of G is the average of the colors of the edges incident with υ, and is an integer. The minimum k for which G has a twin k-edge mean coloring is called the twin chromatic mean index of G and is denoted by $\chi _{tm}^\prime (G)$. First, we establish lower and upper bounds for $\chi _{tm}^\prime (G)$ under general or more specific assumptions. Then we determine the twin chromatic mean indices of paths, cycles, and stars.

The eigenvalues of matrix representation hypergraph have the possibility that all of it can be an integer or otherwise. The Laplacian integral hypergraphs are those hypergraphs whose Laplacian spectrum consists entirely of integers likewise the definition of signless Laplacian integral and Seidel integral. This research focuses on the properties of the entry matrix and formulates the spectrum of the Laplacian matrix, Signless Laplacian matrix, and Seidel Matrix of complete r-uniform hypergraphs. Hence, it can determine the integrality of the representation matrix respectively. The result concludes that complete r-uniform hypergraphs are Laplacian integral, signless Laplacian integral, and Seidel integral.

Let G = (V, E) be a simple finite connected and undirected graph with n vertices and m edges. The n vertices are assigned the colors through mapping c : V [G] → I⁺. An r-dynamic coloring is a proper k-coloring of a graph G such that each vertex of G receive colors in at least min{deg(υ),r} different color classes. The minimum k such that the graph G has r-dynamic k coloring is called the r-dynamic chromatic number of graph G denoted as χ_r(G). Let G₁ and G₂ be a graphs with n₁ and n₂ vertices and m₁ and m₂ edges. The central vertex join of G₁ and G₂ is the graph ${G_1}\,\dot V\,{G_2}$ is obtained from C(G₁) and G₂ joining each vertex of G₁ with every vertex of G₂. The aim of this paper is to obtain the lower bound for r-dynamic chromatic number of central vertex join of path with a graph G, central vertex join of cycle with a graph G and r-dynamic chromatic number of ${P_m}\dot V\,{P_n},\,{P_m}\dot V\,{K_n},\,{P_m}\dot V\,{K_n},\,{P_m}\dot V\,{C_n},\,{C_m}\dot V\,{K_n}$ and ${C_m}\dot V\,{C_n}$ respectively.

The increasing number of patient infected by Covid-19 viruses in Indonesia, causing each personal to be more vigilant in doing activities outside. Many patients who are positively exposed to the corona viruses are self isolating in their own house because the hospital is full. Patiens who have recovered and tested negative from the corona viruses can work outside the house. The purpose of this study is to provide information regarding patients infected with Covid-19 in certain area through a tracing application. This apllication can help public to find out how many individuals are infected with Covid-19 in the surrounding environment by priorizing patient privacy and in real time anonymously. The method used is a combination of labelling graph theory and the GPS tracing system applied to the gadget. The programming language use in this gadget cases is flutter. The stages that will be carried out are starting from tracing patients infected with Covid-19 based on the position of tracing area, then predicted through a graph model approach based on distance and percentage of transmission. The result of this research is the percentage of prediction about personal vulnerability. The initiation of prediction divide into saveral categories, including vulnerable, moderate, or safe.

Bulog is a state-owned public company engaged in food logistics. There are about 18 Bulog warehouses in East Java Province with an uneven distribution. Because the scope of Bulog's business includes logistics or warehousing, surveys and pest eradication, provision of plastic bags, transportation business, food commodity trading and retail business, there must be good coordination between regional sub-divisions and warehouse complexes. In this study, the minimum regional sub-division recommendations in the East Java region were determined using the theory of connected domination number in graphs. The location of the warehouse complex is described as the vertex and adjacent warehouse complexes are connected by edges. In this research, we also determine the connected domination number of unicyclic graph and vertex amalgamation operations for several classes of graphs.

Consider the graph G = (V, E). It is a connected graph. It is a simple graph too. A node w ∈ V, then we call vertex, determined two elements of graph. There are vertices and edges of graphs. Any two vertices x, y ∈ E ∪ V if d(w, x) ≠ d(w, y), which d(w, x) and d(w, y) is the mixed distance of the element w (vertices or edges) in graph G. A set of vertices in a graph G is represented by the symbol R_m that defines a mixed metric generator for G, if the elements of vertices or edges are stipulated by several vertex set of R_m. There's a chance that some mixed metric generators have varied cardinality. We choose one whose the minimum cardinality and it is called the mixed metric dimension of graph G, denoted by dim_m(G). This research examines the mixed metric dimension of gear G_n, helm H_n, sunflower SF_n, and friendship graph Fr_n. We call these graphs by wheel-like graphs. Our findings include the mixed metric dimension of gear graph G_n of order n ≥ 4 is dim_m(G_n) = n, helm graph H_n of order n ≥ 4 is dim_m(H_n) = n, sunflower graph SF_n of order n ≥ 5 is dim_m (SF_n) = n and friendship graph Fr_n of order n ≥ 3 is dim_m(Fr_n) = 2n.

Let G be an edge-colored connected graph of order n ≥ 3, where adjacent edges may be colored the same. Let k be an integer with 2 ≤ k ≤ n and S ⊆ V (G) with |S| = k. The Steiner distance d(S) of S is the minimum size of a tree in G connecting S. The strong k-rainbow index srx_k (G) of G is the minimum number of colors required to color the edges of G so that every set S in G is connected by a tree of size d(S) whose edges have distinct colors. We focus on k = 3. In this paper, we first characterize the graphs G with srx₃ (G) = 2. According to the definition, it is clearly that ||G|| is the trivial upper bound for srx₃(G). Several previous researchers have shown that there exist some connected graphs G such that srx₃(G) = ||G||. Hence, in this paper, we provide another graph G such that srx₃(G) = ||G||.

We use finite, connected, and undirected graph denoted by G. Let V (G) and E(G) be a vertex set and edge set respectively. A subset D of V (G) is an efficient dominating set of graph G if each vertex in G is either in D or adjoining to a vertex in D. A subset W of V (G) is a resolving set of G if any vertex in G is differently distinguished by its representation respect of every vertex in an ordered set W. Let W = {w₁, w₂, w₃, ..., w_k} be a subset of V (G). The representation of vertex υ ∈ G in respect of an ordered set W is r(υ|W) = (d(υ, w₁),d(υ, w₂), ..., d(υ, w_k)). The set W is called a resolving set of G if r(u|W) ≠ r(υ|W) ∀ u, υ ∈ G. A subset Z of V (G) is called the resolving efficient dominating set of graph G if it is an efficient dominating set and r(u|Z) ≠ r(υ|Z) ∀ u, υ ∈ G. Suppose γ_re(G) denotes the minimum cardinality of the resolving efficient dominating set. In other word we call a resolving efficient domination number of graphs. We obtained γ_reG of some comb product graphs in this paper, namely P_m ⊲ P_n, S_m ⊲ P_n, and K_m ⊲ P_n.

We examine that all graphs in this paper are limited, simple and connected. A graceful k-coloring of a graph is a proper vertex coloring f₁ : V (G) → {1, 2,..., k} where k ≥ 2 which induces a proper edge coloring f₂ : E (G) → {1, 2,..., k − 1} characterized by f₂(uυ) = |f₁(u) — f₂ (υ)|. Nethermost k for which a graph G has a graceful k-coloring is named a graceful chromatic number of a graph G, denoted by χ_g (G). In our research, we will obtain the exact value of the graceful chromatic number of some graphs.

The purpose of this study is to develop rainbow antimagic coloring. This study is a combination of two notions, namely antimagic and rainbow concept. If every vertex of graph G is labeled with the antimagic labels and then edge weight of antimagic labels are used to assign a rainbow coloring. The minimum number of colors for a rainbow path to exist with the condition satisfying the edge weights w(x) ≠ w(y) for any two vertices x and y is the definition of the rainbow antimagic connection number rac(G). In this study, we use connected graphs and simple graphs in obtaining the rainbow antimagic connection number. This paper will explain the rainbow antimagic coloring on some graphs and get their formula of the rainbow antimagic connection number. We have obtained rac(G) where G is vertex amalgamation of graphs, namely path, star, broom, paw, fan, and triangular book graph.

This study aims to analyse the resolving strong dominating set. This concept combinations of two notions, they are metric dimension and strong domination set. By a resolving strong domination set, we mean a set D_s ⊂ V(G) which satisfies the definition of strong dominating set as well as resolving set. The resolving strong domination number of graph G, denoted by γ_rst(G), is the minimum cardinality of resolving strong dominating set of G. In this paper, we determine the resolving strong domination number of some wheel related graphs, namely helm graph H_n, gear graph G_n, and flower graph Fl_n. Through this paper, we will use the notations γ_st(G) and dim(G) which show the strong domination and dimension numbers.

Let H be simple, non-isolated vertex, connected and directionless graphs with vertex set V (H), edge set E(H). With the use of c-coloring of graph H, using the formula c : υ(H) → S, where |S| = c, the colors of the adjacent vertex are different. A proper c-coloring of H is an r-dynamic coloring if it's applied to every vertex υ ∈ V (H) satisfies |c(N(υ))| ⩾ min {r, d(υ)}. The minimum c such that H has an r-dynamic coloring with c colors is called an r-dynamic chromatic number, denoted by χ_r (H). In this study, we will obtain the exact value of r-dynamic chromatic number of subdivision by wheel graph.

Nowadays, cryptosystems can be applied in several areas in life. One of them is in transaction data. In transaction data, a very strong cryptosystem is needed so that the transaction data is safe. Cryptosystems are better with a strong keystream. In this case, we use rainbow antimagic as a cryptosystem key to improve the robustness of the keystream by using affine cipher. The algorithm uses the edge weights of rainbow antimagic vertex labeling of graphs as a key for encryption and decryption. In this paper, we found the rainbow antimagic connection number of tadpole graphs and two algorithms to straighten affine ciphers.

Let χ(G) be a chromatic number of proper coloring on G. For an injection f : V (G) → {0, 2, . . . ; 2k_υg} and f : E(G) → }1, 2, . . . , k_e}, where k = max{k_e, 2k_χ} for k_υ, k_e are natural number. The associated weight of a vertex u, υ ∈ V (G) under f is w(u) = f(u) + ∑_uυ∈E(G)f(uυ). The function f is called a local vertex irregular reflexive k-labeling if every two adjacent vertices has distinct weight. When we assign each vertex of G with a color of the vertex weight w(uυ), thus we say the graph G admits a local vertex irregular reflexive coloring. The smallest number of vertex weights needed to color the vertices of G such that no two adjacent vertices share the same color is called a local vertex irregular reflexive chromatic number, denoted by _χirvs(G). Furthermore, the minimum k required such that _χlrvs(G) = χ(G) is called a local reflexive vertex color strength, denoted by lrvcs(G). In this paper, we will obtain the lrvcs(G) and characterize the existence of a graph with given its local reflexive vertex color strength.

Let G(V (G),E(G)) be a connected, simple, and finite graph. Let f be a bijective function of labeling on graph G from the edge set E(G) to natural number up to the number of edges of G. A rainbow vertex antimagic labeling of graph G is a function f under the condition all internal vertices of a path u – υ, Ɐu, υ ∈ V (G) have different weight (denoted by w(u)), where w(u) = ∑_uu'∈E(G)f (uu'). If G has a rainbow vertex antimagic labeling, then G is a rainbow vertex antimagic coloring, where the every vertex is assigned with the color w(u). The rvac(G) is a notation of rainbow vertex antimagic connection number of graph G which means the minimum colors taken over all rainbow vertex antimagic coloring induced by rainbow vertex antimagic labeling of graph G. The results of this research are the exact value of the rainbow vertex antimagic connection number of star (S_n), double star (DS_n), and broom graph (Br_{n, m}).

The kidney is organ that plays an important role in the body's metabolism, especially the process of filtration and reabsorption of food waste. Currently the determination of kidney parts through kidney histology is still done manually by experts based on experience and knowledge. Therefore, to make it easier to determine the parts of the kidney, a histological image segmentation of the kidney was carried out. In the segmentation process, it is necessary to extract the color features of the parts of the kidney, namely the glomerulus and proximal tubule. The color features used are Hue, saturation, value (HSV) color space. The hue means the representation of color type. The saturation defines the amount of white color is mixed with hue. The value in HSV color space denotes the intensity or lightness or brightness of the color. The method consists of three steps such as pre-processing step, extraction feature HSV and statistical analysis. The result of statistical analysis showed that the hue and value features, glomerulus and proximal tubule had different ranges of values. However, the features of saturation, glomerulus and proximal tubule is overlap.

"Usaha Kecil Mikro dan Menengah" (UMKM) is a productive business unit of individuals or business entities in each economic sector. Currently, many UMKMs face difficulty in developing their business due to a lack of working capital. Therefore, the government provides business funding for the UMKM through "Dinas Koperasi dan UMKM" (Diskopum). Diskopum has various business funding; one of them is business funding for a beginner UMKM. The beginner UMKM that can get the business funding must complete the requirements that Diskopum requested. Among the requirements requested, there are several fuzzy criteria. This research solves the problem of determining the business funding for the beginner UMKM using the fuzzy TOPSIS method. The method was chosen because the output is in the form of ranking. Since the data used in this study is the submission data from 2019, the data already has the actual results. There are several differences between the actual ranking and the result using the fuzzy TOPSIS method, but the difference is insignificant. That result proved that the fuzzy TOPSIS method could determine the ranking of the business capital fund as an alternative method.

Indonesia is a country with a very prominent marine charm, and it is the largest archipelago in the world, covering about 50% of the coral triangle area, providing marine tourist resorts. Therefore tourism development is quite promising. For that purpose, simple boats are of necessity for tourists to enjoy the beauty of such marine tourism. One solution to support such marine tourism sector is the availability of Autonomous Surface Vehicle (ASV). This vehicle will be the interest of this paper. This study used Touristant ASV with dimensions of 1.5 m in diameter, 4 meters in length and 1.3 meters in height. The purpose of this paper is to conduct a study with a focus on the estimation of ASV position with ASV motion influenced by wind speed and wave height by applying the H-infinity method. The position error generated from the simulation shows that the position error has an accuracy of about 96%.

Blood Transfusion Unit (UTD) as a blood supply provider is required to meet the demand for blood, but in reality, the blood stock does not always meet the blood demand. The blood type stocks in the Blood Transfusion Unit (UTD) relies on blood donors voluntarily donating their blood. Red blood cells only have a life span of 35 days as of the blood donation date. If overdue the blood cannot be used for transfusion. Fulfillment of the availability of blood is a very important thing. On one hand, too much blood stock results in significant losses, such as expiration. On the other hand, too low blood stock makes the people's blood needs unfulfilled. Therefore, this paper is an effort to estimate the blood supply at Indonesian Red Cross Bojonegoro by using the Modified Kalman Filter method. The Modified Kalman Filter is a comparison of two Kalman Filter development methods, those are Extended Kalman Filter (EKF) and Fuzzy Kalman Filter (FKF). The simulation results showed that the EKF method was accurate than the FKF method, with an error of 3 % generated by the EKF and that of 9% by the FKF.

Two dimensional human's arm is one of the optimal control application. This arm model consists of joint angles consisting of shoulder joint and elbow joint. Beside that, there are also muscle force vectors consisting of pectoralis major, posterior deltoid, brachialis, lateral head of triceps brachii, biceps brachii, and longhead of triceps. Linear Quadratic Tracking (LQT) is constructed to obtain solution of state and optimal control. From state solution and optimal control obtained, they will be used estimation by Backpropagation and ANFIS. From data resulted from LQT simulation, the input used are muscle force vectors. They will be used for estimation the output i.e. angle of shoulder joint and angle of elbow joint. From the LQT simulation, the angle position can follow the given reference function. Then Backpropagation and ANFIS can make estimation in angle of shoulder joint and angle of elbow joint based on six muscle force vectors with small RMSE. In Backpropagation, the estimation result of angle of shoulder joint between target and output with RMSE is 0.0954 and the estimation result of angle elbow joint between target and output with RMSE is 0.2528. In ANFIS, the estimation result of angle of shoulder joint between target and output with RMSE is 0.0062 and the estimation result of angle elbow joint between target and output with RMSE is 0.0526.

Distribution optimization has an important role to distribute products to consumers. The selection of the right route will have an impact on the distribution process resulting in minimal costs. The application of graph theory that can be used to determine the optimum route in the distribution process is the study of the Vehicle Routing Problem (VRP) variant. The VRP variants discussed in this article are MDVRP and VRPTW. The method used to solve the VRP variant of this article is the ACS-RVND algorithm. The ACS-RVND algorithm consists of several main stages, namely the initial solution formation stage using the ACS algorithm, the solution improvement stage using the RVND procedure and the acceptance criteria stage. The data needed for the application of the ACS-RVND algorithm in solving the distribution optimization problem of MDVRP cases are the number of depots, the number of customers, the capacity of the vehicle, the number of ants, the number of iterations, the number of customer requests and the distance between customers. While in the case of VRPTW data multiple depots are replaced by time windows depot and service time. The results of solving distribution optimization problems in the form of the route, the total distance traveled and the result of the route in the graph model. The performance of the ACS RVND algorithm can be compared with the performance of the ant colony optimization (ACO) algorithm and the Hybrid Ant Coloy Optimization (HACO) algorithm. Analysis of the results using several dataset test cases showed that the ACS RVND algorithm on MDVRP obtained a better solution than the ACO algorithm and the ACS RVND algorithm on VRPTW was better than the Hybrid Ant Coloy Optimization (HACO) algorithm when viewed from the total distance distribution route.

Salt is one of the marine resources that is quite a lot needed as a supplementary food for the people of Indonesia. However, efforts to increase salt production have not been in demand, including in efforts to improve its quality, because many factors affect sea salt content or salinity, including the evaporation process, location and size of the sea, wind, air humidity and sea water temperature in this study are expected to produce the best salinity modeling by taking into account the factors that affect salinity. In this study, the method used was probit bivariate. The parameter estimation method used in the bivariate probit is the Maximum Likelihood Estimation (MLE). After the initial bivariate probit regression model is formed, then testing is carried out to determine the significance of each predictor variable to the response variable. After that the model that is formed identifies the criteria of goodness using the smallest Akaike Information Criterion (AIC) value of -9.03 so that the modeling results are good.

One strategy for a company to develop and grow bigger and stronger in competition is by business expansion. According to Moin (2010:2), there are two strategic ways to maintain and expand a business, that is, an internal expansion strategy by building a new business or business unit from scratch and an external expansion strategy in the form of a business merger by buying an existing company through a merger, acquisitions and consolidations which are fast-track to new markets. Profitability is a factor that gets important attention because it can attract investors to make investment in the company. Profit is the gab beetwen revenue and expenses in a certain period in a company. It has very important role for either internal or external of the company. One way to reduce the risk of company losses is by using an estimation method to find out the company's estimated profit for the next month or next year. In this study the estimation method for travel company was used, that is, by using the Ensemble Kalman Filter (EnKF) and H-infinity, as a policy making chart in order to maintain and increase company profits. Based on the analysis of results computation with 100, 200 and 300 iterations, it showed an error of less than 3%.

We established new single-condition criteria for the oscillation of all solutions to a second-order half-linear advanced equation of the form ∆(φ(ζ)(∆x(ζ))^ν) + ρ(ζ)x^ν(ζ + η) = 0; ζ≥ζ₀ under the conditions that $\sum\nolimits_{s = \zeta }^\infty {{1 \over {\varphi {1 \over v}\left( s \right)}} < \infty }$. We derive new single-condition constraints for the oscillation of all unimprovable constant solutions to equation. Even in the linear case, the significant result is new and improves all of the prior results to the best of our knowledge. The advantage of our technique is the simple proof, solely relying on the monotonicities of a positive solution sequentially improved. Examples of our conclusions are presented.

Ministry of Health established the Indonesian Red Cross (PMI) as an organization to anticipate the need for blood by obligation to provide enough proper blood for use. Its process of delivering information related to blood donation requires the public always come to PMI. In such way it is less efficient and effective. In addition, there is no system for estimating blood stock to anticipate the blood supply needed in the next period. Blood transfusion is needed in terms of both quality and quantity by patients suffering from various health problems. Due to the urgency of blood transfusion, maintaining the stability of blood stock is a must so as not to cause blood loss due to excessive of the blood stock. To minimize such loss, blood stock prediction is needed. The objective of this study was to estimated the blood demand for blood type of Thrombocyte Concentrate (TC) or concentrated red blood cells at PMI Gresik by applying the method of Unscented Kalman Filter (UKF) and Square Root Ensemble Kalman Filter (SR-EnKF). The simulation results showed that both methods have high accuracy with an error of less than 3%.. The best simulation showed that the error between the real data and the simulation with SR-EnKF was in the order of 0.0023574 with generated 300 ensembles. Where as that with UKF was some 0.025566.

Covid-19 entered Indonesia in March 2020, which had an extraordinary impact on all aspects of life. The real impact is the economic and social sectors. Various efforts and policies from the Indonesian government were made to suppress the increase in the rate of Covid-19 cases. The spread of Covid-19 cases in Indonesia has been evenly distributed in various provinces, one of which is East Java. East Java has 38 districts/cities, where the case of each district is different, there are green, yellow, red, and black zones. To find out the pattern of spread of each district/city zone, clustering is used. The method used in this study was to use the hybrid method of clustering with K-means and classification with its algorithm Decision Tree. The purpose of this study to prepare mitigation measures to inhibit the rate of spread of Covid-19 in East Java Province. The variables used include the number of positive, the number of dead, the number of recovered, the number of suspects, and the number of probable. With this grouped data, it is expected to help make the right decision in reducing the spread and minimizing the number of positive patients. Based on the results of the study, there will be cluster results, namely 7 very high-risk areas (C0), 1 high risk district (C1), 29 moderate risk districts (C2), and 1 low-risk district (C3). It also has a validity index level of 0.356 as measured by the Davies-Bouldin Index.

The world is currently facing with COVID-19 pandemic. One way to prevent the spread of COVID-19 is to do physical distancing. However, this has an impact on the continuity of the economy and business. The Ministry of Trade, Cooperatives, SMEs, and Industry announced that the Covid-19 pandemic affected the activities of SMEs. One of the SMEs that impacted is the commercial sector, such as markets, essential food stores, food stalls, coffee shops, etc. Before the Covid-19 pandemic, the business process carried out was face-to-face with customers without any distance. So that when the physical distancing rules are implemented, the service flow will be disrupted. With this conveyor, the SMEs service process flow can support business process activities properly and smoothly while still complying with physical distancing rules. The process of moving business products from the seller to the consumer is done automatically. Based on these problems, it is necessary to design a conveyor table that will be used as a media for physical distancing tools that are in according needs of the user using the Quality Function Deployment method and statistical analysis of anthropometric data approach.

PT KAEF is one of the pharmaceutical manufacturing industries in Indonesia that produces various kinds of drug variants. Currently, PT KAEF is experiencing problems in the form of product defects that exceed the company's standard, which is 1%. By using the DMAIC Six Sigma Statistical tool (Define, Measure, Analyze, Improve, and Control), it is possible to evaluate the possibility of failure of the production system so that the cause of each product defect can be identified and get the right problem-solving solution and with Failure Mode Effects Mode can be known the solutions for the priority problems. From the search results, it can be seen that liquid products are the products with the most defects, with the causes of defects caused by errors in work procedures and the use of old machines. From the improvement results, it was found that the level of product defects decreased from 2,26% to 0,93% or in sigma level increase from 4,18 to 4,46.

A new symbolization of Yusof-Goode (Y-G) splicing system was introduced by Yusof in 2012, is inspired by the framework of Formal Language Theory introduced by Head in 1987. Y-G splicing system is intended to present the biological process of DNA splicing in a translucent way. In this paper, starting with some relevant preliminaries, one theorem is proposed via Y-G approach using one initial string and one rule with different characteristics of the restriction enzyme. Additionally, the theorem showed the behavior of the splicing languages generated at single stage splicing. Two cases are considered in the theorem by conducting splicing using palindromic rule and palindromic recognition site with same left and right context for Case I and different left and right context for Case II. Furthermore, two molecular examples are discussed to validate two cases proposed in the theorem, which shows the real meaning of the theorem in biological aspect. From the proposed theorem, based on the splicing language generated, the type of splicing language can be determined. It is discovered that, the generated languages are in the form of limit and transient.

Sorting coffee bean nowadays is still done manually, although there is already a support machine for separation through size, but to determine the quality of the seeds remain manual using human power. This coffee bean sorting is in the spotlight to research whether it can be more effective if there is a tool that can directly find out the quality of coffee. This system will make it easier for workers in the field. In addition to saving time, costs will decrease and also the work of workers will be reduced. This paper present the implementation of machine learning method to classify the coffee bean quality. The dataset use 90 coffee bean for three classes and 30 for each class. From the experimental result, the highest accuracy obtain 83%.

This study aims to estimate fruit tree biomass with a high-order Gaussian kernel estimator. The source of the data was obtained by estimating the relationship between tree diameter (x) and tree biomass (y) which was obtained through the allometric equation y = 0.11ρx^2.62 for branched trees. Data samples were taken as many as 250 obtained from 5 sub-district locations in critical land on longan and mango fruit tree vegetation. The relationship between x and y is then estimated in the form of an equation y_i = m (x_i) + ε_i where, i = 1, 2, n. The results of the analysis using the kernel estimator showed that the tree biomass estimation resulted in a smooth regression curve at an optimal bandwidth (h) score of 1.3 (GCV = 122.92) longan and 2.6 (GCV = 3523.25) mango. The relationship between MSE and bandwidth shows a very strong negative correlation with a score of r = -0.959 (p.value = 0.04) in the estimated longan biomass and r = -0.964 (p.value = 0.03) in the estimated mango biomass and is significant (α = 0.05). This means that a parallel increase in the bandwidth score will decrease the MSE score when GCV is controlled.

PBL has become a popular topic in educational research studies. Several studies examine the effect of PBL toward students' mathematical connection abilities. A total of 8 articles qualified for inclusion. This study analyzed them using Meta Analysis with the Comprehensive Meta-Analysis (CMA) application by selecting the Hedge's equation to determine its effect size and bias publication was assessed by the funnel plot, and Rosenthal's fail-safe N (FSN) test. Based on the analysis result, the overall effect size is 0.797 according to random-effect model with a 95% confidence interval (CI). It was classified as a moderate level. The findings of the study showed that the overall implementation of PBL had a larger positive effect significantly compared to conventional learning on the students' mathematical connection's ability. Because, in the implementation of the PBL model, students are faced with problems that are closely related to everyday life. This shows that mathematical connection ability is needed one of which is the aspects of the connection between mathematics and daily life. Doing this research can support the development of learning and can be an alternative learning model to improving students' mathematical connections ability.

Learning independence is something that is expected in this digital era. So much knowledge can be obtained from various sources, not only from learning at school. For this reason, qualitative research is needed to analyze it. The purpose of this qualitative research with the case study method is to analyze student learning independence in online learning mathematics based on google classroom. The technique used is by giving questionnaires to students through a google form that is distributed in google classroom. This study was applied to 30 students grade VII-A of SMP Santo Yoseph Medan in the 2021/2022 Academic Year. Based on the learning independence questionnaire that has been filled out by students, the results show that the average percentage of students' dependence on others is 86.27, students have self-confidence is 71.07, students behave in a disciplined manner is 72.86, students have a sense of responsibility are 72.67, students have behaviour based on their own initiative is 91.33, students do self-control is 77.55. So, based on overall indicators of learning independence, it is concluded that students are independent in learning mathematics with an average percentage of 78.63. From several indicators of learning independence, it was found that the attitude on one's own initiative was more dominant than some other indicators.

High order thinking skills are important for prospective mathematics teachers. This study aims to describe whether High Order Thinking Skills (HOTS) can appear when prospective teachers solve controversial math problems. This research has been conducted using descriptive qualitative research. The instruments that have been used are controversial math test questions and interviews. The research subjects used were 150 prospective mathematics teachers, and three people who experienced controversy were taken to find out their HOTS. The results showed that from the three subjects, information was obtained that analysis and evaluation had emerged when solving controversial problems, but only one subject appeared for creating. Suggestions for the next researcher is to combine critical thinking and HOTS to bring up aspects of creating.

This study is inspired by the result of a previous study which found that student skills in managing mathematical concepts to solve mathematics are very low. Students find difficulties in searching, applying, or choosing the problem-solving procedures. By considering this issue, the researchers aim to discover the process of managing knowledge to find flexible solutions with conceptual basis while understanding the symbols used, both as the process and concept to solve mathematical problems. Procept in this paper is defined as the symbol that expresses process and concept. This study was a qualitative-explorative descriptive research. The research subject was determined by giving mathematics skill test to 42 Junior High School students as the subject, thus, five high-skilled students were acquired, while 22 students fell into the moderate category, and 15 students fell into the low category. The characterization for the illustration of procept skills of each category is formulated. Data collecting was conducted by implementing a task-based interview, and was analysed by applying the qualitative data analysis technique performed through data reduction, data presentation, and conclusion drawing. Research results show that in the formation stages of procept (pre-procedure, procedure, multi-procedure, process, procept), subjects with high and moderate skills of mathematics have reached the procept stage, while subjects with low mathematical skills are in the stage between the procedural and multi-procedural.

Problem-solving can grow if students are trained to have metaliteracy. Metaliteracy is the ability to think that focuses on critical thinking skills and collaborative efforts. This study aims to determine the impact of the implementation of RBL-STEM to analyze the metaliteracy of students in solving rainbow antimagic coloring problems. The methods used in this study were a combination of quantitative and qualitative methods. This research used two classes, experimental and control. Both classes were given the same treatments with different experiment classes using LKM that have been developed with the RBL model. The analysis of the results of the homogeneity test on the pre-test items showed that the two classes were homogeneous with a significant value is ≥ 0.05, and the results of the independent sample t-test on post test result showed that the sig (2-tailed) value is 0.000 (p ≤ 0.05) so its significant. It can be concluded that the RBL-STEM model can improve the metaliteracy level of the students in solving rainbow antimagic coloring.

The purpose of this study was to measure the achievement of students' science process skills (SPS) on cells and tissues concept during pandemic. The research was conducted in January 2021 at high school in Depok City. The sampling technique used purposive random sampling. SPS tested consist of 7 aspects (observing, applying concepts, interpreting, asking, communicating, classifying, and concluding). Data collection using an essay test with 16 questions and teacher-student interviews. The instrument was validated by five expert validators and calculated with the Aiken's V formula reaches 0.74 (valid) and the reliability test value with Cronbach-Alpha reaches 0.81 (reliable). The non-parametric normality test reach 0.361 (sample is normally distributed). The non-parametric Mann-Whitney test reach 0.011 (hypothesis accepted; there is a difference in achievement between grade XI and XII). The results of the survey showed that the students' SPS were in the moderate (grade XII) and less category (grade XI). The easiest aspect of SPS in both is the questioning aspect. The aspect that gets the least category is communicating (grade XII) and classification (grade XI). This can be influenced by the level of students' understanding of the concept and scientific process, experience in observing, and doing all scientific process.

Analogy learning model is a learning that use analogies, namely comparing concepttarget and concept analog to find related features both of them then make conclusion. The purpose of this research was to know students' mathematical intuitive thinking ability between students taught with Teaching with analogy model and those taught using a scientific learning. The research was conducted at senior high school in Depok. The method of research used quasi experiment method with posttest-only control group design. The samples are 71 students, they are 37 students in experimental group and 34 students in control group by cluster random sampling technique. Data collection to measure the ability of students' mathematical intuitive thinking used by test instrument. The result of this research shows that the value of sig.=0,000 less than signification standard 0,05 on hypothesis test. This indicates that the average of students' mathematical intuitive thinking abilityon teaching sequences and series taught using teaching with analogy model is higher than those taught with scientific learning. This research concludes that learning mathematics using teaching with analogy model has an effect on students' mathematical intuitive thinking ability.

Mathematical reasoning ability can be obtained through the process of understanding students in learning mathematics. However, not a few students experience learning barriers, one of which is in studying three-dimensional material. The purpose of this study is to identify the epistemological obstacle focused to Reasoning and Proof indicator in the three dimensional and overcome them by developing mathematical learning designs in high school. This research was held at SMAN 9 Tangerang. The reasearch method is Didactical Design Research. This method is consist of three stages, namely analysis before learning (prospective analysis), during learning (metapeda didactic), and after learning (retrosfective). Based on the results of the preresearch, 80,48% of 38 students who took the identification of student obstacle test had epistimological obstacles in the concepot three dimensional. To overcome the epistemological obstacle in the concept of three dimensional, are needed learning design that are developed based of student's learning obstacle, repersonalization, and recontextualization, so that it results the hypothetical learning trajectory which composed the various student activities and predictions of student responses follows with the anticipation, and result the generates student worksheet. The results of the study show that the design can be used to overcome student difficulties, it can be seen from the effectiveness of anticipation given to overcome student difficulties during learning.

Teachers in the 21st century are required to have the ability to integrate technology for content knowledge and teaching strategies known as TPACK. 21^st-century teachers must have the knowledge and skills to use various technological tools, both traditional and modern, to facilitate learning and improve learning outcomes. For this reason, it is necessary to prepare prospective teachers who have the knowledge and skills to integrate technology into education. This research aims to design a learning model to develop TPACK of prospective elementary teachers in mathematics learning. This literature study is based on related articles or books and analyzed to formulate applicable learning models. The results showed that The synthesis of qualitative evidence-based learning by design could improve the TPACK of prospective teachers. Because it provides an authentic context to learn about educational technology by starting from the difficulties of students. Also, it enhances prospective teachers' self-regulated learning and collaboration.

The research proposed to develop teaching-learning material with metaphor phase in mathematics for students at High School. The teaching-learning materials developed in this study consist of three kinds of metaphors: grounding metaphors, linking metaphors, and redefinitional metaphors. The selection subject matter in modules is composition and inverse function. Hopefully, it would help students learn mathematics independently and students are expected to be able to understand abstract material concepts with more concrete and meaningful concepts. The method research is R&D with 3D models (Define, Design and Develop). Using the questionnaire, the teaching-learning material was validated by three lecturers at mathematics education and five mathematics teachers who teach at high school. Some notes from the validator provide improvement. And finally, teaching-learning material was tested on 27 students at State High School 1 Jawilan-Serang City class XII. The result shows that the teaching-learning material in review by validator is very feasible criteria (89%) and review from students shows suitable criteria for use in teaching-learning mathematics (86%), so the conclusion is the teaching-learning material is feasible to use in teaching and learning mathematics especially in subject composition and inverse function.

Online learning prefers to use electronic teaching materials, one of the teaching materials used is e-modules as a learning resource that can improve students' abilities. This form of inquisition is oriented to R&D (Research & Development) with the application of the ADDIE model (Analysis, Design, Development, Implementation, Evaluation). Research for implementation of e-module based using pre-experiment design with One Group Pretest-Posttest Design. The sample selection was done by purposive sampling technique, the samples studied were students of SMA Negeri 1 Tanjungbalai as many as 32 students. The instruments used are the BSNP questionnaire and thedescription test High Order Thinking Skill (HOTS). The results showed that the development of SETS-based e-modules with the PjBL model on colloidal learning: (1) the average feasibility of developing e-modules for all BSNP criteria was eligible (content feasibility = 3.54, language eligibility = 3.59, presentation feasibility = 3.84 and the feasibility of graphics = 3.68, then the e-module is feasible to use, and (2) its use has an effect on increasing High Order Thinking Skill students'(HOTS) (with an N-gain of 0.44).

Virtual Laboratory (virtual lab) is a series of virtual experiment laboratories that have been designed and programmed to be used by students for practicum, especially during the Covid-19 pandemic. The virtual lab is helpful for student to build content knowledge which usually they do in real practicum activities. The virtual lab is arranged systematically. Therefore, the result should be close to the real value. Here we report our study on pendulum whether the virtual lab experiment yield the same result as the real laboratory (real lab). We compare both results of experimental data using data analytics and also graphic analytics. The results from the study, shows that there is no significant difference between virtual lab and real lab. Thus, the virtual laboratory is a comparable pendulum experimental result for students doing a remote practicum in physics.