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Recursive digital hydrographic is an automatic and recommended method of separating baseflow to obtain reproducible results. Digital filters help assess the contribution of water to the total flow of a river, while measuring the flow of the riverbed requires sensitive and accurate flow separation techniques. Therefore, this study aims to analyze the analysis of one-way ANOVA digital filter methods for the hydrological characteristics of the small island watershed of Ambon City, including RDF one parameter algorithm, two-parameter algorithm, RDF Lyne & Holick, RDF Chapman, and RDF Eckhard. The one-factor Fingerprint Analysis (ANOVA) results for the five RDF methods of baseflow separation showed that the distribution of baseflow data was generally with a Shapiro-Wilk coefficient greater than α 0.05 and homogeneity with a Levene coefficient of 0.560 greater>α 0.05. The baseflow separation of the five RDF methods has a significant difference with a significance value of 0.001<α 0.05, and the highest average base flow value of the five RDF methods in a row is the Two-parameter algorithm method, followed by the One-parameter algorithm, Eckhardt algorithm, Lyne &Hollick algorithm, and Chapman algorithm. In conjunction with the Turkish test, this calculation showed that the flow separation for the four RDF methods, Lyne &Hollick algorithm, Eckhardt algorithm, One-parameter algorithm, and two-parameter algorithm, have significant similarities and differ significantly from the RDF-Chapman method. These results are strongly influenced by the hydrological characteristics of small island watersheds with limited rain catchment areas and are vulnerable to global environmental changes. [ABSTRACT FROM AUTHOR]

Rational enhancement of convective heat transfer process is implemented in the studied heat transfer surface reliably controlled by changing the values of the channel parameters and it has been experimentally proved. The values of the maximum assessment are established as well as the implementation conditions and the ranges of values of the current estimates of the rational enhancement of convective heat transfer process are established too. This experimental method is proposed for directly determining the coefficient of pressure loss of friction in the channels of the heat transfer apparatus even of very small sizes. A universal working area of aerodynamic tube has been developed for this purpose. This graphic method has been proposed and implemented for determining and observing a continuous change in the values of current performance evaluations of the rational enhancement of convective heat transfer process. It is required for construction of dimensionless parameters of plate-ribbed sliced heat transfer surface across the entire rational enhancement of convective heat transfer process implementation area according to Reynold’s creation values. Thermal and aerodynamic characteristics are obtained in the investigated heat transfer surface in the criteria for providing reliable design calculations of full-sized heat transfer apparatus for various purposes. The possibility of reducing the volume and mass of heat transfer apparatus has been proved in using plate-chat-ribbed heat transfer surface with channels and with diaphragm. [ABSTRACT FROM AUTHOR]

Verification activity in a streamline manufacturing system is one of the most important activity to make sure that the design requirements and the actual product specifications are met. It helps designer or manufacturing engineer as a feedback by detecting issue at early stage. However, we have to select the most effective verification method that will lead to low cost and relatively fast production. Many industries make machined components that are mounted to welded frame, the locations of the components may float with a larger tolerance to the welded frame than the feature to feature tolerance needed for mounting hole pattern. The composite tolerance is needed for this particular case. The most suitable method for gathering measurement data for small batch production is either automatically using CMM or manually using pin gages and size measurement devices. While, the data processing step can be done by graphic analysis or paper gage method for inspecting composite positional tolerance. The innovation of this journal is changing the way of data processing method by reducing the papers (coordinate grid and polar overlay) required for graphic analysis and converting them into mathematical model that can be processed by computer. Hence, we call this virtual graphic analysis. The benefits of using virtual graphic analysis are reducing cost and time of overall inspection process. [ABSTRACT FROM AUTHOR]

A graph is a set of vertices and edges where each edge connects two vertices in the graph. There are several ways to represent a graph, e.g., it can be represented as a matrix: its adjacency matrix, anti-adjacency matrix, Laplacian matrix, or distance matrix. Two matrices which will be explored in this paper are the adjacency matrix and distance matrix. The adjacency matrix represents the presence or absence of an edge connecting two vertices, while the distance matrix represents the shortest path between two vertices. A graph with diameter two is a graph such that the longest distance between any two vertices is equal to two. Examples of two-diameter graphs include bipartite graphs, wheel graphs, and fan graphs. The relation between the distance and adjacency matrices is already known. The purpose of this paper is to find the relation between the square of the distance matrix and the square of the adjacency matrix of a two diameter graph and to find the characteristic polynomial of the distance matrix of a complete bipartite graph Kn,n(which is a special type of two-diameter graph). We prove that D² = 4(J-I)Ā + A2 where D is the distance matrix, J is the matrix all of whose entries are 1, I is the identity matrix, A is the adjacency matrix and Ā is the complement of A Moreover, we also find that the characteristic polynomial of the distance matrix of a complete p bipartite graph is P(λ) = (λ+2)2n-2(λ-(n-2))(λ-(3n-2)). [ABSTRACT FROM AUTHOR]

Let G be a connected graph, let V(G) be the vertex set of graph G, and let E(G) be the edge set of graph G. Thus, the bijective function f : V(G) ∪ E(G) -→ {1, 2, 3, ..., |V(G)| + |E(G)|} is called a local antimagic total edge labeling if for two adjacent edges e1 and e2, wt(e1) = wt(e2), where for e = uv ∈ G, wt(e) = f (u) + f (v) + f (uv). Thus, the local antimagic total edge labeling by induces a proper edge coloring of a graph G if each edge e is assigned the color wt(e). The local antimagic total edge coloring, denoted by γleat(G) is the minimum number of colors taken over all colorings induced by local antimagic total edge labelings of a graph G. In this research, we determine the local super antimagic total edge coloring of some wheel related graph including fan, wheel, gear and friendship graph. [ABSTRACT FROM AUTHOR]

Let G be a nontrivial and connected graph of order n. Define a bijection function g: V(G) -→ {1, 2, . . ., n}. For any vertex v ∈ V(G), the neighbor sum g(v) + Σu∈N(v)g(u) is a called the weight of the vertices v, denoted by w(v). If w(x) ≠ w(y) for any two distinct vertices x and y, then g is called an inclusive distance antimagic labeling. In this paper, we present several results on inclusive distance antimagic labeling of graphs namely joint product, friendship, complete graph, path graph, cyle graph, star graph, doubel star, broom and wheel graph. [ABSTRACT FROM AUTHOR]

An unicyclic graph is a graph containing exactly one cycle. Let G = (V, E) be a simple, nontrivial, finite, and connected graph with vertex set V(G) and edge sets E(G). Let k ∈ N, a mapping fw: V(G) → N defined by fw(v) = Σv∈e w(e) is called as a k - edge - weighting of graph G. A vertex coloring is an edge-weighting w where fw(u) ≠ fw(v) for any edges uv. We define the vertex coloring as the minimum k such that for every graph G has a vertex-coloring k - edge - weighting and we denoted it by μ(G). In this paper, we analyze the exact value of vertex coloring edge weighting of some unicyclic graphs and it's lower bound. [ABSTRACT FROM AUTHOR]

Collision problems play an important role in many daily life applications. The concept of collision usually describes in momentum and impulse. Concepts that are included in collision process can be represented in multiple representations, such as verbal, visual, graph, and mathematical. The aims of the research were to analyze students' conception and their multiple representations skill in the collision. The method used in this research is descriptive survey method. The subjects of this research are university students from physics education program. Subjects consisted 34 students of 2nd semester who had learned Introduction Physics course. Data collected by using two-tier test and interview. Interview used to clarify and empower students answer. The results showed that 42.1% students have correct conception and 43.17% students have multiple representations skill. Almost all of students prefer to answer the question by using verbal representation and can't write an equation or mathematical representation. Some students also do not understand the concept correctly, even though the material has taught before. It can happen because they answer the question based on their intuition. Intuition easily traps students to the wrong concepts. The results of this research can be used to encourage lecturers to utilize appropriate learning method and learning media that improve students' conception in the collision. [ABSTRACT FROM AUTHOR]

All graphs in this paper are a simple, nontrivial and connected graph G. A set W = {w1, w2,w3,..., wk} of vertex set of G, r(v\W) = (d(v,w1),d(v,w2), --, d(v,wk)) is a representation of vertex v to W, the distance between the vertex v and the vertex w, denoted by d(v,w). A set W is called a resolving set of G if every vertices of G have different representation. The minimum cardinality of resolving set W is metric dimension, denoted by dim(G). Furthermore, the resolving set W of G, is called the non-isolated resolving set if there does not for all v ∊ W induced by the non-isolated vertex. A non-isolated resolving number, denoted by nr(G), is minimum cardinality of non-isolated resolving set in G. In this research, we obtain the lower bound of the non isolated resolving number of graphs with homogeneous pendant edges, nr(G ⊙ mK1) ≤ |V(G)|m for m ≤ 2 and these results of the non isolated resolving number of graphs with homogeneous pendant edges with G with a path Pn, complete graph Kn and cycle Cn. [ABSTRACT FROM AUTHOR]

The energy of a graph of a group G is the sum of all absolute values of the eigenvalues of the adjacency matrix. An adjacency matrix is a square matrix where the rows and columns consist of 0 or 1-entry depending on the adjacency of the vertices of the graph. A conjugacy class graph is a graph whose vertex set is the non-central conjugacy classes of the group. Two vertices are connected if their orders are not coprime. Meanwhile, a group G is said to be metabelian if there exists a normal subgroup H in G such that both H and the factor group G/H are abelian. In this research, the energy of the conjugacy class graphs for all nonabelian metabelian groups of order 24 are determined. The computations are assisted by Groups, Algorithm and Programming (GAP) and Maple2016 software. The results show that the energy of graphs of the groups in the study must be an even integer in the case that the energy is rational. [ABSTRACT FROM AUTHOR]

There are various aspects of combinatorial information that are stored in the coefficients of graph polynomials such as the independence polynomial, the matching polynomial and the clique polynomial. The independence polynomial of a graph is defined as a polynomial in which its coefficients are the number of independent sets in the graph. The independent set of a graph is a set of pairwise non-adjacent vertices. The matching polynomial of a graph is the polynomial in which the coefficients are the number of matching sets in the graph. The matching set of a graph is a set of pairwise edges which do not have common vertices. The clique polynomial of a graph is the polynomial in which the coefficients are the number of cliques in the graph. The clique of a graph is the set of pairwise adjacent vertices. Meanwhile, a graph of group G is called conjugate graph if the vertices are noncentral elements of G and two distinct vertices are connected if they are conjugate. In this research, the independence polynomial, the matching polynomial and the clique polynomial of the conjugate graph of dihedral groups of order at most twelve are computed. [ABSTRACT FROM AUTHOR]

In this research, G is a finite 3-generator 2-group of order 16, where G can be a graph which is called the orbit graph. The orbit graph is a graph whose vertices are non-central orbits under the group action of G on a set. The two vertices are adjacent when they are conjugated to each other. Based on the definition of the orbit graph and group action, the orbit graph is determined for G in the case that G acts on itself by conjugation. Throughout this research, the graph that will be considered is a simple undirected graph. [ABSTRACT FROM AUTHOR]

The graph model networks are investigated to determine centrality, weights and the significance of vertices. For centrality analysis appliesa typical method that includesany one of the properties of graph vertices. In graph theory, methods of analyzing centrality are used: in terms by degree, closeness, betweenness, radiality, eccentricity, page-rank, status, Katz and eigenvector. We have proposed a new method of multi-parametric centrality, which includes a number of basic properties of the network member. The mathematical model of multi-parametric centrality method is developed. Comparison of results for the presented method with the centrality methods is carried out. For evaluate the results for the multi-parametric centrality methodthe graph model with hundreds of vertices is analyzed. The comparative analysis showed the accuracy of presented method, includes simultaneously a number of basic properties of vertices. [ABSTRACT FROM AUTHOR]

A labeling f : V (G) → Z+ such that |f(u) − f(v)|≥diam(G) + 1 − d(u, v) holds for every u, v ∈ V (G), is called a radio labeling of G. We define the radio degree of a labeling f : V (G) → {1, 2, … |V (G)|} as the number of pairs of vertices u, v ∈ V (G) satisfying the condition |f(u) - f(v)|≥diam(G) + 1 - d(u, v) and denote it by rdeg(f). The maximum value of rdeg(f) taken over all such labelings is defined as the radio degree of the graph denoted by rdeg(G). In this paper, we find the radio degree of some standard graphs like paths, cycles, complete graphs, complete bipartite graphs and also obtain a characterization of graphs of diameter two that achieve the maximum radio degree. [ABSTRACT FROM AUTHOR]

An algorithm for constructing super-large semantic networks has been developed in current work. Algorithm was tested using the "Cosmos" category of the Internet encyclopedia "Wikipedia" as an example. During the implementation, a parser for the syntax analysis of Wikipedia pages was developed. A graph based on list of articles and categories was formed. On the basis of the obtained graph analysis, algorithms for finding domains of high connectivity in a graph were proposed and tested. Algorithms for constructing a domain based on the number of links and the number of articles in the current subject area is considered. The shortcomings of these algorithms are shown and explained, an algorithm is developed on their joint use. The possibility of applying a combined algorithm for obtaining the final domain is shown. The problem of instability of the received domain was discovered when starting an algorithm from two neighboring vertices related to the domain. [ABSTRACT FROM AUTHOR]

During the survey, the respondents are often allowed to tick more than one answer option for a question. Analysis and visualization of such data have difficulties because of the need for processing multiple response variables. With standard representation such as pie and bar charts, information about the association between different answer options is lost. The author proposes a visualization approach for multiple response variables based on Venn diagrams. For a more informative representation with a large number of overlapping groups it is suggested to use similarity and association matrices. Some aggregate indicators of dissimilarity (similarity) are proposed based on the determinant of the similarity matrix and the maximum eigenvalue of association matrix. The application of the proposed approaches is well illustrated by the example of the analysis of advertising sources. Intersection of sets indicates that the same consumer audience is covered by several advertising sources. This information is very important for the allocation of the advertising budget. The differences between target groups in advertising sources are of interest. To identify such differences the hypothesis of homogeneity and independence are tested. Recent approach to the problem are briefly reviewed and compared. An alternative procedure is suggested. It is based on partition of a consumer audience into pairwise disjoint subsets and includes hypothesis testing of the difference between the population proportions. It turned out to be more suitable for the real problem being solved. [ABSTRACT FROM AUTHOR]

The restricted detour distance D*(u,v) between two vertices u and v of G is the length of a longest u-v path P in G such that =P. The restricted detour polynomial of the graph G is denoted by D*(G;x) and defined as D*(G;x) = ηu,vxD*(u,v). The restricted detour index dd*(G) of a connected graph G is the Wiener index with respect to restricted detour distance, that is dd* (G) = ηu,v D*(u,v). In this paper, the restricted detour polynomial and restricted detour index of edge identification of two wheel graphs are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we study with some graph descriptors also called topological indices. These descriptors are useful in determination of some properties of chemical structures and preferred to some earlier descriptors as they are more practical. Especially the first and second Zagreb indices together with the first and second multiplicative Zagreb indices are considered and they are calculated in terms of the smallest and largest vertex degrees and vertex number for some well-known classes of graphs. [ABSTRACT FROM AUTHOR]

Information security control in software defined networks (SDN) is connected with execution of the security policy rules regulating information accesses and protection against distribution of the malicious code and harmful influences. The paper offers a representation of a security policy in the form of hierarchical structure which in case of distribution of resources for the solution of tasks defines graphs of admissible interactions in a networks. These graphs define commutation tables of switches via the SDN controller. [ABSTRACT FROM AUTHOR]

Knowledge patterns are closely related to ontologies and knowledge bases. They represent general patterns of knowledge, which can be used in various ontologies. We propose to represent knowledge patterns in RDF language. This paper presents the possibilities of visualization of knowledge patterns in available editors of RDF graphs. [ABSTRACT FROM AUTHOR]

Let G be a graph with V(G) = {v1, ..., vn} and E(G) = {e1, ... em}. We only consider undirected graphs with no multiple edges in this paper. The adjacency matrix of G, denoted by A(G), is the n x n matrix A = [aij], where aij = 1 if e = vivj ∈ E(G) or otherwise aij = 0. The anti adjacency matrix of G, denoted by B(G), is the n x n matrix B = [bij], where bij = 0 if e = vivj ∈ E(G) or otherwise bij = 1. Properties of the determinant of the adjacency matrix of some simple graphs have been studied by many researchers. However, the determinant of the anti-adjacency matrix has not been explored yet. If G1 and G2 are disjoint graphs, then the joining of two graphs G1 and G2, denoted G1 ▽ G2 is defined by taking copies of G1 and G2 and adding edges so that each vertex in G1 is adjacent to every vertex in G2. In this paper, we show the properties of the determinant of joining two graphs, G1 and G2. Union of two graphs, denote G1 ∪ G2 is a graph formed by taking copies of G1 and G2. The objectives of this paper are to identify some properties of the determinant anti adjacency matrix of joining and union operation from two disjoint graphs. This paper also emphasizes on investigating the determinant of some special graph class formed by joining and unioning operation of two disjoint of several classes of graphs, such as Bipartite graphs, Cycles, Complete graphs, Stars, and Wheels. [ABSTRACT FROM AUTHOR]

Maximum Standard Deviation Reduction (MSDR) is a graph clustering algorithm to minimize the distance variation within a cluster. In this paper we propose a modified MSDR by replacing one technical step in MSDR which uses polynomial regression, with a new and simpler step. This leads to our new algorithm called Modified MSDR (MMSDR). We implement the new algorithm to separate a domestic flight network of an Indonesian airline into two large clusters. Further analysis allows us to discover a weak link in the network, which should be improved by adding more flights. [ABSTRACT FROM AUTHOR]

Maximal clique enumeration is a graph clustering method for finding all vertices that have the most influence in a graph. The Bron-Kerbosch algorithm is one of the fastest algorithms to find all maximal cliques. Hence, this paper will focus on that algorithm to find all maximal cliques. Counting all maximal cliques of a graph usually uses an adjacency matrix of the graph to find all vertices in the graph that have the most influence. But, in this paper, a complement matrix of a graph will be used in counting all maximal cliques. This research uses a graph that represents a domestic flight route of one of the airlines in Indonesia. By using Bron-Kerbosch algorithm, all maximal cliques of the graph will be listed, so that it will come up with the vertices which are the most influential in this graph. The graph will be represented in complement matrix. The result of applying the Bron-Kerbosch algorithm with the complement matrix of graph will determine vertices that have the most influence in the graph. Besides that, by using a complement matrix, the result gives more information on the vertices which are only connected to the vertices that have the most influence. [ABSTRACT FROM AUTHOR]

Let F, G, and H be simple graphs. We say F → (G,H) if for every 2-coloring of the edges of F there exist a monochromatic G or H in F. The Ramsey number r(G,H) is min {v(F): F → (G,H)}, the size Ramsey number r* (G,H) is min {e(F) : F → (G,H)}, and the restricted size Ramsey number r* (G,H) is min {e(F) : F → (G,H), (F) = r(G,H)}. In 1972, Chvátal and Harary gave the Ramsey number for P3 versus any graph H with no isolates. In 1983, Harary and Miller started the investigation of the (restricted) size Ramsey number for some pairs of small graphs with order at most four. In1983, Faudree and Sheehan continued the investigation and summarized the complete results on the (restricted) size Ramsey number for all pairs of small graphs with order at most four. In 1998, Lortz and Mengenser gave both the size Ramsey number and the restricted size Ramsey number for all pairs of small forests with order at most five. Lately, we investigate the restricted size Ramsey number for a path of order three versus all connected graphs of order five. In this work, we continue the investigation on the restricted size Ramsey number for a pair of small graphs. In particularly, for a path of order three versus connected graphs of order six. [ABSTRACT FROM AUTHOR]

The rainbow connection number of a graph (G), denoted rc(G), is the smallest number of colors needed to color the edges of G so that any two vertices are connected by a path whose edges all have different colors. Similarly we define the strong rainbow connection number of G, denoted by sc(G), by replacing "path" with "geodesic". n this paper, we study the rc and src of a very specific construction known as splitting. For any graph H and any m ∈ N, its m-splitting is a new graph denoted by Splm(G) constructed as follows. Suppose V(H) = {h1, ..., hn}. Then for each hi we introduce m new vertices vi¹ ..., vim and we join each new vertex vij to all neighbors of the original vertex hi H. In this paper we determine the rc and src of Splm (P3) for all m ∈ N, where P3 is the 3-path, i.e. path with three vertices. [ABSTRACT FROM AUTHOR]

This study discusses a process of material development towards teaching the subject of the graphs of quadratic functions (parabola) by utilizing computer algebra systems. Additionally, the results obtained during and after the process of developing materials are summarized. The last section of the study provides recommendations for teachers and researchers who want to develop computer-assisted instruction materials. [ABSTRACT FROM AUTHOR]

In this study, electromagnetic pollution at the 50-3500 MHz. band of frequency spectrum was investigated in central of Sinop. Measurement was conducted at coordinate information determined by GPS 10 different checkpoints about 30 times including 15 nights and 15 days for every checkpoints. According to the results of measurement; electromagnetic pollution is not higher than determined value limit by ICTA in the central of Sinop. Measurement data was removed computer and average values was determined. Obtained data was demonstrated on google map and graphs with different color at rate of electronic pollution. International and national limit values compared with obtained values and to make data and resource is presented. [ABSTRACT FROM AUTHOR]

Hurwitz groups are the nontrivial finite quotients of the (2, 3, 7) triangle group of

In this paper, we introduce notations of neutrosophic soft graphs, neutrosophic soft subgraphs and strong neutrosophic soft graphs. We also give some properties and related examples of them. [ABSTRACT FROM AUTHOR]

In this paper, we define union and intersection operations of fuzzy soft graphs and present some important properties related of them. [ABSTRACT FROM AUTHOR]

Economic order quantity (EOQ) model has been used extensively over a century. Many studies have altered the model to imitate the actual inventory problem. This paper extends the traditional EOQ model and considers an inventory condition where items received are partly with imperfect quality and noninstantaneous deterioration after inspection. We assume the imperfect quality items are discarded immediately by the end of the 100% screening process. A mathematical model is developed and numerical examples along with graphical representation and sensitivity analysis are provided to illustrate the model. [ABSTRACT FROM AUTHOR]

The commuting graph C(G,X), where G is a finite group and X is a subset of G, is the graph whose vertex set is X and two distinct elements of X being joined by an edge whenever they commute in the group G. Here the Δ1 (t)-orbit representatives and the number of elements in the first disc Δ1 (t) of Δ1 (t), is studied when G is a symmetric group of degree n, Sym(n) and X is a conjugacy class of elements of order three. [ABSTRACT FROM AUTHOR]

Let G be a group with nonempty subsets A and B. The graph G(A; B) is the simple graph obtained by deleting all loops from the graph whose vertex set is A and where vertices x and y are adjacent if and only if there is a b ∊ B such that xb = y or yb = x. In this paper, we present realizations of some cacti as G(A; B)'s. [ABSTRACT FROM AUTHOR]

Let mK3 = (Vm; Em) be a finite disconnected graph consisting of m disjoint triangles K3, where Vm is the set of vertices, Em is the set of edges and both Vm and Em are of the same size 3m. A total labelling of mK3 is a function f which maps the elements in Vm and Em to positive integer values, i.e. f : Vm ∪ Em → f1; 2; 3; …g. Let c be a positive integer. A triangle is said have a c-Erd"osian triangle labelling if it is a total labelling f : Vm ∪ Em → {c; c + 1; …, c + 6m - 1} such that f (x) + f (y) = f (xy) for any x; y 2 Vm and an edge xy 2 Em joining them. In order to find all the c-Erd"osian triangle labelling, a straightforward is to use the exhaustive search. However, the exhaustive search is only able to find c-Erd"osian triangle labelling for m ⩽ 5 due to combinatorial explosion. By studying the constant sum of vertex labels, we propose a strong permutation approach, which allows us to generate a certain classes of c-Erd"osian triangle labelling up until m = 8. [ABSTRACT FROM AUTHOR]

Singular trajectories are rarely used because of issues during realization. A method of planning trajectories for given set of points in task space with use of graphs and neural networks is presented. In every desired point the inverse kinematics problem is solved in order to derive all possible solutions. A graph of solutions is made. The shortest path is determined to define required nodes in joint space. Neural networks are used to define the path between these nodes. [ABSTRACT FROM AUTHOR]

Let G be a graph with V(G) = {v1,...,vn} and E(G) = {e1,...,.em}. In this paper, only graphs with no multiple edges are observed. The n × n matrix A = [aij}, where aij = 1 if e = v1vj and aij = 0 otherwise, is the adjacency matrix of G and is denoted by A(G). The n × n matrix B = [bij], where bij = 0 if e = vivj ϵ E (G) and bij = 1 otherwise, is the antiadjacency matrix of G and is denoted by B(G). Boolean operations on two graphs have been examined by Harary and Wilcox. Hence, this paper will consider Boolean operations on two adjancency and antiadjancency matrices of two graphs G1 and G2 with V(G2) = V(G2). Boolean operations which are reviewed on this paper are OR (V), AND (Λ), XOR(⊕), and NXOR(⊕) However, the paper only focus on operation ⊕ and ⊕. The purposes of this paper are to introduce the operations on two adjacency and antiadjacency matrices of two graphs G1 and G2 with V(G1) = V(G2), to reveal the effect on the represented graph using operations ⊕ and ⊕ on both adjacency and antiadjacency matrices, and to compare the largest eigenvalues between the matrices generated by the Boolean operations. [ABSTRACT FROM AUTHOR]

Let G be a graph with V(G) = {v1,...,vn} and E(G) = {e1,...,.em}. We only consider graphs with no multiple edges in this paper. The adjacency matrix of G, denoted by A(G), is the n × n matrix A = [aij], where aij = 1 if e = vivj ϵ E(G) or aij = 0 otherwise. The antiadjacency matrix of G, denoted by B(G), is the n ×n matrix B = [bij], where bij = 0 if e = vivj ϵ E (G) or Bij = 1 otherwise. Harary and Wilcox have considered Boolean operations on two graphs G1 and G2, resulting a new graph G whose V(G1) × V (G) equals V(G1) × V(G2). On this paper, Boolean operations are defined for two adjacency and two antiadjacency matrices of graphs G1 and G2 with V(G1) = V(G2) rather than looking at the two graphs themselves. Boolean operations which are reviewed on this paper are V and Λ. The objectives of this paper are to introduce the operations on two adjacency or two antiadjacency matrices of graph G, to discover some characteristics of the operations on the matrices, to construct a new graph which is generated using the operators on two adjacency or antiadjacency matrices, and to reveal the similarity between operators on adjacency matrix and operators on antiadjacency matrix based on the represented graph. This paper also emphasizes on investigating the relationship between the operators and on comparing the largest eigenvalue between graphs which are constructed by Boolean operators on both adjacency and antiadjacency matrices. [ABSTRACT FROM AUTHOR]

It is shown that only a part of contributions in the full expression for the (amputated) two-leg graphs in effective single-scalar S-matrix theory can be considered as the self-energy function. This part is uniquely fixed by two requirements: the correct wave function normalization and the true (physical) position of the 2-leg Green function pole. On the one-loop level there is no need in fixing the other unknown constants because they turn out absorbed by the parameters that appear only in one-loop S-matrix graphs with n ≥ 3 legs. This means that the problem of fixing the dimensional coupling constants turns out shifted to the next stage of the renormalization procedure. Also, it is shown that the same is true with respect to the multi-component effective scalar theory. In this case the requirements of diagonalizability and correctness of pole positions turn out sufficient for one-loop renormalization of two-leg S-matrix graphs. [ABSTRACT FROM AUTHOR]

The analysis of the deformation and fracture peculiarities of two kinds of aluminum alloys with different deformation behavior types using AE method was carried out. It is shown that an effective description of deformation mechanisms with the use of AE method can be made by sorting and identification of AE signal sources. Strain stages identified through the strain hardening diagrams are consistent with AE activity graphs for different types of AE sources at these stages. AE activity at the stage of strain hardening substantially depends on heterogeneous structure characteristics of materials under loading. [ABSTRACT FROM AUTHOR]

The effect of graph size on segmentation performance and speed is investigated, where segmentation is based on the graph cuts algorithm. The study is performed on lung extraction in 50 complete multi detector computed tomography (MDCT) datasets, and a fully automatic procedure. The experiments were performed on different graph sizes for both 2-D (4 and 8 neighbours) and 3-D (6 and 26 neighbours) graphs. Five slices from each segmented dataset were compared to the reference delineation provided by a radiologist. Our evaluations highlight the fact that when medical image segmentation is performed using graph cuts, increasing graph and neighbourhood connection size does not necessarily improve the segmentation performance, but also increase the running time dramatically. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the bounds of path number in a directed graph, especially in the tournament Tn=(X,U), where we prove that: [formula] and from this remarkable result, we give some subclasses of tournaments for which we have [formula] (i.e. lower bound of P(G)=upper bound of P(G)) especially if An = (X,U) is the tournament having exactly m-n+1 elementary circuits we have: P(An) = e(An) = n2/4-2. Also we give a general theorem concerning the classes of directed graphs satisfying P(G)=e(G). The result obtained: 1. A procedure that allows a directed graph of order n satisfying P(G)=e(G), another class of directed graph G1 of order n+1 such that P(G1)=e(G1). 2. Generalized certain results proved by Alspach and Ore concerning the path partition number in directed graphs. [ABSTRACT FROM AUTHOR]

Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms even for nonlinear and non-Gaussian signal inference problems. IFT algorithms exploit spatial correlations of the signal fields and benefit from techniques developed to investigate quantum and statistical field theories, such as Feynman diagrams, re-normalisation calculations, and thermodynamic potentials. The theory can be used in many areas, and applications in cosmology and numerics are presented. [ABSTRACT FROM AUTHOR]

We investigate introductory physics students' difficulties in translating between mathematical and graphical representations and the effect of scaffolding on students' performance. We gave a typical problem that can be solved using Gauss's law involving a spherically symmetric charge distribution (a conducting sphere concentric with a conducting spherical shell) to 95 calculus-based introductory physics students. We asked students to write a mathematical expression for the electric field in various regions and asked them to graph the electric field. We knew from previous experience that students have great difficulty in graphing the electric field. Therefore, we implemented two scaffolding interventions to help them. Students who received the scaffolding support were either (1) asked to plot the electric field in each region first (before having to plot it as a function of distance from the center of the sphere) or (2) asked to plot the electric field in each region after explicitly evaluating the electric field at the beginning, mid and end points of each region. The comparison group was only asked to plot the electric field at the end of the problem. We found that students benefited the most from intervention (1) and that intervention (2), although intended to aid students, had an adverse effect. Also, recorded interviews were conducted with a few students in order to understand how students were impacted by the aforementioned interventions. [ABSTRACT FROM AUTHOR]

Plug-and-play visual components in a Dynamic Geometry Software (DGS) enable development of visually attractive, rich and highly interactive dynamic drawings. We are developing SLGeometry, a DGS that contains a custom programming language, a computer algebra system (CAS engine) and a graphics subsystem. The basic extensibility framework on SLGeometry supports dynamic addition of new functions from attribute annotated classes that implement runtime metadata registration in code. We present a general plug-in framework for dynamic importing of arbitrary Silverlight user interface (UI) controls into SLGeometry at runtime. The CAS engine maintains a metadata storage that describes each imported visual component and enables two-way communication between the expressions stored in the engine and the UI controls on the screen. [ABSTRACT FROM AUTHOR]

There are many methods that can be applied to each one of the control charts, for instance, Daudin's methodology, which proposal is to set two stages of decision, and a rule to go on with the second stage. It is always taken two samples and, at first, it is only analyzed the first sample. Then, depending on the rule, it is analyzed the second sample or not, so that a good decision can be made. It is stated that in the existing bibliography there are several studies about variable control charts, concretely, average control charts. On the other hand there are fewer contributions for the attribute control chart. [ABSTRACT FROM AUTHOR]

Physics students are expected to apply the mathematics learned in their mathematics courses to physics concepts and problems. Few PER studies have distinguished between difficulties students have with physics concepts and those with either mathematics concepts and their application or the representations used to connect the math and the physics. We are conducting empirical studies of student responses to mathematics questions dealing with graphical representations of (single-variable) integration. Reasoning in written responses could roughly be put into three major categories related to particular features of the graphs: area under the curve, position of the function, and shape of the curve. In subsequent individual interviews, we varied representational features to explore the depth and breadth of the contextual nature of student reasoning, with an emphasis on negative integrals. Results suggest an incomplete understanding of the criteria that determine the sign of a definite integral. [ABSTRACT FROM AUTHOR]

In upper division electricity and magnetism, the manipulation and interpretation of vector functions is pervasive and a significant challenge to students. At CSU San Marcos, using in-class activities adapted from the Oregon State University Paradigms in Physics Curriculum, students' difficulties with vector functions become evident in two types of in-class activities: sketching vector functions and relating vector and scalar functions (e.g., electric field and electric potential). For many students, the cause of these difficulties is a failure to fully distinguish between the components of a vector function and its coordinate variables. To address this difficulty, we implement an additional inclass activity requiring students to translate between graphical and algebraic representations of vector functions. We present our experience with these issues, how to address them, and how in-class activities can provide evidence of student thinking that facilitates curricular refinement. [ABSTRACT FROM AUTHOR]

The Physics Education Group at the University of Washington is examining the extent to which students are able to use graphs of potential energy vs. position to infer kinematic and dynamic quantities for a system. The findings indicate that many students have difficulty in relating the graphs to real-world systems. Some problems seem to be graphical in nature (e.g., interpreting graphs of potential energy vs. position as graphs of position vs. time). Others involve relating the graphs to total, kinetic, and potential energies, especially when the potential energy is negative. The results have implications beyond the introductory level since graphs of potential energy are used in advanced courses on classical and quantum mechanics. [ABSTRACT FROM AUTHOR]

Constant temperature molecular dynamics simulations have been performed on ZnS at different temperatures ranging from 300 K to 1400 K with the objective of establishing and validating the temperature dependent structural and thermodynamic properties. The simulations were carried out in canonical ensemble (NVT) using Lennard-Jones pair potential. Radial distribution functions have been calculated. RDF peaks are found to be broadened and decrease in heights with increasing temperature, reflecting enhanced atomic motions. Energy temperature graph does not show any break, however a break in the specific heat curve and a λ type transformation are observed indicating second order phase transformation. Mean Square Displacement (MSD) for Zn and S atoms separately have been measured and almost identical graph were obtained. The MSD curve exhibits the existence of maximum disorderness at 1100 K and 1400 K which indicates phase transformations around them. [ABSTRACT FROM AUTHOR]

A new design of an optimized optical system for the reduction of a laser beam size at a certain wavelength is presented. The technique of this design is based upon replacing the elements of a four-lenses optical system, which is designed for this purpose, by one element made of an axial gradient index material. The optical performance of this new design, which has a power as that of its counterpart, is tested by the evaluation of many merit functions. The graphical comparisons between the corresponding values of both systems merit functions show that the new design has a less amount of geometrical aberrations relative to that of its counterpart. [ABSTRACT FROM AUTHOR]