Deg Graph
by admin on Saturday, October 16th, 2010 | Comments Off
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The curve (pic prov w/ link) is graph of deg 4 polynomial and goes thru the point (5, -405) Find polynomial?
The curve (pic prov w/ link) is graph of deg 4 polynomial and goes thru the point (5, -405) Find polynomial?
Picture of the degree 4 polynomial graph: http://www.flickr.com/photos/45798231@N04/4293882880/
Slightly confused as to what I should do here. I started with the function...
f(x) = ax^4 + bx^3 + cx^2 + dx + e
found e to be zero through observation, so e is irrelevant.
Determined that: -405 = a(5)^4 + b(5)^3 + c(5)^2 + d(5) which is then simplified to...
-405 = 625a + 125b + 25c + 5d
Then I found the derivative which is f ' (x) = 4ax^3 + 3bx^2 + 2cx + d
Is my format for the polynomial correct so far? What can I do with this derivative with the graph that I have been given? What is this darn polynomial???
Thanks for all of your help, I appreciate it.
From the picture it has a root at -4 and a double root at 0, and a root at 2, so it must have the form y = a x^2 (x+4) (x-2) where a must be determined using the fact that (5,-405) is on the graph. So plug in (x,y) = (5,-405) and get 675 a = -405, so a = -405/675 = -3/5. Hence the polynomial is:
(-3/5) x^2 (x+4) (x-2)
A former 32nd degree Freemason 2/4
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Split Graph $70.1 High Quality Content by WIKIPEDIA articles In graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split graphs were first studied by Foldes and Hammer (1977a, 1977b), and independently introduced by Tyshkevich and Chernyak (1979). Note that the partition into a clique and an independent set need not be unique; for instance, the path abc is a split graph, the vertices of which can be partitioned in three different ways: 1. the clique {a, b} and the independent set {c} 2. the clique {b, c} and the independent set {a} 3. the clique {b} and the independent set {a, c} Split graphs can be characterized in terms of their forbidden induced subgraphs: a graph is split if and only if no induced subgraph is a cycle on four or five vertices, or a pair of disjoint edges (the complement of a 4cycle). Author: Surhone, Lambert M./ Tennoe, Mariam T./ Henssonow, Susan F. Binding Type: Paperback Number of Pages: 90 Publication Date: 2010/08/13 Language: English Dimensions: 6.00 x 9.02 x 0.22 inches |
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Pancyclic Graph $74.88 High Quality Content by WIKIPEDIA articles In the mathematical study of graph theory, a pancyclic graph is a directed or undirected graph that contains cycles of all possible lengths from three up to the number of vertices in the graph. Pancyclic graphs are a generalization of Hamiltonian graphs, graphs which have a cycle of the maximum possible length. A tournament is a directed graph with one directed edge between each pair of vertices. Intuitively, a tournament can be used to model a roundrobin sports competition, by drawing an edge from the winner to the loser of each game in the competition. A tournament is called strongly connected or strong if and only if it cannot be partitioned into two subsets L and W of losers and winners, such that every competitor in W beats every competitor in L. Every strong tournament is pancyclic and nodepancyclic. Author: Miller, Frederic P./ Vandome, Agnes F./ McBrewster, John Binding Type: Paperback Number of Pages: 76 Publication Date: 2010/10/09 Language: English Dimensions: 6.00 x 9.02 x 0.18 inches |
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TwoDimensional Graph $81.25 High Quality Content by WIKIPEDIA articles A twodimensional graph is the graph of a function of one variable f(x). Provided that x and f(x) are real numbers, the graph can be represented as a straight or curved curve in a twodimensional Cartesian coordinate system.A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin. The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as a signed distances from the origin. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 104 Publication Date: 2010/08/09 Language: English Dimensions: 5.98 x 9.00 x 0.25 inches |
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Dual Graph $79.66 High Quality Content by WIKIPEDIA articles In mathematics, a dual graph of a given planar graph G is a graph which has a vertex for each plane region of G, and an edge for each edge in G joining two neighboring regions, for a certain embedding of G. The term dual is used because this property is symmetric, meaning that if H is a dual of G, then G is a dual of H (if G is connected). The same notation of duality may also be used for more general embeddings of graphs on manifolds. Author: Surhone, Lambert M./ Tennoe, Mariam T./ Henssonow, Susan F. Binding Type: Paperback Number of Pages: 112 Publication Date: 2010/08/15 Language: English Dimensions: 6.00 x 9.02 x 0.27 inches |
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Brian Leetch In Air Horizontal graph $149.99 Brian Leetch In Air Horizontal graph - Photo |
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Hulk Hogan B/W graph $209.99 Hulk Hogan B/W graph - Photo |
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Microsoft Graph $113.11 High Quality Content by WIKIPEDIA articles Microsoft Graph (also known as Microsoft Chart) is an OLE application that is deployed by a number of the Microsoft Office programs such as Excel and Access to create charts and graphs. The program can also be hosted as an OLE application object in Visual Basic. Microsoft Graph supports many different types of charts, however, it is a legacy application and the charts produced are not modernlooking and polished. Office 2003 was the last version to use Microsoft Graph for hosting charts inside Office applications as OLE objects. Office 2007, specifically, Excel 2007 includes a new integrated highquality charting engine and the charts created are native to the applications. The new engine supports advanced formatting, including 3D rendering, transparencies and shadows. Chart layouts can also be customized to highlight various trends in the data. Microsoft Graph still exists for compatibility reasons, but the entry points are removed. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 184 Publication Date: 2010/08/11 Language: English Dimensions: 6.00 x 9.02 x 0.42 inches |
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CauseEffect Graph $81.25 High Quality Content by WIKIPEDIA articles In software testing, a causeeffect graph is a directed graph that maps a set of causes to a set of effects. The causes may be thought of as the input to the program, and the effects may be thought of as the output. Usually the graph shows the nodes representing the causes on the left side and the nodes representing the effects on the right side. There may be intermediate nodes in between that combine inputs using logical operators such as AND and OR. Constraints may be added to the causes and effects. These are represented as edges labelled with the constraint symbol using a dashed line. For causes, valid constraint symbols are E (exclusive), O (one and only one), and I (at least one). The exclusive constraint states that both causes1 and cause2 cannot be true simultaneously. The Inclusive (at least one) cons Author: Surhone, Lambert M./ Tennoe, Mariam T./ Henssonow, Susan F. Binding Type: Paperback Number of Pages: 112 Publication Date: 2010/09/20 Language: English Dimensions: 6.00 x 9.02 x 0.27 inches |
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Tanner Graph $71.7 High Quality Content by WIKIPEDIA articles A Tanner graph is a bipartite graph used to specify constraints or equations which specify error correcting codes. In coding theory, Tanner graphs are used to construct longer codes from smaller ones. Both encoders and decoders employ these graphs extensively. Tanner graphs were proposed by Michael Tanner as a means to create larger error correcting codes from smaller ones using recursive techniques. He generalized the techniques of Elias for product codes. Tanner discussed lower bounds on the codes obtained from these graphs irrespective of the specific characteristics of the codes which were being used to construct larger codes. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 82 Publication Date: 2010/08/10 Language: English Dimensions: 6.00 x 9.02 x 0.20 inches |
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Managing and Mining Graph Data $159 Deals with graph data analytics. This book contains surveys on the graph topics like graph languages, indexing, clustering, data generation, pattern mining, classification, keyword search, pattern matching, and privacy. It also studies various domain-specific scenarios like stream mining, web graphs, social networks, chemical and biological data. |
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Self Complementary Graph $60.54 High Quality Content by WIKIPEDIA articles A selfcomplementary graph is a graph which is isomorphic to its complement. The simplest selfcomplementary graphs are the 4vertex path graph and the 5vertex cycle graph.Selfcomplementary graphs are interesting in their relation to the graph isomorphism problem: the problems of checking whether two selfcomplementary graphs are isomorphic and of checking whether a given graph is selfcomplementary are polynomialtime equivalent to the general graph isomorphism problem. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 64 Publication Date: 2010/08/10 Language: English Dimensions: 5.98 x 9.00 x 0.15 inches |
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Trellis (Graph) $60.54 High Quality Content by WIKIPEDIA articles A trellis is a graph of which the nodes are ordered into vertical slices (time) and each node at each time is connected to (at least) one node at an earlier and (at least) one node at a later time. The earliest and latest times in the trellis have only one node.Trellises are used in encoders and decoders for communication theory and encryption. They are also the central datatype used in BaumWelch algorithm for Hidden Markov Models. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 70 Publication Date: 2010/08/10 Language: English Dimensions: 6.00 x 9.02 x 0.17 inches |
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Some Topics in Graph Theory $70 This book provides a rapid introduction to topics in graph theory typically covered in a graduate course. |
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Graph Spectra for Complex Networks $92 A concise and self-contained introduction to the theory of graph spectra and its applications to the study of complex networks. |
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Graph theory in modern engineering $93 Graph theory in modern engineering; computer aided design, control, optimization, reliability analysis |
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Algorithmic Aspects of Graph Connectivity $79 The first really thorough book to discuss this central notion in graph and network theory, emphasising its algorithmic aspects. |
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Graph Rewriting by Trev, Nuadha [Paperback] $78.07 Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Graph transformation, or Graph rewriting, concerns the technique of creating a new graph out of an original graph using some automatic machine. It has numerous applications, ranging from software verification to layout algorithms. Graph transformations can be used as a computation abstraction. The basic idea is that the state of a computation can be represented as a graph, further steps in that computation can then be represented as transformation rules on that graph. Such rules consist of an original graph, which is to be matched to a subgraph in the complete state, and a replacing graph, which will replace the matched subgraph. Formally, a graph rewriting system consists of a set of graph rewrite rules of the form, with L being called pattern graph and R being called replacement graph. A graph rewrite rule is applied to the host graph by searching for an occurrence of the pattern graph and by replacing the found occurrence by an instance of the replacement graph. Author: Trev, Nuadha Binding Type: Paperback Number of Pages: 84 Publication Date: 2011/08/16 Language: English Dimensions: 9.02 x 5.98 x 0.20 inches |
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Zefal Twin Graph Tire Gauge $20.99 Zefal Twin Graph Tire Gauge fits Presta and Schrader valves. |
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Hybrid Graph Theory and Network Analysis $24 Contains work on applications of graph-theory to electrical network analysis. |
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A Java Library of Graph Algorithms and Optimization $99.95 Provides the source code for a library of Java programs that can be used to solve problems in graph theory and combinatorial optimization. This book covers random graph generation and connectivity procedures. It deals with topics such as graph coloring, graph matching, network flow, and packing and covering, including the assignment, and others. |
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Logical Graph $101.96 High Quality Content by WIKIPEDIA articles A logical graph is a special type of diagramatic structure in any one of several systems of graphical syntax that Charles Sanders Peirce developed for logic. In his papers on qualitative logic, entitative graphs, and existential graphs, Peirce developed several versions of a graphical formalism, or a graphtheoretic formal language, designed to be interpreted for logic. In the century since Peirce initiated this line of development, a variety of formal systems have branched out from what is abstractly the same formal base of graphtheoretic structures. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 154 Publication Date: 2010/08/11 Language: English Dimensions: 6.00 x 9.02 x 0.36 inches |
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Schreier Coset Graph $71.7 High Quality Content by WIKIPEDIA articles High Quality Content by WIKIPEDIA articles In the area of mathematics called combinatorial group theory, the Schreier coset graph is a graph associated to a group G, a generating set { xi: i in I }, and a subgroup H G. The vertices of the graph are the right cosets Hg = { hg: h in G } for g in G. The edges of the graph are of the form (Hg, Hgxi). The Cayley graph of the group G with { xi: i in I } is the Schreier coset graph for H = { 1G }. The graph is named after Otto Schreier. The graph is useful to understand coset enumeration and the ToddCoxeter algorithm. A spanning tree of a Schreier coset graph corresponds to a Schreier transversal, as in Schreiers subgroup lemma, (Conder 2003). Coset graphs can be used to form large permutation representations of groups and were used by Graham Higman to show that the alternating groups of large enough degree are Hurwitz groups, (Conder 2003). Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 90 Publication Date: 2010/08/10 Language: English Dimensions: 6.00 x 9.02 x 0.22 inches |
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Analysis and Correctness of Algebraic Graph and Model Transformations $79.95 Analysis and Correctness of Algebraic Graph and Model Transformations |
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Hulk Hogan vs. Andre the Giant graph $209.99 Hulk Hogan vs. Andre the Giant graph - Photo |
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Billy Smith Islanders Sliding Save graph $39.99 Billy Smith Islanders Sliding Save graph - Photo |
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Tiki Barber Run Vs. Oakland graph $89.99 Tiki Barber Run Vs. Oakland graph - Photo |
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Joe Torre w/ Giuliani Single graph $229.99 Joe Torre w/ Giuliani Single graph - Photo |
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Clark Gillies Cup Over Head graph $34.99 Clark Gillies Cup Over Head graph - Photo |
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Vertex (Graph Theory) $71.7 High Quality Content by WIKIPEDIA articles In graph theory, a vertex (plural vertices) or node is the fundamental unit out of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices). From the point of view of graph theory, vertices are treated as featureless and indivisible objects, although they may have additional structure depending on the application from which the graph arises; for instance, a semantic network is a graph in which the vertices represent concepts or classes of objects. The two vertices forming an edge are said to be its endpoints, and the edge is said to be incident to the vertices. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 78 Publication Date: 2010/08/09 Language: English Dimensions: 6.00 x 9.02 x 0.19 inches |
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Graph Theory and Combinatorial Optimization $104 The techniques of graph theory have been used in solving many classical problems. This book explores the field's classical foundations and its developing theories, ideas and applications to new problems. It also examines the geometric properties of graph theory and its widening uses in combinatorial optimization theory and application. |
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Existential Graph $93.99 High Quality Content by WIKIPEDIA articles An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote his first paper on graphical logic in 1882, and continued to develop the method until his death in 1914.Peirce notated predicates using intuitive English phrases; the standard notation of contemporary logic, capital Latin letters, may also be employed. A dot asserts the existence of some individual in the domain of discourse. Multiple instances of the same object are linked by a line, called the line of identity. There are no literal variables or quantifiers in the sense of firstorder logic. A line of identity connecting two or more predicates can be read as asserting that the predicates share a common variable. The presence of lines of identity requires modifying the alpha rules of Equivalence. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 134 Publication Date: 2010/08/11 Language: English Dimensions: 6.00 x 9.02 x 0.31 inches |
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Hyperspace Graph of Connected Subgraphs $108.33 This book creates a new door to a whole new field for research. It was originated by creating analogous ideas from topology to graph theory. Nevertheless, everyone that has taken an undergraduate course in graph theory will be able to understand this work. Given a connected graph, we can construct a new connected graph whose vertices represent all the connected subgraphs of the original graph. This defines the Hyperspace Graph of Connected Subgraphs. One of the objectives is finding relations between the properties of a graph and its corresponding Hyperspace Graph of Connected Subgraphs. In this book, we explore just a few of this relations and give just a little tiny view of this vast field of open questions and problems. This book is intended to invite mathematicians young and old, novice and experienced to explore and expand the ideas presented. The work within this pages is not a end, a solution, but a beginning, a question and a generator for new results. Author: Simon Romero, Likin Binding Type: Paperback Number of Pages: 108 Publication Date: 2009/07/01 Language: English Dimensions: 9.00 x 6.00 x 0.26 inches |
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Convexity and Graph Theory $210 Among the participants discussing recent trends in their respective fields and in areas of common interest in these proceedings are such world-famous geometers as H.S.M. Coxeter, L. Danzer, D.G. Larman and J.M. Wills, and equally famous graph-theorists B. Bollobás, P. Erdös and F. Harary. In addition to new results in both geometry and graph theory, this work includes articles involving both of these two fields, for instance ``Convexity, Graph Theory and Non-Negative Matrices'', ``Weakly Saturated Graphs are Rigid'', and many more. The volume covers a broad spectrum of topics in graph theory, geometry, convexity, and combinatorics. The book closes with a number of abstracts and a collection of open problems raised during the conference. |
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Matching (Graph Theory) $73.28 High Quality Content by WIKIPEDIA articles In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices. It may also be an entire graph consisting of edges without common vertices. Author: Miller, Frederic P./ Vandome, Agnes F./ McBrewster, John Binding Type: Paperback Number of Pages: 92 Publication Date: 2010/09/29 Language: English Dimensions: 6.00 x 9.02 x 0.22 inches |
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Neighbourhood (Graph Theory) $60.54 High Quality Content by WIKIPEDIA articles In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge. The neighbourhood of a vertex v in a graph G is the induced subgraph of G consisting of all vertices adjacent to v and all edges connecting two such vertices. For example, the image shows a graph of 6 vertices and 7 edges. Vertex 5 is adjacent to vertices 1, 2, and 4 but it is not adjacent to 3 and 6. The neighbourhood of vertex 5 is the graph with three vertices, 1, 2, and 4, and one edge connecting vertices 1 and 2. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 70 Publication Date: 2010/08/10 Language: English Dimensions: 6.00 x 9.02 x 0.17 inches |
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Layered Percolation on the Complete Graph. $115.71 We present a generalized (multitype) version of percolation on the complete graph, in which we divide the vertices of the graph into a fixed number of sets (called layers) and perform percolation where the probability of {u, v} being in our edge set depends on the respective layers of u and v. Many results analogous to usual percolation on the complete graph are determined. In addition, we determine the exponential rate function for the probability that a giant component occupies a fixed fraction of the graph, while all other components are small. We also determine the exponential rate function for the probability that a particular exploration process on the random graph will discover a certain fraction of vertices in each layer, without encountering a giant component. Author: Smith, S. Alex Binding Type: Paperback Number of Pages: 58 Publication Date: 2011/09/03 Language: English Dimensions: 9.69 x 7.44 x 0.12 inches |
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The Grbner Annihilator Graph of a Ring $111.53 In recent years, graph theory has been used as a tool to study rings in the form of several different graphs, many of which are based on the zero divisor structure of the ring. We dene here the annihilator graph of a ring to try to harness the best possible graphical representation of a ring. This paper lays the foundation for the theory of annihilator graphs and the extension of them to a more general form, the Grbner annihilator graph. We will study the relationships between the algebraic properties of a ring, and the graph theoretic properties of the Grbner annihilator graph of that ring. We will state some concise results while also formally stating areas in which the author feels further research is needed. This work is an extension of recent work on Zero Divisor Graphs, and Annihilator graphs, with an emphasis on simultaneous generalizations of both. Author: McGuire, Trevor Binding Type: Paperback Number of Pages: 68 Publication Date: 2009/09/01 Language: English Dimensions: 9.00 x 6.00 x 0.16 inches |