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Journal articles on the topic 'Terminal Vertices'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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1

Sciriha, Irene. "Polynomial reconstruction and terminal vertices." Linear Algebra and its Applications 356, no. 1-3 (2002): 145–56. http://dx.doi.org/10.1016/s0024-3795(02)00385-3.

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Xie, Sun, Haixing Zhao, and Jun Yin. "Uniformly Most Reliable Three-Terminal Graph of Dense Graphs." Mathematical Problems in Engineering 2021 (April 19, 2021): 1–10. http://dx.doi.org/10.1155/2021/6664959.

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A graph G with k specified target vertices in vertex set is a k -terminal graph. The k -terminal reliability is the connection probability of the fixed k target vertices in a k -terminal graph when every edge of this graph survives independently with probability p . For the class of two-terminal graphs with a large number of edges, Betrand, Goff, Graves, and Sun constructed a locally most reliable two-terminal graph for p close to 1 and illustrated by a counterexample that this locally most reliable graph is not the uniformly most reliable two-terminal graph. At the same time, they also determ

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3

Babujee, J. Baskar, and J. Senbagamalar. "On Wiener and terminal Wiener index of graphs." International Journal of Biomathematics 08, no. 05 (2015): 1550066. http://dx.doi.org/10.1142/s1793524515500667.

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The Wiener index is a topological index defined as the sum of distances between all pairs of vertices in a graph. It was introduced as a structural descriptor for molecular graphs of alkanes, which are trees with vertex degrees of four at the most. The terminal Wiener index is defined as the sum of distances between all pairs of pendent vertices in a graph. In this paper we investigate Wiener and terminal Wiener for graphs derived from certain operations.

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Deutsch, Emeric, and Juan Alberto Rodríguez-Velázquez. "The Terminal Hosoya Polynomial of Some Families of Composite Graphs." International Journal of Combinatorics 2014 (April 16, 2014): 1–4. http://dx.doi.org/10.1155/2014/696507.

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Let G be a connected graph and let Ω(G) be the set of pendent vertices of G. The terminal Hosoya polynomial of G is defined as TH(G,t)∶=∑x,y∈Ω(G):x≠ytdG(x,y), where dG(x,y) denotes the distance between the pendent vertices x and y. In this note paper we obtain closed formulae for the terminal Hosoya polynomial of rooted product graphs and corona product graphs.

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Renuka, Sahu, and Kumar Sharma Animesh. "Understanding the Unique Properties of Fuzzy Concept in Binary Trees." Indian Journal of Science and Technology 16, no. 33 (2023): 2631–36. https://doi.org/10.17485/IJST/v16i33.874.

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Abstract <strong>Objective:</strong> This study investigated the properties of fuzzy binaries, a type of rooted trees, and explored their implications in different domains. <strong>Method:</strong> This investigation included analyzing the structural properties of fuzzy binary tree, such as the number of vertices, the height, and the degree to which edges were assigned membership. Theorem: Combinatorial analysis and mathematical induction were used to derive the relation between the number of vertex and height of a fuzzy binary tree based on its internal vertex. The conditions t

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Ramane, H. S., A. B. Ganagi, K. P. Narayankar, and S. S. Shirkol. "Terminal Hosoya Polynomial of Line Graphs." Journal of Discrete Mathematics 2013 (June 13, 2013): 1–3. http://dx.doi.org/10.1155/2013/857908.

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The terminal Hosoya polynomial of a graph G is defined as TH(G,λ)=∑k≥1‍dT(G,k)λk, where dT(G,k) is the number of pairs of pendant vertices of G that are at distance k. In this paper we obtain terminal Hosoya polynomial of line graphs.

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KAUFMANN, MICHAEL, SHAODI GAO, and K. THULASIRAMAN. "AN ALGORITHM FOR STEINER TREES IN GRID GRAPHS AND ITS APPLICATION TO HOMOTOPIC ROUTING." Journal of Circuits, Systems and Computers 06, no. 01 (1996): 1–13. http://dx.doi.org/10.1142/s0218126696000029.

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In this paper we present an algorithm for Steiner minimal trees in grid graphs with all terminals located on the boundary of the graph. The algorithm runs in O(min{k4, k2n}) time, where k and n are the numbers of terminals and vertices of the graph, respectively. It can handle non-convex boundaries and is the fastest known for this case. We also consider the homotopic routing problem and apply our Steiner tree algorithm to construct minimum-length wires for multi-terminal nets.

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Xie, Sun, Haixing Zhao, Jun Yin, and Jinyu Zou. "Judgment Criteria for Reliability Comparison of Three-Terminal Graphs with High Edge Failure Probability." Axioms 14, no. 6 (2025): 457. https://doi.org/10.3390/axioms14060457.

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A three-terminal graph is defined as a simple graph comprising three specified target vertices. The reliability of three-terminal graphs represents the probability that these three target vertices remain connected, given that each edge fails independently with a constant probability q. In this paper, we focus on exploring the characteristics of more reliable three-terminal graphs when the edge failure probability approaches 1. Three reliability comparison criteria are proposed to characterize the locally most reliable three-terminal graph progressively when the number of edges m is in the rang

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Khadka, Shree Ram, and Phanindra Prasad Bhandari. "Lexicographic Earliest Arrival Contraflow Evacuation Problem on UPL-TTSP Network." International Journal of Operational Research/Nepal 9, no. 1 (2020): 1–7. http://dx.doi.org/10.3126/ijorn.v9i1.51842.

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An evacuation plan proposes a way out for maximum utilization of an existing transportation system so that the safest tour and most efficient evacuation time of all expected evacuees could be ensured. This paper studies the auto-based earliest arrival contraflow problem modeled on network with capacitated intermediate vertices. The vertices serve as trans-shipment vertices as well as temporary shelters of given priority order. It also proposes an efficient solution procedure to the problem for the uniform path length two terminal series parallel (UPL-TTSP) network.

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PAUL, SOMNATH. "ON THE MAXIMAL DISTANCE SPECTRAL RADIUS IN A CLASS OF BICYCLIC GRAPHS." Discrete Mathematics, Algorithms and Applications 04, no. 04 (2012): 1250061. http://dx.doi.org/10.1142/s1793830912500619.

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Bicyclic graphs are connected graphs in which the number of edges equals the number of vertices plus one. Let Pp+1 = x1x2⋯xp+1, Pt+1 = y1y2⋯yt+1 and Pq+1 = z1z2⋯zq+1 be three vertex-disjoint paths. Identifying the initial vertices as u0 and the terminal vertices as v0, the resultant graph, denoted by θ(p; t; q), is called a θ-graph. Let [Formula: see text] be the class of all bicyclic graphs on n vertices, which contain a θ-graph as an induced subgraph. In this paper, we study the distance spectral radius of bicyclic graphs in [Formula: see text], and determine the graph with the largest dista

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Khalid, Sohaib, and Akbar Ali. "On the zeroth-order general Randić index, variable sum exdeg index and trees having vertices with prescribed degree." Discrete Mathematics, Algorithms and Applications 10, no. 02 (2018): 1850015. http://dx.doi.org/10.1142/s1793830918500155.

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The zeroth-order general Randić index (usually denoted by [Formula: see text]) and variable sum exdeg index (denoted by [Formula: see text]) of a graph [Formula: see text] are defined as [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] is degree of the vertex [Formula: see text], [Formula: see text] is a positive real number different from 1 and [Formula: see text] is a real number other than [Formula: see text] and [Formula: see text]. A segment of a tree is a path [Formula: see text], whose terminal vertices are branching or/and pendent, and all non-termin

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Kitamura, Ryuichi, Toshiyuki Yamamoto, Keiko Kishizawa, and Ram M. Pendyala. "Stochastic Frontier Models of Prism Vertices." Transportation Research Record: Journal of the Transportation Research Board 1718, no. 1 (2000): 18–26. http://dx.doi.org/10.3141/1718-03.

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A methodology to estimate the location and size of space-time prisms that govern individuals’ activity and travel is presented. Because the vertices of a prism are unobservable, stochastic frontier models are formulated to locate prism vertices along the time axis using observable trip starting or ending times as the dependent variable and commute characteristics, personal and household attributes, and area characteristics as explanatory variables. Models are estimated successfully with coherent behavioral indications. A mean difference of 1.46 h is found between the observed trip ending time

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Øbro, Mikkel. "Classification of terminal simplicial reflexive d-polytopes with 3d − 1 vertices." manuscripta mathematica 125, no. 1 (2007): 69–79. http://dx.doi.org/10.1007/s00229-007-0133-z.

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Schweickert, Richard, and Xiaofang Zheng. "Tree Inference: Response Time and Other Measures in a Binary Multinomial Processing Tree, Representation and Uniqueness of Parameters." Mathematics 10, no. 2 (2022): 267. http://dx.doi.org/10.3390/math10020267.

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A Multinomial Processing Tree (MPT) is a directed tree with a probability associated with each arc and partitioned terminal vertices. We consider an additional parameter for each arc, a measure such as time. Each vertex represents a process. An arc descending from a vertex represents selection of a process outcome. A source vertex represents processing beginning with stimulus presentation and a terminal vertex represents a response. An experimental factor selectively influences a vertex if changing the factor level changes parameter values on arcs descending from that vertex and no others. Ear

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Tosa, Cristian, Tomio Miwa, and Takayuki Morikawa. "Space-Time Prism Vertices for Morning and Evening Commuters in Cluj-Napoca, Romania." Advanced Engineering Forum 21 (March 2017): 573–78. http://dx.doi.org/10.4028/www.scientific.net/aef.21.573.

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This paper investigates socio-demographic characteristics in the origin and terminal vertices of the time-space prism, by using the stochastic frontier method for morning and evening full time workers in the metropolitan area of Cluj-Napoca, Romania. Observed trip starting and ending times are used as dependent variables, while trip distance and time, as well as spatial characteristics to distinguish among commuters are independent variables. The results discuss spatial and temporal patterns of the commuting trips in estimating the temporal vertices of time-space prisms in a former socialist,

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Abayo, Sylvester Arthur, Isaac Owino Okoth, and Donnie Munyao Kasyoki. "Reachability in complete t-ary trees." Annals of Mathematics and Computer Science 18 (October 1, 2023): 67–89. http://dx.doi.org/10.56947/amcs.v18.191.

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Mathematical trees such as Cayley trees, plane trees, binary trees, noncrossing trees, t-ary trees among others have been studied extensively. Reachability of vertices as a statistic has been studied in Cayley trees, plane trees, noncrossing trees and recently in t-ary trees where all edges are oriented from vertices of lower label towards vertices of higher label. In this paper, we obtain closed formulas as well as asymptotic formulas for the number of complete t-ary trees in which there are paths of a given length such that the terminal vertex is a sink, leaf sink, first child and non-first

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17

Stanić, Zoran. "On determination of caterpillars with four terminal vertices by their Laplacian spectrum." Linear Algebra and its Applications 431, no. 11 (2009): 2035–48. http://dx.doi.org/10.1016/j.laa.2009.06.041.

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18

Ferretti, V., and D. Sankoff. "The empirical discovery of phylogenetic invariants." Advances in Applied Probability 25, no. 2 (1993): 290–302. http://dx.doi.org/10.2307/1427653.

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An invariant Φ of a tree T under a k-state Markov model, where the time parameter is identified with the edges of T, allows us to recognize whether data on N observed species can be associated with the N terminal vertices of T in the sense of having been generated on T rather than on any other tree with N terminals. The invariance is with respect to the (time) lengths associated with the edges of the tree. We propose a general method of finding invariants of a parametrized functional form. It involves calculating the probability f of all kN data possibilities for each of m edge-length configur

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Ferretti, V., and D. Sankoff. "The empirical discovery of phylogenetic invariants." Advances in Applied Probability 25, no. 02 (1993): 290–302. http://dx.doi.org/10.1017/s0001867800025350.

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An invariant Φ of a tree T under a k-state Markov model, where the time parameter is identified with the edges of T, allows us to recognize whether data on N observed species can be associated with the N terminal vertices of T in the sense of having been generated on T rather than on any other tree with N terminals. The invariance is with respect to the (time) lengths associated with the edges of the tree. We propose a general method of finding invariants of a parametrized functional form. It involves calculating the probability f of all kN data possibilities for each of m edge-length configur

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20

Bi, Bo, Muhammad Kamran Jamil, Khawaja Muhammad Fahd, Tian-Le Sun, Imran Ahmad, and Lei Ding. "Algorithms for Computing Wiener Indices of Acyclic and Unicyclic Graphs." Complexity 2021 (May 3, 2021): 1–6. http://dx.doi.org/10.1155/2021/6663306.

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Let G = V G , E G be a molecular graph, where V G and E G are the sets of vertices (atoms) and edges (bonds). A topological index of a molecular graph is a numerical quantity which helps to predict the chemical/physical properties of the molecules. The Wiener, Wiener polarity, and the terminal Wiener indices are the distance-based topological indices. In this paper, we described a linear time algorithm (LTA) that computes the Wiener index for acyclic graphs and extended this algorithm for unicyclic graphs. The same algorithms are modified to compute the terminal Wiener index and the Wiener pol

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21

Huang, Zejun, and Xingzhi Zhan. "Extremal digraphs whose walks with the same initial and terminal vertices have distinct lengths." Discrete Mathematics 312, no. 15 (2012): 2203–13. http://dx.doi.org/10.1016/j.disc.2012.04.008.

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22

Wahlström, Magnus. "Quasipolynomial Multicut-mimicking Networks and Kernels for Multiway Cut Problems." ACM Transactions on Algorithms 18, no. 2 (2022): 1–19. http://dx.doi.org/10.1145/3501304.

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We show the existence of an exact mimicking network of k O ( log k ) edges for minimum multicuts over a set of terminals in an undirected graph, where k is the total capacity of the terminals, i.e., the sum of the degrees of the terminal vertices. Furthermore, using the best available approximation algorithm for Small Set Expansion , we show that a mimicking network of k O ( log3 k ) edges can be computed in randomized polynomial time. As a consequence, we show quasipolynomial kernels for several problems, including Edge Multiway Cut , Group Feedback Edge Set for an arbitrary group, and Edge M

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Sunoj, B. S*1 &. Mathew Varkey T. K. 2. "LINEAR PRIME LABELING OF SOME DIRECT TREE GRAPHS." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 5, no. 7 (2018): 154–60. https://doi.org/10.5281/zenodo.1307142.

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Linear prime labeling of a graph is the labeling of the vertices with {0,1,2---,p-1} and the direct edges with twice the value of the terminal vertex plus value of the initial vertex. The greatest common incidence number of a vertex (gcin) of in degree greater than one is defined as the greatest common divisor of the labels of the incident edges. If the gcin of each vertex of in degree greater than one is one, then the graph admits linear prime labeling. Here we investigate some direct tree graphs for linear prime labeling.

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Kim, Tae-Yang. "An Algorithm Design about Psychological Counseling Platform Using the Derivative Works." International Journal of Membrane Science and Technology 10, no. 1 (2023): 98–107. http://dx.doi.org/10.15379/ijmst.v10i1.1434.

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The psychological counseling platform using the derivative works in this study includes four main modules and two sub modules. The first main one is a content database that stores a plurality of derivative works in which keywords are set. The second is a message input module including a request message providing unit that displays a request message input from the client terminal on the counselor's terminal, and a counseling message input unit that receives a counseling message written based on the request message from the counselor's terminal. The third main module is a keyword extraction modu

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de Melo, Alexsander A., Celina M. H. de Figueiredo, and Uéverton S. Souza. "On the Computational Difficulty of the Terminal Connection Problem." RAIRO - Theoretical Informatics and Applications 57 (2023): 3. http://dx.doi.org/10.1051/ita/2023002.

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A connection tree of a graph G for a terminal set W is a tree subgraph T of G such that leaves(T) ⊆ W ⊆ V(T). A non-terminal vertex is called linker if its degree in T is exactly 2, and it is called router if its degree in T is at least 3. The Terminal connection problem (TCP) asks whether G admits a connection tree for W with at most ℓ linkers and at most r routers, while the Steiner tree problem asks whether G admits a connection tree for W with at most k non-terminal vertices. We prove that, if r ≥ 1 is fixed, then TCP is polynomial-time solvable when restricted to split graphs. This result

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Suryaningsih, Ratih, and Edy Tri Baskoro. "The locating-chromatic number and partition dimension of fibonacene graphs." Indonesian Journal of Combinatorics 3, no. 2 (2020): 116. http://dx.doi.org/10.19184/ijc.2019.3.2.5.

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<p>Fibonacenes are unbranched catacondensed benzenoid hydrocarbons in which all the non-terminal hexagons are angularly annelated. A hexagon is said to be angularly annelated if the hexagon is adjacent to exactly two other hexagons and possesses two adjacent vertices of degree 2. Fibonacenes possess remarkable properties related with Fibonacci numbers. Various graph properties of fibonacenes have been extensively studied, such as their saturation numbers, independence numbers and Wiener indices. In this paper, we show that the locating-chromatic number of any fibonacene graph is 4 and th

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Sunoj, B.S, and Varkey T.K Mathew. "Linear Incidence Edge Prime Labeling – More Results on Path Related Di Graphs." Indian Journal of Science and Technology 13, no. 2 (2020): 141–48. https://doi.org/10.17485/ijst/2020/v13i02/148783.

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Abstract <strong>Objectives:</strong> Our aim is to find new families of di graphs that admit linear incidence edge prime labeling. <strong>Methods/statistical analysis: </strong>Here the vertices are assigned with 0,1,…,m−1 and edges with 2g(v) + g(u), where u is the initial vertex and v is the terminal vertex and g is the vertex labeling function. The graph is prime when the greatest common incidence number of vertices with in degree greater than one is one. <strong>Findings:</strong> Here we prove that di graph of corona product of P<sub>n</sub> with K<sub>2

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Sadanandan, Indulekha Thekkethuruthel, and Bhadrachalam Chitturi. "Optimal Algorithms for Sorting Permutations with Brooms." Algorithms 15, no. 7 (2022): 220. http://dx.doi.org/10.3390/a15070220.

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Sorting permutations with various operations has applications in genetics and computer interconnection networks where an operation is specified by its generator set. A transposition tree T=(V,E) is a spanning tree over n vertices v1,v2,…vn. T denotes an operation in which each edge is a generator. A value assigned to a vertex is called a token or a marker. The markers on vertices u and v can be swapped only if the pair (u,v)∈E. The initial configuration consists of a bijection from the set of vertices v1,v2,…,vn to the set of markers (1,2,⋯,n−1,n). The goal is to sort the initial configuration

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Papyan, Vardan, X. Y. Han, and David L. Donoho. "Prevalence of neural collapse during the terminal phase of deep learning training." Proceedings of the National Academy of Sciences 117, no. 40 (2020): 24652–63. http://dx.doi.org/10.1073/pnas.2015509117.

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Modern practice for training classification deepnets involves a terminal phase of training (TPT), which begins at the epoch where training error first vanishes. During TPT, the training error stays effectively zero, while training loss is pushed toward zero. Direct measurements of TPT, for three prototypical deepnet architectures and across seven canonical classification datasets, expose a pervasive inductive bias we call neural collapse (NC), involving four deeply interconnected phenomena. (NC1) Cross-example within-class variability of last-layer training activations collapses to zero, as th

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Srochko, V. A., and E. V. Aksenyushkina. "On Resolution of an Extremum Norm Problem for the Terminal State of a Linear System." Bulletin of Irkutsk State University. Series Mathematics 34 (2020): 3–17. http://dx.doi.org/10.26516/1997-7670.2020.34.3.

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We study extremum norm problems for the terminal state of a linear dynamical system using methods of parameterization of admissible controls. Piecewise continuous controls are approximated in the class of piecewise linear functions on a uniform grid of nodes of the time interval by linear combinations of special support functions. In this case, the restriction of a control of the original problem to the interval induces the same restrictions for the variables of the finite-dimensional problems. The finite-dimensional version of a minimum norm problem can effectively be resolved with the help o

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Putri, Azizah Riana, Syafrizal Sy, and Monika Rianti Helmi. "Bilangan Kromatik Lokasi Graf Tentakel." Limits: Journal of Mathematics and Its Applications 22, no. 2 (2025): 45–53. https://doi.org/10.12962/limits.v22i2.3462.

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The locating-chromatic number of a graph was introduced by Chartrand et al. in 2002, which is a combined concept between the vertex coloring and partition dimension of a graph. The locating-chromatic number of a graph is a grouping of vertices on a graph based on color, which is called a color class, provided that each vertex on the graph has a different color code. Determining the locating-chromatic number of a graph is done by constructing the lower and upper bound of the locating-chromatic number of the graph. In this paper, we determine the locating-chromatic number of the tentacle graph,

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Liang, Binmei, and Jianzhou Zhang. "KmsGC: An Unsupervised Color Image Segmentation Algorithm Based onK-Means Clustering and Graph Cut." Mathematical Problems in Engineering 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/464875.

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For unsupervised color image segmentation, we propose a two-stage algorithm, KmsGC, that combinesK-means clustering with graph cut. In the first stage,K-means clustering algorithm is applied to make an initial clustering, and the optimal number of clusters is automatically determined by a compactness criterion that is established to find clustering with maximum intercluster distance and minimum intracluster variance. In the second stage, a multiple terminal vertices weighted graph is constructed based on an energy function, and the image is segmented according to a minimum cost multiway cut. A

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Kamalov, A. A., S. T. Matskeplishvili, M. E. Chaliy, et al. "Assessing the influence of cardiovascular risk factors on the severity of erectile dysfunction: a multivariate statistical analysis." Vestnik Urologii 10, no. 1 (2022): 15–31. http://dx.doi.org/10.21886/2308-6424-2022-10-1-15-31.

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Introduction. The American Heart Association identifies 7 major factors that affect the condition of the vascular wall: smoking, blood pressure, total cholesterol, glucose, body mass index, physical activity, and diet. The vascular wall lesions most often manifest clinically as vasculogenic erectile dysfunction (ED). Consequently, evaluating patients for the presence of the above risk factors can not only help in the treatment of ED, but can also significantly increase the chances of early detection of cardiac pathology.Purpose of the study. To assess cardiovascular disorder markers’ role in p

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Rohaľ-Ilkiv, Boris, Martin Gulan, and Peter Minarčík. "Computationally Efficient Continuous-Time Model Predictive Control of a 2-DOF Helicopter via B-Spline Parameterization." Sensors 23, no. 9 (2023): 4463. http://dx.doi.org/10.3390/s23094463.

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This paper investigates one way to reduce the computational burden of continuous-time model predictive control (MPC) laws by representing the input/output signals and related models using B-spline functions. Such an approximation allows to implement the resulting feedback control law more efficiently, requiring less online computational effort. As a result, the proposed controller formulates the control signals as continuous polynomial spline functions. All constraints assumed over the prediction horizon are then expressed as constraints acting on the B-splines control polygon vertices. The pe

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Alexopoulou, Konstantina I., Catherine P. Raptopoulou, Vassilis Psycharis, et al. "Solvent-Dependent Access to Two Different Ni4II Core Topologies from the First Use of Pyridine-2,6-dimethanol in Nickel(II) Cluster Chemistry." Australian Journal of Chemistry 65, no. 12 (2012): 1608. http://dx.doi.org/10.1071/ch12424.

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The use of pyridine-2,6-dimethanol, pdmH2, in reactions with nickel(ii) acetate has led to two Ni4 clusters, depending on the solvent. [Ni4(O2CMe)4(pdmH)4]·MeCN (1·MeCN) can be obtained from MeCN and [Ni4(O2CMe)6(pdmH)2(EtOH)2]·1.2EtOH (2·1.2EtOH) from EtOH. Each cluster can be converted into the other in the appropriate solvent. The tetranuclear cluster molecule 1 possesses a distorted cubane {Ni4(μ3-OR)4}4+ core (RO– = pdmH–) with the NiII atoms and the alkoxide-type oxygen atoms from the η3 : η1 : μ3 pdmH– ligands occupying alternate vertices of the cube; four η1 : η1 : μ MeCO2– groups cap

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Suwandi, Selfa, Nurdin Nurdin, and Muh Nur. "Edge-Magic Total Labeling on Vertex Amalgamation Graphs of a Star Graph with a Path Graph." Journal of Social Science 5, no. 4 (2024): 1140–51. http://dx.doi.org/10.46799/jss.v5i4.881.

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One of the topic graph theories is graph labeling. Let be a finite simple connected graph, a bijection from to where and is called an edge-magic total labeling of if there exists a contant (called the magic sum of ) such that for any edge of . The super edge-magic total labeling on a graph is the edge-magic total labeling which maps into the set . Let be a connected graph with a fixed vertex . The vertex amalgamation of graph onto a fixed vertex called terminal denoted by is a graph formed by taking all elements (vertices and edges) in with . In this study, we will show that vertex amalgamatio

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Zhang, Panpan, and Hosam Mahmoud. "The degree profile and weight in Apollonian networks and k-trees." Advances in Applied Probability 48, no. 1 (2016): 163–75. http://dx.doi.org/10.1017/apr.2015.11.

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Abstract We investigate the degree profile and total weight in Apollonian networks. We study the distribution of the degrees of vertices as they age in the evolutionary process. Asymptotically, the (suitably-scaled) degree of a node with a fixed label has a Mittag-Leffler-like limit distribution. The degrees of nodes of later ages have different asymptotic distributions, influenced by the time of their appearance. The very late arrivals have a degenerate distribution. The result is obtained via triangular Pólya urns. Also, via the Bagchi–Pal urn, we show that the number of terminal nodes asymp

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Короткий, Виктор, Viktor Korotkiy, Е. Усманова, and E. Usmanova. "Second Order Curves on Computer Screen." Geometry & Graphics 6, no. 2 (2018): 100–112. http://dx.doi.org/10.12737/article_5b55a829cee6c0.74112002.

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Modern computer graphics is based on methods of computational geometry. The curves and surfaces’ description is based on apparatus of spline functions, which became the main tool for geometric modeling. Methods of projective geometry are almost not applying. One of the reasons for this is impossibility to exactly construct a second-order curve passing through given points and tangent to given straight lines. To eliminate this defect a computer program for second order curves construction has been developed. The program performs the construction of second-order curve’s metric (center, vertices,

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Chernousova, T. G. "Mathematical and Graph Models of Specialized Multi-Agent Systems with Distributed Solution of Applied Problems." LETI Transactions on Electrical Engineering & Computer Science 16, no. 6 (2023): 81–95. http://dx.doi.org/10.32603/2071-8985-2023-16-6-81-95.

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The concept of a specialized multi-agent system (SMAS) as a system designed for a distributed solution of either one applied problem or a highly limited range of applied problems is considered. Such problems frequently require a large number of homogeneous operations, which can lead to a significant increase in the size of the system and, as a result, to inefficient control and a drop in performance. Therefore, it is advisable to divide a large-sized open SMAS into classes of agents and find relationships between them. This corresponds to dividing the applied task T into subtasks and determini

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Villanueva-Valencia, José Ramon, Efthymios Tsimtsirakis, and Alex Evilevitch. "Role of HSV-1 Capsid Vertex-Specific Component (CVSC) and Viral Terminal DNA in Capsid Docking at the Nuclear Pore." Viruses 13, no. 12 (2021): 2515. http://dx.doi.org/10.3390/v13122515.

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Penetration of the viral genome into a host cell nucleus is critical for initiation of viral replication for most DNA viruses and a few RNA viruses. For herpesviruses, viral DNA ejection into a nucleus occurs when the capsid docks at the nuclear pore complex (NPC) basket with the correct orientation of the unique capsid portal vertex. It has been shown that capsid vertex-specific component (CVSC) proteins, which are located at the twelve vertices of the human herpes simplex virus type 1 (HSV-1) capsid, interact with nucleoporins (Nups) of NPCs. However, it remained unclear whether CVSC protein

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Li, Zhihai, Xiao Zhang, Lili Dong, et al. "CryoEM structure of the tegumented capsid of Epstein-Barr virus." Cell Research 30, no. 10 (2020): 873–84. http://dx.doi.org/10.1038/s41422-020-0363-0.

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Abstract Epstein-Barr virus (EBV) is the primary cause of infectious mononucleosis and has been shown to be closely associated with various malignancies. Here, we present a complete atomic model of EBV, including the icosahedral capsid, the dodecameric portal and the capsid-associated tegument complex (CATC). Our in situ portal from the tegumented capsid adopts a closed conformation with its channel valve holding the terminal viral DNA and with its crown region firmly engaged by three layers of ring-like dsDNA, which, together with the penton flexibility, effectively alleviates the capsid inne

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Xiao, Chuan, Carol M. Bator, Valorie D. Bowman, et al. "Interaction of Coxsackievirus A21 with Its Cellular Receptor, ICAM-1." Journal of Virology 75, no. 5 (2001): 2444–51. http://dx.doi.org/10.1128/jvi.75.5.2444-2451.2001.

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ABSTRACT Coxsackievirus A21 (CAV21), like human rhinoviruses (HRVs), is a causative agent of the common cold. It uses the same cellular receptor, intercellular adhesion molecule 1 (ICAM-1), as does the major group of HRVs; unlike HRVs, however, it is stable at acid pH. The cryoelectron microscopy (cryoEM) image reconstruction of CAV21 is consistent with the highly homologous crystal structure of poliovirus 1; like other enteroviruses and HRVs, CAV21 has a canyon-like depression around each of the 12 fivefold vertices. A cryoEM reconstruction of CAV21 complexed with ICAM-1 shows all five domain

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Narvekar, Kedar U., and Bikshandarkoil R. Srinivasan. "Crystal structures of two isostructural bivalent metal N-benzoylglycinates." Acta Crystallographica Section E Crystallographic Communications 76, no. 8 (2020): 1260–65. http://dx.doi.org/10.1107/s2056989020009287.

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The crystal structures of two coordination compounds of N-benzoylglycine, viz. catena-poly[[[diaquabis(N-benzoylglycinato)cobalt(II)]-μ-aqua] dihydrate], {[Co(C9H8NO3)2(H2O)3]·2H2O} n , 1, and catena-poly[[[diaquabis(N-benzoylglycinato)nickel(II)]-μ-aqua] dihydrate], {[Ni(C9H8NO3)2(H2O)3]·2H2O} n , 2, are described. The structures of 1 and 2 were reported previously [Morelock et al. (1979). J. Am. Chem. Soc. 101, 4858–4866] and redetermined in this work to determine the H-atom coordinates. In the isostructural compounds, the central metal is located on an inversion centre and exhibits a distor

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Rashid, Muhammad Aamer, Sarfraz Ahmad, Muhammad Kamran Siddiqui, and Mohammed K. A. Kaabar. "On Computation and Analysis of Topological Index-Based Invariants for Complex Coronoid Systems." Complexity 2021 (October 18, 2021): 1–12. http://dx.doi.org/10.1155/2021/4646501.

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In chemical graph theory, benzenoid systems are interrogated as they exhibit the chemical compounds known as benzenoid hydrocarbons. Benzenoid schemes are circumscribed as planar connected finite graphs having no cut vertices wherein the entire internal sections are collaboratively congruent regular hexagon. The past couple of decennium has acknowledged an extravagant development regarding implementation of information theoretic framework in miscellaneous ramification of science, for instance, in social sciences, biological, physical, and engineering. Explicitly, this tremendous improvement ha

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Reddy, Vijay, and Glen Nemerow. "Structure and function of cement proteins in human adenovirus." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C1603. http://dx.doi.org/10.1107/s205327331408396x.

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Human adenoviruses (HAdVs) are large (~150nm in diameter, 150MDa) nonenveloped double-stranded DNA (dsDNA) viruses that cause respiratory, ocular, and enteric diseases. The capsid shell of adenovirus (Ad) comprises multiple copies of three major capsid proteins (MCP: hexon, penton base and fiber) and four minor/cement proteins (IIIa, VI, VIII and IX) that are organized with pseudo T=25 icosahedral symmetry. In addition, six other proteins (V, VII, μ, IVa2, terminal protein and protease) are encapsidated along with the 36Kb dsDNA genome inside the capsid. The crystal structures of all three MCP

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Berger, Raphael J. F., Michael A. Schmidt, Jonas Jusélius, Dage Sundholm, Peter Sirsch та Hubert Schmidbaur. "Tetraberyllium-η4-oxo-hexa(arylcarboxylates)". Zeitschrift für Naturforschung B 56, № 10 (2001): 979–89. http://dx.doi.org/10.1515/znb-2001-1004.

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Abstract Tetraberyllium-oxo-hexabenzoate and -hexa(mesitylcarboxylate) were prepared from benzoic / mesitylcarboxylic acid and freshly precipitated beryllium hydroxide in a tetrahydrofuran / water two-phase system. The crystal structure of the benzoate was deter mined from Be4O(OCOPh)6(C6H6)3 , and that of the mesitylcarboxylate from the phase Be4O(OCOMes)6(CCl4). The two clusters have the μ4-oxo cage structure also detected for the acetate and nitrate complexes, and for the related hexacarbonato hexaanion. The high symmetry of the cluster allows the observation of 9Be and l7O signals in the

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Fuchs, Renate, and Dieter Blaas. "Productive Entry Pathways of Human Rhinoviruses." Advances in Virology 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/826301.

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Currently, complete or partial genome sequences of more than 150 human rhinovirus (HRV) isolates are known. Twelve species A use members of the low-density lipoprotein receptor family for cell entry, whereas the remaining HRV-A and all HRV-B bind ICAM-1. HRV-Cs exploit an unknown receptor. At least all A and B type viruses depend on receptor-mediated endocytosis for infection. In HeLa cells, they are internalized mainly by a clathrin- and dynamin-dependent mechanism. Upon uptake into acidic compartments, the icosahedral HRV capsid expands by~4% and holes open at the 2-fold axes, close to the p

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Yulianti, Lyra, Des Welyyanti, Yanita Yanita, Muhammad Rafif Fajri, and Suhadi Wido Saputro. "On the metric dimension of Buckminsterfullerene-net graph." Indonesian Journal of Combinatorics 7, no. 2 (2023): 63. http://dx.doi.org/10.19184/ijc.2023.7.2.2.

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The metric dimension of an arbitrary connected graph <em>G</em>, denoted by dim(<em>G</em>), is the minimum cardinality of the resolving set <em>W</em> of <em>G</em>. An ordered set <em>W = </em>{<em>w<sub>1</sub>, w<sub>2</sub>,..., w<sub>k</sub></em>} is a resolving set of <em>G</em> if for all two different vertices in <em>G</em>, their metric representations are different with respect to <em>W</em>. The metric representation of a vertex <em>v

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Duan, Ruofei, Hao Pei, Kaiyuan Shi, et al. "Force analysis and improvement of main transformer bushing terminal structure." Journal of Physics: Conference Series 2876, no. 1 (2024): 012017. http://dx.doi.org/10.1088/1742-6596/2876/1/012017.

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Abstract After investigation, it was found that due to natural environmental conditions such as rain and snow temperature, equipment such as down conductor above the terminals, and natural swings of wires, the terminal blocks of the down conductor bushing on the high voltage side of the main transformer of a 500kV substation will deteriorate and deform. Following the force analysis and experiment on the down conductor bushing terminal block on the high voltage side of the main transformer, it is found that the weak structure of the bushing terminal block lies in the vertical orientation of the

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Khayat, Reza, Chi-yu Fu, Alice C. Ortmann, Mark J. Young, and John E. Johnson. "The Architecture and Chemical Stability of the Archaeal Sulfolobus Turreted Icosahedral Virus." Journal of Virology 84, no. 18 (2010): 9575–83. http://dx.doi.org/10.1128/jvi.00708-10.

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ABSTRACT Viruses utilize a diverse array of mechanisms to deliver their genomes into hosts. While great strides have been made in understanding the genome delivery of eukaryotic and prokaryotic viruses, little is known about archaeal virus genome delivery and the associated particle changes. The Sulfolobus turreted icosahedral virus (STIV) is a double-stranded DNA (dsDNA) archaeal virus that contains a host-derived membrane sandwiched between the genome and the proteinaceous capsid shell. Using cryo-electron microscopy (cryo-EM) and different biochemical treatments, we identified three viral m

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