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Journal articles on the topic 'Interior vertex'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Sunil, M. P., and J. Suresh Kumar. "On Null Vertex in Fuzzy Graphs." International Journal of Analysis and Applications 22 (March 4, 2024): 43. http://dx.doi.org/10.28924/2291-8639-22-2024-43.

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We introduce a new type of vertex in fuzzy graphs, namely null vertex, which is neither a boundary vertex nor an interior vertex. Here, we initiate a study on the null vertex in fuzzy graphs, explore its properties and establish its presence in various types of fuzzy graphs.

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2

Iwundu, M. P., and S. U. Ekpo. "Rules for Identifying the Initial Design Points for Use in the Quick Convergent Inflow Algorithm." International Journal of Statistics and Probability 5, no. 1 (2015): 98. http://dx.doi.org/10.5539/ijsp.v5n1p98.

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The starting point of search is an important factor in optimal design construction as a poor starting point may require a longer time before convergence is reached. Hence the location of the initial design points for use in the Quick Convergent Inflow Algorithm on segmented regions is examined with the aim of developing useful criteria for identifying the initial design points. Proportional allocation of design points to go into the initial design measures is proposed. The allocation of 100% vertex points, 100% boundary points and 100% boundary points as well as the allocation of 50% vertex an

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Osborne, M. R. "An interior point method for linear programming." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 31, no. 4 (1990): 367–78. http://dx.doi.org/10.1017/s033427000000672x.

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AbstractDesign of an interior point method for linear programming is discussed, and results of a simulation study reported. Emphasis is put on guessing the optimal vertex at as early a stage as possible.

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4

Annadhifi, Muhammad Ilham Nurfaizi, Robiatul Adawiyah, Dafik Dafik, and I. Nengah Suparta. "RAINBOW VERTEX CONNECTION NUMBER OF BULL GRAPH, NET GRAPH, TRIANGULAR LADDER GRAPH, AND COMPOSITION GRAPH (P_n [P_1 ])." BAREKENG: Jurnal Ilmu Matematika dan Terapan 18, no. 3 (2024): 1665–72. http://dx.doi.org/10.30598/barekengvol18iss3pp1665-1672.

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The rainbow connection was first introduced by Chartrand in 2006 and then in 2009 Krivelevich and Yuster first time introduced the rainbow vertex connection. Let graph be a connected graph. The rainbow vertex-connection is the assignment of color to the vertices of a graph , if every vertex on the graph is connected by a path graph that has interior vertices in different colors. The minimum number of colors from the rainbow vertex coloring in the graph is called rainbow vertex connection number which is denoted . The results of the research are the rainbow vertex connection number of bull grap

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Dudko, Anastasia, Oleksandr Lesechko, and Vyacheslav Pivovarchik. "Recovering the shape of an equilateral quantum tree with the Dirichlet conditions at the pendant vertices." Opuscula Mathematica 44, no. 5 (2024): 689–705. http://dx.doi.org/10.7494/opmath.2024.44.5.689.

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We consider two spectral problems on an equilateral rooted tree with the standard (continuity and Kirchhoff's type) conditions at the interior vertices (except of the root if it is interior) and Dirichlet conditions at the pendant vertices (except of the root if it is pendant). For the first (Neumann) problem we impose the standard conditions (if the root is an interior vertex) or Neumann condition (if the root is a pendant vertex) at the root, while for the second (Dirichlet) problem we impose the Dirichlet condition at the root. We show that for caterpillar trees the spectra of the Neumann p

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Bradly, C. J., E. J. Janse van Rensburg, A. L. Owczarek, and S. G. Whittington. "Adsorbed self-avoiding walks pulled at an interior vertex." Journal of Physics A: Mathematical and Theoretical 52, no. 40 (2019): 405001. http://dx.doi.org/10.1088/1751-8121/ab3cb1.

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7

Mehrotra, Sanjay. "On finding a vertex solution using interior point methods." Linear Algebra and its Applications 152 (July 1991): 233–53. http://dx.doi.org/10.1016/0024-3795(91)90277-4.

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8

Dicks, Warren, and Zoran Šunić. "Orders on Trees and Free Products of Left-ordered Groups." Canadian Mathematical Bulletin 63, no. 2 (2020): 335–47. http://dx.doi.org/10.4153/s0008439519000389.

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AbstractWe construct total orders on the vertex set of an oriented tree. The orders are based only on up-down counts at the interior vertices and the edges along the unique geodesic from a given vertex to another.As an application, we provide a short proof (modulo Bass–Serre theory) of Vinogradov’s result that the free product of left-orderable groups is left-orderable.

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Inkulu, R., K. Sowmya, and Nitish P. Thakur. "Dynamic Algorithms for Visibility Polygons in Simple Polygons." International Journal of Computational Geometry & Applications 30, no. 01 (2020): 51–78. http://dx.doi.org/10.1142/s021819592050003x.

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We devise the following dynamic algorithms for both maintaining as well as querying for the visibility and weak visibility polygons amid vertex insertions and deletions to the simple polygon. A fully-dynamic algorithm for maintaining the visibility polygon of a fixed point located interior to the simple polygon amid vertex insertions and deletions to the simple polygon. The time complexity to update the visibility polygon of a point [Formula: see text] due to the insertion (resp. deletion) of vertex [Formula: see text] to (resp. from) the current simple polygon is expressed in terms of the num

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Dosiyev, A. A., and S. Cival Buranay. "A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/864865.

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The integral representations of the solution around the vertices of the interior reentered angles (on the “singular” parts) are approximated by the composite midpoint rule when the boundary functions are from These approximations are connected with the 9-point approximation of Laplace's equation on each rectangular grid on the “nonsingular” part of the polygon by the fourth-order gluing operator. It is proved that the uniform error is of order where and is the mesh step. For the -order derivatives () of the difference between the approximate and the exact solutions, in each “ singular” part or

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11

Katz, Eric, Hannah Markwig, and Thomas Markwig. "The Tropicalj-Invariant." LMS Journal of Computation and Mathematics 12 (2009): 275–94. http://dx.doi.org/10.1112/s1461157000001522.

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AbstractIf (Q,A) is a marked polygon with one interior point, then a general polynomialfbelonging toK[x,y] with supportAdefines an elliptic curveCfon the toric surfaceXA. IfKhas a non-archimedean valuation intoRwe can tropicalizeCfto get a tropical curve Trop(Cf). If in the Newton subdivision induced byfis a triangulation and the interior point occurs as the vertex of a triangle, then Trop(Cf) will be a graph of genus one and we show that the lattice length of the cycle of that graph is the negative of the valuation of thej-invariant ofCf.

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12

Solymosi, József, and Ching Wong. "Intersecting Hexagons in 3-Space." Studia Scientiarum Mathematicarum Hungarica 59, no. 1 (2022): 30–39. http://dx.doi.org/10.1556/012.2022.01514.

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Two hexagons in the space are said to intersect heavily if their intersection consists of at least one common vertex as well as an interior point. We show that the number of hexagons on n points in 3-space without heavy intersections is o(n2), under the assumption that the hexagons are ‘fat’.

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13

Lynch, Thomas B. "Variance Reduction for Sector Sampling." Forest Science 52, no. 3 (2006): 251–61. http://dx.doi.org/10.1093/forestscience/52.3.251.

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Abstract Variance reduction techniques used in Monte Carlo integration including control variates and importance sampling can use estimated or actual shapes of vegetated land areas to reduce the variance of estimators from sector sampling. The estimated shapes of forested areas could come from maps, aerial photos, or similar sources. Antithetic variates for variance reduction in Monte Carlo integration can be applied to sector sampling without using any estimated shape or map. Sector sampling selects as samples all trees or other vegetation of interest located in randomly chosen sectors that h

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14

Max, Nelson. "Constructing and Visualizing Uniform Tilings." Computers 12, no. 10 (2023): 208. http://dx.doi.org/10.3390/computers12100208.

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This paper describes a system which takes user input of a pattern of regular polygons around one vertex and attempts to construct a uniform tiling with the same pattern at every vertex by adding one polygon at a time. The system constructs spherical, planar, or hyperbolic tilings when the sum of the interior angles of the user-specified regular polygons is respectively less than, equal to, or greater than 360∘. Other works have catalogued uniform tilings in tables and/or illustrations. In contrast, this system was developed as an interactive educational tool for people to learn about symmetry

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15

Zhou, Mengyun, and Qingfeng Guan. "A 25-Intersection Model for Representing Topological Relations between Simple Spatial Objects in 3-D Space." ISPRS International Journal of Geo-Information 8, no. 4 (2019): 182. http://dx.doi.org/10.3390/ijgi8040182.

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With the rapid development of the economy, urgent needs for 3-D Geographical Information System (GIS) have sprung up in many application fields. The precise expression of three-dimensional topological relations is the foundation of spatial analysis, topological query, and spatial reasoning in three-dimensional space. In this paper, we subdivide the topological part “boundary” into face, edge, and vertex and propose a 25-intersection model (25IM) to represent topological relations between two simple spatial objects (point, line, region, and body) in 3-D space. An object in the 25IM has five top

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16

Eskandari, Marzieh, Bahram Sadeghi Bigham, and Mazyar Zahedi-Seresht. "Lower Bound for Sculpture Garden Problem: Localization of IoT Devices." Applied Sciences 13, no. 4 (2023): 2597. http://dx.doi.org/10.3390/app13042597.

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The purpose of the current study is to investigate a special case of art gallery problem, namely a sculpture garden problem. In this problem, for a given polygon P, the ultimate goal is to place the minimum number of guards (landmarks) to define the interior polygon P by applying a monotone Boolean formula composed of the guards. Using this problem, it can replace the operation-based method with time-consuming, pixel-based algorithms. So, the processing time of some problems in the fields of machine vision, image processing and gamification can be strongly reduced. The problem has also many ap

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17

Bezrodnykh, S. I., and V. I. Vlasov. "Analysis of Defects and Harmonic Grid Generation in Domains with Angles and Cutouts." Журнал вычислительной математики и математической физики 63, no. 12 (2023): 2096–129. http://dx.doi.org/10.31857/s0044466923120062.

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A survey of works concerning difficulties associated with harmonic grid generation in plane domains with angles and cutouts is given, and some new results are presented. It is well known that harmonic grids produced by standard methods in domains with cutouts or reentrant angles (i.e., interior angles greater than π) may contain defects, such as self-overlappings or exit beyond the domain boundary. It is established that, near the vertex of a reentrant angle, these defects follow from the asymptotics constructed for the underlying harmonic mapping, according to which the grid line leaving the

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Eskandari, Marzieh, Bigham Bahram Sadeghi, and Mazyar Zahedi-Seresht. "Lower Bound for Sculpture Garden Problem: Localization of IoT Devices." Applied Sciences 13, no. 4 (2024): 2597. https://doi.org/10.3390/app13042597.

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The purpose of the current study is to investigate a special case of art gallery problem, namely a sculpture garden problem. In this problem, for a given polygon P, the ultimate goal is to place the minimum number of guards (landmarks) to define the interior polygon P by applying a monotone Boolean formula composed of the guards. Using this problem, it can replace the operation-based method with time-consuming, pixel-based algorithms. So, the processing time of some problems in the fields of machine vision, image processing and gamification can be strongly reduced. The problem has also many ap

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19

Abello, James, Vladimir Estivill-Castro, Thomas Shermer, and Jorge Urrutia. "Illumination of Orthogonal Polygons with Orthogonal Floodlights." International Journal of Computational Geometry & Applications 08, no. 01 (1998): 25–38. http://dx.doi.org/10.1142/s0218195998000035.

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We provide the first tight bound for covering an orthogonal polygon with n vertices and h holes with vertex floodlights (guards with restricted angle of vision). In particular, we provide tight bounds for the number of orthogonal floodlights, placed at vertices or on the boundary, sufficient to illuminate the interior or the exterior of an orthogonal polygon with holes. Our results lead directly to very simple linear, and thus optimal, algorithms for computing a covering of an orthogonal polygon.

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20

Károlyi, Gy, J. Pach, and G. Tóth. "A modular version of the Erdős– Szekeres theorem." Studia Scientiarum Mathematicarum Hungarica 38, no. 1-4 (2001): 245–60. http://dx.doi.org/10.1556/sscmath.38.2001.1-4.17.

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Bialostocki, Dierker, and Voxman proved that for any n = p +2, there is an integer B(n; p) with the following property. Every set of B(n; p) points in general position in the plane has n points in convex position such that the number of points in the interior of their convex hull is 0 mod p. They conjectured that the same is true for all pairs n = 3, p =2. In this note, we show that every su&ciently large point set determining no triangle with more than one point in its interior has n elements that form the vertex set of an empty convex n-gon. As a consequence, we show that the above conje

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21

Wei, Xian-Biao, Yan-Hsiou Cheng, and Yu-Ping Wang. "The Partial Inverse Spectral and Nodal Problems for Sturm–Liouville Operators on a Star-Shaped Graph." Mathematics 10, no. 21 (2022): 3971. http://dx.doi.org/10.3390/math10213971.

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We firstly prove the Horváth-type theorem for Sturm–Liouville operators on a star-shaped graph and then solve a new partial inverse nodal problem for this operator. We give some algorithms to recover this operator from a dense nodal subset and prove uniqueness theorems from paired-dense nodal subsets in interior subintervals having a central vertex. In particular, we obtain some uniqueness theorems by replacing the information of nodal data on some fixed edge with part of the eigenvalues under some conditions.

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22

Manzoor, Shahid, Michael G. Edwards, Ali H. Dogru, and Tareq M. Al-Shaalan. "Interior boundary-aligned unstructured grid generation and cell-centered versus vertex-centered CVD-MPFA performance." Computational Geosciences 22, no. 1 (2017): 195–230. http://dx.doi.org/10.1007/s10596-017-9686-4.

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23

FREIDLIN, MARK, and MATTHIAS WEBER. "ON STOCHASTICITY OF SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH A SMALL DELAY." Stochastics and Dynamics 05, no. 03 (2005): 475–86. http://dx.doi.org/10.1142/s0219493705001547.

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We show that solutions of a class of differential equations with a small delay can be approximated, in a sense, by a stochastic process on a graph associated with the equation. This process moves as a deterministic motion inside any edge of the graph, but, after reaching an interior vertex of the graph, the process chooses one of the other adjacent edges to proceed there with a certain probability. These probabilities are calculated explicitly. The stochasticity is an intrinsic property of the differential equation with small delay.

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24

Snyman, J. A., and M. Van Rooyen. "An experimental investigation of a new multiplex method for linear programming." Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 6, no. 2 (1987): 82–88. http://dx.doi.org/10.4102/satnt.v6i2.948.

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Karmarkar’s recent internal and iterative method for linear programming problems has resulted in a renewed interest in some older alternatives, other than the simplex method. Here a new multiplex and geometric method, which has some features in common with the older methods, is proposed and implemented. In this method the solution is found by following a gradient path through the interior of the feasible region and through subspaces of reduced dimension corresponding to the bounding hyper-surfaces of the feasible region. The path moves from an initial feasible point through a sequence of linea

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Zhang, Jin, and Xiaowei Liu. "Supercloseness of the continuous interior penalty method for singularly perturbed problems in 1D: Vertex-cell interpolation." Applied Numerical Mathematics 123 (January 2018): 88–98. http://dx.doi.org/10.1016/j.apnum.2017.09.003.

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Krivonozhko, V. E., and F. R. Førsund. "The relationship between returns-to-scale properties of interior points and vertex points in DEA models." Doklady Mathematics 81, no. 1 (2010): 159–63. http://dx.doi.org/10.1134/s1064562410010436.

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27

Saputra, Fuad Adi. "Bilangan Rainbow Connection dari Hasil Operasi Penjumlahan dan Perkalian Kartesius Dua Graf." CAUCHY 2, no. 3 (2012): 125. http://dx.doi.org/10.18860/ca.v2i3.3122.

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<div class="standard"><a id="magicparlabel-268">Graf dengan pewarnaan sisi disebut pelangi sisi terhubung, jika setiap titik pada graf dihubungkan oleh lintasan yang memiliki sisi-sisi dengan warna yang berbeda. Rainbow connection pada graf yang terhubung, disimbolkan oleh yaitu bilangan terkecil dari warna yang dibutuhkan untuk membuat graf menjadi pelangi sisi terhubung. Sedangkan graf dengan pewarnaan titik adalah pelangi titik terhubung, jika setiap titik pada graf dihubungkan oleh lintasan yang memiliki titik-titik interior dengan warna yang berbeda. Rainbow vertex-connection

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28

GUHA, SUMANTA. "PARALLEL COMPUTATION OF INTERNAL AND EXTERNAL FARTHEST NEIGHBORS IN SIMPLE POLYGONS." International Journal of Computational Geometry & Applications 02, no. 02 (1992): 175–90. http://dx.doi.org/10.1142/s0218195992000111.

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We present efficient parallel algorithms for two problems in simple polygons: the all-farthest neighbors problem and the external all-farthest neighbors problem. The all-farthest neighbors problem is that of computing, for each vertex p of a simple polygon P, a point ψ(p) in P farthest from p when the distance between p and ψ(p) is measured by the shortest path between them constrained to lie inside P. The external all-farthest neighbors problem is that of computing, for each vertex p of a simple polygon P, a point ϕ(p) on (the boundary of) P farthest from p when the distance between p and ϕ(p

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Nigolian, Valentin Zénon, Marcel Campen, and David Bommes. "A Progressive Embedding Approach to Bijective Tetrahedral Maps driven by Cluster Mesh Topology." ACM Transactions on Graphics 43, no. 6 (2024): 1–14. http://dx.doi.org/10.1145/3687992.

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We present a novel algorithm to map ball-topology tetrahedral meshes onto star-shaped domains with guarantees regarding bijectivity. Our algorithm is based on the recently introduced idea of Shrink-and-Expand, where images of interior vertices are initially clustered at one point (Shrink-), before being sequentially moved to non-degenerate positions yielding a bijective map (-and-Expand). In this context, we introduce the concept of the cluster mesh , i.e. the unexpanded interior mesh consisting of geometrically degenerate simplices. Using local, per-vertex connectivity information solely from

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30

Wang, Zhihua, and Hongmei Kang. "A Polynomial Splines Identification Method Based on Control Nets." Complexity 2020 (August 19, 2020): 1–12. http://dx.doi.org/10.1155/2020/7103963.

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In this study, based on Polynomial Splines with control nets, an identification method is investigated. We introduce polynomial splines with control nets defined over T-mesh. The basic idea is to extend T-vertices such that those T-vertices become interior cross vertices or boundary vertices. To this end, we introduce the design-suitable T-mesh for constructing polynomial splines with control net. In design-suitable T-meshes, there are no extra basis vertices produced by an appropriate extension of T-vertices. The basis functions are defined over each vertex in a design-suitable T-mesh by the

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31

Manzoor, Shahid, Michael G. Edwards, Ali H. Dogru, and Tareq M. Al-Shaalan. "Correction to: Interior boundary-aligned unstructured grid generation and cell-centered versus vertex-centered CVD-MPFA performance." Computational Geosciences 22, no. 1 (2017): 231. http://dx.doi.org/10.1007/s10596-017-9699-z.

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Almalki, Norah, and Pawaton Kaemawichanurat. "Domination and Independent Domination in Hexagonal Systems." Mathematics 10, no. 1 (2021): 67. http://dx.doi.org/10.3390/math10010067.

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A vertex subset D of G is a dominating set if every vertex in V(G)\D is adjacent to a vertex in D. A dominating set D is independent if G[D], the subgraph of G induced by D, contains no edge. The domination number γ(G) of a graph G is the minimum cardinality of a dominating set of G, and the independent domination number i(G) of G is the minimum cardinality of an independent dominating set of G. A classical work related to the relationship between γ(G) and i(G) of a graph G was established in 1978 by Allan and Laskar. They proved that every K1,3-free graph G satisfies γ(G)=i(H). Hexagonal syst

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Khan, M. Asif, and Judy M. Vance. "Mesh Reduction Using an Angle Criterion Approach." Journal of Mechanical Design 118, no. 2 (1996): 300–305. http://dx.doi.org/10.1115/1.2826884.

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Surface polygonization is the process by which a representative polygonal mesh of a surface is constructed for rendering or analysis purposes. This work presents a new surface polygonization algorithm specifically tailored to be applied to a large class of models which are created with parametric surfaces having triangular meshes. This method has particular application in the area of building virtual environments from computer-aided-design (CAD) models. The algorithm is based on an edge reduction scheme that collapses two vertices of a given triangular polygon edge onto one new vertex. A two s

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Fox, M. D., and J. R. Goggins. "Morley’s diagram generalised." Mathematical Gazette 87, no. 510 (2003): 453–67. http://dx.doi.org/10.1017/s0025557200173632.

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Morley’s theorem is well-known: if we trisect the interior angles of any triangle A0A1A2, then the common point of each pair of trisectors adjacent to a side is a vertex of the Morley triangle, M0M1M2, which is always equilateral (Figure 1). Less well-known is that the two triangles are in perspective, that is, the three lines AiMi, concur at a point M.The pairs of trisectors further from the sides meet at W0, W1 and W2, the vertices of the anti-Morley (or perhaps the Worley) triangle. It, too, is in perspective with A0A1A2, the centre of perspective being W. Also, the Morley and anti-Morley t

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Nguyen, Tuan-Minh, and Stanislav Volkov. "On a class of random walks in simplexes." Journal of Applied Probability 57, no. 2 (2020): 409–28. http://dx.doi.org/10.1017/jpr.2020.19.

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AbstractWe study the limit behaviour of a class of random walk models taking values in the standard d-dimensional ( $d\ge 1$ ) simplex. From an interior point z, the process chooses one of the $d+1$ vertices of the simplex, with probabilities depending on z, and then the particle randomly jumps to a new location z′ on the segment connecting z to the chosen vertex. In some special cases, using properties of the Beta distribution, we prove that the limiting distributions of the Markov chain are Dirichlet. We also consider a related history-dependent random walk model in [0, 1] based on an urn-ty

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Swachhatoya, Ghosal, and Bhavana Vinaya. "Is the Sum of Interior Angles of a Triangle Always 180 Degree." International Journal of Trend in Scientific Research and Development 2, no. 2 (2018): 247–49. https://doi.org/10.31142/ijtsrd9397.

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In 19th century we have the concept of Non Euclidean geometry that is divided into two parts spherical geometry and hyperbolic geometry. Euclidean plane is not quite the same as the Cartesian plane. In geometry a plane is a flat, two dimensional surface that extends infinitely far but has no thickness. In reality it is bit difficult to visualise or think a plane. The actual concept of plane is imaginary on the surface of the earth. In broader sense it is no longer true that the sum of a triangle is 180 degree, however to some extent it may be true for very small triangle because from the persp

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Kaliuzhnyi-Verbovetskyi, D., and V. Pivovarchik. "RECOVERING THE SHAPE OF A QUANTUM CATERPILLAR TREE BY TWO SPECTRA." Mechanics And Mathematical Methods 5, no. 1 (2023): 14–24. http://dx.doi.org/10.31650/2618-0650-2023-5-1-14-24.

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existence of co-spectral (iso-spectral) graphs is a well-known problem of the classical graph theory. However, co-spectral graphs exist in the theory of quantum graphs also. In other words, the spectrum of the Sturm-Liouville problem on a metric graph does not determine alone the shape of the graph. Сo-spectral trees also exist if the number of vertices exceeds eight. We consider two Sturm-Liouville spectral problems on an equilateral metric caterpillar tree with real L2 (0,l) potentials on the edges. In the first (Neumann) problem we impose standard conditions at all vertices: Neumann boundar

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Custódio, Lis, and Sinesio Pesco. "Derivation of Mean Value Coordinates Using Interior Distance and Their Application on Mesh Deformation." Revista de Informática Teórica e Aplicada 25, no. 2 (2018): 11. http://dx.doi.org/10.22456/2175-2745.76189.

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The deformation methods based on cage controls became a subject of considerable interest due its simplicity and intuitive results. In this technique, the model is enclosed within a simpler mesh (the cage) and its points are expressed as function of the cage elements. Then, by manipulating the cage, the respective deformation is obtained on the model in its interior.In this direction, in the last years, extensions of barycentric coordinates, such as Mean Value coordinates, Positive Mean Value Coordinates, Harmonic coordinates and Green's coordinates, have been proposed to write the points of th

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Wigley, Neil M. "Corner Behavior of Solutions of Semilinear Dirichlet Problems." Canadian Journal of Mathematics 37, no. 6 (1985): 1025–46. http://dx.doi.org/10.4153/cjm-1985-055-x.

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In recent years there has been considerable attention paid to the behavior of solutions of elliptic boundary value problems in domains with piecewise smooth boundary. In two dimensions the study concerns the behavior of a solution near a corner, and in three (or more) dimensions two cases have been given considerable attention: a conical vertex on the boundary, or an edge.The solution of such a problem may be singular at the nonsmooth boundary points. The standard example in two dimensions is a solution in polar coordinates of the Dirichlet problem near a corner of interior angle πα;u = r1/α s

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Rodenberg, O. B. P. M., E. Verbree, and S. Zlatanova. "INDOOR A* PATHFINDING THROUGH AN OCTREE REPRESENTATION OF A POINT CLOUD." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences IV-2/W1 (October 5, 2016): 249–55. http://dx.doi.org/10.5194/isprs-annals-iv-2-w1-249-2016.

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There is a growing demand of 3D indoor pathfinding applications. Researched in the field of robotics during the last decades of the 20th century, these methods focussed on 2D navigation. Nowadays we would like to have the ability to help people navigate inside buildings or send a drone inside a building when this is too dangerous for people. What these examples have in common is that an object with a certain geometry needs to find an optimal collision free path between a start and goal point. <br><br> This paper presents a new workflow for pathfinding through an octree representati

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Zhao, Yan, Yuki Endo, Yoshihiro Kanamori, and Jun Mitani. "A Computational Design Method for Tucking Axisymmetric Origami Consisting of Triangular Facets." Symmetry 10, no. 10 (2018): 469. http://dx.doi.org/10.3390/sym10100469.

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Three-dimensional (3D) origami, which can generate a structure through folding a crease pattern on a flat sheet of paper, has received considerable attention in art, mathematics, and engineering. With consideration of symmetry, the user can efficiently generate a rational crease pattern and make the fabricated shape stable. In this paper, we focus on a category of axisymmetric origami consisting of triangular facets and edit the origami in 3D space for expanding its variations. However, it is difficult to retain the developability, which requires the sum of the angles around each interior vert

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BAI, XIAOLIANG, and SHUSHENG ZHANG. "HIERARCHICAL PARAMETERIZATION OF TRIANGULAR MESH WITH A BOUNDARY POLYGON TRIANGULATION." International Journal of Image and Graphics 10, no. 03 (2010): 449–66. http://dx.doi.org/10.1142/s0219467810003858.

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Parameterizing a 3D triangular mesh is the process of finding an isomorphic planar mesh. It is widely used in graphics, as it is required, for instance, for surface fitting, texture mapping and re-meshing. In this paper, we present a new 3D approach to triangular mesh parameterization, which includes three steps: (1) construct a boundary polygon triangulation by mesh simplification; (2) parameterize the boundary polygon triangulation by first smoothing and then flattening it; (3) parameterize the interior vertices by parameterizing the vertex-split-cells one by one while refining the boundary

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Iordanishvili, A. K., L. N. Soldatova, V. S. Soldatov, and M. M. Shvetsov. "Methods of application of ozone therapy for the treatment of peri-implantation mucositis." Medical alphabet, no. 2 (March 30, 2021): 7–12. http://dx.doi.org/10.33667/2078-5631-2021-2-7-12.

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The effectiveness of using «Asepta plus remineralization» special toothpaste, combination of the same toothpaste and «Asepta parodontal fresh» rinse or «Asepta remineralizing gel» (Vertex CJSC, St. Petersburg, Russia) using analysis technique of the structure and severity of the interior disease sight based on psychosensorial-anatomy-functional desadaptation syndrome. It was established that patients who used «Asepta plus remineralization» toothpaste and «Asepta remineralizing gel» on day 3 showed adaptation to the conditions of their existence. Among the patients using «Asepta plus reminerali

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Fan, Tiffany, David I. Shuman, Shashanka Ubaru, and Yousef Saad. "Spectrum-Adapted Polynomial Approximation for Matrix Functions with Applications in Graph Signal Processing." Algorithms 13, no. 11 (2020): 295. http://dx.doi.org/10.3390/a13110295.

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We propose and investigate two new methods to approximate f(A)b for large, sparse, Hermitian matrices A. Computations of this form play an important role in numerous signal processing and machine learning tasks. The main idea behind both methods is to first estimate the spectral density of A, and then find polynomials of a fixed order that better approximate the function f on areas of the spectrum with a higher density of eigenvalues. Compared to state-of-the-art methods such as the Lanczos method and truncated Chebyshev expansion, the proposed methods tend to provide more accurate approximati

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Bonatsos, D., S. Karampagia, and R. F. Casten. "Line of approximate SU(3) symmetry inside the symmetry triangle of the Interacting Boson Model." HNPS Proceedings 19 (January 1, 2020): 16. http://dx.doi.org/10.12681/hnps.2510.

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The U(5), SU(3), and O(6) symmetries of the Interacting Boson Model (IBM) have been traditionally placed at the vertices of the symmetry triangle, while an O(5) symmetry is known to hold along the U(5)–O(6) side of the triangle. We construct [1] for the first time a symmetry line in the interior of the triangle, along which the SU(3) symmetry is preserved. This is achieved by using the contraction of the SU(3) algebra to the algebra of the rigid rotator in the large boson number limit of the IBM. The line extends from the SU(3) vertex to near the critical line of the first order shape/phase tr

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Carstensen, Carsten, and Friederike Hellwig. "Constants in Discrete Poincaré and Friedrichs Inequalities and Discrete Quasi-Interpolation." Computational Methods in Applied Mathematics 18, no. 3 (2018): 433–50. http://dx.doi.org/10.1515/cmam-2017-0044.

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AbstractThis paper provides a discrete Poincaré inequality innspace dimensions on a simplexKwith explicit constants. This inequality bounds the norm of the piecewise derivative of functions with integral mean zero onKand all integrals of jumps zero along all interior sides by its Lebesgue norm times{C(n)\operatorname{diam}(K)}. The explicit constant{C(n)}depends only on the dimension{n=2,3}in case of an adaptive triangulation with the newest vertex bisection. The second part of this paper proves the stability of an enrichment operator, which leads to the stability and approximation of a (discr

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McCarthy, J. M. "The Synthesis of Planar RR and Spatial CC Chains and the Equation of a Triangle." Journal of Mechanical Design 117, B (1995): 101–6. http://dx.doi.org/10.1115/1.2836441.

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This paper formulates the planar and spatial versions of an equation that determines one vertex of a triangle in terms of the other two vertices and their interior angles. The fact that a slight modification of Sandor and Erdman’s standard form equation for the design of RR chains yields this planar triangle equation is the basis for identifying the equivalent equation for a spatial triangle as the standard form equation for CC chains. The simultaneous solution of two of the planar equations yields an analytical expression of Burmester’s relationship between the fixed pivot of an RR chain and

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McCarthy, J. M. "The Synthesis of Planar RR and Spatial CC Chains and the Equation of a Triangle." Journal of Vibration and Acoustics 117, B (1995): 101–6. http://dx.doi.org/10.1115/1.2838647.

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This paper formulates the planar and spatial versions of an equation that determines one vertex of a triangle in terms of the other two vertices and their interior angles. The fact that a slight modification of Sandor and Erdman’s standard form equation for the design of RR chains yields this planar triangle equation is the basis for identifying the equivalent equation for a spatial triangle as the standard form equation for CC chains. The simultaneous solution of two of the planar equations yields an analytical expression of Burmester’s relationship between the fixed pivot of an RR chain and

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Chladek, Grzegorz, Michał Nowak, Wojciech Pakieła, and Anna Mertas. "Effect of Candida albicans Suspension on the Mechanical Properties of Denture Base Acrylic Resin." Materials 15, no. 11 (2022): 3841. http://dx.doi.org/10.3390/ma15113841.

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Yeast-like fungi such as Candida albicans (C. albicans) are the primary pathogenic microorganism in the oral cavity of denture wearers. The research available so far, conducted according to a protocol based on the exposure of specimens to a C. albicans suspension and their cutting with water cooling, shows that hard polymethyl methacrylate (PMMA) prosthetic materials are not only surface colonized, but also penetrated by microorganisms in a short time. This justifies the hypothesis that exposure to a suspension of the C. albicans strain causes the changes in mechanical properties due to surfac

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Tang, Yunyi, and Yuanpeng Zhu. "Image Zooming Based on Two Classes of C1-Continuous Coons Patches Construction with Shape Parameters over Triangular Domain." Symmetry 12, no. 4 (2020): 661. http://dx.doi.org/10.3390/sym12040661.

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Image interpolation is important in image zooming. To improve the quality of image zooming, in this work, we proposed a class of rational quadratic trigonometric Hermite functions with two shape parameters and two classes of C 1 -continuous Coons patches constructions over a triangular domain by improved side–side method and side–vertex method. Altering the values of shape parameters can adjust the interior shape of the triangular Coons patch without influencing the function values and partial derivatives of the boundaries. In order to deal with the problem of well-posedness in image zooming,

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