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1

Sadhu, Sanjib, Sasanka Roy, Soumen Nandi, Subhas C. Nandy, and Suchismita Roy. "Efficient Algorithm for Computing the Triangle Maximizing the Length of Its Smallest Side Inside a Convex Polygon." International Journal of Foundations of Computer Science 31, no. 04 (2020): 421–43. http://dx.doi.org/10.1142/s0129054120500173.

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Given a convex polygon with [Formula: see text] vertices, we study the problem of identifying a triangle with its smallest side as large as possible among all the triangles that can be drawn inside the polygon. We show that at least one of the vertices of such a triangle must coincide with a vertex of the polygon. We also propose an [Formula: see text] time algorithm to compute such a triangle inside the given convex polygon.
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2

BRADLEY, DAVID M., ANDRÉ KHALIL, ROBERT G. NIEMEYER, and ELLIOT OSSANNA. "THE BOX-COUNTING DIMENSION OF PASCAL’S TRIANGLE r mod p." Fractals 26, no. 05 (2018): 1850071. http://dx.doi.org/10.1142/s0218348x18500718.

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We consider Pascal’s Triangle [Formula: see text] to be the entries of Pascal’s Triangle that are congruent to [Formula: see text]. Such a representation of Pascal’s Triangle exhibits fractal-like structures. When the Triangle is mapped to a subset of the unit square, we show that such a set is nonempty and exists as a limit of a sequence of coarse approximations. We then show that for any given prime [Formula: see text], any such sequence converges to the same set, regardless of the residue(s) considered. As an obvious consequence, this allows us to conclude that the fractal (box-counting) di
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3

DAI, F. Z., Z. D. ZHANG, J. Z. ZHOU, J. Z. LU, and Y. K. ZHANG. "ANALYSIS OF SURFACE ROUGHNESS AT OVERLAPPING LASER SHOCK PEENING." Surface Review and Letters 23, no. 03 (2016): 1650012. http://dx.doi.org/10.1142/s0218625x16500128.

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The overlapping effects on surface roughness are studied when samples are treated by laser shock peening (LSP). Surface roughness of overlapped circular laser spot is calculated by ISO 25178 height parameters. The usually used overlapping styles namely isosceles-right-triangle-style (AAP) and equilateral-triangle-style (AAA) are carefully investigated when the overlapping degree in x-axis ([Formula: see text]) is below 50%. Surface roughness of isosceles-right-triangle-style attains its minimum value at [Formula: see text] of 29.3%, and attains its maximum value at [Formula: see text] of 43.6%
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4

Kou, Shuai, Chengfu Qin, and Weihua Yang. "Contractible Edges in 3-Connected Cubic Graphs." Parallel Processing Letters 31, no. 03 (2021): 2150014. http://dx.doi.org/10.1142/s0129626421500146.

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An edge [Formula: see text] in a 3-connected graph [Formula: see text] is contractible if the contraction [Formula: see text] is still [Formula: see text]-connected. Let [Formula: see text] be the set of contractible edges of [Formula: see text], [Formula: see text] be the set of vertices adjacent to three vertices of a triangle △. It has been proved that [Formula: see text] in a 3-connected graph [Formula: see text] of order at least 5. In this note [Formula: see text] is a 3-connected cubic graph containing [Formula: see text] triangles, at least [Formula: see text] vertices and with every [
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5

Zhang, Pu, and Lin Zhu. "Objective Triangle Functors in Adjoint Pairs." Algebra Colloquium 24, no. 04 (2017): 639–46. http://dx.doi.org/10.1142/s1005386717000426.

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An additive functor [Formula: see text] → [Formula: see text] between additive categories is objective if any morphism f in [Formula: see text] with F(f) = 0 factors through an object K with F(K) = 0. We consider when a triangle functor in an adjoint pair is objective. We show that a triangle functor is objective provided that its adjoint (whatever left adjoint or right adjoint) is full or dense. We also give an example to show that the adjoint of a faithful triangle functor is not necessarily objective. In particular, the adjoint of an objective triangle functor is not necessarily objective.
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6

Ahmia, Moussa, and Hacène Belbachir. "Preserving log-concavity for p,q-binomial coefficient." Discrete Mathematics, Algorithms and Applications 11, no. 02 (2019): 1950017. http://dx.doi.org/10.1142/s1793830919500174.

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We study the log-concavity of a sequence of [Formula: see text]-binomial coefficients located on a ray of the [Formula: see text]-Pascal triangle for certain directions, and we establish the preserving log-concavity of linear transformations associated to [Formula: see text]-Pascal triangle.
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7

Xu, Liqiong, Shuming Zhou, and Weihua Yang. "Fault-Tolerant Maximal Local-Connectivity on Cayley Graphs Generated by Transpositions." International Journal of Foundations of Computer Science 30, no. 08 (2019): 1301–15. http://dx.doi.org/10.1142/s0129054119500278.

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An interconnection network is usually modeled as a graph, in which vertices and edges correspond to processors and communication links, respectively. Connectivity is an important metric for fault tolerance of interconnection networks. A graph [Formula: see text] is said to be maximally local-connected if each pair of vertices [Formula: see text] and [Formula: see text] are connected by [Formula: see text] vertex-disjoint paths. In this paper, we show that Cayley graphs generated by [Formula: see text]([Formula: see text]) transpositions are [Formula: see text]-fault-tolerant maximally local-co
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8

Goodman, Samantha, Lana Vanderlee, Rachel Acton, Syed Mahamad, and David Hammond. "The Impact of Front-of-Package Label Design on Consumer Understanding of Nutrient Amounts." Nutrients 10, no. 11 (2018): 1624. http://dx.doi.org/10.3390/nu10111624.

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A between-groups experiment examined the salience of front-of-package (FOP) symbols. Adults from Canada, the US, Australia, and the UK completed an online survey (n = 11,617). Respondents were randomized to view cereal boxes displaying one of 11 FOP label conditions for ‘high’ levels of sugar and saturated fat: control (no FOP symbol), red circle, red ‘stop sign’, magnifying glass, magnifying glass + exclamation mark, and ‘caution’ triangle + exclamation mark, plus each of these five conditions accompanied by a ‘high in’ text descriptor. Participants identified the amount of saturated fat and
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9

Azari, Mahdieh. "On ordinary and weighted Harary indices of Mycielski graphs." Discrete Mathematics, Algorithms and Applications 09, no. 02 (2017): 1750022. http://dx.doi.org/10.1142/s1793830917500227.

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The Mycielski’s construction is a well-known construction on graphs which transforms a [Formula: see text]-chromatic triangle-free graph [Formula: see text] into a [Formula: see text]-chromatic triangle-free graph [Formula: see text] which is called the Mycielski graph of [Formula: see text]. In this paper, we compute the Harary index, additively weighted Harary index, and multiplicatively weighted Harary index of the Mycielski graph of any simple connected graph with girth greater than [Formula: see text].
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10

Guo, C. Q., Y. Yan, L. Li, et al. "Stable local structure in LSMCO system and its relationship with pseudogap." International Journal of Modern Physics B 29, no. 25n26 (2015): 1542028. http://dx.doi.org/10.1142/s021797921542028x.

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Pseudogap is a unique property of high-[Formula: see text] superconductors. However, it was also found that there is a similar pseudogap in giant magnetoresistive La–Sr–Mn–O materials, which are not superconductors. In our previous research, we suggested that the origin of the pseudogap is correlated with the stability of [Formula: see text] plane. We call it a steady “fixed triangle” local structure. If our assumption is correct, it will be expected to find a similar stable local structure in the La–Sr–Mn–O system, which is similar to the [Formula: see text] plane in cuprates. We synthesized
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11

BABENKO, MAXIM, ALEXEY GUSAKOV, and ILYA RAZENSHTEYN. "TRIANGLE-FREE 2-MATCHINGS REVISITED." Discrete Mathematics, Algorithms and Applications 02, no. 04 (2010): 643–54. http://dx.doi.org/10.1142/s1793830910000930.

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A 2-matching in an undirected graph G = (VG, EG) is a function x: EG → {0, 1, 2} such that for each node v ∈ VG the sum of values x(e) for all edges e incident to v does not exceed 2. The size of x is the sum ∑e x(e). If {e ∈ EG|x(e) ≠ 0} contains no triangles then x is called triangle-free. Cornuéjols and Pulleyblank devised a combinatorial O(mn)-algorithm that finds a maximum triangle free 2-matching of size (hereinafter n ≔ |VG|, m ≔ |EG|) and also established a min-max theorem. We claim that this approach is, in fact, superfluous by demonstrating how these results may be obtained directly
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12

ETTESTAD, DAVID, and JOAQUIN CARBONARA. "THE SIERPINSKI TRIANGLE PLANE." Fractals 26, no. 01 (2018): 1850003. http://dx.doi.org/10.1142/s0218348x18500032.

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The Sierpinski Triangle (ST) is a fractal which has Haussdorf dimension [Formula: see text] that has been studied extensively. In this paper, we introduce the Sierpinski Triangle Plane (STP), an infinite extension of the ST that spans the entire real plane but is not a vector subspace or a tiling of the plane with a finite set of STs. STP is shown to be a radial fractal with many interesting and surprising properties.
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13

SU, XIAOLE, HONGWEI SUN, and YUSHENG WANG. "TOPONOGOV-TYPE AREA COMPARISON THEOREM OF 2-DIMENSIONAL MANIFOLDS." Communications in Contemporary Mathematics 15, no. 03 (2013): 1350007. http://dx.doi.org/10.1142/s0219199713500077.

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Let △p1p2p3 be a geodesic triangle on M, a complete 2-dimensional Riemannian manifold of curvature ≥ k, and let [Formula: see text] be its comparison triangle on [Formula: see text] (a complete and simply connected 2-dimensional manifold of constant curvature k). Our main result is that if △p1p2p3 is areable, then its area is not less than that of [Formula: see text].
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14

Dobrinen, Natasha. "The Ramsey theory of the universal homogeneous triangle-free graph." Journal of Mathematical Logic 20, no. 02 (2020): 2050012. http://dx.doi.org/10.1142/s0219061320500129.

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The universal homogeneous triangle-free graph, constructed by Henson [A family of countable homogeneous graphs, Pacific J. Math. 38(1) (1971) 69–83] and denoted [Formula: see text], is the triangle-free analogue of the Rado graph. While the Ramsey theory of the Rado graph has been completely established, beginning with Erdős–Hajnal–Posá [Strong embeddings of graphs into coloured graphs, in Infinite and Finite Sets. Vol.[Formula: see text] , eds. A. Hajnal, R. Rado and V. Sós, Colloquia Mathematica Societatis János Bolyai, Vol. 10 (North-Holland, 1973), pp. 585–595] and culminating in work of S
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15

PALAGALLO, JUDITH, and MATTHEW PALMER. "ANALYSIS OF AN IRREGULAR SIERPINSKI TRIANGLE." Fractals 12, no. 01 (2004): 137–44. http://dx.doi.org/10.1142/s0218348x04002239.

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An irregular Sierpinski triangle is a non-empty compact set F satisfying [Formula: see text] where each Ti is a contracting affine transformation. The irregular Sierpinski triangle is not generated with similarity transformations. Therefore, the calculation of its fractal dimension is not straightforward. We associate with each irregular Sierpinski triangle a self-similar regularization. The dimension of the regularization dictates the shape of the irregular Sierpinski triangle. We also describe properties of the regularizations and show their relationship to the classic Sierpinski triangle.
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16

Miao, Xiaofang, Peng Wu, and Baoyin Zhao. "Optimum design for a novel large mode area fiber with triangle-platform-index core." Modern Physics Letters B 33, no. 18 (2019): 1950207. http://dx.doi.org/10.1142/s0217984919502075.

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A triangle-platform-index core fiber is proposed, in which the refractive index distribution in the cross-section of the fiber core is composed of several closely connected triangles and a platform at the outermost layer. The simulation results show that the proposed fiber possesses an extremely large mode field area of [Formula: see text] at the wavelength of [Formula: see text], and achieves single-mode operation state near a bend radius of 17 cm. Furthermore, several different mode field distributions, including Gauss-like distribution, flatten distribution and hollow distribution, are achi
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17

T, Sivakumar, Pauvithraa K.T, and Durga Devi V. "ENCRYPTION METHOD USING PASCAL’S TRIANGLE BASED SUBSTITUTION AND SIERPINSKI TRIANGLE BASED PERMUTATION." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 15, no. 13 (2016): 7362–67. http://dx.doi.org/10.24297/ijct.v15i13.4806.

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Text messages are often created, shared and a person sends at least ten messages a day. Because of its frequent usage those messages are not been encrypted. Thus it is unable to send confidential messages via SMS service. In this paper, we develop a new encryption technique using the notions of Pascals Triangle and Sierpinski Triangle. The proposed method uses the Pascals triangle for substitution and Sierpinski triangle for permutation. The method is simple and easy to implement in real time. It is difficult for the attackers to predict the original message contained in the ciphertext. The pr
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18

Yang, Xiu-Yi, and Hong-Na Li. "The hypergeometric system for one-loop triangle integral." International Journal of Modern Physics A 34, no. 35 (2019): 1950232. http://dx.doi.org/10.1142/s0217751x19502324.

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We derive the holonomic hypergeometric system for the [Formula: see text] function with two equal virtual masses, and present the expression of [Formula: see text] in hypergeometric series in corresponding convergent region. Combining the Horn’s convergence theory with Gröbner basis of polynomial ideal, one can calculate the convergence region of the corresponding multiple series concretely. Using the system given here, one can analytically continue [Formula: see text] to whole parameter space.
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19

AL-Khassawneh, Yazan Alaya, Naomie Salim, and Mutasem Jarrah. "Improving Triangle-Graph Based Text Summarization using Hybrid Similarity Function." Indian Journal of Science and Technology 10, no. 8 (2017): 1–15. http://dx.doi.org/10.17485/ijst/2017/v10i8/108907.

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20

NAVARRO, J. C., and J. D. ROSSI. "NONLINEAR MEAN-VALUE FORMULAS ON FRACTAL SETS." Fractals 26, no. 06 (2018): 1850091. http://dx.doi.org/10.1142/s0218348x18500913.

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In this paper we study the solutions to nonlinear mean-value formulas on fractal sets. We focus on the mean-value problem [Formula: see text] in the Sierpiński gasket with prescribed values [Formula: see text], [Formula: see text] and [Formula: see text] at the three vertices of the first triangle. For this problem we show existence and uniqueness of a continuous solution and analyze some properties like the validity of a comparison principle, Lipschitz continuity of solutions (regularity) and continuous dependence of the solution with respect to the prescribed values at the three vertices of
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21

Kim, Hyoungjun, Thomas Mattman, and Seungsang Oh. "More intrinsically knotted graphs with 22 edges and the restoring method." Journal of Knot Theory and Its Ramifications 27, no. 10 (2018): 1850059. http://dx.doi.org/10.1142/s0218216518500591.

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A graph is called intrinsically knotted if every embedding of the graph contains a knotted cycle. Johnson, Kidwell and Michael, and, independently, Mattman, showed that intrinsically knotted graphs have at least 21 edges. Recently, Lee, Kim, Lee and Oh, and, independently, Barsotti and Mattman, showed that [Formula: see text] and the 13 graphs obtained from [Formula: see text] by [Formula: see text] moves are the only intrinsically knotted graphs with 21 edges. Also Kim, Lee, Lee, Mattman and Oh showed that there are exactly three triangle-free intrinsically knotted graphs with 22 edges having
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22

Hajossy, Rudolf. "Plimpton 322 : A Universal Cuneiform Table for Old Babylonian Mathematicians, Builders, Surveyors and Teachers." Tatra Mountains Mathematical Publications 67, no. 1 (2016): 1–40. http://dx.doi.org/10.1515/tmmp-2016-0027.

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Abstract This article deals with the damaged and incomplete Old Babylonian tablet Plimpton 322 which contains 4 columns and 15 rows of a cuneiform mathematical text. It has been shown that the presumed original table with its 7 columns and 39 rows represented: a table of square roots of numbers from 0 to 2 for mathematicians; an earliest rudiments of a trigonometric table for builders and surveyors where angles are not measured as an arc in a unit circle but as a side of a unit right-angled triangle; a list of the 39 exercises on reciprocal pairs, unit and integer-side right triangles (rectang
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23

Uchimura, Keisuke. "Attracting Basins of Certain Nonholomorphic Maps." International Journal of Bifurcation and Chaos 08, no. 07 (1998): 1517–26. http://dx.doi.org/10.1142/s0218127498001169.

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Attractive basins of a function [Formula: see text] are considered. The function Fc(z) is obtained by a perturbation of a "two-dimensional tent map" [Formula: see text]. We prove that the immediate attractive basins of the function F4/3(z) consist of six triangular regions which are subdivisions of a equilateral triangle by three medians.
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24

Carter, J. Scott. "Fractal simplices." Journal of Knot Theory and Its Ramifications 25, no. 09 (2016): 1641003. http://dx.doi.org/10.1142/s0218216516410030.

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There are three constructions of which I know that yield higher dimensional analogues of Sierpinski’s triangle. The most obvious is to remove the open convex hull of the midpoints of the edges of the [Formula: see text]-simplex. The complement is a union of simplices. Continue the removal recursively in each of the remaining sub-simplices. The result is an uncountably infinite figure in [Formula: see text]-dimensional space that is Cantor-like in a manner analogous to the Sierpinski triangle. A countable analogue is obtained by means of playing the chaos game in the [Formula: see text]-simplex
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25

MÓRA, PÉTER. "ESTIMATE OF THE HAUSDORFF MEASURE OF THE SIERPINSKI TRIANGLE." Fractals 17, no. 02 (2009): 137–48. http://dx.doi.org/10.1142/s0218348x09004296.

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It is well-known that the Hausdorff dimension of the Sierpinski triangle Λ is s = log 3/ log 2. However, it is a long standing open problem to compute the s-dimensional Hausdorff measure of Λ denoted by [Formula: see text]. In the literature the best existing estimate is [Formula: see text] In this paper we improve significantly the lower bound. We also give an upper bound which is weaker than the one above but everybody can check it easily. Namely, we prove that [Formula: see text] holds.
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Adeboye, Ilesanmi, and Daryl Cooper. "The area of convex projective surfaces and Fock–Goncharov coordinates." Journal of Topology and Analysis 12, no. 02 (2018): 533–46. http://dx.doi.org/10.1142/s1793525319500560.

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The area of a convex projective surface of genus [Formula: see text] is at least [Formula: see text] where [Formula: see text] is the vector of triangle invariants of Bonahon–Dreyer and [Formula: see text] are the Fock–Goncharov triple ratios.
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27

Wang, Shiying, Kai Feng, and Yubao Guo. "Sufficient Conditions for Maximally k-Isoperimetric Edge Connectivity of Graphs." International Journal of Foundations of Computer Science 26, no. 05 (2015): 583–98. http://dx.doi.org/10.1142/s012905411550032x.

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The k-isoperimetric edge connectivity is a more refined network reliability index than edge connectivity. The k-isoperimetric edge connectivity of a connected graph G is defined as γk(G) = min{|[X, [Formula: see text]]| : X ⊆ V (G), |X| ≥ k, |[Formula: see text]| ≥ k}. Let βk(G) = min{|[X,[Formula: see text]]| : X ⊆ V (G), |X| = k}. A graph G is called a γk-optimal graph if γk(G) = βk(G). An edge cut S = [X,[Formula: see text]] is called a γk-cut if |S| = γk(G), X ⊆ V (G), |X| ≥ k and |[Formula: see text]| ≥ k. Moreover, G is called a super-γk graph if every γk-cut [X,[Formula: see text]] of G
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Han, Zhike, Xiuchao Wu, Meng Chi, Jun Tang, and Lijing Yang. "A Novel Approach to Transform Bitmap to Vector Image for Data Reliable Visualization considering the Image Triangulation and Color Selection." Security and Communication Networks 2020 (November 2, 2020): 1–13. http://dx.doi.org/10.1155/2020/8871588.

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Vector image is a type of image composed of many geometric primitives. Compared with bitmaps, vector images have the ability to save memory as well as to enlarge without distortion. Meanwhile, it has been commonly adopted in data visualization (image data) because it can be scaled to multiple sizes to fit different scenes. For instance, it can be applied for the illustrations in newspapers and magazines, the logo on the web, the background for poster, the design of text, and traffic signs. However, transforming a bitmap to vector image is still a challenging problem because of the complicated
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Wichianpaisarn, Tanawat, and Chariya Uiyyasathian. "Graphs with large clique-chromatic numbers." Discrete Mathematics, Algorithms and Applications 07, no. 04 (2015): 1550055. http://dx.doi.org/10.1142/s179383091550055x.

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The clique-chromatic number of a graph [Formula: see text], [Formula: see text], is the least number of colors on [Formula: see text] without a monocolored maximal clique of size at least two. If [Formula: see text] is triangle-free, [Formula: see text]; we then consider only graphs with a triangle. Unlike the chromatic number, the clique-chromatic number of a graph is not necessary to be at least those of its subgraphs. Thus, for any family of graphs [Formula: see text], the boundedness of [Formula: see text][Formula: see text] has been investigated. Many families of graphs are proved to have
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BRADLEY, DAVID M., DANIEL D’ALESSIO, ANDRÉ KHALIL, et al. "ON THE RELATIVE FREQUENCY OF RESIDUE CLASSES IN PASCAL’S TRIANGLE MODULO A PRIME." Fractals 27, no. 06 (2019): 1950098. http://dx.doi.org/10.1142/s0218348x19500981.

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When the entries of Pascal’s triangle which are congruent to a given nonzero residue modulo a fixed prime are mapped to corresponding locations of the unit square, a fractal-like structure emerges. In a previous publication, Bradley, Khalil, Niemeyer and Ossanna [The box-counting dimension of Pascal’s triangle [Formula: see text] mod [Formula: see text], Fractals 26(5) (2018) 1850071] showed that this mapping yields a nonempty compact set which can be realized as a limit of a sequence of sets representing incrementally refined approximations. Moreover, it was shown therein that for any fixed p
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31

Luo, Tao. "CP Violation Sensitivity at the Belle II Experiment." International Journal of Modern Physics: Conference Series 46 (January 2018): 1860061. http://dx.doi.org/10.1142/s2010194518600613.

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The sensitivity on the measurements of the angles of the CKM unitarity triangle, i.e. [Formula: see text], [Formula: see text] and [Formula: see text], for Belle II experiment is presented in this letter, the CKM mechanism is expected to be tested at 1% level on Belle II.
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32

Pan, Hong Yu, and Feng Qi Zhao. "Free polaron energy levels in AlyGa1−yN/AlxGa1−xN triangle quantum well structures." Modern Physics Letters B 31, no. 17 (2017): 1750187. http://dx.doi.org/10.1142/s0217984917501871.

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In this work, a variational method is used to examine the problems relevant to the free polaron energy spectrum in a wurtzite Al[Formula: see text]Ga[Formula: see text]N/Al[Formula: see text]Ga[Formula: see text]N triangle quantum well structure. The numerical calculations for the ground state energy, transition energy and polaron energy shifts as the functions of well-width [Formula: see text] and composition [Formula: see text] are carried out by considering the anisotropies of the parameters, such as the optical phonon frequency, dielectric constant and electron effective mass, as well as t
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NOMURA, K., and A. H. MACDONALD. "NUMERICAL KUBO FORMULA STUDY OF FRICTIONAL DRAG IN THE INTEGER QUANTUM HALL REGIME." International Journal of Modern Physics B 18, no. 27n29 (2004): 3621–24. http://dx.doi.org/10.1142/s0217979204027141.

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We study interlayer frictional drag between two-dimensional electron systems in the strong magnetic field limit by evaluating the weak-coupling Kubo formula for interlayer drag numerically. The key quantity in this theory is the disorder averaged "triangle function", a product of three Greens functions of electrons that represents the dc current response of electrons in one layer to charge fluctuations in a remote current-carrying layer. We find that the disorder averaged triangle functions are proportional to the momentum transfer [Formula: see text] at small [Formula: see text] and that they
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34

Escobar-Ruiz, A. M., R. Linares, Alexander V. Turbiner, and Willard Miller. "Classical n-body system in geometrical and volume variables: I. Three-body case." International Journal of Modern Physics A 36, no. 18 (2021): 2150140. http://dx.doi.org/10.1142/s0217751x21501402.

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We consider the classical three-body system with [Formula: see text] degrees of freedom [Formula: see text] at zero total angular momentum. The study is restricted to potentials [Formula: see text] that depend solely on relative (mutual) distances [Formula: see text] between bodies. Following the proposal by J. L. Lagrange, in the center-of-mass frame we introduce the relative distances (complemented by angles) as generalized coordinates and show that the kinetic energy does not depend on [Formula: see text], confirming results by Murnaghan (1936) at [Formula: see text] and van Kampen–Wintner
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35

AL-Khassawneh, Yazan Alaya. "The use of Semantic Role Labelling with Triangle-Graph Based Text Summarization." International Journal of Emerging Trends in Engineering Research 8, no. 4 (2020): 1162–69. http://dx.doi.org/10.30534/ijeter/2020/34842020.

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36

McKee, Terry A. "Requiring adjacent chords in cycles." Discrete Mathematics, Algorithms and Applications 10, no. 01 (2018): 1850003. http://dx.doi.org/10.1142/s1793830918500039.

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Define a new class of graphs by cycles of length 5 or more always having adjacent chords. This is equivalent to cycles of length 5 or more always having noncrossing chords, which is a property that has a known forbidden induced subgraph characterization. Another characterization comes from viewing the graphs in this class in contrast to distance-hereditary graphs (which are characterized by cycles of length 5 or more always having crossing chords). Moreover, the graphs in the new class are those in which every edge of every cycle [Formula: see text] of length 5 or more forms a triangle with a
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37

SILVESTRINI, LUCA. "RARE DECAYS AND CP VIOLATION BEYOND THE STANDARD MODEL." International Journal of Modern Physics A 21, no. 08n09 (2006): 1738–49. http://dx.doi.org/10.1142/s0217751x06032721.

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We review the status of rare decays and CP violation in extensions of the Standard Model. We analyze the determination of the unitarity triangle and the model-independent constraints on new physics that can be derived from this analysis. We find stringent bounds on new contributions to [Formula: see text] and [Formula: see text] mixing, pointing either to models of minimal flavour violation or to models with new sources of flavour and CP violation in b → s transitions. We discuss the status of the universal unitarity triangle in minimal flavour violation, and study rare decays in this class of
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38

POHL, ANKE D. "Odd and even Maass cusp forms for Hecke triangle groups, and the billiard flow." Ergodic Theory and Dynamical Systems 36, no. 1 (2014): 142–72. http://dx.doi.org/10.1017/etds.2014.64.

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By a transfer operator approach to Maass cusp forms and the Selberg zeta function for cofinite Hecke triangle groups, Möller and the present author found a factorization of the Selberg zeta function into a product of Fredholm determinants of transfer-operator-like families:$$\begin{eqnarray}Z(s)=\det (1-{\mathcal{L}}_{s}^{+})\det (1-{\mathcal{L}}_{s}^{-}).\end{eqnarray}$$In this article we show that the operator families${\mathcal{L}}_{s}^{\pm }$arise as families of transfer operators for the triangle groups underlying the Hecke triangle groups, and that for$s\in \mathbb{C}$,$\text{Re}s={\text
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39

Yu, Pei, Qiang Guo, Ren-De Li, Jing-Ti Han, and Jian-Guo Liu. "Roles of clustering properties for degree-mixing pattern networks." International Journal of Modern Physics C 28, no. 03 (2017): 1750029. http://dx.doi.org/10.1142/s0129183117500292.

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The clustering coefficients have been extensively investigated for analyzing the local structural properties of complex networks. In this paper, the clustering coefficients for triangle and square structures, namely [Formula: see text] and [Formula: see text], are introduced to measure the local structure properties for different degree-mixing pattern networks. Firstly, a network model with tunable assortative coefficients is introduced. Secondly, the comparison results between the local clustering coefficients [Formula: see text] and [Formula: see text] are reported, one can find that the squ
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40

LIU, JIA-BAO, JING ZHAO, JIE MIN, and JINDE CAO. "THE HOSOYA INDEX OF GRAPHS FORMED BY A FRACTAL GRAPH." Fractals 27, no. 08 (2019): 1950135. http://dx.doi.org/10.1142/s0218348x19501354.

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The computational complexity of the Hosoya index of a given graph is NP-Complete. Let [Formula: see text] be the graph constructed from [Formula: see text] by a triangle instead of all vertices of the initial graph [Formula: see text]. In this paper, we characterize the Hosoya index of the graph [Formula: see text]. To our surprise, it shows that the Hosoya index of [Formula: see text] is thoroughly given by the order and degrees of all the vertices of the initial graph [Formula: see text].
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41

Grechuk, Bogdan, and Sittichoke Som-am. "A Convex Cover for Closed Unit Curves has Area at Least 0.0975." International Journal of Computational Geometry & Applications 30, no. 02 (2020): 121–39. http://dx.doi.org/10.1142/s0218195920500065.

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We combine geometric methods with a numerical box search algorithm to show that the minimal area of a convex set in the plane which can cover every closed plane curve of unit length is at least [Formula: see text]. This improves the best previous lower bound of [Formula: see text]. In fact, we show that the minimal area of the convex hull of circle, equilateral triangle, and rectangle of perimeter [Formula: see text] is between [Formula: see text] and [Formula: see text].
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42

YÈCHE, CHRISTOPHE. "CP VIOLATION AT BABAR." International Journal of Modern Physics A 23, no. 21 (2008): 3273–76. http://dx.doi.org/10.1142/s0217751x08041967.

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We report recent measurements of the three CKM angles of the Unitarity Triangle using about 383 millions [Formula: see text] pairs collected with the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC.
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43

Mohan, S., and K. Somasundaram. "Total coloring of the prismatic graphs." Discrete Mathematics, Algorithms and Applications 12, no. 03 (2020): 2050032. http://dx.doi.org/10.1142/s1793830920500329.

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A total coloring of a graph is an assignment of colors to all the elements of the graph such that no two adjacent or incident elements receive the same color. A graph [Formula: see text] is prismatic, if for every triangle [Formula: see text], every vertex not in [Formula: see text] has exactly one neighbor in [Formula: see text]. In this paper, we prove the total coloring conjecture (TCC) for prismatic graphs and the tight bound of the TCC for some classes of prismatic graphs.
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44

SCHUBERT, KLAUS R. "CP VIOLATION IN B-MESON DECAYS." International Journal of Modern Physics A 20, no. 02n03 (2005): 385–98. http://dx.doi.org/10.1142/s0217751x05021555.

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After a short introduction on CP asymmetries in K and B meson decays, I discuss a few recent results related to CP violation, mainly from the BABAR experiment: CPT tests in [Formula: see text] mixing, search for CP violation in [Formula: see text] and [Formula: see text] decays, and measurements of the unitarity-triangle angle α in B →ππ and B →ρρ decays. I conclude with the result of a CKM-matrix fit to all relevant observations.
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45

RAMÍREZ, JOSÉ L., GUSTAVO N. RUBIANO, and BORUT JURČIČ ZLOBEC. "GENERATING FRACTAL PATTERNS BY USING p-CIRCLE INVERSION." Fractals 23, no. 04 (2015): 1550047. http://dx.doi.org/10.1142/s0218348x15500474.

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In this paper, we introduce the [Formula: see text]-circle inversion which generalizes the classical inversion with respect to a circle ([Formula: see text]) and the taxicab inversion [Formula: see text]. We study some basic properties and we also show the inversive images of some basic curves. We apply this new transformation to well-known fractals such as Sierpinski triangle, Koch curve, dragon curve, Fibonacci fractal, among others. Then we obtain new fractal patterns. Moreover, we generalize the method called circle inversion fractal be means of the [Formula: see text]-circle inversion.
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MA, YONG-LIANG, and YUE-LIANG WU. "ANOMALY AND ANOMALY-FREE TREATMENT OF QFT's BASED ON SYMMETRY-PRESERVING LOOP REGULARIZATION." International Journal of Modern Physics A 21, no. 31 (2006): 6383–456. http://dx.doi.org/10.1142/s0217751x0603309x.

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The triangle anomaly in massless and massive QED is investigated by adopting the symmetry-preserving loop regularization method proposed recently in Refs. 1 and 2. The method is realized in the initial dimension of theory without modifying the original Lagrangian, it preserves symmetries under non-Abelian gauge and Poincaré transformations in spite of the existence of two intrinsic mass scales Mc and μs which actually play the roles of UV- and IR-cutoff respectively. The axial-vector–vector-vector (AVV) triangle diagrams in massless and massive QED are evaluated explicitly by using the loop re
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Qing-Quan, Gou, Zhang Jian-Ping, and Li Ping. "Formation Mechanism and Binding Energy for Equilateral Triangle Structure of $\text {He}^+_3$ Cluster." Communications in Theoretical Physics 38, no. 5 (2002): 597–600. http://dx.doi.org/10.1088/0253-6102/38/5/597.

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48

Gallego Torromé, Ricardo. "A note on Clifford bundles and certain Finsler type spaces." International Journal of Geometric Methods in Modern Physics 18, no. 10 (2021): 2150162. http://dx.doi.org/10.1142/s0219887821501620.

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We study a relation between certain extensions of the Clifford bundle and Finsler type structures that naturally generalize the standard Clifford relation between (pseudo)-Riemannian metric structures and Dirac matrices. We show for flat metrics that there is a triangle map between Finsler structures constructed from a (pseudo)-Riemannian metric and [Formula: see text]-forms on [Formula: see text], the extension of the Clifford bundle and relevant Dirac type operators.
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49

Palumbo, Lidia. "Soul, Triangle and Virtue. On the Figure of Implicit Comparison in Plato’s Meno." Peitho. Examina Antiqua 8, no. 1 (2017): 201–12. http://dx.doi.org/10.14746/pea.2017.1.12.

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Plato’s dialogues can be regarded as the most important documents of the extraordinary mimetic power of visual writing, i.e., writing capable of “showing” and “drawing images” by using words only. Thanks to the great lesson of the Attic theater, Plato makes his readers see: when reading the dialogues, they see not only the characters talking but owing to the visual power of mimetic writing, they also see that which the characters are actually talking about. There are numerous rhetorical devices employed by Plato the writer that make this visual rendering of philosophy possible. In this text, I
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50

Palumbo, Lidia. "Soul, Triangle and Virtue. On the Figure of Implicit Comparison in Plato’s Meno." Peitho. Examina Antiqua, no. 1(8) (October 24, 2017): 201–12. http://dx.doi.org/10.14746/peitho.2017.12225.

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Plato’s dialogues can be regarded as the most important documents of the extraordinary mimetic power of visual writing, i.e., writing capable of “showing” and “drawing images” by using words only. Thanks to the great lesson of the Attic theater, Plato makes his readers see: when reading the dialogues, they see not only the characters talking but owing to the visual power of mimetic writing, they also see that which the characters are actually talking about. There are numerous rhetorical devices employed by Plato the writer that make this visual rendering of philosophy possible. In this text, I
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