Adjacent Triangles Research Articles

Ultrasound-guided ablation for T1N0M0 papillary thyroid carcinoma adjacent and non-adjacent danger triangle area: a retrospective comparative study

Objectives To compare the safety and efficacy of ultrasound-guided radiofrequency ablation (RFA) in the treatment of T1N0M0 papillary thyroid carcinoma (PTC) with adjacent and non-adjacent danger triangle area (DTA). Materials and methods This retrospective study involved collecting clinical data of all T1N0M0 PTC patients who underwent RFA between January 2018 and December 2020 at the hospital. A total of 211 patients were enrolled in the study (mean age 43.25 ± 12.30 years, male-to-female ratio = 1:3). Among them, 91 had adjacent DTA involvement, while 120 had non-adjacent DTA involvement. Comparisons were made between the two groups patients regarding tumor volume changes, technical success rates, tumor disappearance, disease progression, complications. Results In both groups, the technical success rate was 100%, with a median follow-up period of 30 months. The rates of complete tumor disappearance were 78% (71/91) and 74.2% (89/120) for the adjacent and non-adjacent DTA(p = .517). Disease progression rates were 2.2% (2/91) and 1.7% (2/120) (p > .99), Complication rates were 3.3%(3/91) in the adjacent DTA group and 1.7% (2/120) in the non-adjacent DTA group (p = .654). At 6th month after ablation, the volume reduction rate (VRR) in the non-adjacent DTA group (42.3%) was higher than in the adjacent DTA group (37.3%) (p = .002). However, no significant differences were observed in VRR between the two groups at 1, 3, 12, 18, 24, 30, and 36 months (p > .05). Conclusion In the treatment of T1N0M0 PTC, the complication rates and short-term efficacy of RFA in adjacent to the DTA did not differ from those of non-adjacent DTA.

Light 3-faces in 3-polytopes without adjacent triangles

Over the last decades, a lot of research has been devoted to structural and coloring problems on plane graphs that are sparse in this or that sense.In this note we deal with the densest among sparse 3-polytopes, namely those having no adjacent 3-cycles. Borodin (1996) proved that such 3-polytopes have a vertex of degree at most 4 and, moreover, an edge with the degree-sum of its end-vertices at most 9, where both bounds are sharp.By d(v) denote the degree of a vertex v. An edge e=xy in a 3-polytope is an (i,j)-edge if d(x)≤i and d(y)≤j. The well-known (3,5;4,4)-Archimedean solid corresponds to a plane quadrangulation in which every edge joins a 3-vertex with a 5-vertex.We prove that every 3-polytope with neither adjacent 3-cycles nor (3,5)-edges has a 3-face with the degree-sum of its incident vertices (weight) at most 16, which bound is sharp.

Minimal lateral damage fabrication of high-temperature superconducting nanowires via focused helium ion beam irradiation

Abstract The low temperature superconducting nanowire single-photon detectors have become a key infrared photon counting technology in communication and astronomy applications. However, the constrained physical space of devices demands for high-performance superconducting detectors capable of operation at higher temperature. To date, the fabrication of high temperature superconductor nanowires is still facing seriously uneven lateral damage during ion etching process. In this work, we report a promising fabricating method for high-temperature superconducting YBa2Cu3O7−x (YBCO) nanowires, using a focused helium ion beam to minimize the lateral damage of the cut. Based on the simulation, we designed tangent circles and adjacent isosceles triangles to replace lines in cutting nanowires for reducing the superimposed damage of He+ ions. The lateral damage of single helium ion cut has been reduced with a superimposed damage width decrease from 58.8 nm to 29.7 nm. This work provides a platform for boosting the YBCO nanowires to achieve single photon detection.

An Improved [formula omitted] rational Bernstein–Bézier triangular patch for scattered data interpolation

Scattered data interpolation is important in sciences, engineering, and medical-based problems. The degree smoothness attained is either C1 or C2. However, based on our simulations, we found that, Hussain and Hussain (2011) scheme is not producing C1 everywhere. Motivated by this, in this study we will propose an improve sufficient condition for the C1 on each adjacent triangle. Our scheme is guaranteed to produce C1 everywhere. To support our claim, we have implemented both schemes and perform some numerical comparison including error measurement. From the results, our proposed scheme is producing C1 interpolating surface while the interpolating surface produced by Hussain and Hussain (2011) is not C1 everywhere. Furthermore, our proposed scheme give smaller error compared with Hussain and Hussain (2011) scheme. All numerical and graphical results are presented by using MATLAB programming.

Light 3-Paths in 3-Polytopes without Adjacent Triangles

Light 3-Paths in 3-Polytopes without Adjacent Triangles

Construction of a new class of quadrilateral spline elements based on the scaled boundary coordinates

The scaled boundary finite element method (SBFEM) is a semi-analytical numerical approach based on the scaled boundary coordinates. Recently, the method which uses interpolations in both the circumferential and radial directions has also been developed based on the scaled boundary representation. However, the stress fields are always discontinuous within the S-elements by both the original SBFEM and the latter method. In this paper, a new class of quadrilateral elements with interior smoothness is constructed by extending the B-net method based on the area coordinates into the S-net method based on the scaled boundary coordinates. In the S-net method, the Bernstein bases are separately applied to discretize both circumferential and radial directions in each sub-triangle of an S-element (or quadrilateral element), and the smoothness conditions between adjacent triangles can be simply represented in the form of linear equations. Then, by using the S-net method, we obtain a new class of quadrilateral elements with interior smoothness and high-order completeness. The shape functions or interpolation bases can be obtained explicitly and determined by the same interpolation nodes of the S-element as the original SBFEM. Some numerical tests also show that the proposed elements can obtain good results.

Thermal Hall effects due to topological spin fluctuations in YMnO3

The thermal Hall effect in magnetic insulators has been considered a powerful method for examining the topological nature of charge-neutral quasiparticles such as magnons. Yet, unlike the kagome system, the triangular lattice has received less attention for studying the thermal Hall effect because the scalar spin chirality cancels out between adjacent triangles. However, such cancellation cannot be perfect if the triangular lattice is distorted. Here, we report that the trimerized triangular lattice of multiferroic hexagonal manganite YMnO3 produces a highly unusual thermal Hall effect under an applied magnetic field. Our theoretical calculations demonstrate that the thermal Hall conductivity is related to the splitting of the otherwise degenerate two chiralities of its 120˚ magnetic structure. Our result is one of the most unusual cases of topological physics due to this broken Z2 symmetry of the chirality in the supposedly paramagnetic state of YMnO3, due to strong topological spin fluctuations with the additional intricacy of a Dzyaloshinskii-Moriya interaction.

An Efficient Slicing Algorithm for Additive Manufacturing in Arbitrary Directions Based on Adjacent Triangles

An Efficient Slicing Algorithm for Additive Manufacturing in Arbitrary Directions Based on Adjacent Triangles

Tiling billards on triangle tilings, and interval exchange transformations

AbstractWe consider the dynamics of light rays in triangle tilings where triangles are transparent and adjacent triangles have equal but opposite indices of refraction. We find that the behavior of a trajectory on a triangle tiling is described by an orientation‐reversing three‐interval exchange transformation on the circle, and that the behavior of all the trajectories on a given triangle tiling is described by a polygon exchange transformation. We observe that, for a particular choice of triangle tiling, certain trajectories appear to approach the Rauzy fractal, under rescaling.

Growing uniform planar maps face by face

AbstractWe provide “growth schemes” for inductively generating uniform random ‐angulations of the sphere with faces, as well as uniform random simple triangulations of the sphere with faces. In the case of ‐angulations, we provide a way to insert a new face at a random location in a uniform ‐angulation with faces in such a way that the new map is precisely a uniform ‐angulation with faces. Similarly, given a uniform simple triangulation of the sphere with faces, we describe a way to insert two new adjacent triangles so as to obtain a uniform simple triangulation of the sphere with faces. The latter is based on a new bijective presentation of simple triangulations that relies on a construction by Poulalhon and Schaeffer.

The Number of Perfect Matchings in (3,6)-Fullerene

A [see formula in PDF]-fullerene is a connected cubic plane graph whose faces are only triangles and hexagons, and has the connectivity [see formula in PDF] or [see formula in PDF]. The [see formula in PDF]-fullerenes with connectivity [see formula in PDF] are the tubes consisting of [see formula in PDF] concentric hexagonal layers such that each layer consists of two hexagons, capped on each end by two adjacent triangles, denoted by [see formula in PDF]. A [see formula in PDF]-fullerene [see formula in PDF] with [see formula in PDF] vertices has exactly [see formula in PDF] perfect matchings. The structure of a [see formula in PDF]-fullerene [see formula in PDF] with connectivity [see formula in PDF] can be determined by only three parameters [see formula in PDF], [see formula in PDF] and[see formula in PDF], thus we denote it by [see formula in PDF], where [see formula in PDF] is the radius (number of rings), [see formula in PDF] is the size (number of spokes in each layer, [see formula in PDF], [see formula in PDF] is even), and [see formula in PDF] is the torsion ([see formula in PDF]). In this paper, the counting formula of the perfect matchings in [see formula in PDF]is given, and the number of perfect matchings is obtained. Therefore, the correctness of the conclusion that every bridgeless cubic graph with [see formula in PDF] vertices has at least [see formula in PDF] perfect matchings proposed by Esperet et al is verified for [see formula in PDF]-fullerene [see formula in PDF].

Local and global measures of the shear moduli of jammed disk packings.

Strain-controlled isotropic compression gives rise to jammed packings of repulsive, frictionless disks with either positive or negative global shear moduli. We carry out computational studies to understand the contributions of the negative shear moduli to the mechanical response of jammed disk packings. We first decompose the ensemble-averaged, global shear modulus as 〈G〉=(1-F_{-})〈G_{+}〉+F_{-}〈G_{-}〉, where F_{-} is the fraction of jammed packings with negative shear moduli and 〈G_{+}〉 and 〈G_{-}〉 are the average values from packings with positive and negative moduli, respectively. We show that 〈G_{+}〉 and 〈|G_{-}|〉 obey different power-law scaling relations above and below pN^{2}∼1. For pN^{2}>1, both 〈G_{+}〉N and 〈|G_{-}|〉N∼(pN^{2})^{β}, where β∼0.5 for repulsive linear spring interactions. Despite this, 〈G〉N∼(pN^{2})^{β^{'}} with β^{'}≳0.5 due to the contributions from packings with negative shear moduli. We show further that the probability distribution of global shear moduli P(G) collapses at fixed pN^{2} and different values of p and N. We calculate analytically that P(G) is a Γ distribution in the pN^{2}≪1 limit. As pN^{2} increases, the skewness of P(G) decreases and P(G) becomes a skew-normal distribution with negative skewness in the pN^{2}≫1 limit. We also partition jammed disk packings into subsystems using Delaunay triangulation of the disk centers to calculate local shear moduli. We show that the local shear moduli defined from groups of adjacent triangles can be negative even when G>0. The spatial correlation function of local shear moduli C(r[over ⃗]) displays weak correlations for pn_{sub}^{2}<10^{-2}, where n_{sub} is the number of particles within each subsystem. However, C(r[over ⃗]) begins to develop long-ranged spatial correlations with fourfold angular symmetry for pn_{sub}^{2}≳10^{-2}.

Signed planar graphs with Δ ≥ 8 are Δ-edge-colorable

A well-known theorem due to Vizing states that every graph with maximum degree Δ is Δ- or (Δ+1)-edge-colorable. Recently, Behr extended the concept of edge coloring in a natural way to signed graphs. He also proved that an analogue of Vizing's Theorem holds for all signed graphs. Adopting Behr's definition, Zhang et al. proved that a signed planar graph G with maximum degree Δ is Δ-edge-colorable if either Δ≥10 or Δ∈{8,9} and G contains no adjacent triangles. They also proposed the conjecture that every signed planar graph with Δ≥6 is Δ-edge-colorable, as a generalization of Vizing's Planar Graph Conjecture. In this paper, we prove that every signed planar graph with Δ≥8 is Δ-edge-colorable.

Pressure Regulating Self-Trapped States toward Remarkable Emission Enhancement of Zero-Dimensional Lead-Free Halides Nanocrystals.

Copper(I)-based halides have recently attracted increasing attention as a substitute for lead halides, owing to their nontoxicity, abundance, unique structure, and optoelectric properties. However, exploring an effective strategy to further improve their optical activities and revealing structure-optical property relationships still remain a great concern. Here, by using high pressure technique, a remarkable enhancement of self-trapped exciton (STE) emission associated with the energy exchange between multiple self-trapped states in zero-dimensional lead-free halide Cs3 Cu2 I5 NCs is successfully achieved. Furthermore, high-pressure processing endows the piezochromism of Cs3 Cu2 I5 NCs by experiencing a white light and a strong purple light emission, which is able to be stabilized at near-ambient pressure. The distortion of [Cu2 I5 ] clusters composing of tetrahedral [CuI4 ] and trigonal planar [CuI3 ] and the decreased Cu-Cu distance between the adjacent Cu-I tetrahedron and triangle are responsible for the significant STEs emission enhancement under high pressure. The experiments combined with first-principles calculations not only shed light on the structure-optical property relationships of [Cu2 I5 ] clusters halide, but also provide guidance for improving emission intensity that is highly desirable in solid-state lighting applications.

The Decomposability of Toroidal Graphs without Adjacent Triangles or Short Cycles

A graph G has a (d,h)-decomposition if there is a pair (D,F) such that F is a subgraph of G and D is an acyclic orientation of G−E(F), where the maximum degree of F is no more than h and the maximum out-degree of D is no more than d. This paper proves that toroidal graphs having no adjacent triangles are (3,1)-decomposable, and for {i,j}⊆{3,4,6}, toroidal graphs without i- and j-cycles are (2,1)-decomposable. As consequences of these results, toroidal graphs without adjacent triangles are 1-defective DP-4-colorable, and toroidal graphs without i- and j-cycles are 1-defective DP-3-colorable for {i,j}⊆{3,4,6}.

Finding globally shortest paths through a sequence of adjacent triangles by the method of orienting curves

Finding globally shortest paths through a sequence of adjacent triangles by the method of orienting curves

Augmented DNA Nanoarchitectures: A Structural Library of 3D Self-Assembling Tensegrity Triangle Variants.

The DNA tensegrity triangle is known to reliably self-assemble into a 3D rhombohedral crystalline lattice via sticky-end cohesion. Here, the library of accessible motifs is expanded throughcovalent extensions of intertriangle regions and sticky-end-coordinated linkages of adjacent triangles with double helical segmentsusing both geometrically symmetric and asymmetric configurations. The molecular structures of 18self-assembled architectures at resolutions of 3.32-9.32Å are reported; the observed cell dimensions, cavity sizes, and cross-sectional areas agree with theoretical expectations. These data demonstrate that fine control over triclinic and rhombohedral crystal parameters and the customizability of more complex 3D DNA lattices are attainable via rational design. It is anticipated that augmented DNA architectures may be fine-tuned for the self-assembly of designer nanocages, guest-host complexes, and proscriptive 3D nanomaterials, as originally envisioned. Finally, designer asymmetric crystalline building blocks can be seen as a first step toward controlling and encoding information in three dimensions.

Diagram of the phase composition of the Fe - Si - Al system and its isothermal sections

The diagram of the phase composition of the Fe &ndash; Si &ndash; Al system and its isothermal sections within the temperature range of 300-3000 K are plotted. Thermodynamic data of Fe3Si, Fe2Si, Fe5Si3, FeSi, FeSi2 silicides, FeAl, FeAl2, FeAl3, Fe2Al5 aluminides and Al2Fe2Si, Al3FeSi, Al2FeSi, Al11Fe3Si6, Al14Fe3Si3 ternary compounds are used. The diagram consists of 20 elementary triangles of coexisting phases, the number of which decreases to 6 at the temperature 1900 K and more. At the temperatures above 2900 K, the equilibrium of the condensed phases is disturbed due to the transition of such metal components of the low-melting aluminum corner of the diagram as Al, Al2, Fe, Si and Si2, leading to losses of valuable elements, to the gas phase. Crystallization fields are assessed by calculating the squares of elementary triangles, as well as the prevalence of each compound in the phase space by taking into account its participation in the construction of adjacent triangles. Using our own method, the mathematical model of the diagram was created in the form of equations for dependence of the amount of the formed phase on the chemical composition of examined metal. The computer program was developed based on the established equations. The examples of calculation of the phase composition of two grades of ferrosilicon FeSi65 and FeSi75, which are the most common in metallurgy, as well as two grades of ferrosilicoaluminum FeSi45Al15 and FeSi55Al20 are presented. Correspondence of the calculated and instrumentally found phase composition of the industrial metal has been revealed. Presence of mathematical models makes it possible to accelerate selection of the metal with the required composition and properties from the set of planned for smelting. This research is funded by the Science Committee of&nbsp;the Ministry of Education and Science of the Republic of&nbsp;Kazakhstan (Grant No. AP09259368).

Strain energy form coefficients for bending of short beams having full and thin-walled arbitrary cross section with application for FEM and Airfoils

The aim of this work is to develop a new generalized formula and a numerical computation program for evaluating the energy form coefficient of a complex and arbitrary cross section for full and thin-walled cross section with respect to any central axis, for the bending of beams of small lengths in comparison with the transverse dimension of the section. This coefficient plays a very important role in the calculation of the deformation energy of beams subjected to bending under the effect of a shearing force for short beams. It also enters in the formulation of FEM bending model, in order to calculate the stresses and the strains due to the external forces. The application is made for complex sections used in various fields of construction and in particular for airfoils designed for aerospace construction. A method is developed to calculate this coefficient as a function of the rotation of the central axes. The calculation of the area, the moments, and the product of inertias with respect to the central axes is necessary. The formula for calculating this coefficient is presented as a definite integral of a non-analytical function determined point by point along the direction of the application of the shear force. This function is based on the calculation of the partial static moments. The calculation of the latter is based on the development of a technique by subdividing the upper part of the section into adjacent common triangles at one point for the full solid section or by segments on the boundary for the thin-walled section. To speed up the process of numerically calculating this integral with high precision and reduced time, Gauss Legendre quadrature of order 40 is used. The calculation of the distribution of the tangential stress as well as its maximum value is determined. A shear shape coefficient is therefore determined. In the second part of this work, an application is made for the static calculation by the FEM of a hyper static beam with a view to determining the influence of this coefficient on all the parameters of resistance and bending stiffness as a correction of the classical model of bending by the FEM. A study of the error made by the classical bending model on our shear effect model is presented. A coefficient of efficiency of a section is presented.

Experimental study on physical and mechanical characteristics of rock-concrete combined body under complex stress conditions

Tidal waves and vehicle loadings forming a complex stress condition in coastal regions have a significant effect on the stability of engineering structures. It is therefore necessary to understand the physical and mechanical behaviors for rock-concrete combined structures under complex stress conditions for realizing the safe design of structures. Therefore, the complex stress condition tests of rock-concrete samples of varying roughness are performed in this study. The stress–strain curves of the rock-concrete samples show that hysteresis occurred under complex stress conditions. As the confining pressure increases, the hysteresis loop area increases. Furthermore, the elastic modulus increases accordingly as the roughness increases. The lateral deformation ratio (κ) of the loaded rock-concrete sample increases as the number of cycles increases, but decreases as the height of roughness increases. The Mohr-Coulomb (M−C) criterion and the Hoek-Brown (H-B) criterion are used to fit the testing data and for discussion. The H-B strength criterion is suitable for describing the strength characteristics of the rock-concrete combined body under complex stress conditions. Ultimately, with the increasing axial loading and decreasing confining loading, the relative slipping on the adjacent triangle rock base and concrete resulted in the occurrence of the tensile crack.