A Remark on the Characterization of Triangulated Graphs

In this study, we consider the problem of triangulated graphs. Precisely we give a necessary and sufficient condition for a graph to be triangulated. This gives an alternative characterization of triangulated graphs. Our method is based on the so-called perfectly nested sequences.

RESEARCH ON ADAPTIVE DATA COMPRESSION METHOD FOR TRIANGULATED SURFACES

NC code or STL file can be generated directly from measuring data in a fastreverse-engineering mode. Compressing the massive data from laser scanner is the key of the newmode. An adaptive compression method based on triangulated-surfaces model is put forward.Normal-vector angles between triangles are computed to find prime vertices for removal. Ring datastructure is adopted to save massive data effectively. It allows the efficient retrieval of allneighboring vertices and triangles of a given vertices. To avoid long and thin triangles, a newre-triangulation approach based on normalized minimum-vertex-distance is proposed, in which thevertex distance and interior angle of triangle are considered. Results indicate that the compressionmethod has high efficiency and can get reliable precision. The method can be applied in fastreverse engineering to acquire an optimal subset of the original massive data.

Seismic traveltime inversion of 3D velocity model with triangulated interfaces

Seismic traveltime tomographic inversion has played an important role in detecting the internal structure of the solid earth. We use a set of blocks to approximate geologically complex media that cannot be well described by layered models or cells. The geological body is described as an aggregate of arbitrarily shaped blocks,which are separated by triangulated interfaces. We can describe the media as homogenous or heterogeneous in each block. We define the velocities at the given rectangle grid points for each block,and the heterogeneous velocities in each block can be calculated by a linear interpolation algorithm. The parameters of the velocity grid positions are independent of the model parameterization,which is advantageous in the joint inversion of the velocities and the node depths of an interface. We implement a segmentally iterative ray tracer to calculate traveltimes in the 3D heterogeneous block models.The damped least squares method is employed in seismic traveltime inversion,which includes the partial derivatives of traveltime with respect to the depths of nodes in the triangulated interfaces and velocities defined in rectangular grids. The numerical tests indicate that the node depths of a triangulated interface and homogeneous velocity distributions can be well inverted in a stratified model.

Layer-Constrained Triangulated Irregular Network Algorithm Based on Ground Penetrating Radar Data and Its Application

In this paper,a layer-constrained triangulated irregular network（ LC-TIN） algorithm is proposed for three-dimensional（ 3 D） modelling,and applied to construct a 3 D model for geological disease information based on ground penetrating radar（ GPR） data. Compared with the traditional TIN algorithm,the LCTIN algorithm introduced a layer constraint to the discrete data points during the 3 D modelling process,and it can dynamically construct networks from layer to layer and implement 3 D modelling for arbitrary shapes with high precision. The experimental results validated this method,the proposed algorithm not only can maintain the rationality of triangulation network,but also can obtain a good generation speed. In addition,the algorithm is also introduced to our self-developed 3 D visualization platform,which utilized GPR data to model geological diseases. Therefore the feasibility of the algorithm is verified in the practical application.

Torsion Pairs in Triangulated Categories

We study the properties of torsion pairs in triangulated category by introducing the notions of d-Ext-projectivity and d-Ext-injectivity. In terms of -mutation of torsion pairs, we investigate the properties of torsion pairs in triangulated category under some conditions on subcategories and in .

Balanced Pairs on Triangulated Categories

Let C be a triangulated category.We first introduce the notion of balanced pairs in C,and then establish the bijective correspondence between balanced pairs and proper classesξwith enoughξ-projectives andξ-injectives.Assume thatξ:=ξX=ξ^(Y) is the proper class induced by a balanced pair(X,Y).We prove that(C,Eξ,sξ)is an extriangulated category.Moreover,it is proved that(C,Eξ,sξ)is a triangulated category if and only if X=Y=0,and that(C,Eξ,sξ)is an exact category if and only if X=Y=C.As an application,we produce a large variety of examples of extriangulated categories which are neither exact nor triangulated.

From recollement of triangulated categories to recollement of abelian categories

In this paper,we prove that if a triangulated category D admits a recollement relative to triangulated categories D' and D″,then the abelian category D/T admits a recollement relative to abelian categories D'/i(T) and D″/j(T) where T is a cluster tilting subcategory of D and satisfies i i (T) T,j j (T) T.

SAR imaging simulation for an inhomogeneous undulated lunar surface based on triangulated irregular network

Based on the statistics of the lunar cratered terrain, e.g., population, dimension and shape of craters, the terrain feature of cratered lunar surface is numerically generated. According to the inhomogeneous distribution of the lunar surface slope, the triangulated irregular network （TIN） is employed to make the digital elevation of lunar surface model. The Kirchhoff approximation of surface scattering is then applied to simulation of lunar surface scattering. The synthetic aperture radar （SAR） image for compre- hensive cratered lunar surface is numerically generated using back projection （BP） algorithm of SAR imaging. Making use of the digital elevation and Clementine UVVIS data at Apollo 15 landing site as the ground truth, an SAR image at Apollo 15 landing site is simulated. The image simulation is verified using real SAR image and echoes statistics.

Resolving Subcategories of Triangulated Categories and Relative Homological Dimension

We introduce and study （pre）resolving subcategories of a triangulated category and the homological dimension relative to these subcategories. We apply the obtained properties to relative Gorenstein categories.

Cohomology Theories in Triangulated Categories

Let C be a triangulated category with a proper class g of triangles. We prove that there exists an Avramov-Martsinkovsky type exact sequence in g, which connects ε-cohomology, ε-Tate cohomology and ε-Corenstein cohomology.

Relative Quotient Triangulated Categories

Let A be a finite dimensional algebra over a field k. We consider a subfunc- tor F of Ext1A（-, -）, which has enough projectives and injectives such that P（F） is of finite type, where P（F） denotes the set of F-projectives. One can get the relative derived category Db（A） of A-rood. For an F-self-orthogonal module TF, we discuss the relation between the relative quotient triangulated category Db（A）/Kb（addTF） and the relative stable category of the Frobenius category of TF-Cohen-Macaulay modules. In particular, for an F-Gorenstein algebra A and an F-tilting A-module TF, we get a triangle equiva- lence between DbF（A）/Kb（add TF） and the relative stable category of TF-Cohen-Macaulay modules. This gives the relative version of a result of Chen and Zhang.

Triangulated Structures Induced by Triangle Functors

Given a triangle functor F : A → B, the authors introduce the half image hIm F,which is an additive category closely related to F. If F is full or faithful, then hIm F admits a natural triangulated structure. However, in general, one can not expect that hIm F has a natural triangulated structure. The aim of this paper is to prove that hIm F admits a natural triangulated structure if and only if F satisfies the condition(SM). If this is the case, hIm F is triangle-equivalent to the Verdier quotient A/Ker F.

Cluster Structures in 2-Calabi-Yau Triangulated Categories of Dynkin Type with Maximal Rigid Objects

In this paper, we consider two kinds of 2-Calabi-Yau triangulated categories with finitely many indecomposable objects up to isomorphisms, called An,t =D^b（KA（2t＋1）（n＋1）-3）/τ^t（n＋1）-1[1], where n,t ≥ 1, and Dn,t = Db（KD2t（n＋1））/τ^（n＋1）φ^n, where n,t ≥ 1, and φ is induced by an automorphism of D2t（n＋1） of order 2. Except the categories An,1, they all contain non-zero maximal rigid objects which are not cluster tilting. An,1 contain cluster tilting objects. We define the cluster complex of An,t （resp. Dn,t） by using the geometric description of cluster categories of type A （resp. type D）. We show that there is an isomorphism from the cluster complex of An,t （resp. Dn,t） to the cluster complex of root system of type Bn. In particular, the maximal rigid objects are isomorphic to clusters. This yields a result proved recently by Buan-Palu-Reiten： Let RAn,t, resp. RDn,t, be the full subcategory of An,t, resp. Dn,t, generated by the rigid objects. Then RAn,t≈RAn,1 and TDn,t≈TAn,1 as additive categories, for all t 〉 1.

Rigidity of the Hexagonal Delaunay Triangulated Plane

We show the rigidity of the hexagonal Delaunay triangulated plane under Luo’s PL conformality.As a consequence,we obtain a rigidity theorem for a particular type of locally finite convex ideal hyperbolic polyhedra.

The Psychosomatic Traits of“People with the Five Elements in Traditional Chinese Medicine”:A Qualitative Study

Objective To identify the representative attributes of the five elements of a person with a qualitative methodology and provide the basis for the clinical diagnosis and treatment of“people with the five elements in traditional Chinese medicine(TCM).”Methods Data collected from the literature review,two sessions of brainstorming of experts with related experience in“people with the five elements in TCM”from October 2020 to December 2020,and six rounds of in-depth interviews with 30 participants who had various attributes of the five elements from March 2021 to October 2021 were analyzed.Triangulation was used in this study,and theming and synthesizing were used to analyze the data.Results A total of 31 experts and 30 interviewees participated in this study.The median age of the experts and interviewees were 48.0 and 38.5 years,respectively;51.66%and 54.8%of experts and interviewees,respectively,were men.The descriptors of facial diagrams of“people with the five elements in TCM”were complexion,shape,distribution state of facial bones,convergence trend of facial muscles,and facial expression.A theoretical model of“people with the five elements in TCM”was shaped based on these findings.Conclusion The study suggests a possibility for bridging the gap between personality and bodily state,identifying an avenue for personality research from the perspective of TCM.

Flexible robotic endoscopy for treating gastrointestinal neoplasms

Therapeutic flexible endoscopic robotic systems have been developed primarily as a platform for endoscopic submucosal dissection(ESD)in the treatment of earlystage gastrointestinal cancer.Since ESD can only be performed by highly skilled endoscopists,the goal is to lower the technical hurdles to ESD by introducing a robot.In some cases,such robots have already been used clinically,but they are still in the research and development stage.This paper outlined the current status of development,including a system by the author’s group,and discussed future challenges.

Ruppert's Delaunay Triangulation Refinement Scheme for Optimal RSUs Placement in Vehicle to Infrastructure Communication Network

Road Side Units(RSUs)are the essential component of vehicular communication for the objective of improving safety and mobility in the road transportation.RSUs are generally deployed at the roadside and more specifically at the intersections in order to collect traffic information from the vehicles and disseminate alarms and messages in emergency situations to the neighborhood vehicles cooperating with the network.However,the development of a predominant RSUs placement algorithm for ensuring competent communication in VANETs is a challenging issue due to the hindrance of obstacles like water bodies,trees and buildings.In this paper,Ruppert’s Delaunay Triangulation Refinement Scheme(RDTRS)for optimal RSUs placement is proposed for accurately estimating the optimal number of RSUs that has the possibility of enhancing the area of coverage during data communication.This RDTRS is proposed by considering the maximum number of factors such as global coverage,intersection popularity,vehicle density and obstacles present in the map for optimal RSUs placement,which is considered as the core improvement over the existing RSUs optimal placement strategies.It is contributed for deploying requisite RSUs with essential transmission range for maximal coverage in the convex map such that each position of the map could be effectively covered by at least one RSU in the presence of obstacles.The simulation experiments of the proposed RDTRS are conducted with complex road traffic environments.The results of this proposed RDTRS confirmed its predominance in reducing the end-to-end delay by 21.32%,packet loss by 9.38%with improved packet delivery rate of 10.68%,compared to the benchmarked schemes.

Study on Flow Field Simulation at Transmission Towers in Loess Hilly Regions Based on Circular Boundary Constraints

When using high-voltage transmission lines for energy transmission in loess hilly regions,local extreme wind fields such as turbulence and high-speed cyclones occur from time to time,which can cause many kinds of mechanical and electrical failures,seriously affecting the reliable and stable energy transmission of the power grid.The existing research focuses on the wind field simulation of ideal micro-terrain and actual terrain with mostly single microterrain characteristics.Model boundary constraints and the influence of constrained boundaries are the main problems that need to be solved to accurately model and simulate complex flow fields.In this paper,a flow field simulation method based on circular boundary constraints is carried out.During the study,the influence of the model boundary and the selection conditions of themodeling range are systematically analyzed.It is more suitable to make sure that the air domain is 4 times higher than the height of the hill undulations,in addition to ensuring that there should be a minimum of 400 m between the study region and the boundary.Then,an actual terrain model of a power grid line in Shanxi is established,through the method proposed in this paper,the wind speed at the location of the transmission tower line under different wind directions is analyzed,and it is found that when the incidence direction is 45 degrees north by east the wind speed is the highest.The findings demonstrate that the circular boundary model has the advantage of more easily adjusting the wind incidence direction,in addition to theoretically reducing the errors caused by traditional models in boundary processing.It can accurately obtain the distribution characteristics of the flow field affected by the terrain,and quickly screen out the extreme working conditions that are most harmful to the transmission lines in the actual transmission line for energy transmission in complex loess hilly regions.

Accurate surface normal representation to facilitate gradient coil optimization on curved surface

The design methods for gradient coils are mostly based on discrete extrinsic methods(e.g.,the BioteSavart integration calculation),for which the surface normal vector strongly influences any numerical calculation of the discretized surface.Previous studies are mostly based on regular or analytical surfaces,which allow normal vectors to be expressed analytically.For certain applications,design methods for extending currentcarrying surfaces from developable or analytic geometries to arbitrary surfaces generated from a scanned point cloud are required.The key task is to correctly express the discretized normal vectors to ensure geometrical accuracy of the designed coils.Mathematically,it has been proven that applying a Delaunay triangulation to approximate a smooth surface can result in the discrete elemental normal vectors converging to those of the original surface.Accordingly,this article uses Delaunay triangulation to expand upon previous design methods so that they encompass arbitrary piecewise continuous surfaces.Two design methods,the stream function and the so-called solid isotropic material with penalization(SIMP)method,are used to design circumvolute and noncircumvolute gradient coils on general surfaces.

基于不规则三角形网格和有限体积法的物理性流域水文模型

传统的栅格离散方式不能很好反映流域水文过程的边界特征,且难以实现流域水文过程的多尺度模拟。采用有限体积法构建了基于不规则三角形网格的物理性水文模型,将物理性描述的偏微分方程组在控制体积内积分得到空间半离散的常微分方程组,保证数值求解中的水量平衡,并可与概念性描述部分水文过程(如截留、填洼等)的常微分方程组更好地耦合;建立了数值求解方案,采用Triangle对计算区域进行离散,并在沁河上游流域进行了验证,结果表明模型具有较高的模拟精度和良好的应用前景。