Let G = （V, E） be a simple connected graph, and ｜V（G）｜ ≥ 2. Let f be a mapping from V（G） ∪ E（G） to {1,2…, k}. If arbitary uv ∈ E（G）,f（u） ≠ f（v）,f（u） ≠ f（uv）,f（v） ≠ f（uv）; arbitary uv, uw...Let G = （V, E） be a simple connected graph, and ｜V（G）｜ ≥ 2. Let f be a mapping from V（G） ∪ E（G） to {1,2…, k}. If arbitary uv ∈ E（G）,f（u） ≠ f（v）,f（u） ≠ f（uv）,f（v） ≠ f（uv）; arbitary uv, uw ∈ E（G）（v ≠ w）, f（uv） ≠ f（uw）;arbitary uv ∈ E（G） and u ≠ v, C（u） ≠ C（v）, whereC（u）={f（u）}∪{f（uv）｜uv∈E（G）}.Then f is called a k-adjacent-vertex-distinguishing-proper-total coloring of the graph G（k-AVDTC of G for short）. The number min{k｜k-AVDTC of G} is called the adjacent vertex-distinguishing total chromatic number and denoted by χat（G）. In this paper we prove that if △（G） is at least a particular constant and δ ≥32√△ln△, then χat（G） ≤ △（G） ＋ 10^26 ＋ 2√△ln△.展开更多
A proper k-edge coloring of a graph G is called adjacent vertex distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the color set of edges incident to u is not equal to the color set of edges ...A proper k-edge coloring of a graph G is called adjacent vertex distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the color set of edges incident to u is not equal to the color set of edges incident to v, where uv ∈E（G）. The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by χ＇αα（G）, is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. In this paper we prove that if G（V, E） is a graph with no isolated edges, then χ＇αα（G）≤32△.展开更多
The biggest bottleneck in DNA computing is exponential explosion, in which the DNA molecules used as data in information processing grow exponentially with an increase of problem size. To overcome this bottleneck and ...The biggest bottleneck in DNA computing is exponential explosion, in which the DNA molecules used as data in information processing grow exponentially with an increase of problem size. To overcome this bottleneck and improve the processing speed, we propose a DNA computing model to solve the graph vertex coloring problem. The main points of the model are as follows： The exponential explosion prob- lem is solved by dividing subgraphs, reducing the vertex colors without losing the solutions, and ordering the vertices in subgraphs; and the bio-operation times are reduced considerably by a designed parallel polymerase chain reaction （PCR） technology that dramatically improves the processing speed. In this arti- cle, a 3-colorable graph with 61 vertices is used to illustrate the capability of the DNA computing model. The experiment showed that not only are all the solutions of the graph found, but also more than 99% of false solutions are deleted when the initial solution space is constructed. The powerful computational capability of the model was based on specific reactions among the large number of nanoscale oligonu- cleotide strands. All these tiny strands are operated by DNA self-assembly and parallel PCR. After thou- sands of accurate PCR operations, the solutions were found by recognizing, splicing, and assembling. We also prove that the searching capability of this model is up to 0（3^59）. By means of an exhaustive search, it would take more than 896 000 years for an electronic computer （5 x 10^14 s-1） to achieve this enormous task. This searching capability is the largest among both the electronic and non-electronic computers that have been developed since the DNA computing model was proposed by Adleman＇s research group in 2002 （with a searching capability of 0（2^20））.展开更多
This paper proposes a vertex-estimation-based, feature-preserving smoothingtechnique for meshes. A robust mesh smoothing operator called mean value coordinates flow isintroduced to modify mean curvature flow and make ...This paper proposes a vertex-estimation-based, feature-preserving smoothingtechnique for meshes. A robust mesh smoothing operator called mean value coordinates flow isintroduced to modify mean curvature flow and make it more stable. Also the paper proposes athree-pass vertex estimation based on bilateral filtering of local neighbors which is transferredfrom image processing settings and a Quasi-Laplacian operation, derived from the standard Laplacianoperator, is performed to increase the smoothness order of the mesh rapidly whilst denoising meshesefficiently, preventing volume shrinkage as well as preserving sharp features of the mesh. Comparedwith previous algorithms, the result shows it is simple, efficient and robust.展开更多
LetG be a graph with vertex setV (G) and edge setE (G), and letg andf be two integer-valued functions defined on V(G) such thatg(x)?(x) for every vertexx ofV(G). It was conjectured that ifG is an (mg +m - 1,mf -m+1)-g...LetG be a graph with vertex setV (G) and edge setE (G), and letg andf be two integer-valued functions defined on V(G) such thatg(x)?(x) for every vertexx ofV(G). It was conjectured that ifG is an (mg +m - 1,mf -m+1)-graph andH a subgraph ofG withm edges, thenG has a (g,f)-factorization orthogonal toH. This conjecture is proved affirmatively.展开更多
Introduction: Breech birth has always been a subject of great interest because of its risks of perinatal morbidity and mortality. Aim: The aim of our study was to compare the maternal and perinatal prognosis of breech...Introduction: Breech birth has always been a subject of great interest because of its risks of perinatal morbidity and mortality. Aim: The aim of our study was to compare the maternal and perinatal prognosis of breech delivery with that of vertex delivery. Patients and Method: This was a retrospective case-control analytical study carried out in the obstetrics and gynaecology department of Ségou hospital over a 2-year period from 1 January 2020 to 31 December 2021, involving 242 breech deliveries compared with 484 top deliveries with a live single foetus without foetal malformation of gestational age ≥ 35 SA. The statistical tests used were: chi² (p Results: The frequency of breech delivery was 3.3%, with a predominance of caesarean section for breech presentation (64.88%) compared with 32.85% for vertex (P: 0.00;CI: (0.191 - 0.367). The perinatal prognosis of fetuses with breech presentations was marked by a higher rate of neonatal asphyxia (Apgar score Conclusion: Breech birth is relatively rare in our department. It carries a higher risk of maternal morbidity and neonatal morbidity than breech delivery. However, the vital prognosis for the mother was identical in both groups.展开更多
Let G be a finite group with order ｜G｜=p1^α1p2^α2……pk^αk, where p1 〈 p2 〈……〈 Pk are prime numbers. One of the well-known simple graphs associated with G is the prime graph （or Gruenberg- Kegel graph） den...Let G be a finite group with order ｜G｜=p1^α1p2^α2……pk^αk, where p1 〈 p2 〈……〈 Pk are prime numbers. One of the well-known simple graphs associated with G is the prime graph （or Gruenberg- Kegel graph） denoted .by г（G） （or GK（G））. This graph is constructed as follows： The vertex set of it is π（G） = {p1,p2,…,pk} and two vertices pi, pj with i≠j are adjacent by an edge （and we write pi - pj） if and only if G contains an element of order pipj. The degree deg（pi） of a vertex pj ∈π（G） is the number of edges incident on pi. We define D（G） ：= （deg（p1）, deg（p2）,..., deg（pk））, which is called the degree pattern of G. A group G is called k-fold OD-characterizable if there exist exactly k non- isomorphic groups H such that ｜H｜ = ｜G｜ and D（H） = D（G）. Moreover, a 1-fold OD-characterizable group is simply called OD-characterizable. Let L ：= U3（5） be the projective special unitary group. In this paper, we classify groups with the same order and degree pattern as an almost simple group related to L. In fact, we obtain that L and L.2 are OD-characterizable; L.3 is 3-fold OD-characterizable; L.S3 is 6-fold OD-characterizable.展开更多
Cultural relics line graphic serves as a crucial form of traditional artifact information documentation,which is a simple and intuitive product with low cost of displaying compared with 3D models.Dimensionality reduct...Cultural relics line graphic serves as a crucial form of traditional artifact information documentation,which is a simple and intuitive product with low cost of displaying compared with 3D models.Dimensionality reduction is undoubtedly necessary for line drawings.However,most existing methods for artifact drawing rely on the principles of orthographic projection that always cannot avoid angle occlusion and data overlapping while the surface of cultural relics is complex.Therefore,conformal mapping was introduced as a dimensionality reduction way to compensate for the limitation of orthographic projection.Based on the given criteria for assessing surface complexity,this paper proposed a three-dimensional feature guideline extraction method for complex cultural relic surfaces.A 2D and 3D combined factor that measured the importance of points on describing surface features,vertex weight,was designed.Then the selection threshold for feature guideline extraction was determined based on the differences between vertex weight and shape index distributions.The feasibility and stability were verified through experiments conducted on real cultural relic surface data.Results demonstrated the ability of the method to address the challenges associated with the automatic generation of line drawings for complex surfaces.The extraction method and the obtained results will be useful for line graphic drawing,displaying and propaganda of cultural relics.展开更多
In this paper, an efficient and easy-to-implement coarsening algorithm is proposed for adaptive grids obtained using the newest vertex bisection method in two dimemsions. The new coarsening algorithm does not require ...In this paper, an efficient and easy-to-implement coarsening algorithm is proposed for adaptive grids obtained using the newest vertex bisection method in two dimemsions. The new coarsening algorithm does not require storing the binary refinement tree explicitly. Instead, the structure is implicitly contained in a special ordering of triangular elements. Numerical experiments demonstrate that the proposed coarsening algorithm is efficient when applied for multilevel preconditioners and mesh adaptivity for time-dependent problems.展开更多
The human eye is an asymmetric optical system and the real cornea is not a rotationally symmetrical volume.Each optical element in the eye has its own optical and neural axes.Defining the optimum center for laser abla...The human eye is an asymmetric optical system and the real cornea is not a rotationally symmetrical volume.Each optical element in the eye has its own optical and neural axes.Defining the optimum center for laser ablation is difficult with many available approaches.We explain the various centration approaches(based on these reference axes)in refractive surgery and review their clinical outcomes.The line-of-sight(LOS)(the line joining the entrance pupil center with the fixation point)is often the recommended reference axis for representing wavefront aberrations of the whole eye(derived from the definition of chief ray in geometrical optics);however pupil centration can be unstable and change with the pupil size.The corneal vertex(CV)represents a stable preferable morphologic reference which is the best approximate for alignment to the visual axis.However,the corneal light reflex can be considered as non-constant,but dependent on the direction of gaze of the eye with respect to the light source.A compromise between the pupil and CV centered ablations is seen in the form of an asymmetric offset where the manifest refraction is referenced to the CV while the higher order aberrations are referenced to the pupil center.There is a need for a flexible choice of centration in excimer laser systems to design customized and non-customized treatments optimally.展开更多
A vertex distinguishing equitable total coloring of graph G is a proper total coloring of graph G such that any two distinct vertices＇ coloring sets are not identical and the difference of the elements colored by any...A vertex distinguishing equitable total coloring of graph G is a proper total coloring of graph G such that any two distinct vertices＇ coloring sets are not identical and the difference of the elements colored by any two colors is not more than 1. In this paper we shall give vertex distinguishing equitable total chromatic number of join graphs Pn VPn, Cn VCn and prove that they satisfy conjecture 3, namely, the chromatic numbers of vertex distinguishing total and vertex distinguishing equitable total are the same for join graphs Pn V Pn and Cn ∨ Cn.展开更多
基金the Natural Science Foundation of Gansu Province （No. 3ZS051-A25-025） the Foundation of Gansu Provincial Department of Education （No. 0501-03）.
文摘Let G = （V, E） be a simple connected graph, and ｜V（G）｜ ≥ 2. Let f be a mapping from V（G） ∪ E（G） to {1,2…, k}. If arbitary uv ∈ E（G）,f（u） ≠ f（v）,f（u） ≠ f（uv）,f（v） ≠ f（uv）; arbitary uv, uw ∈ E（G）（v ≠ w）, f（uv） ≠ f（uw）;arbitary uv ∈ E（G） and u ≠ v, C（u） ≠ C（v）, whereC（u）={f（u）}∪{f（uv）｜uv∈E（G）}.Then f is called a k-adjacent-vertex-distinguishing-proper-total coloring of the graph G（k-AVDTC of G for short）. The number min{k｜k-AVDTC of G} is called the adjacent vertex-distinguishing total chromatic number and denoted by χat（G）. In this paper we prove that if △（G） is at least a particular constant and δ ≥32√△ln△, then χat（G） ≤ △（G） ＋ 10^26 ＋ 2√△ln△.
基金Supported by the Natural Science Foundation of Gansu Province(3ZS051-A25-025)
文摘A proper k-edge coloring of a graph G is called adjacent vertex distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the color set of edges incident to u is not equal to the color set of edges incident to v, where uv ∈E（G）. The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by χ＇αα（G）, is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. In this paper we prove that if G（V, E） is a graph with no isolated edges, then χ＇αα（G）≤32△.
基金The authors are grateful for the support from the National Natural Science Foundation of China （61632002, 61379059, and 61572046）.
文摘The biggest bottleneck in DNA computing is exponential explosion, in which the DNA molecules used as data in information processing grow exponentially with an increase of problem size. To overcome this bottleneck and improve the processing speed, we propose a DNA computing model to solve the graph vertex coloring problem. The main points of the model are as follows： The exponential explosion prob- lem is solved by dividing subgraphs, reducing the vertex colors without losing the solutions, and ordering the vertices in subgraphs; and the bio-operation times are reduced considerably by a designed parallel polymerase chain reaction （PCR） technology that dramatically improves the processing speed. In this arti- cle, a 3-colorable graph with 61 vertices is used to illustrate the capability of the DNA computing model. The experiment showed that not only are all the solutions of the graph found, but also more than 99% of false solutions are deleted when the initial solution space is constructed. The powerful computational capability of the model was based on specific reactions among the large number of nanoscale oligonu- cleotide strands. All these tiny strands are operated by DNA self-assembly and parallel PCR. After thou- sands of accurate PCR operations, the solutions were found by recognizing, splicing, and assembling. We also prove that the searching capability of this model is up to 0（3^59）. By means of an exhaustive search, it would take more than 896 000 years for an electronic computer （5 x 10^14 s-1） to achieve this enormous task. This searching capability is the largest among both the electronic and non-electronic computers that have been developed since the DNA computing model was proposed by Adleman＇s research group in 2002 （with a searching capability of 0（2^20））.
文摘This paper proposes a vertex-estimation-based, feature-preserving smoothingtechnique for meshes. A robust mesh smoothing operator called mean value coordinates flow isintroduced to modify mean curvature flow and make it more stable. Also the paper proposes athree-pass vertex estimation based on bilateral filtering of local neighbors which is transferredfrom image processing settings and a Quasi-Laplacian operation, derived from the standard Laplacianoperator, is performed to increase the smoothness order of the mesh rapidly whilst denoising meshesefficiently, preventing volume shrinkage as well as preserving sharp features of the mesh. Comparedwith previous algorithms, the result shows it is simple, efficient and robust.
文摘LetG be a graph with vertex setV (G) and edge setE (G), and letg andf be two integer-valued functions defined on V(G) such thatg(x)?(x) for every vertexx ofV(G). It was conjectured that ifG is an (mg +m - 1,mf -m+1)-graph andH a subgraph ofG withm edges, thenG has a (g,f)-factorization orthogonal toH. This conjecture is proved affirmatively.
基金supported in part by the National Natural Science Foundation of China(Grant No.10471034)Famous Youth Foundation of Henan Province(Grant No.0512000100)the Natural Science Foundation of Educational Committee of Henan Province(Grant No.2000110010).
文摘In this paper, we define a P-twisted affine Lie algebra, and construct its realizations by twisted vertex operators.
文摘Introduction: Breech birth has always been a subject of great interest because of its risks of perinatal morbidity and mortality. Aim: The aim of our study was to compare the maternal and perinatal prognosis of breech delivery with that of vertex delivery. Patients and Method: This was a retrospective case-control analytical study carried out in the obstetrics and gynaecology department of Ségou hospital over a 2-year period from 1 January 2020 to 31 December 2021, involving 242 breech deliveries compared with 484 top deliveries with a live single foetus without foetal malformation of gestational age ≥ 35 SA. The statistical tests used were: chi² (p Results: The frequency of breech delivery was 3.3%, with a predominance of caesarean section for breech presentation (64.88%) compared with 32.85% for vertex (P: 0.00;CI: (0.191 - 0.367). The perinatal prognosis of fetuses with breech presentations was marked by a higher rate of neonatal asphyxia (Apgar score Conclusion: Breech birth is relatively rare in our department. It carries a higher risk of maternal morbidity and neonatal morbidity than breech delivery. However, the vital prognosis for the mother was identical in both groups.
基金Supported by National Natural Science Foundation of China (Grant No. 10871032)the SRFDP of China (Grant No. 20660285002)a subproject of National Natural Science Foundation of China (Grant No. 50674008) (Chongqing University, Nos. 104207520080834, 104207520080968)
文摘Let G be a finite group with order ｜G｜=p1^α1p2^α2……pk^αk, where p1 〈 p2 〈……〈 Pk are prime numbers. One of the well-known simple graphs associated with G is the prime graph （or Gruenberg- Kegel graph） denoted .by г（G） （or GK（G））. This graph is constructed as follows： The vertex set of it is π（G） = {p1,p2,…,pk} and two vertices pi, pj with i≠j are adjacent by an edge （and we write pi - pj） if and only if G contains an element of order pipj. The degree deg（pi） of a vertex pj ∈π（G） is the number of edges incident on pi. We define D（G） ：= （deg（p1）, deg（p2）,..., deg（pk））, which is called the degree pattern of G. A group G is called k-fold OD-characterizable if there exist exactly k non- isomorphic groups H such that ｜H｜ = ｜G｜ and D（H） = D（G）. Moreover, a 1-fold OD-characterizable group is simply called OD-characterizable. Let L ：= U3（5） be the projective special unitary group. In this paper, we classify groups with the same order and degree pattern as an almost simple group related to L. In fact, we obtain that L and L.2 are OD-characterizable; L.3 is 3-fold OD-characterizable; L.S3 is 6-fold OD-characterizable.
基金National Natural Science Foundation of China(Nos.42071444,42101444)。
文摘Cultural relics line graphic serves as a crucial form of traditional artifact information documentation,which is a simple and intuitive product with low cost of displaying compared with 3D models.Dimensionality reduction is undoubtedly necessary for line drawings.However,most existing methods for artifact drawing rely on the principles of orthographic projection that always cannot avoid angle occlusion and data overlapping while the surface of cultural relics is complex.Therefore,conformal mapping was introduced as a dimensionality reduction way to compensate for the limitation of orthographic projection.Based on the given criteria for assessing surface complexity,this paper proposed a three-dimensional feature guideline extraction method for complex cultural relic surfaces.A 2D and 3D combined factor that measured the importance of points on describing surface features,vertex weight,was designed.Then the selection threshold for feature guideline extraction was determined based on the differences between vertex weight and shape index distributions.The feasibility and stability were verified through experiments conducted on real cultural relic surface data.Results demonstrated the ability of the method to address the challenges associated with the automatic generation of line drawings for complex surfaces.The extraction method and the obtained results will be useful for line graphic drawing,displaying and propaganda of cultural relics.
基金supported in part by NSF Grant DMS-0811272in part by NIH Grant P50GM76516 and R01GM75309supported by NSF Grant DMS-0915153
文摘In this paper, an efficient and easy-to-implement coarsening algorithm is proposed for adaptive grids obtained using the newest vertex bisection method in two dimemsions. The new coarsening algorithm does not require storing the binary refinement tree explicitly. Instead, the structure is implicitly contained in a special ordering of triangular elements. Numerical experiments demonstrate that the proposed coarsening algorithm is efficient when applied for multilevel preconditioners and mesh adaptivity for time-dependent problems.
文摘The human eye is an asymmetric optical system and the real cornea is not a rotationally symmetrical volume.Each optical element in the eye has its own optical and neural axes.Defining the optimum center for laser ablation is difficult with many available approaches.We explain the various centration approaches(based on these reference axes)in refractive surgery and review their clinical outcomes.The line-of-sight(LOS)(the line joining the entrance pupil center with the fixation point)is often the recommended reference axis for representing wavefront aberrations of the whole eye(derived from the definition of chief ray in geometrical optics);however pupil centration can be unstable and change with the pupil size.The corneal vertex(CV)represents a stable preferable morphologic reference which is the best approximate for alignment to the visual axis.However,the corneal light reflex can be considered as non-constant,but dependent on the direction of gaze of the eye with respect to the light source.A compromise between the pupil and CV centered ablations is seen in the form of an asymmetric offset where the manifest refraction is referenced to the CV while the higher order aberrations are referenced to the pupil center.There is a need for a flexible choice of centration in excimer laser systems to design customized and non-customized treatments optimally.
基金the Xianyang Normal University Foundation for Basic Research(No.06XSYK266)Com~2 MaCKOSEP(R11-1999-054)
文摘A vertex distinguishing equitable total coloring of graph G is a proper total coloring of graph G such that any two distinct vertices＇ coloring sets are not identical and the difference of the elements colored by any two colors is not more than 1. In this paper we shall give vertex distinguishing equitable total chromatic number of join graphs Pn VPn, Cn VCn and prove that they satisfy conjecture 3, namely, the chromatic numbers of vertex distinguishing total and vertex distinguishing equitable total are the same for join graphs Pn V Pn and Cn ∨ Cn.
