Objective To summarize clinical experience for treating anterior mitral leaflet prolapse with an artificial chordal loop. Methods From January 2008 to August 2009,pre-measured ePTFE loops were used to treat anterior l...Objective To summarize clinical experience for treating anterior mitral leaflet prolapse with an artificial chordal loop. Methods From January 2008 to August 2009,pre-measured ePTFE loops were used to treat anterior leaflet prolapse in 8 patients,5 males and 3 females, aged from 28 to 68 (average 56.0±8.9) years. The heart展开更多
The minimum number of colors needed to properly color the vertices and edges of a graph G is called the total chromatic number of G and denoted by χ'' (G). It is shown that if a planar graph G has maximum deg...The minimum number of colors needed to properly color the vertices and edges of a graph G is called the total chromatic number of G and denoted by χ'' (G). It is shown that if a planar graph G has maximum degree Δ≥9, then χ'' (G) = Δ + 1. In this paper, we prove that if G is a planar graph with maximum degree 8 and without intersecting chordal 4-cycles, then χ ''(G) = 9.展开更多
Background Repair of anterior mitral leaflet （AML） prolapse is still a technical challenge for cardiac surgeons. It is an important issue to find a way to repair the AML prolapse with a reliable and reproducible tec...Background Repair of anterior mitral leaflet （AML） prolapse is still a technical challenge for cardiac surgeons. It is an important issue to find a way to repair the AML prolapse with a reliable and reproducible technique.Methods Between January 2002 and June 2009, the operation of chordal transfer based on the ＂edge-to-edge＂technique was performed in 21 patients with serious mitral valve regurgitation because of prolapse of the anterior leaflet.After the operation, echocardiography was performed in each patient before discharge and at the time of follow-up.Results All patients survived the operation. One patient required mitral valve replacement because of anterior leaflet perforation 3 days after the operation. The other patients were free from reoperation. At the time of follow-up, all these patients were in New York Heart Association （NYHA） functional class I. In all these patients, pre-discharge and follow-up echocardiography showed neither stenosis nor significant regurgitation of the mitral valve： the cross-sectional area of the mitral valve was 3.3-4.8 cm2 （mean （3.78：±0.52） cm2）, the mean regurgitation area was （0.45：±0.22） cm2. At the same time, both dimension of left atrium and left ventricle reduced significantly （left atrium diameter： pre-operation （48.26±11.12） mm, post-operation （37.57±9.56） mm, P 〈0.05; the end-diastolic diameter of the left ventricle：pre-operation （61.43±8.24） mm, post-operation （42.35±10.79） mm, P〈0.01）.Conclusion ＂Edge-to-edge＂ chordal transfer technique is a simple, reliable, and reproducible technique that can provide good results for repair of anterior leaflet prolapse of mitral valve.展开更多
A k-total-coloring of a graph G is a coloring of vertices and edges of G using k colors such that no two adjacent or incident elements receive the same color.In this paper,it is proved that if G is a planar graph with...A k-total-coloring of a graph G is a coloring of vertices and edges of G using k colors such that no two adjacent or incident elements receive the same color.In this paper,it is proved that if G is a planar graph with Δ（G） ≥ 7 and without chordal 7-cycles,then G has a（Δ（G） ＋ 1）-total-coloring.展开更多
In this paper, we study the notion of chordality and cycles in clutters from a commutative algebraic point of view. The corresponding concept of chordality in commutative algebra is having a linear resolution. We main...In this paper, we study the notion of chordality and cycles in clutters from a commutative algebraic point of view. The corresponding concept of chordality in commutative algebra is having a linear resolution. We mainly consider the generalization of chordality proposed by Bigdeli et al. in 2017 and the concept of cycles introduced by Can- non and Faridi in 2013, and study their interrelations and algebraic interpretations. In particular, we investigate the relationship between chordality and having linear quotients in some classes of clutters. Also, we show that if e is a clutter such that （ ） is a vertex decomposable simplicial complex or I（ ） is squarefree stable, then is chordal.展开更多
In a matrix-completion problem the aim is to specify the missing entries of a matrix in order to produce a matrix with particular properties. In this paper we survey results concerning matrix-completion problems where...In a matrix-completion problem the aim is to specify the missing entries of a matrix in order to produce a matrix with particular properties. In this paper we survey results concerning matrix-completion problems where we look for completions of various types for partial matrices supported on a given pattern. We see that the existence of completions of the required type often depends on the chordal properties of graphs associated with the pattern.展开更多
文摘Objective To summarize clinical experience for treating anterior mitral leaflet prolapse with an artificial chordal loop. Methods From January 2008 to August 2009,pre-measured ePTFE loops were used to treat anterior leaflet prolapse in 8 patients,5 males and 3 females, aged from 28 to 68 (average 56.0±8.9) years. The heart
基金supported by Natural Science Foundation of Shandong Province (Grant No. ZR2009AM009)Scientific Research Foundation for the Excellent Middle-Aged and Youth Scientists of Shandong Province (Grant No. BS2012SF016)National Natural Science Foundation of China (Grant Nos.11001055 and 11101243)
文摘The minimum number of colors needed to properly color the vertices and edges of a graph G is called the total chromatic number of G and denoted by χ'' (G). It is shown that if a planar graph G has maximum degree Δ≥9, then χ'' (G) = Δ + 1. In this paper, we prove that if G is a planar graph with maximum degree 8 and without intersecting chordal 4-cycles, then χ ''(G) = 9.
文摘Background Repair of anterior mitral leaflet （AML） prolapse is still a technical challenge for cardiac surgeons. It is an important issue to find a way to repair the AML prolapse with a reliable and reproducible technique.Methods Between January 2002 and June 2009, the operation of chordal transfer based on the ＂edge-to-edge＂technique was performed in 21 patients with serious mitral valve regurgitation because of prolapse of the anterior leaflet.After the operation, echocardiography was performed in each patient before discharge and at the time of follow-up.Results All patients survived the operation. One patient required mitral valve replacement because of anterior leaflet perforation 3 days after the operation. The other patients were free from reoperation. At the time of follow-up, all these patients were in New York Heart Association （NYHA） functional class I. In all these patients, pre-discharge and follow-up echocardiography showed neither stenosis nor significant regurgitation of the mitral valve： the cross-sectional area of the mitral valve was 3.3-4.8 cm2 （mean （3.78：±0.52） cm2）, the mean regurgitation area was （0.45：±0.22） cm2. At the same time, both dimension of left atrium and left ventricle reduced significantly （left atrium diameter： pre-operation （48.26±11.12） mm, post-operation （37.57±9.56） mm, P 〈0.05; the end-diastolic diameter of the left ventricle：pre-operation （61.43±8.24） mm, post-operation （42.35±10.79） mm, P〈0.01）.Conclusion ＂Edge-to-edge＂ chordal transfer technique is a simple, reliable, and reproducible technique that can provide good results for repair of anterior leaflet prolapse of mitral valve.
基金Supported by National Natural Science Foundation of China(Grant No.11271006)
文摘A k-total-coloring of a graph G is a coloring of vertices and edges of G using k colors such that no two adjacent or incident elements receive the same color.In this paper,it is proved that if G is a planar graph with Δ（G） ≥ 7 and without chordal 7-cycles,then G has a（Δ（G） ＋ 1）-total-coloring.
文摘In this paper, we study the notion of chordality and cycles in clutters from a commutative algebraic point of view. The corresponding concept of chordality in commutative algebra is having a linear resolution. We mainly consider the generalization of chordality proposed by Bigdeli et al. in 2017 and the concept of cycles introduced by Can- non and Faridi in 2013, and study their interrelations and algebraic interpretations. In particular, we investigate the relationship between chordality and having linear quotients in some classes of clutters. Also, we show that if e is a clutter such that （ ） is a vertex decomposable simplicial complex or I（ ） is squarefree stable, then is chordal.
文摘In a matrix-completion problem the aim is to specify the missing entries of a matrix in order to produce a matrix with particular properties. In this paper we survey results concerning matrix-completion problems where we look for completions of various types for partial matrices supported on a given pattern. We see that the existence of completions of the required type often depends on the chordal properties of graphs associated with the pattern.
