Pub Date : 2019-02-06DOI: 10.15673/tmgc.v12i1.1377
S. Das, M. Cenanovic, Junfeng Zhang
In this note, we derive an approximation for the mean curvature normal vector on vertices of triangulated surface meshes from the Young-Laplace equation and the force balance principle. We then demonstrate that the approximation expression from our physics-based derivation is equivalent to the discrete Laplace-Beltrami operator approach in the literature. This work, in addition to providing an alternative expression to calculate the mean curvature normal vector, can be further extended to other mesh structures, including non-triangular and heterogeneous meshes.
{"title":"A Physics-Based Estimation of Mean Curvature Normal Vector for Triangulated Surfaces","authors":"S. Das, M. Cenanovic, Junfeng Zhang","doi":"10.15673/tmgc.v12i1.1377","DOIUrl":"https://doi.org/10.15673/tmgc.v12i1.1377","url":null,"abstract":"In this note, we derive an approximation for the mean curvature normal vector on vertices of triangulated surface meshes from the Young-Laplace equation and the force balance principle. We then demonstrate that the approximation expression from our physics-based derivation is equivalent to the discrete Laplace-Beltrami operator approach in the literature. This work, in addition to providing an alternative expression to calculate the mean curvature normal vector, can be further extended to other mesh structures, including non-triangular and heterogeneous meshes.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"113 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72623834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-21DOI: 10.15673/TMGC.V11I3.1202
Koji Matsumoto
In 1994 N.~Papaghiuc introduced the notion of semi-slant submanifold in a Hermitian manifold which is a generalization of $CR$- and slant-submanifolds, cite{MR0353212}, cite{MR760392}. In particular, he considered this submanifold in Kaehlerian manifolds, cite{MR1328947}. Then, in 2007, V.~A.~Khan and M.~A.~Khan considered this submanifold in a nearly Kaehler manifold and obtained interesting results, cite{MR2364904}. Recently, we considered semi-slant submanifolds in a locally conformal Kaehler manifold and we gave a necessary and sufficient conditions of the two distributions (holomorphic and slant) be integrable. Moreover, we considered these submanifolds in a locally conformal Kaehler space form. In the last paper, we defined $2$-kind warped product semi-slant submanifolds in almost hermitian manifolds and studied the first kind submanifold in a locally conformal Kaehler manifold. Using Gauss equation, we derived some properties of this submanifold in an locally conformal Kaehler space form, cite{MR2077697}, cite{MR3728534}. In this paper, we consider same submanifold with the parallel second fundamental form in a locally conformal Kaehler space form. Using Codazzi equation, we partially determine the tensor field $P$ which defined in~eqref{1.3}, see Theorem~ref{th4.1}. Finally, we show that, in the first type warped product semi-slant submanifold in a locally conformal space form, if it is normally flat, then the shape operators $A$ satisfy some special equations, see Theorem~ref{th5.2}.
1994年N. Papaghiuc在厄米流形中引入了半倾斜子流形的概念，它是$CR$和倾斜子流形的推广，cite{MR0353212}, cite{MR760392}。特别地，他考虑了Kaehlerian流形中的子流形cite{MR1328947}。然后，在2007年，V. a . Khan和M. a . Khan在一个近Kaehler流形中考虑了这个子流形，得到了有趣的结果，cite{MR2364904}。本文研究了局部共形Kaehler流形中的半倾斜子流形，给出了两种分布(全纯分布和倾斜分布)可积的充分必要条件。此外，我们考虑了这些子流形的局部共形Kaehler空间形式。在最后一篇文章中，我们定义了几乎厄米流形中的$2$ -类翘曲积半倾斜子流形，并研究了局部共形Kaehler流形中的第一类子流形。利用高斯方程，我们得到了该子流形在局部共形Kaehler空间形式下的一些性质，cite{MR2077697}, cite{MR3728534}。在局部共形Kaehler空间中，考虑具有平行第二基本形式的同一子流形。利用Codazzi方程，我们部分确定了在eqref{1.3}中定义的张量场$P$，见定理ref{th4.1}。最后，我们证明了在局部共形空间形式的第一类翘曲积半斜子流形中，如果它通常是平坦的，那么形状算子$A$满足一些特殊方程，见定理ref{th5.2}。
{"title":"Warped product semi-slant submanifolds in locally conformal Kaehler manifolds II","authors":"Koji Matsumoto","doi":"10.15673/TMGC.V11I3.1202","DOIUrl":"https://doi.org/10.15673/TMGC.V11I3.1202","url":null,"abstract":"In 1994 N.~Papaghiuc introduced the notion of semi-slant submanifold in a Hermitian manifold which is a generalization of $CR$- and slant-submanifolds, cite{MR0353212}, cite{MR760392}. \u0000In particular, he considered this submanifold in Kaehlerian manifolds, cite{MR1328947}. \u0000Then, in 2007, V.~A.~Khan and M.~A.~Khan considered this submanifold in a nearly Kaehler manifold and obtained interesting results, cite{MR2364904}. \u0000Recently, we considered semi-slant submanifolds in a locally conformal Kaehler manifold and we gave a necessary and sufficient conditions of the two distributions (holomorphic and slant) be integrable. \u0000Moreover, we considered these submanifolds in a locally conformal Kaehler space form. \u0000In the last paper, we defined $2$-kind warped product semi-slant submanifolds in almost hermitian manifolds and studied the first kind submanifold in a locally conformal Kaehler manifold. \u0000Using Gauss equation, we derived some properties of this submanifold in an locally conformal Kaehler space form, cite{MR2077697}, cite{MR3728534}. \u0000In this paper, we consider same submanifold with the parallel second fundamental form in a locally conformal Kaehler space form. \u0000Using Codazzi equation, we partially determine the tensor field $P$ which defined in~eqref{1.3}, see Theorem~ref{th4.1}. \u0000Finally, we show that, in the first type warped product semi-slant submanifold in a locally conformal space form, if it is normally flat, then the shape operators $A$ \u0000satisfy some special equations, see Theorem~ref{th5.2}.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89322273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-21DOI: 10.15673/TMGC.V11I3.1200
Віталій Станіславович Шпаківський
Для n-вимірної (2 ⩽ n < 1) комутативної асоціативної алгебри
{"title":"Про моногенні функції на розширеннях комутативної алгебри","authors":"Віталій Станіславович Шпаківський","doi":"10.15673/TMGC.V11I3.1200","DOIUrl":"https://doi.org/10.15673/TMGC.V11I3.1200","url":null,"abstract":"Для n-вимірної (2 ⩽ n < 1) комутативної асоціативної алгебри","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"109 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76007567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-21DOI: 10.15673/TMGC.V11I3.1201
Любовь Михайловна Пиджакова, Александр Михайлович Шелехов
Как известно, функция двух переменных z=f(x, y) задает на плоскости (x, y) в окрестности регулярной точки некоторую три-ткань, образованную слоениями x=const, y=const и f(x, y)=const. Три-ткань называется регулярной, если она эквивалентна (локально диффеоморфна) три-ткани, образованной тремя семействами параллельных прямых. В этом случае уравнение ткани имеет вид $z=fleft(alpha(x)+beta(y)right)$. В одной из работ авторов этой статьи были найдены все регулярные три-ткани, определяемые некоторыми известными уравнениями в частных производных, в частности, определяемые гармоническими функциями. В настоящей работе результаты обобщаются для плюригармонических функций вида u=f(x_1, ...., x_r, y_1, ... , y_r). Во-первых, функция такого вида определяет на многообразии размерности 2r (2r + 1)-ткань, образованную слоениями коразмерности 1 вида x_i=const, y_i=const, i=1, 2, ..., r и u=const. (2r + 1)-ткань называется регулярной, если в некоторых локальных координатах ее уравнение может быть записано в виде $$ u=fleft(varphi_1(x_1)+ldots + varphi_1(x_r)+psi_1(y_1)+ldots +psi_r( y_r)right). $$ В этой статье мы находим все плюригармонические функции, задающие регулярные (2r + 1)-ткани (теорема 1). С другой стороны, каждая плюригармоническая функция u=f(x_1,..., x_r, y_1, ... , y_r) определяет на 2r-мерном многообразии три-ткань W(r,r,2r-1), образованную двумя r-мерными слоениями x_i=const и y_i=const и слоением u=const коразмерности 1. Эта ткань называется регулярной, если в некоторых локальных координатах ее уравнение может быть записано в виде $$ u=fleft(varphi(x_1, x_2,ldots, x_r)+psi(y_1, y_2,ldots, y_r)right). $$ В этой работе найдены все плюригармонические функции, определяющие регулярные три-ткани W(r,r,2r-1) (теорема 2)
{"title":"О регулярных тканях, определенных плюригармоническими функциями","authors":"Любовь Михайловна Пиджакова, Александр Михайлович Шелехов","doi":"10.15673/TMGC.V11I3.1201","DOIUrl":"https://doi.org/10.15673/TMGC.V11I3.1201","url":null,"abstract":"Как известно, функция двух переменных z=f(x, y) задает на плоскости (x, y) в окрестности регулярной точки некоторую три-ткань, образованную слоениями x=const, y=const и f(x, y)=const. \u0000Три-ткань называется регулярной, если она эквивалентна (локально диффеоморфна) три-ткани, образованной тремя семействами параллельных прямых. \u0000В этом случае уравнение ткани имеет вид $z=fleft(alpha(x)+beta(y)right)$. \u0000В одной из работ авторов этой статьи были найдены все регулярные три-ткани, определяемые некоторыми известными уравнениями в частных производных, в частности, определяемые гармоническими функциями. \u0000В настоящей работе результаты обобщаются для плюригармонических функций вида \u0000u=f(x_1, ...., x_r, y_1, ... , y_r). \u0000Во-первых, функция такого вида определяет на многообразии размерности 2r (2r + 1)-ткань, образованную слоениями коразмерности 1 вида x_i=const, y_i=const, i=1, 2, ..., r и u=const. \u0000(2r + 1)-ткань называется регулярной, если в некоторых локальных координатах ее уравнение может быть записано в виде \u0000$$ \u0000u=fleft(varphi_1(x_1)+ldots + varphi_1(x_r)+psi_1(y_1)+ldots +psi_r( y_r)right). \u0000$$ \u0000В этой статье мы находим все плюригармонические функции, задающие регулярные (2r + 1)-ткани (теорема 1). \u0000С другой стороны, каждая плюригармоническая функция u=f(x_1,..., x_r, y_1, ... , y_r) \u0000определяет на 2r-мерном многообразии три-ткань W(r,r,2r-1), образованную двумя r-мерными слоениями x_i=const и y_i=const и слоением u=const коразмерности 1. \u0000Эта ткань называется регулярной, если в некоторых локальных координатах ее уравнение может быть записано в виде \u0000$$ \u0000u=fleft(varphi(x_1, x_2,ldots, x_r)+psi(y_1, y_2,ldots, y_r)right). \u0000$$ \u0000В этой работе найдены все плюригармонические функции, определяющие регулярные три-ткани W(r,r,2r-1) (теорема 2)","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90265931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-11DOI: 10.15673/tmgc.v12i3.1488
I. Kuznietsova, S. Maksymenko
Let $B$ be a M"obius band and $f:B to mathbb{R}$ be a Morse map taking a constant value on $partial B$, and $mathcal{S}(f,partial B)$ be the group of diffeomorphisms $h$ of $B$ fixed on $partial B$ and preserving $f$ in the sense that $fcirc h = f$. Under certain assumptions on $f$ we compute the group $pi_0mathcal{S}(f,partial B)$ of isotopy classes of such diffeomorphisms. In fact, those computations hold for functions $f:Btomathbb{R}$ whose germs at critical points are smoothly equivalent to homogeneous polynomials $mathbb{R}^2tomathbb{R}$ without multiple factors. Together with previous results of the second author this allows to compute similar groups for certain classes of smooth functions $f:Ntomathbb{R}$ on non-orientable compact surfaces $N$.
设$B$为Möbius带，$f:B to mathbb{R}$为在$partial B$上取常数值的莫尔斯映射，$mathcal{S}(f,partial B)$为$B$的差同群$h$固定在$partial B$上，并保留$f$在$fcirc h = f$的意义上。在$f$的某些假设下，我们计算了这类微分同形的同位素类的群$pi_0mathcal{S}(f,partial B)$。事实上，这些计算适用于函数$f:Btomathbb{R}$，其在临界点处的细菌光滑等效于齐次多项式$mathbb{R}^2tomathbb{R}$，没有多因子。结合第二作者之前的结果，这允许计算某些类光滑函数$f:Ntomathbb{R}$在不可定向紧致曲面$N$上的相似群。
{"title":"Homotopy properties of smooth functions on the Möbius band","authors":"I. Kuznietsova, S. Maksymenko","doi":"10.15673/tmgc.v12i3.1488","DOIUrl":"https://doi.org/10.15673/tmgc.v12i3.1488","url":null,"abstract":"Let $B$ be a M\"obius band and $f:B to mathbb{R}$ be a Morse map taking a constant value on $partial B$, and $mathcal{S}(f,partial B)$ be the group of diffeomorphisms $h$ of $B$ fixed on $partial B$ and preserving $f$ in the sense that $fcirc h = f$. \u0000Under certain assumptions on $f$ we compute the group $pi_0mathcal{S}(f,partial B)$ of isotopy classes of such diffeomorphisms. \u0000In fact, those computations hold for functions $f:Btomathbb{R}$ whose germs at critical points are smoothly equivalent to homogeneous polynomials $mathbb{R}^2tomathbb{R}$ without multiple factors. \u0000Together with previous results of the second author this allows to compute similar groups for certain classes of smooth functions $f:Ntomathbb{R}$ on non-orientable compact surfaces $N$.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78620277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-24DOI: 10.15673/tmgc.v12i2.1436
K. Eftekharinasab
Darboux theorem to more general context of Frechet manifolds we face an obstacle: in general vector fields do not have local flows. Recently, Fr'{e}chet geometry has been developed in terms of projective limit of Banach manifolds. In this framework under an appropriate Lipchitz condition The Darboux theorem asserts that a symplectic manifold $(M^{2n},omega)$ is locally symplectomorphic to $(R^{2n}, omega_0)$, where $omega_0$ is the standard symplectic form on $R^{2n}$. This theorem was proved by Moser in 1965, the idea of proof, known as the Moser’s trick, works in many situations. The Moser tricks is to construct an appropriate isotopy $ ff_t $ generated by a time-dependent vector field $ X_t $ on $M$ such that $ ff_1^{*} omega = omega_0$. Nevertheless, it was showed by Marsden that Darboux theorem is not valid for weak symplectic Banach manifolds. However, in 1999 Bambusi showed that if we associate to each point of a Banach manifold a suitable Banach space (classifying space) via a given symplectic form then the Moser trick can be applied to obtain the theorem if the classifying space does not depend on the point of the manifold and a suitable smoothness condition holds. If we want to try to generalize the local flows exist and with some restrictive conditions the Darboux theorem was proved by Kumar. In this paper we consider the category of so-called bounded Fr'{e}chet manifolds and prove that in this category vector fields have local flows and following the idea of Bambusi we associate to each point of a manifold a Fr'{e}chet space independent of the choice of the point and with the assumption of bounded smoothness on vector fields we prove the Darboux theorem.
{"title":"On the generalization of the Darboux theorem","authors":"K. Eftekharinasab","doi":"10.15673/tmgc.v12i2.1436","DOIUrl":"https://doi.org/10.15673/tmgc.v12i2.1436","url":null,"abstract":"Darboux theorem to more general context of Frechet manifolds we face an obstacle: in general vector fields do not have local flows. Recently, Fr'{e}chet geometry has been developed in terms of projective limit of Banach manifolds. In this framework under an appropriate Lipchitz condition The Darboux theorem asserts that a symplectic manifold $(M^{2n},omega)$ is locally symplectomorphic to $(R^{2n}, omega_0)$, where $omega_0$ is the standard symplectic form on $R^{2n}$. This theorem was proved by Moser in 1965, the idea of proof, known as the Moser’s trick, works in many situations. The Moser tricks is to construct an appropriate isotopy $ ff_t $ generated by a time-dependent vector field $ X_t $ on $M$ such that $ ff_1^{*} omega = omega_0$. Nevertheless, it was showed by Marsden that Darboux theorem is not valid for weak symplectic Banach manifolds. However, in 1999 Bambusi showed that if we associate to each point of a Banach manifold a suitable Banach space (classifying space) via a given symplectic form then the Moser trick can be applied to obtain the theorem if the classifying space does not depend on the point of the manifold and a suitable smoothness condition holds. \u0000 If we want to try to generalize the local flows exist and with some restrictive conditions the Darboux theorem was proved by Kumar. In this paper we consider the category of so-called bounded Fr'{e}chet manifolds and prove that in this category vector fields have local flows and following the idea of Bambusi we associate to each point of a manifold a Fr'{e}chet space independent of the choice of the point and with the assumption of bounded smoothness on vector fields we prove the Darboux theorem.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"130 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73131705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-15DOI: 10.15673/TMGC.V11I2.1025
Олена В'ячеславівна Ноздрінова, Ольга Віталіївна Починка
In the paper it is proved that any orientable surface admits an orientation-preserving diffeomorphism with one saddle orbit. It distinguishes in principle the considered class of systems from source-sink diffeomorphisms existing only on the sphere. It is shown that diffeomorphisms with one saddle orbit of a positive type on any surface have exactly three node orbits. In addition, all possible types of periodic data for such diffeomorphisms are established. Namely, formulas are found expressing the periods of the sources through the periods of the sink and the saddle.
{"title":"A calculation of periodic data of surface diffeomorphisms with one saddle orbit.","authors":"Олена В'ячеславівна Ноздрінова, Ольга Віталіївна Починка","doi":"10.15673/TMGC.V11I2.1025","DOIUrl":"https://doi.org/10.15673/TMGC.V11I2.1025","url":null,"abstract":"In the paper it is proved that any orientable surface admits an orientation-preserving diffeomorphism with one saddle orbit. It distinguishes in principle the considered class of systems from source-sink diffeomorphisms existing only on the sphere. It is shown that diffeomorphisms with one saddle orbit of a positive type on any surface have exactly three node orbits. In addition, all possible types of periodic data for such diffeomorphisms are established. Namely, formulas are found expressing the periods of the sources through the periods of the sink and the saddle.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78032804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-15DOI: 10.15673/TMGC.V11I2.1026
L. Plachta
We study two measures of nonplanarity of cubic graphs G, the genus γ (G), and the edge deletion number ed(G). For cubic graphs of small orders these parameters are compared with another measure of nonplanarity, the rectilinear crossing number (G). We introduce operations of connected sum, specified for cubic graphs G, and show that under certain conditions the parameters γ(G) and ed(G) are additive (subadditive) with respect to them.The minimal genus graphs (i.e. the cubic graphs of minimum order with given value of genus γ) and the minimal edge deletion graphs (i.e. cubic graphs of minimum order with given value of edge deletion number ed) are introduced and studied. We provide upper bounds for the order of minimal genus and minimal edge deletion graphs.
{"title":"On measures of nonplanarity of cubic graphs","authors":"L. Plachta","doi":"10.15673/TMGC.V11I2.1026","DOIUrl":"https://doi.org/10.15673/TMGC.V11I2.1026","url":null,"abstract":"We study two measures of nonplanarity of cubic graphs G, the genus γ (G), and the edge deletion number ed(G). For cubic graphs of small orders these parameters are compared with another measure of nonplanarity, the rectilinear crossing number (G). We introduce operations of connected sum, specified for cubic graphs G, and show that under certain conditions the parameters γ(G) and ed(G) are additive (subadditive) with respect to them.The minimal genus graphs (i.e. the cubic graphs of minimum order with given value of genus γ) and the minimal edge deletion graphs (i.e. cubic graphs of minimum order with given value of edge deletion number ed) are introduced and studied. We provide upper bounds for the order of minimal genus and minimal edge deletion graphs.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88097561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-15DOI: 10.15673/TMGC.V11I2.1027
V. Lyubashenko
It is proven that Rankin-Cohen brackets form an associativedeformation of the algebra of polynomials whose coeffcients are holomorphicfunctions on the upper half-plane.
证明了Rankin-Cohen括号是系数为上半平面全纯函数的多项式代数的一种关联变形。
{"title":"Moyal and Rankin-Cohen deformations of algebras","authors":"V. Lyubashenko","doi":"10.15673/TMGC.V11I2.1027","DOIUrl":"https://doi.org/10.15673/TMGC.V11I2.1027","url":null,"abstract":"It is proven that Rankin-Cohen brackets form an associativedeformation of the algebra of polynomials whose coeffcients are holomorphicfunctions on the upper half-plane.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77350646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Злата Кибалко, Олександр Олегович Пришляк, Roman Shchurko
We consider optimal Morse flows on closed surfaces. Up to topological trajectory equivalence such flows are determined by marked chord diagrams. We present list all such diagrams for flows on nonorientable surfaces of genus at most 4 and indicate pairs of diagrams corresponding to the flows and their inverses.
{"title":"Trajectory equivalence of optimal Morse flows on closed surfaces","authors":"Злата Кибалко, Олександр Олегович Пришляк, Roman Shchurko","doi":"10.15673/TMGC.V11I1.916","DOIUrl":"https://doi.org/10.15673/TMGC.V11I1.916","url":null,"abstract":"We consider optimal Morse flows on closed surfaces. Up to topological trajectory equivalence such flows are determined by marked chord diagrams. We present list all such diagrams for flows on nonorientable surfaces of genus at most 4 and indicate pairs of diagrams corresponding to the flows and their inverses.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"719 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77795650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：