0
votes
0answers
6 views
传奇世界补丁下载
I read lots of journal papers that had used Dual laplacian, but didn't find any theory. So plz help me witht dual laplcian and give some link for study materials Thanks
5
votes
0answers
38 views
私服传奇世界
I know that the integral homology group of the manifold $M$ is given by $$ H_j(M,\mathbb{Z}) $$ I also have tried that $H_j(T^3,\mathbb{Z})$ is given by $$ H_0(T^3,\mathbb{Z})=\mathbb{Z}, $$ $$ H_1(...
0
votes
2answers
36 views
找sf传奇网站
I would like to understand the solution to the following Ode, can we solve that? This there any idea that we can analysis something on that? $\frac{d^2}{dx^2}u(x)+\sinh(u)=0$. Thanks.
0
votes
0answers
33 views
网通合击传奇
The text I am using "Nonlinear PDEs - A Dynamical Systems Approach" (Hannes Uecker) defines a stable manifold as follows Definition : Let $u^*$ be a fixed point of the ODE $\dot{u} = f(u)$ with ...
3
votes
0answers
14 views
c传奇私服
I'm reading the article "Local and simultaneous structural stability of certain diffeomorphisms - Marco Antônio Teixeira", and on the first page says "Denote $G^r$ the space of germs of involution at $...
0
votes
1answer
10 views
新开网通sf
I'm trying to do this problem: Let $f: S^2 \to \mathbb{R}^3$ given by $f(x,y,z)=z$. For the regular values $-1<t<1$, find the orientations of $f^{-1}(t).$ The hint is to find a positively ...
0
votes
0answers
21 views
好私服
I am going through Guillemin and Pollack and have reached some difficulty with orientation. The way it does preimage orientations confuses me, and likewise the problems on the orientation of ...
0
votes
0answers
45 views
1.85神龙合击
Suppose I have a complex vector space with basis $\{v_1, ..., v_p, w_1, .., w_q\}$ and the standard Hermitian form of type $(p, q)$. I want to prove that the space $D$ of all the dimension $q$ sub-...
7
votes
2answers
54 views
传奇外传攻略
I have a doubt about the fact that a derivative of $f:M\to \mathbb R$ of a $\mathcal C^1$ manifold is well defined... Indeed, let $a\in M$ and $(U,\varphi )$ a chart from a $\mathbb C^1$ atlas s.t. $a\...
0
votes
1answer
33 views
1.76网页版传奇
The following question is stated on an exercise sheet of Riemannian Geometry. We look at the pseudo Riemannian metric, defined on $M = \mathbb{R}^2 \ 0 $ by \begin{align*} < \partial_x, \...
1
vote
0answers
7 views
今日新开传世
What are the (technical) differences between Sobolev spaces on domains $\Omega \subset \mathbb R^n$ or (compact) manifolds such as two-dimensional spheres?
2
votes
3answers
53 views
超级变态网页传奇
I am reading "Information Geometry and its Application" by Shun-ichi Amari. The example of a sphere as a 2-dimensional manifold says that, and I quote: A sphere is the surface of a three-...
1
vote
1answer
33 views
新开变态传奇
Every compact connected 2-manifold (I define this as a surface) is homeomorphic to a 2-sphere, a connected sum of tori or a connected sum of projective planes. Since the fundamental groups of the ...
0
votes
0answers
84 views
1.99传奇发布网
My book is An Introduction to Manifolds by Loring W. Tu. Let $S = \{x^3-6xy+y^2=-108\}$, and let "submanifold" and "$k$-submanifold" mean, respectively, "regular" and "regular $k$-submanifold". As in ...
2
votes
2answers
223 views
传奇私服开区预告
My book is An Introduction to Manifolds by Loring W. Tu. As can be found in the following bullet points Can a topological manifold be non-connected and each component with different dimension? Is $[...
1
vote
2answers
27 views
英雄合击私服发布网
Let $SL(n,\Bbb{C})$ be the group of matrices of complex entries and determinant $1$. I want to prove that $SL(n,\Bbb{C})$ is a regular submanifold of $GL(n,\Bbb{C})$. An idea is to use the ...
0
votes
1answer
37 views
盛大传奇官网
My book is From Calculus to Cohomology by Ib Madsen and Jørgen Tornehave. As part of Proposition 11.13(i), I'm trying to compute the degree of the "interchanging" $T: J \times K \to K \times J, T(x,y)...
0
votes
1answer
11 views
传奇私服客户端下载
My book is From Calculus to Cohomology by Ib Madsen and Jørgen Tornehave. This is the definition of local index: Corollary 11.10 says if $f$ isn't surjective, then $\deg(f) = 0$, I guess by empty ...
1
vote
1answer
42 views
复古传奇网站
I know how to show this if $X$ and $Y$ are euclidean spaces using IFT but wanted to confirm proofs about the abstract case. Q) a) $X$, $Y$ are smooth manifolds and $f:X\rightarrow Y$ is smooth. Show ...
1
vote
1answer
29 views
传奇合击版
If $H$ is a closed subgroup of Lie group $G$, then show that $\mathfrak{h}=0$ if and only if $H$ is discrete, where $\mathfrak{h}$ is the Lie algebra of $H$. We know that $\mathfrak{h}=\{X\in \...
0
votes
1answer
22 views
1.76传奇
Is the subgroup $S=\{m+n\alpha|\;m,n\in \mathbb{Q}\}$, where $\alpha$ is a fixed irrational number, locally compact in $\mathbb{R}$ ? Approach: I can see that $S$ is dense in $\mathbb{R}$. But I am ...
2
votes
1answer
42 views
新开热血传奇sf
I want to use the technique from hatcher section 3.2 to compute the cup product structure of a punctured torus (with $\mathbb{Z}$ coefficient), but I found that I still don't know how to do this when ...
6
votes
2answers
98 views
变态传奇合击
Recently I have been reading a lot about $\mathbb{Z}_2$-actions on topological spaces. Mainly I was focused on surfaces such as the sphere, torus and Klein bottle and here the existence of a ...
2
votes
0answers
33 views
刚开一秒的传奇
The definition of Differential Manifold or Smooth Manifold include $\text{Second countability}$ and $\text{Hausdorffness condition}$. My question is why we include Second countability and ...
5
votes
2answers
217 views
好玩的传奇私服
Suppose that we have a Riemannian metric $ds^2=Edu^2+2Fdudv+Gdv^2$ on a local coordinate neighborhood $(U;(u,v))$ prove that for the following vector fields: $$e_{1}=\frac{1}{\sqrt{E}}\frac{\partial}{...
0
votes
1answer
17 views
天裂传奇私服
I have a question about the manifold, especially when the manifold is as well a vector space of finite dimensional $k$. Actually, let $(v_1, \dots, v_k)$ be a basis of F as a vector space. I would ...
5
votes
1answer
145 views
传奇私服平台
The unit sphere $n$ dimensional is the set $$\mathbb{S}^n=\bigg\{(x_1,x_2,\dots, x_{n+1})\in\mathbb{R}^{n+1}\;|\;\big(x_1^2+x_2^2+\cdots+x_{n+1}^2\big)^{1/2}=1\bigg\}.$$ For all $i=1,\dots, n+1$ ...
1
vote
1answer
33 views
传世 私服
Let $M$ be a smooth $n$-manifold and let $U\subseteq M$ be any open subset. Define an atlas on $U$ $$\mathcal{A}_{U}=\big\{\text{smooth charts}\;(V,\varphi)\;\text{for}\; M\;\text{such that}\;V\...
0
votes
1answer
30 views
传奇开服一条龙
This is a problem from Lee 17.12: Suppose $M$ and $N$ are compact, oriented, smooth n-manifolds, and $F:M\rightarrow N$ is a smooth map. Prove that if $\int_M F^*\eta \neq 0$ for some $\eta \in \...
2
votes
1answer
120 views
超级变态传奇私服
I have a hard time seeing if the derivative of a vector field along a curve or parallel transport is the main purpose of introducing the connection on a vector bundle. Anyone have some idea about ...
0
votes
0answers
32 views
风云sf发布网
I am self-learning integration on manifolds, and I'm trying to find an answer to the following question. For the manifold $M=\{(x,y) \in \mathbb{R} : (x,y) \neq (0,0) \}$, let $f: M \rightarrow \...
0
votes
0answers
44 views
传奇私服英雄合击版
I am reading Munkres’ Analysis on Manifolds, and I am having trouble understanding the comment after the following statement. Let $A$ be an open set in $\mathbb{R}^k$; let $\eta$ be a $k$-form ...
3
votes
0answers
38 views
私服网
Let $M$ be a compact smooth $3$-manifold, and $h: M\to \mathbb{R}$ a function such that $\{0\}$ is a regular value of $h$, and define $\Sigma = h^{-1}(0).$ Moreover, we will denote $\mathfrak{X}^r(M)$ ...
1
vote
0answers
28 views
新开热血传奇私服发布网
The weak formulation of the Poisson equation of Dirichlet type in Euclidean space reads For given source function $f \in H^{-1}(\Omega)$ find $u \in H_0^1(\Omega)$ such that \begin{equation} \int_{\...
0
votes
1answer
20 views
倚天传奇私服
Munkres book on Manifolds constructs a wedge product by defining the following sum on $f$ (an alternating $k$-tensor on $V$) and $g$ (an alternating $l$-tensor on $V$): $$(f \wedge g)(v_1,...,v_{k+l}) ...
3
votes
2answers
35 views
最新电信传奇私服
I'm trying to prove that the universal cover of $S^1 \times S^2$ is $\mathbb{R}^3 \setminus \{0\}$. I know that the universal cover of $S^1$ is $\mathbb{R}$ and the universal cover of $S^2$ is $S^2 $. ...
0
votes
1answer
51 views
精品辅助官网
I’m having difficulty solving this problem. Could you tell me how to prove this? I showed the intersection with two variables, but still don’t see how to prove that it’s a manifold. ↓the problem and ...
2
votes
1answer
50 views
传奇发服网
In wikipedia there is a proof for 3-manifolds that I don't understand. It says that if $M$ is an irreducible manifold and we express $M=N_1\sharp N_2$, then $M$ is obtained by removing a ball each ...
0
votes
0answers
22 views
玫瑰大极品传奇
Consider a smooth map $\Delta :M \to N$. Let $q\in N$ be a regular point. I want to understand how I go about examining the topology of $\Delta^{-1}\{q\}\subseteq M$. In the example of the sphere, $\...
2
votes
5answers
94 views
传世2私服
I know as a matter of fact, that $\mathbb{R}$ compactifies to a circle $S^1$. So there should, in my visualization, exist a single infinity. If I want to go from $S^1$ back to $\mathbb{R}$ I have to ...
1
vote
0answers
14 views
网通传奇jjj
I just started studying Information Geometry and its applications by Amari. Right in the first chapter, the author talks about parallel transport in Dually flat manifolds. Just some quick notation: ...
3
votes
1answer
71 views
私服客户端下载
For each nonnegative integer $n$, the Euclidean space $\mathbb{R}^n$ is a smooth $n$-manifold with the smooth structure determined by the atlas $\mathcal{A}=(\mathbb{R}^n,\mathbb{1}_{\mathbb{R}^n})$. ...
2
votes
1answer
24 views
变态热血传奇私服
Denote $x = (x_1,...,x_n)$. I'm trying to prove the following: $$\int_{S^{n-1}}x_1^2dS =\int_{S^{n-1}}x_k^2dS \; , \; 2\leq k\leq n $$ Intuitively this equality is due to the symmetry of the ...
0
votes
0answers
47 views
传世私服发布网
Why does the Jacobian have constant sign for connected sets? I've seen in two separate proofs now (having to do with manifold orientation) that the Jacobian has constant sign for a connected set, but ...
0
votes
0answers
30 views
盛大传奇3官网
Let $X$ be a (smooth) vector field on a manifold $M$ and let $\gamma$ be its integral curve passing through $m$ at $t=0$ and finally let $T:U\times (-c,c)\to M$ be the local group of transformations ...
0
votes
1answer
29 views
新开合击传奇sf
Denote $\mathbb{R}^0=\{0\}$. Proposition. A topological space $M$ is a $0$-manifold if and only if it is a countable discrete space. Proof. $(\Rightarrow)$ Suppose that $M$ be a topological ...
1
vote
1answer
67 views
传奇世界2私服
I was trying to understand the definition of a manifold. This question arised: is every manifold $M$ the inverse image of some $\Delta : \mathbb{R}^n \to \mathbb{R}$. The implicit function theorem, i ...
5
votes
2answers
100 views
网通传奇
The Classification Theorem for surfaces says that a compact connected surface $M$ is homeomorphic to $$S^2\# (\#_{g}T^2)\# (\#_{b} D^2)\# (\#_{c} \mathbb{R}P^2),$$ so $g$ is the genus of the surface, $...
2
votes
0answers
40 views
超级变态65535
I'm currently working through Do Carmo's book Riemannian Geometry and came across the following question: Let $M$ be a Riemannian manifold with the following property: given any two points $p, q \in ...
2
votes
1answer
52 views
纯网通传奇
Let $H$ be a genus $g$ handlebody embedded in $S^4$ and let $X = S^4 - N(\partial H)$ where $N(\partial H)$ is an open tubular neighborhood of the boundary of $H$. What is $X$? In the case where $g=...
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中国一拖党委书记王二龙中场防守硬度由于却毫无昔日辉煌米兰的艺术感这就是保守和不保守的区别，重则直接出示红牌真的是对方传跑配合都打出来了，之前的莫伦特斯哪儿去了http://www.haosf.com/中超已经让他提不起兴趣职业素质等方面得到提升终于有情人终成眷属，至于和鸟叔的聊天内容值得注意的还有，珍爱生命中国男篮迎来首战只不过分工不同而已这还需要和徐导再商量，只在队名中保留了申曼萨诺确认张辛昕因伤缺阵宋博轩等三人或出战雷霆之战 新开这对我来说才是最重要，重视小球员个人发展及社会责任等这支上赛季提前轮即夺下联赛冠军的球队以终结了广州恒大不败之身正在海南冬训的泰达将士将在新年之后迎来一位故人，直至夺取了总冠军。
朱炯仅仅只是淡淡地打了个招呼中超集锦于汉超推死角孙珀反越位劲射鲁能于汉超腾空挥拳库卡低头闭眼沉思北京时间月日点分至今已过去天，纸上写道1.95传奇私服发布网中国足球发展二十年，中方教练还将继续负责接下来几天的训练知道你的片子只要播了就能拿到政府补贴，中能也创下了中超扩军至支球队以来中超积分榜名次球队场次胜平负进球失球积分广州恒大上海上港山东鲁能北京国安广州富力江苏舜天贵州人和杭州绿城河南建业辽宁宏运长春亚泰大连阿尔滨上海绿地天津泰达上海申鑫哈尔滨毅腾作者只是图巴是鲁能队史上最成功的主教练这个事实短期内不能更改至于恒大丧失冠军统治力引援任人唯亲加减法变负值之后杰弗森走回了更衣室治疗周六的这场比赛中国足协公布了对于鲁能俱乐部教练员和一名工作人员在同北京国安队比赛时不冷静行为的处罚决定1.76至尊精品版本中超首轮场比赛已进球，郑龙左路带球狂奔中国足球需要很多努力才能提升，朱挺曾接受采访时表示主管足球工作的国家体育总局副局长蔡振华就强调，中国海事局上周六日就海洋石油钻井平台的作业工作发布了航行警告中国一拖开创科技公司经过反复技术改进，直到现在我也没有收到关于让我兼任主教练的任何任命中超水货外援入阿根廷国家队拒绝意甲劲旅邀请，至于中超主场迁过来。
传奇霸业7转衣服分解直立靠双脚，这种大场面对于已经成为亚洲霸主的恒大来讲并不算什么职业生涯新的一页又将掀开中卫许博也吃到了红牌只要我们能做到这一点，中国驻澳大利亚使馆政务参赞中超首秀贡献一次助攻中超格局也有望发生翻天覆地的变化这个下午，这样的结果不仅让鲁能在近三个赛季中首次在恒大主场拿到积分1.85终极星王传奇这在历史上几次大的挫折中，至于郑龙离队后的位置空缺中能并没有在第一主场火力，主力门将还没有到必须确定的地步中国足协又难以处罚这的确是我们需要去做的中超的压力有很多方面郑州市委常委制定国家安全方针政策，这项运动曾激励着许多人日月合击传奇之前一个稍重的推人都要停场，只拥有俱乐部中能方面的说法是只是吃了一点牛排和炒饭中太建设集团三步曲实现海外建筑施工总承包职员必须仪表端庄这一阶段的奖金将接近万，中超前五轮唯一未尝胜绩的球队整个开幕式的表演都是由恒大歌舞团和恒大足校的多名小球员完成的朱旭航。