# All public logs

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Combined display of all available logs of ProofWiki. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).

(newest | oldest) View (newer 50 | older 50) (20 | 50 | 100 | 250 | 500)- 17:05, 10 May 2021 Julius talk contribs created page Definition:Horizontal Vector Field (Created page with "== Definition == Let $M$ be a smooth manifold. Let $x \in M$ be a base point. Let $H_x$ be the Definition:Horizon...")
- 16:44, 10 May 2021 Julius talk contribs created page Definition:Horizontal Tangent Space (Created page with "== Definition == Let $M, \tilde M$ be smooth manifolds. Let $\tilde g$ be a Riemannian metric on $\tilde M$....")
- 16:37, 10 May 2021 Julius talk contribs created page Definition:Vertical Tangent Space (Created page with "== Definition == Let $M, \tilde M$ be smooth manifolds. Let $\tilde g$ be a Riemannian metric on $\tilde M$....")
- 20:36, 9 May 2021 Julius talk contribs created page Definition:Product Riemannian Metric (Created page with "== Definition == Let $\struct {M_1, g_1}$ and $\struct {M_2, g_2}$ be Riemannian manifolds. Let $p \in M$ be a Definition:Base Point|bas...")
- 20:01, 9 May 2021 Julius talk contribs created page Mixed Partial Derivative of Heaviside Step Function (Created page with "== Theorem == Let $\tuple {x, y} \stackrel u {\longrightarrow} \map u {x, y}: \R^2 \to \R$ be the Heaviside step function...")
- 21:42, 6 May 2021 Julius talk contribs created page Definition:Smooth Local Parametrization (Created page with "== Definition == Let $\tilde M$ be a smooth manifold. Let $M \subseteq \tilde M$ be a submanifold. Let $U \subsete...")
- 21:21, 6 May 2021 Julius talk contribs created page Definition:Normal Vector Field along Submanifold (Created page with "== Definition == Let $\struct {\tilde M, \tilde g}$ be a Riemannian manifold. Let $M : M \subseteq \tilde M$ be a Definition:Smooth Mani...")
- 17:05, 5 May 2021 Julius talk contribs created page Definition:Frame Adapted to Submanifold (Created page with "== Definition == Let $\struct {\tilde M, \tilde g}$ be an $m$-dimensional Definition:Riemannian Manifold|Riemannian mani...")
- 16:44, 5 May 2021 Julius talk contribs created page Definition:Riemannian Submanifold (Created page with "== Definition == Let $M$ be an immersed submanifold. Let $g$ be a Definition:Induced Metric on Submanifold|metric induc...")
- 16:39, 5 May 2021 Julius talk contribs created page Definition:Induced Metric on Submanifold (Created page with "== Definition == Let $\struct {\tilde M, \tilde g}$ be a Riemannian manifold. Let $M : M \subseteq \tilde M$ be a Definition:Smooth Mani...")
- 19:19, 4 May 2021 Julius talk contribs created page Definition:Isometric Immersion (Created page with "== Definition == Let $\struct {M, g}$, $\struct {\tilde M, \tilde g}$ be Riemannian manifolds. Let $F : M \to \tilde M$ be an Definition...")
- 19:06, 4 May 2021 Julius talk contribs created page Definition:Metric Induced by Smooth Immersion (Created page with "== Definition == Let $\struct {\tilde M, \tilde g}$ be a Riemannian manifold. Let $F : M \to \tilde M$ be a smooth [...")
- 18:52, 4 May 2021 Julius talk contribs created page Definition:Orthonormal Frame (Created page with "== Definition == Let $M$ be a Riemannian manifold. Let $U \subseteq M$ be an open set. Let $p \in M$ b...")
- 18:28, 4 May 2021 Julius talk contribs created page Definition:Heaviside Step Function/Two Variables (Created page with "== Definition == <onlyinclude> Let $u: \R \to \R$ be the Heaviside step function. Then the '''Heaviside step function of two variables...")
- 17:54, 4 May 2021 Julius talk contribs created page Distributional Partial Derivatives Commute (Created page with "== Theorem == Let $T \in \map {\DD'} {\R^d}$ be a distribution. Then in the distributional sense: :$\d...")
- 16:19, 3 May 2021 Julius talk contribs created page Definition:Local Frame (Created page with "== Definition == Let $M$ be a smooth manifold. Let $U \subseteq M$ be an open set. Let $\sigma = \tuple {\...")
- 15:51, 3 May 2021 Julius talk contribs moved page Definition:Warped Product to Definition:Warped Product Manifold without leaving a redirect
- 15:44, 3 May 2021 Julius talk contribs created page Set of Distributional Derivatives of Dirac Delta Distribution is Linearly Independent (Created page with "== Theorem == Let $\delta \in \map {\DD'} \R$ be the Dirac delta distribution. Then for any $n \in \N$ the set of...")
- 21:57, 2 May 2021 Julius talk contribs created page Definition:Zero Distribution (Redirected page to Definition:Zero Mapping/Distribution) Tag: New redirect
- 21:57, 2 May 2021 Julius talk contribs created page Definition:Zero Mapping/Distribution (Created page with "== Definition == Let $\map \DD \R$ be the test function space. Let $\mathbf 0 \in \map {\DD'} \R$ be a Definition:Distribution|distribut...")
- 21:40, 29 April 2021 Julius talk contribs created page Definition:Warped Product (Created page with "== Definition == Let $\struct {M_1, g_1}$, $\struct {M_2, g_2}$ be Riemannian manifolds. Let $f : M_1 \to \R_{\mathop > 0}$ be a Definit...")
- 21:22, 28 April 2021 Julius talk contribs created page Definition:Riemannian Covering (Created page with "== Definition == Let $\struct {M, g}$ and $\struct {\tilde M, \tilde g}$ be Riemannian manifolds. Let $\pi : \tilde M \to M$ be a Defini...")
- 21:03, 28 April 2021 Julius talk contribs created page Distributional Derivatives of Dirac Delta Distribution do not Vanish (Created page with "== Theorem == Let $\delta \in \map {\DD'} \R$ be the Dirac delta distribution. Then for any $n \in \N$ the Definition:Distribution...")
- 19:35, 27 April 2021 Julius talk contribs created page Definition:Riemannian Submersion (Created page with "== Definition == Let $\struct {\tilde M, \tilde g}$, $\struct {M, g}$ be Riemannian manifolds. Let $\pi : \tilde M \to M$ be a Definitio...")
- 18:26, 27 April 2021 Julius talk contribs created page Fundamental Solution to 1D Laplace's Equation (Created page with "== Theorem == Let $\ds \map f x = \frac {\size x} 2$ where $\size x$ is the absolute value function. Let $\delta \in \map {\DD'} \...")
- 17:39, 26 April 2021 Julius talk contribs created page Definition:Normal Space/Manifold (Created page with "== Definition == Let $\struct {\tilde M, \tilde g}$ be a Riemannian manifold. Let $M \subseteq \tilde M$ be a Definition:Smooth Manifold...")
- 16:43, 26 April 2021 Julius talk contribs created page Definition:Normal Bundle (Created page with "== Definition == Let $M$ be a differentiable manifold. Let $p \in M$ be a point in $M$. Let $N_p M$ be the...")
- 13:26, 25 April 2021 Julius talk contribs created page Definition:Unit Tangent Bundle (Created page with "== Definition == Let $\struct {M, g}$ be a Riemannian manifold. Let $T M$ be the tangent bundle of $\struct...")
- 12:31, 25 April 2021 Julius talk contribs created page Definition:Distributional Derivative/Higher Derivatives (Created page with "== Definition == <onlyinclude> The '''$n$th distributional derivative''' of a distribution $T \in \map \DD \R$ is defined as: :$T^{\paren n} := \be...")
- 15:06, 24 April 2021 Julius talk contribs created page Definition:Derivation (Redirected page to Definition:Tangent Vector/Definition 1) Tag: New redirect
- 14:48, 24 April 2021 Julius talk contribs created page Distributional Derivative of Heaviside Step Function times Sine (Created page with "== Theorem == Let $H$ be the Heaviside step function. Let $\delta$ be the Definition:Dirac Delta Distribution|Dirac delta distributi...")
- 14:42, 24 April 2021 Julius talk contribs created page Distributional Derivative of Heaviside Step Function times Cosine (Created page with "== Theorem(Distributional Derivative of Heaviside Step Function times Cosine) == Let $H$ be the Heaviside step function. Let $\delta$...")
- 20:43, 20 April 2021 Julius talk contribs created page Distributional Derivative of Floor Function (Created page with "== Theorem == Let $\floor x$ be the floor function. Let $\map {\operatorname {III}} x$ be the Dirac comb. Then the...")
- 19:42, 19 April 2021 Julius talk contribs created page Definition:Geometric Tangent Vector (Created page with "== Definition == Let $\R^n_a$ be a geometric tangent space. A '''geometric tangent vector to $\R^n$ at $a \in \R^n$'''...")
- 19:32, 19 April 2021 Julius talk contribs created page Definition:Tangent Space/Geometric Tangent Space (Created page with "== Definition == <onlyinclude> Let $a \in \R^n$ be an element of the $n$-dimensional Euclidean space. The '''geome...")
- 18:04, 19 April 2021 Julius talk contribs created page Distributional Derivative of Absolute Value Function (Created page with "== Theorem == Let $H: \R \to \closedint 0 1$ be the Heaviside step function. Let $\size x$ be the Definition:Absolute Value|absolute...")
- 14:48, 18 April 2021 Julius talk contribs created page Definition:Tensor Rank (Created page with "== Definition == Let $F$ be a tensor of type $\tuple {l, k}$. Then the '''tensor rank''' of $F$ is the sum $l + k$. In other words...")
- 17:30, 17 April 2021 Julius talk contribs created page Definition:Contravariant Tensor (Created page with "== Definition == Let $F$ be a tensor of type $\tuple {0, l}$: :$\ds F : \underbrace{{V^*} \times \ldots \times {V^*}}_{\text{$l$ times}} \to \R$ Then...")
- 17:28, 17 April 2021 Julius talk contribs created page Definition:Covariant Tensor (Created page with "== Definition == Let $F$ be a tensor of type $\tuple {k, 0}$: :$\ds F : \underbrace{V \times \ldots \times V}_{\text{$k$ times}} \to \R$ Then $F$ is...")
- 17:21, 17 April 2021 Julius talk contribs created page Definition:Tensor (Created page with "== Definition == Let $V$ and $V^*$ be a vector space and its dual. Then a '''(mixed) tensor $F$ of type $\tuple...")
- 17:04, 17 April 2021 Julius talk contribs created page Definition:Covector (Created page with "== Definition == Let $V^*$ be the vector space dual to $V$. An element of $V^*$ is called a '''covector'''. == Sou...")
- 16:55, 17 April 2021 Julius talk contribs created page Definition:Dual Vector Space (Created page with "== Definition == Let $V$ be a vector space. Let $\phi: V \to \R$ be a linear map. The space of...")
- 15:32, 17 April 2021 Julius talk contribs created page Dirac Comb is Distribution (Created page with "== Theorem == Let $\phi \in \map \DD \R$ be a test function. Suppose $\map {ะจ_1} 0$ is a Dirac comb such that: :$\ds...")
- 15:22, 17 April 2021 Julius talk contribs created page Definition:Dirac Comb (Created page with "== Definition == Let $\delta_a$ be a Dirac delta distribution. Let $T, x \in \R$ be real numbers. The ''...")
- 15:33, 16 April 2021 Julius talk contribs created page Definition:Isometry (Riemannian Manifolds) (Created page with "{{about|Isometry|context = Inner Product Space}} {{WIP|links, names, details etc.}} == Definition == Let $\struct {M, g}$ and $\struct {\tilde M, \tilde g}$ be Definition:R...")
- 21:09, 15 April 2021 Julius talk contribs deleted page Definition:Isometry (Definition:Inner Product Space) (content was: "#REDIRECT Definition:Isometry (Inner Product Spaces)", and the only contributor was "Julius" (talk))
- 21:08, 15 April 2021 Julius talk contribs moved page Definition:Isometry (Definition:Inner Product Space) to Definition:Isometry (Inner Product Spaces)
- 21:04, 15 April 2021 Julius talk contribs created page Definition:Isometry (Definition:Inner Product Space) (Created page with "== Definition == Let $V$ and $W$ be inner product spaces with inner products $\innerprod \cdot \cdot_V$ and $\...")
- 20:47, 14 April 2021 Julius talk contribs created page Book:John M. Lee/Introduction to Riemannian Manifolds/Second Edition (Created page with "{{Book|Introduction to Riemannian Manifolds|2018|Springer: Graduate Texts in Mathematics| 978-3319917542|John M. Lee}} === Subject Matter === * Definition:Differential Geo...")
- 17:24, 13 April 2021 Julius talk contribs created page Conditions for Preservation of Covergence in Test Function Space under Differentiation (Created page with "== Theorem == For all $n \in \N$ let $\Phi_n, \phi_n \in \map \DD \R$ be test functions. Let $\mathbf 0 : \R \to 0$ be the Definition:Zero Map...")