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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).
- 00:20, 4 May 2024 Hbghlyj talk contribs created page Vector Space over an Infinite Field is not equal to the Union of Proper Subspaces (add a theorem needed in the proof of primitive element theorem)
- 23:25, 3 May 2024 Hbghlyj talk contribs created page Talk:Separable Degree of Field Extensions is Multiplicative (Created page with "== About different definitions == I read from [https://math.stackexchange.com/questions/591077/multiplicative-nature-of-the-separability-degree stackexchange]: If one starts with separability degree definition 2, as done in the book by Lang, the result follows without much difficulty. But it is intractable if one starts from definition 1 --~~~~")
- 22:56, 3 May 2024 Hbghlyj talk contribs created page Equivalence of Definitions of Separable Degree (Add proof)
- 20:26, 3 May 2024 Hbghlyj talk contribs created page Steinitz's Theorem (A theorem needed in the proof of Primitive Element Theorem. name based on Wikipedia page https://en.wikipedia.org/wiki/Steinitz%27s_theorem_(field_theory))
- 19:53, 3 May 2024 Hbghlyj talk contribs created page Separable Degree of Field Extensions is Multiplicative (Creating the page based on a theorem in Lang's book, which in needed in Transitivity of Separable Field Extensions)
- 19:51, 3 May 2024 Hbghlyj talk contribs created page Separable Degree is At Most Equal To Degree (Creating the page based on a theorem in Lang's book, which in needed in Transitivity of Separable Field Extensions)
- 19:37, 3 May 2024 Hbghlyj talk contribs created page Definition:Separable Degree/Definition 3 (Created page with "== Definition == <onlyinclude> Let $K$ be a normal extension of $F$ that contains $E$. The '''separable degree''' $\index E F_{\operatorname {sep} }$ of $E / F$ is the number of embeddings of $E$ into $K$ that fix $F$. </onlyinclude> Category:Separable Field Extensions")
- 19:35, 3 May 2024 Hbghlyj talk contribs created page Definition:Separable Degree/Definition 2 (Created page with "== Definition == <onlyinclude> Let $\bar F$ be the algebraic closure of $F$. The '''separable degree''' $\index E F_{\operatorname {sep} }$ of $E / F$ is the number of embeddings of $E$ into $\bar F$ that fix $F$. </onlyinclude> Category:Separable Field Extensions")
- 19:32, 3 May 2024 Hbghlyj talk contribs created page Definition:Separable Degree/Definition 1 (Created page with "== Definition == <onlyinclude> Let $S \subseteq E$ be the separable closure of $F$ in $E$. The '''separable degree''' $\index E F_{\operatorname {sep} }$ of $E / F$ is the degree $\index S F$. </onlyinclude> Category:Separable Field Extensions")
- 19:01, 3 May 2024 Hbghlyj talk contribs created page Transitivity of Separable Field Extensions (Create the page which is a non-existent link in Subextensions of Separable Field Extension are Separable)
- 16:14, 3 May 2024 Hbghlyj talk contribs created page Equivalence of Definitions of Purely Inseparable Extension (Created page with "== Theorem == Let $E/F$ be an algebraic field extension. {{TFAE|def = Purely Inseparable Field Extension}} === Definition 1 === {{:Definition:Purely Inseparable Field Extension/Definition 1}} === Definition 2 === {{:Definition:Purely Inseparable Field Extension/Definition 2}} === Definition:Purely In...")
- 16:13, 3 May 2024 Hbghlyj talk contribs created page Definition:Purely Inseparable Field Extension/Definition 3 (Created page with "== Definition == <onlyinclude> Let $F$ have positive characteristic $p$. The extension $E/F$ is '''purely inseparable''' {{iff}} each element of $E$ has a minimal polynomial of the form $X^{p^n} - a$. </onlyinclude> == Also see == * Equivalence of Definitions of Purely Inseparable Extension Category:Definitions/Field Extensions")
- 16:12, 3 May 2024 Hbghlyj talk contribs created page Definition:Purely Inseparable Field Extension/Definition 2 (Created page with "== Definition == <onlyinclude> Let $F$ have positive characteristic $p$. The extension $E/F$ is '''purely inseparable''' {{iff}} for each $\alpha \in E$ there exists $n \in \N$ such that $\alpha^{p^n} \in F$. </onlyinclude> == Also see == * Equivalence of Definitions of Purely Inseparable Extension Category:Definitions/Field Extensions")
- 16:11, 3 May 2024 Hbghlyj talk contribs created page Definition:Purely Inseparable Field Extension/Definition 1 (Created page with "== Definition == <onlyinclude> The extension $E/F$ is '''purely inseparable''' {{iff}} every element $\alpha \in E \setminus F$ is inseparable. </onlyinclude> == Also see == * Equivalence of Definitions of Purely Inseparable Extension Category:Definitions/Field Extensions")
- 12:03, 1 May 2024 Hbghlyj talk contribs created page Group of Units Ring of Integers Modulo p^2 is Cyclic (Created page with "== Theorem == Let $p$ be a prime. Let $\struct {\Z / p^2 \Z, +, \times}$ be the ring of integers modulo $p^2$. Let $U = \struct {\paren {\Z / p^2 \Z}^\times, \times}$ denote the group of units of $\struct {\Z / p^2 \Z, +, \times}$. Then $U$ is cyclic. == Proof == The case $p = 2$ follows from Isomorp...")
- 11:00, 1 May 2024 Hbghlyj talk contribs created page Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n/Lemma (Created page with "=== Lemma === There are only $5$ numbers $n$ with the property that $\map \phi n = 8$, and they are $15$, $16$, $20$, $24$ and $30$. === Proof of lemma === Let $p$ be a prime factor of $n$. By Euler Phi Function is Multiplicative: :$p - 1 = \map \phi p \divides \map \phi n = 8$ so $p \in \set{2, 3, 5}$. Let $i,j,k \in \Z^{\ge 0}$ such that $n = 2^i 3^j 5^k$. By Euler Phi Function is Multiplicative: :$8 = \map \phi n = \map \phi {...")
- 16:03, 21 April 2024 Hbghlyj talk contribs created page Talk:Ideal Contained in Finite Union of Prime Ideals (Other name?: new section)
- 12:24, 12 April 2024 Hbghlyj talk contribs created page Template talk:Journalref (in example?: new section)
- 18:04, 25 March 2024 Hbghlyj talk contribs created page User talk:Sandbox/Du Bois-Reymond Constants/Example/First (Proving the inequality (1): new section)
- 13:05, 24 March 2024 Hbghlyj talk contribs created page User talk:Hbghlyj/Sandbox/James's Theorem (Add a redirect?: new section)
- 12:50, 24 March 2024 Hbghlyj talk contribs created page James's theorem (Created page with "== Theorem == $X$ is a Banach space and its dual space is $X^*$. $X$ is reflexive {{iff}} for all $f \in X^*$, there exists an element $a \in X$ such that :$\norm a \leq 1$ and $\map f a = \norm f$ == Proof == === Sufficient Condition === From a corollary of Hahn-Banach Theorem: :For any nonzero element $z \in V$, : :there exists a Definition:Bounded Linear Functional...")
- 12:13, 24 March 2024 Hbghlyj talk contribs created page Reflexive Riesz Lemma (Created page with "== Theorem == <onlyinclude> Let $X$ be a reflexive normed vector space. Let $Y$ be a proper closed linear subspace of $X$. Then there exists $x_\alpha \in X$ such that: :$\norm {x_\alpha} = 1$ with: :$\inf_{y \in M} \norm {\bar{x}-y} = 1$ for all $y \in Y$. </onlyinclude> == Proof == By Hahn-Banach Theorem, there exists $f \in...")
- 21:12, 23 March 2024 Hbghlyj talk contribs created page File talk:Fontene2.gif (thumbnail not animated: new section)
- 20:57, 23 March 2024 Hbghlyj talk contribs created page Talk:Fontené Theorems/Second (Figure updated: new section)
- 20:51, 23 March 2024 Hbghlyj talk contribs uploaded a new version of File:Fontene2.gif (high resolution)
- 20:34, 23 March 2024 Hbghlyj talk contribs created page Talk:Second Fontené Theorem (Duplicate page?: new section)
- 18:40, 23 March 2024 Hbghlyj talk contribs created page Definition:Isogonal Conjugate (Created page with "== Definition == $X$ is a point in the plane of the triangle $ABC$. Then the reflection of the lines $AX$, $BX$, and $CX$ about the angle bisectors at $A$, $B$, and $C$ concur at the '''isogonal conjugate''' of $X$. == Sources == * {{MathWorld|Isogonal Conjugate|IsogonalConjugate}} Category:Triangles")
- 18:33, 23 March 2024 Hbghlyj talk contribs created page Fontené Theorems/Third (Created page with "== Theorem == <onlyinclude> Denote the isogonal conjugate of $P$ with respect to triangle $A B C$ as $P'$. $O$ is the circumcenter. Then the pedal circle of $P$ is tangent to the nine point circle of triangle $A B C$ {{iff}} $O, P, P'$ are collinear. </onlyinclude> == Proof == By Fontené Theorems/Second we can prove that the second intersection $Q'$ of the Defin...")
- 18:28, 23 March 2024 Hbghlyj talk contribs created page Fontené Theorems/Second (Created page with "== Theorem == <onlyinclude> thumb|center|second Fontené theorem If a point $P$ moves on a fixed line $d$ through the circumcenter $O$, then its pedal circle passes through a fixed point $F$ on the nine point circle as illustrated above. </onlyinclude> == Proof == By Fontené Theorems/First, the point of contact $Q$ of the circle $E$ and the ci...")
- 18:24, 23 March 2024 Hbghlyj talk contribs created page Fontené Theorems/First (Created page with "== Theorem == <onlyinclude> Given triangle $ABC$. Let $P$ be an arbitrary point in the plane. $A_1, B_1, C_1$ are the midpoints of $B C, C A, A B$ $A_2 B_2 C_2$ is the pedal triangle of $P$ with respect to triangle $A B C$. Let $X, Y, Z$ be the intersections of $B_1 C_1$ and $B_2 C_2, A_1 C_1$ and $A_2 C_2, A_1 B_1$ and $A_2 B_2$. Then $A_2 X, B_2 Y, C_2 Z$ concur...")
- 17:49, 23 March 2024 Hbghlyj talk contribs created page Definition talk:Mean Curvature (Different concepts?: new section)
- 17:23, 23 March 2024 Hbghlyj talk contribs created page C^k Function Space is Banach Space (Created page with "== Theorem == Let $I = \closedint a b$ be a closed real interval. Let $\struct {\map {C^k} I, +, \, \cdot \,}_\R$ be the vector space of real-valued functions, k-times differentiable on $I$. Let $x \in \map {C^k} I$ be a real-valued function of differentiability class $k$. Let $\norm {...")
- 16:42, 23 March 2024 Hbghlyj talk contribs created page Talk:If Definite Integral of a(x)h(x) vanishes for any C^0 h(x) then C^0 a(x) vanishes (Other names: new section)
- 15:33, 23 March 2024 Hbghlyj talk contribs created page Talk:Fontené Theorems (Other name of the second Fontené theorem?: new section)
- 15:25, 23 March 2024 Hbghlyj talk contribs created page Definition:Pedal Circle (Created page with "== Definition == <onlyinclude> Let $\triangle ABC$ be a triangle. Let $P$ be a point in the plane of $\triangle ABC$. Let $PD$, $PE$ and $PF$ be perpendiculars dropped from $P$ to $BC$, $AC$ and $AB$ respectively. Let $\triangle DEF$ be the pedal triangle of $P$ with respect to $\triangle ABC$. The Definition:Circumcircle...")
- 15:10, 23 March 2024 Hbghlyj talk contribs created page Fontené Theorems (Created page with "== Theorem == thumb|center|second Fontené theorem The second Fontené theorem states that if a point moves on a fixed line through the circumcenter, then its pedal circle passes through a fixed point on the nine point circle as illustrated above. == Sources == * {{MathWorld|Fontené Theorems|FonteneTheorems}} Category:Triangles Category:Ci...")
- 15:09, 23 March 2024 Hbghlyj talk contribs uploaded File:Fontene2.gif
- 15:09, 23 March 2024 Hbghlyj talk contribs created page File:Fontene2.gif
- 13:44, 23 March 2024 Hbghlyj talk contribs uploaded File:U(x,t)=exp(x)H(t).png
- 13:44, 23 March 2024 Hbghlyj talk contribs created page File:U(x,t)=exp(x)H(t).png
- 11:57, 23 March 2024 Hbghlyj talk contribs created page Talk:Derivative of Composite Function/Jacobians (a typo?: new section)
- 11:18, 23 March 2024 Hbghlyj talk contribs created page Talk:Darboux's Theorem (more than one Darboux's Theorem?: new section)
- 19:54, 20 March 2024 Hbghlyj talk contribs created page Talk:Tartaglia's Formula (Other name?: new section)
- 16:30, 19 March 2024 Hbghlyj talk contribs created page Talk:Space of Bounded Linear Transformations is Banach Space (Created page with "== Similar theorem == Is this theorem the same as Necessary and Sufficient Conditions for Continuous Linear Transformation Space to be Banach Space? --Hbghlyj (talk) 16:30, 19 March 2024 (UTC)")
- 16:21, 19 March 2024 Hbghlyj talk contribs created page Talk:Necessary and Sufficient Conditions for Continuous Linear Transformation Space to be Banach Space (Sufficient Condition: new section)
- 14:01, 19 March 2024 Hbghlyj talk contribs created page Talk:Riesz-Fischer Theorem (Added a corollary: new section)
- 02:21, 18 March 2024 Hbghlyj talk contribs created page Sobolev Norm is Norm (Created page with "== Theorem == Let $k \in \Z_+$ and $1 \le p \le \infty$. Let $U \subset \R^n$ be an open set. Then the Sobolev norm is a norm on the Sobolev space $\map{W^{k,p}} U$. == Proof == === Property $(\text N 1)$ === === Property $(\text N 2)$ === === Property $(\text N 3)$ === Assume $u, v \in \map {W^{k,p}} U$. If $1\le...")
- 01:47, 18 March 2024 Hbghlyj talk contribs created page Sobolev Space is Banach Space (Created page with "== Theorem == The Sobolev space $\map {H^n} {a, b}$ equipped with the Sobolev norm is a Definition:Banach Space. == Proof == {{ProofWanted}} == Sources == * {{BookReference|Partial Differential Equations|2010|Lawrence Craig Evans}} Theorem 2 (Sobolev spaces as function spaces). Category:Definitions/Functional Analysis Category:Category:Banach Spaces")
- 01:19, 18 March 2024 Hbghlyj talk contribs created page Talk:Space of Continuously Differentiable on Closed Interval Real-Valued Functions with C^1 Norm is Banach Space (Generalize to C^k Norm?: new section)
- 01:04, 18 March 2024 Hbghlyj talk contribs created page Talk:C^k Norm is Norm (sum of non-negatives is zero if every element is zero: new section)