- testwiki

General

Display information for equation id:math.2263.68 on revision:2263

* Page found: Vorurteilsfreie Schätzung des statistischen Operators zu einem festen Zeitpunkt (eq math.2263.68)

Occurrences on the following pages:

Vorurteilsfreie Schätzung des statistischen Operators zu einem festen Zeitpunkt Eq: math.2273.68

Hash: 1e1cb700e336ea813e8496da043a9b6d

TeX (original user input):

\begin{align}
  & \sum\limits_{m,n}^{{}}{\left[ {{\left| \left\langle  {{r}_{m}} | {{w}_{n}} \right\rangle  \right|}^{2}}{{r}_{m}}\left( -\ln \frac{{{R}_{n}}}{{{r}_{m}}} \right) \right]}\ge \sum\limits_{m,n}^{{}}{\left[ {{\left| \left\langle  {{r}_{m}} | {{w}_{n}} \right\rangle  \right|}^{2}}{{r}_{m}}\left( 1-\frac{{{R}_{n}}}{{{r}_{m}}} \right) \right]} \\
 & =\sum\limits_{m,n}^{{}}{\left[ {{\left| \left\langle  {{r}_{m}} | {{w}_{n}} \right\rangle  \right|}^{2}}\left( {{r}_{m}}-{{R}_{n}} \right) \right]}=\sum\limits_{m}^{{}}{{{r}_{m}}}=\sum\limits_{n}^{{}}{{{R}_{n}}} \\
\end{align}

TeX (checked):

{\begin{aligned}&\sum \limits _{m,n}^{}{\left[{{\left|\left\langle {{r}_{m}}|{{w}_{n}}\right\rangle \right|}^{2}}{{r}_{m}}\left(-\ln {\frac {{R}_{n}}{{r}_{m}}}\right)\right]}\geq \sum \limits _{m,n}^{}{\left[{{\left|\left\langle {{r}_{m}}|{{w}_{n}}\right\rangle \right|}^{2}}{{r}_{m}}\left(1-{\frac {{R}_{n}}{{r}_{m}}}\right)\right]}\\&=\sum \limits _{m,n}^{}{\left[{{\left|\left\langle {{r}_{m}}|{{w}_{n}}\right\rangle \right|}^{2}}\left({{r}_{m}}-{{R}_{n}}\right)\right]}=\sum \limits _{m}^{}{{r}_{m}}=\sum \limits _{n}^{}{{R}_{n}}\\\end{aligned}}

LaTeXML (experimental; uses MathML) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimental; no images) rendering

MathML (4.405 KB / 520 B) :

\begin{aligned} \sum_{m, n}^{} [{| ⟨ r_{m} | w_{n} ⟩ |}^{2} r_{m} (- \ln \frac{R_{n}}{r_{m}})] \geq \sum_{m, n}^{} [{| ⟨ r_{m} | w_{n} ⟩ |}^{2} r_{m} (1 - \frac{R_{n}}{r_{m}})] \\ = \sum_{m, n}^{} [{| ⟨ r_{m} | w_{n} ⟩ |}^{2} (r_{m} - R_{n})] = \sum_{m}^{} r_{m} = \sum_{n}^{} R_{n} \end{aligned}

<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mo>,</mo><mi>n</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msub><mo>|</mo><msub><mi>w</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>&#x2212;</mo><mi>ln</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msub></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>&#x2265;</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mo>,</mo><mi>n</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msub><mo>|</mo><msub><mi>w</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msub></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mo>,</mo><mi>n</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msub><mo>|</mo><msub><mi>w</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msub><mo>&#x2212;</mo><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><msub><mi>r</mi><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msub><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$m$

$n$

$r_{m}$

$w_{n}$

$r_{m}$

$R_{n}$

$r_{m}$

$m$

$n$

$r_{m}$

$w_{n}$

$r_{m}$

$R_{n}$

$r_{m}$

$m$

$n$

$r_{m}$

$w_{n}$

$r_{m}$

$R_{n}$

$m$

$r_{m}$

$n$

$R_{n}$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

Search