Results for query "&amp"

Mean of a vector

Then $$\mu_n\to(2,2,2,2,2,102,102,102,102,102).The exact rate of convergence will be determined by the second-largest singular value of the matrix
$$M =
\begin{bmatrix}
\tfrac13 & \tfrac13 & \tfrac13 & & & \\
\tfrac13 & \tfrac13 & \tfrac13 & & & \\
\tfrac13 & \tfrac13 & \tfrac13 & & & \\
& & & 1 & & \\
& & & & 1 & \\
& & & & & \ddots
\end{bmatrix}
\begin{bmatrix}
1 & & & & & \\
& \tfrac13 & \tfrac13 & \tfrac13 & & \\
& \tfrac13 & \tfrac13 & \tfrac13 & & \\
& \tfrac13 & \tfrac13 & \tfrac13 & & \\
& & & & 1 & \\
& & & & & \ddots
\end{bmatrix}
\begin{bmatrix}
1 & & & & & \\
& 1 & & & & \\
& & \tfrac13 & \tfrac13 & \tfrac13 & \\
& & \tfrac13 & \tfrac13 & \tfrac13 & \\
& & \tfrac13 & \tfrac13 & \tfrac13 & \\
& & & & & \ddots
\end{bmatrix}
\cdots$$
but I don't know how to compute that.

Iterated semi-direct products

5ex\rlap{\scriptstyle#1}}$

$$
\begin{array}{c}
& & 1 & & 1 & & \\
& & \da{} & & \da{} & & \\
& & C & \ra{=} & C\\
& & \da{} & & \da{} & & \\
1 & \ra{} & A & \ra{} & G & \ra{} & B & \ra{} & 1 \\
& & \da{} & & \da{\pi} & & \da{=} \\
1 & \ra{} & D & \ra{} & E & \ra{} & B & \ra{} & 1 \\
& & \da{} & & \da{} & & \\
& & 1 & & 1 & &
\end{array}
$$
in which all rows and columns are exact.Now $A/[C,D]$ is the direct product $C/[C,D] \times D[C,D]/[C,D]$.

Verifying the correctness of a Sudoku solution

We are thus looking for a solution of the following grid:
$$\begin{array}{|ccc|ccc|ccc|ccc|ccc|}
\hline
1&&&2&&&&&&&&&&&&\\
\strut&&&&&&&&&&&&&&&\\
\strut&&&&&&&&&&&&&&&\\
\hline
&&&1&&&2&&&&&&&&&\\
&&&&&&&&&&&&&&\cdots&\\
&&&&&&&&\ddots&&&&&&&\\
\hline
2&&&&&&&&&1&&&&&&\\
\strut&&&&&&&&&&&&&&&\\
\strut&&&&&&&&&&&&&&&\\
\hline
\strut&&&&&&&&&&&&&&&\\
\strut&&&&\vdots&&&&&&&&&&&\\
\strut&&&&&&&&&&&&&&&\\
\hline
\end{array}$$
where the upper part is a $q'\times q'$ subgrid, $q'=q/2$.$S$ is not included in the complement of a Sudoku permutation of one of the following sets:

a) $\{r_1,r_2\}$

b) $\{r_1,c_1,b_1\}$

c) $\{b_1,b_2,b_4,b_5\}$

d) $\{r_1,r_4,b_1,b_4\}$

e) $\{r_1,c_1,b_2,b_4,b_5\}$

f) $\{b_2,b_3,b_4,b_6,b_7,b_8\}$

g) $\{r_1,r_4,b_1,b_5,b_7,b_8\}$

h) $\{r_1,c_1,b_3,b_5,b_6,b_7,b_8\}$

Maximal incomplete sets http://math.

why do these characters belong to the first group in this JS regex match?

:Dokumentation&&&KKS-Nummer&&&Beschreibung&&&Seite)(&&&([^(&&&)]+)&&&([^(&&&)]+)&&&(\d+))+


The test string:

%5B"Deckblatt: Anlagendokumentation&&&Produktdaten&&&KKS-Nummer&&&Hersteller&&&Typ&&&Artikelnummer&&&MA-KF1&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF11&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF12&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF13&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF14&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF15&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF16&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF17&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF18&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF19&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF20&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF21&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF22&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF23&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF24&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF25&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF26&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF27&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF28&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF29&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF30&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF31&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF32&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF33&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF34&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF35&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF36&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF37&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF38&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF39&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF40&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&MA-KF41&&&Beckhoff&&&EK1100&&&BECK%2EEK1100&&&Dokumentation&&&KKS-Nummer&&&Beschreibung&&&Seite&&&all&&&Vorwort&&&6&&&all&&&Produktübersicht&&&7&&&all&&&Grundlagen&&&8&&&all&&&Montage und Verdrahtung&&&9&&&all&&&Inbetriebnahme%2FAnwendungshinweise&&&10&&&all&&&Fehlerbehandlung und Diagnose&&&11&&&all&&&Anhang 1&&&12&&&all&&&Anhang 2&&&13&&&all&&&Anhang 3&&&14&&&all&&&Anhang 4&&&15&&&all&&&Anhang 5&&&16&&&all&&&Anhang 6&&&17&&&all&&&Anhang 7&&&18&&&all&&&Anhang 8&&&19&&&all&&&Anhang 9&&&20&&&all&&&Anhang 10&&&21&&&all&&&Anhang 11&&&22&&&all&&&Anhang 12&&&23&&&all&&&Anhang 13&&&24&&&all&&&Anhang 14&&&25&&&all&&&Anhang 15&&&26&&&all&&&Anhang 16&&&27&&&all&&&Anhang 17&&&28&&&all&&&Anhang 18&&&29&&&all&&&Anhang 19&&&30&&&all&&&Anhang 20&&&31&&&all&&&Anhang 21&&&32&&&all&&&Anhang 22&&&33&&&all&&&Anhang 23&&&34&&&all&&&Anhang 24&&&35&&&all&&&Anhang 25&&&36&&&all&&&Anhang 26&&&37&&&all&&&Anhang 27&&&38&&&all&&&Anhang 28&&&39&&&all&&&Anhang 29&&&40&&&all&&&Anhang 30&&&41&&&all&&&Anhang 31&&&42&&&all&&&Anhang 32&&&43&&&all&&&Anhang 33&&&44&&&all&&&Anhang 34&&&45&&&all&&&Anhang 35&&&46&&&all&&&Anhang 36&&&47&&&all&&&Anhang 37&&&48&&&all&&&Anhang 38&&&49&&&all&&&Anhang 39&&&50&&&all&&&Anhang 40&&&51&&&all&&&Anhang 41&&&52&&&all&&&Anhang 42&&&53"%5D


The regex I wrote should get a first group, which appears after /Artikelnummer/ and before /Dokumentation&&&/ (etc), as well as a second group, which is what I'm having trouble with:

It should consist of repetitions of this pattern: (&&&([^(&&&)]+)&&&([^(&&&)]+)&&&(\d+)+

By my reckoning, that should capture the entire substring:

&&&all&&&Vorwort&&&6&&&all&&&Produktübersicht&&&7&&&all&&&Grundlagen&&&8&&&all&&&Montage und Verdrahtung&&&9&&&all&&&Inbetriebnahme%2FAnwendungshinweise&&&10&&&all&&&Fehlerbehandlung und Diagnose&&&11&&&all&&&Anhang 1&&&12&&&all&&&Anhang 2&&&13&&&all&&&Anhang 3&&&14&&&all&&&Anhang 4&&&15&&&all&&&Anhang 5&&&16&&&all&&&Anhang 6&&&17&&&all&&&Anhang 7&&&18&&&all&&&Anhang 8&&&19&&&all&&&Anhang 9&&&20&&&all&&&Anhang 10&&&21&&&all&&&Anhang 11&&&22&&&all&&&Anhang 12&&&23&&&all&&&Anhang 13&&&24&&&all&&&Anhang 14&&&25&&&all&&&Anhang 15&&&26&&&all&&&Anhang 16&&&27&&&all&&&Anhang 17&&&28&&&all&&&Anhang 18&&&29&&&all&&&Anhang 19&&&30&&&all&&&Anhang 20&&&31&&&all&&&Anhang 21&&&32&&&all&&&Anhang 22&&&33&&&all&&&Anhang 23&&&34&&&all&&&Anhang 24&&&35&&&all&&&Anhang 25&&&36&&&all&&&Anhang 26&&&37&&&all&&&Anhang 27&&&38&&&all&&&Anhang 28&&&39&&&all&&&Anhang 29&&&40&&&all&&&Anhang 30&&&41&&&all&&&Anhang 31&&&42&&&all&&&Anhang 32&&&43&&&all&&&Anhang 33&&&44&&&all&&&Anhang 34&&&45&&&all&&&Anhang 35&&&46&&&all&&&Anhang 36&&&47&&&all&&&Anhang 37&&&48&&&all&&&Anhang 38&&&49&&&all&&&Anhang 39&&&50&&&all&&&Anhang 40&&&51&&&all&&&Anhang 41&&&52&&&all&&&Anhang 42&&&53


But, for some reason, the only string in group 2 is:

&&&Anhang 42&&&53


Why is this happening?You get &&&all&&&Anhang 42&&&53 in Group 2 because the (pattern)+ is a repeated capturing group that stores only the value captured at the last iteration.

Simplicial “universal extensions”, the hammock localization, and Ext

$$

A morphism of $n$-extensions of $Y$ by $X$ is defined to be a hammock

$$\begin{matrix}
&&A_1&\to&A_2&\to&A_3&\to&\ldots&\to &A_{n-2}&\to &A_{n-1}&\to& A_{n}&&\\
&\nearrow&\downarrow&&\downarrow&&\downarrow&&&&\downarrow&&\downarrow&&\downarrow&\searrow&\\
X&&\downarrow&&\downarrow&&\downarrow&&&&\downarrow&&\downarrow&&\downarrow&&Y\\
&\searrow&\downarrow&&\downarrow&&\downarrow&&&&\downarrow&&\downarrow&&\downarrow&\nearrow&\\
&&B_1&\to&B_2&\to&B_3&\to&\ldots&\to &B_{n-2}&\to &B_{n-1}&\to& B_{n}&&\end{matrix}$$

This detetermines a category $n\operatorname{-ext}(Y,X)$.Questions:

Why can we get $\pi_1$ of the function complex by looking at maps into $N[1]$?

Extract Data from Soap XML with Namespaces

vedaadvantage/dp3/connectors"><enquiryReport><primaryMatch><bureauReference>805917662</bureauReference><individual><individualName><familyName>MOHAMMADINEJAD</familyName><firstGivenName>ALI</firstGivenName><createDate>2014-07-15</createDate></individualName><gender>male</gender><dateOfBirth>1982-01-06</dateOfBirth><driversLicenceNumber><countryCodes>AU</countryCodes><value/></driversLicenceNumber><b:address><b:unitNumber/><b:streetNumber>43</b:streetNumber><b:property>43</b:property><b:streetName>KING EDWARD</b:streetName><b:streetType>AVE</b:streetType><b:suburb>ALBION</b:suburb><b:city/><b:state>VIC</b:state><b:postcode>3020</b:postcode><b:countryCode>AU</b:countryCode><b:addressType>residentialCurrent</b:addressType><b:createDate>2015-09-04</b:createDate></b:address></individual><individualConsumerCreditFile><creditEnquiry><accountType><accountType>UA</accountType><value>Utilities</value></accountType><role><consumerRoleTypeCodesResponse>principal</consumerRoleTypeCodesResponse></role><enquiryAmount><currencyCodeType/><value>0</value></enquiryAmount><coBorrower/><creditEnquirer>AGL ENGY SALES & MKTG LTD</creditEnquirer><clientReference/><consumerCreditEnquiryTypeResponse>creditApplication</consumerCreditEnquiryTypeResponse><enquiryDate>2015-09-04</enquiryDate></creditEnquiry><creditEnquiry><accountType><accountType>TC</accountType><value>Telecommunication Service</value></accountType><role><consumerRoleTypeCodesResponse>principal</consumerRoleTypeCodesResponse></role><enquiryAmount><currencyCodeType/><value>0</value></enquiryAmount><coBorrower/><creditEnquirer>VODAFONE DECISION POINT</creditEnquirer><clientReference>1-DCQJWZG</clientReference><consumerCreditEnquiryTypeResponse>creditApplication</consumerCreditEnquiryTypeResponse><enquiryDate>2014-07-15</enquiryDate></creditEnquiry></individualConsumerCreditFile><individualCommercialCreditFile><creditEnquiry><accountType><commercialAccountTypeCodesResponse>CR</commercialAccountTypeCodesResponse><value>Commercial Rental</value></accountType><enquiryAmount><currencyCodeType/><value>25000</value></enquiryAmount><role><commercialRoleTypeCodesResponse>principal</commercialRoleTypeCodesResponse></role><coBorrower/><creditEnquirer>GOGETTA EQUIPMENT FUNDING</creditEnquirer><clientReference/><commercialCreditEnquiryTypeResponse>creditEnquiry</commercialCreditEnquiryTypeResponse><enquiryDate>2016-04-04</enquiryDate></creditEnquiry></individualCommercialCreditFile><matchType>strong</matchType></primaryMatch><summaryData><summary><name>enquiry-amount</name><summaryType>amount</summaryType><currencyCode>AUD</currencyCode><value>25000</value></summary><summary><name>age-of-file</name><summaryType>months</summaryType><currencyCode/><value>20</value></summary><summary><name>age-of-subject</name><summaryType>years</summaryType><currencyCode/><value>34</value></summary><summary><name>time-at-address</name><summaryType>months</summaryType><currencyCode/><value>7</value></summary><summary><name>time-at-employer</name><summaryType>months</summaryType><currencyCode/><value/></summary><summary><name>defaults</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>total-value-of-outstanding-defaults</name><summaryType>amount</summaryType><currencyCode>AUD</currencyCode><value>0</value></summary><summary><name>defaults-paid</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>defaults-12</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>defaults-12-paid</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>defaults-12-unpaid</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>defaults-24-paid</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>defaults-24-unpaid</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>defaults-36-paid</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>defaults-36-unpaid</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>time-since-last-default</name><summaryType>months</summaryType><currencyCode/><value/></summary><summary><name>total-credit-enquiries</name><summaryType>count</summaryType><currencyCode/><value>3</value></summary><summary><name>credit-enquiries-1</name><summaryType>count</summaryType><currencyCode/><value>1</value></summary><summary><name>credit-enquiries-3</name><summaryType>count</summaryType><currencyCode/><value>1</value></summary><summary><name>credit-enquiries-6</name><summaryType>count</summaryType><currencyCode/><value>1</value></summary><summary><name>credit-enquiries-12</name><summaryType>count</summaryType><currencyCode/><value>2</value></summary><summary><name>credit-enquiries-60</name><summaryType>count</summaryType><currencyCode/><value>3</value></summary><summary><name>time-since-last-enquiry</name><summaryType>months</summaryType><currencyCode/><value>7</value></summary><summary><name>telco-and-utility-defaults</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>telco-and-utility-defaults-12</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>telco-and-utility-enquiries</name><summaryType>count</summaryType><currencyCode/><value>2</value></summary><summary><name>telco-and-utility-enquiries-6</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>telco-and-utility-enquiries-12</name><summaryType>count</summaryType><currencyCode/><value>1</value></summary><summary><name>authorised-agents-enquiries-12</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>authorised-agents-enquiries-60</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>directorships-current</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>directorships-previous</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>judgements</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>proprietorships</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>adverse-on-file</name><summaryType/><currencyCode/><value>No</value></summary><summary><name>file-notes</name><summaryType/><currencyCode/><value>No</value></summary><summary><name>known-identities</name><summaryType>count</summaryType><currencyCode/><value>1</value></summary><summary><name>bankruptcies</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>writs-and-summons</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>external-administration-director</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary></summaryData><scoreData><score><scorecardModel>0303</scorecardModel><relativeRisk>2.9</applicantOdds><contributingFactor><impact>Greatly Decreases Risk</impact><value>Lack of Consumer Adverse Information</value></contributingFactor><contributingFactor><impact>Moderately Decreases Risk</impact><value>Number of Consumer Credit Applications</value></contributingFactor><contributingFactor><impact>Marginally Decreases Risk</impact><value>Individual Shopping Pattern</value></contributingFactor><contributingFactor><impact>Marginally Decreases Risk</impact><value>Current and Historic Credit Type Sought</value></contributingFactor><population><populationOdds>11.

The sharp 3x3 lemma: a proof by universal properties?

I'll reproduce the diagram:

$$\ \ \matrix{
&&0&&0&&0
\cr&&\downarrow&&\downarrow&&\downarrow
\cr &&A_1 & & B_1& &C_1
\cr &&\downarrow & &\downarrow&&\downarrow
\cr &&A_2 & \to & B_2 & \to & C_2 &
\cr &&\downarrow &&\downarrow&&\downarrow
\cr 0&\to&A_3 & \to & B_3 & \to & C_3
}\ \ $$

With all rows and columns exact.Show that there exists an exact sequence $A_1\to B_1\to C_1$ making the diagram commute.

formation and interpretation of a dual LP

The coffee company makes $p_{i,j}$ dollars for each kilogram it produces at farm $i$ and ships to restaurant $j$.$
\begin{array}{l*{12}{r}lr}
\mbox{Maximize} & p_{1,1}x_{1,1} & + & p_{1,2}x_{1,2} & + & p_{1,3}x_{1,3} & + & p_{2,1}x_{2,1} & + & p_{2,2}x_{2,2} & + & p_{2,3}x_{2,3} \\
\mbox{Subject to} & x_{1,1} & + & x_{1,2} & + & x_{1,3} & ~ & ~ & ~ & ~ & ~ & ~ &\leq & s_1 \\
~ & ~ & ~ & ~ & ~ & ~ & ~ & x_{2,1} & + & x_{2,2} & + & x_{2,3} & \leq & s_2 \\
~ & x_{1,1} & ~ & ~ & ~ & ~ & + & x_{2,1} & ~ & ~ & ~ & ~ & \geq & d_1 \\
~ & ~ & ~ & x_{1,2} & ~ & ~ & ~ & ~ & + & x_{2,2} & ~ & ~ & \geq & d_2 \\
~ & ~ & ~ & ~ & ~ & x_{1,3} & ~ & ~ & ~ & ~ & + & x_{2,3} & \geq & d_3 \\
&&&&&&&&&&&x_{i,j} & \geq & 0
\end{array}$

Here we can think of each $x_{i,j}$ as the amount (in kg) that is shipped from farm $i$ to restaurant $j$.

Finding the Smallest Convex Hull of an Adjacency Matrix

How do I know if the convex hull is the smallest possible without using brute force?Here is an example:

We have the 9X9 adjacency matrix,

\begin{Vmatrix}
0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
\end{Vmatrix}

which with dots is:
\begin{Vmatrix}
& & & & \cdot & & & & \\
& & & & & \cdot & & & \\
\cdot & & & & & & & & \\
& & & & & \cdot & & & \\
& & & & & \cdot & & & \\
& & & & & & & & &\\
\cdot & & & & & & & & \\
\cdot & & & & & & & & \\
& & & \cdot & & & & & \\
\end{Vmatrix}

then rearranged is:
\begin{Vmatrix}
& \cdot & & & & & & & \\
& & \cdot & & & & & & \\
\cdot & & & & & & & & \\
& & \cdot & & & & & & \\
& & \cdot & & & & & & \\
\cdot & & & & & & & & \\
\cdot & & & & & & & & \\
& & & \cdot & & & & & \\
& & & & & & & & \\
\end{Vmatrix}

with the convex hull of the latter clearly having the smaller area.

How do you calculate the expected value of geometric distribution without diffrentiation?

Is there any way I can calculate the expected value of geometric distribution without diffrentiation?)
$$
\begin{array}{cccccccccccccccccccccccc}
& 0 & & 1 & & 2 & & 3 & & 4 & & 5 & & 6 \\
\hline
& & & p^1 & + & 2p^2 & + & 3p^3 & + & 4p^4 & + & 5p^5 & + & 6p^6 & + & \cdots & {} \\[12pt]
= & & & p^1 & + & p^2 & + & p^3 & + & p^4 & + & p^5 & + & p^6 & + & \cdots \\
& & & & + & p^2 & + & p^3 & + & p^4 & + & p^5 & + & p^6 & + & \cdots \\
& & & & & & + & p^3 & + & p^4 & + & p^5 & + & p^6 & + & \cdots \\
& & & & & & & & + & p^4 & + & p^5 & + & p^6 & + & \cdots \\
& & & & & & & & & & + & p^5 & + & p^6 & + & \cdots \\
& & & & & & & & & & & & + & p^6 & + & \cdots \\
& & & & & & & & & & & & & & + & \cdots \\
& & & & & & & & & & & & & & \vdots
\end{array}
$$
First sum each (horizontal) row.

What wrong with the proof for extreme rays?

Let $ C=\{y\in \mathbb{R}^8: y A \geq 0\}$ be a polyhedral cone, where

$A=\begin{pmatrix}
-1 & -1 & & & & & & \\
& & -1 & -1 & & & & \\
& & & &-1 & -1 & & \\
& & & & & & -1 & -1 \\
1 & && & 1 && & &1&& \\
&1 && & &1 & & &&1&\\
& &1 & & & &1 & & &&1&\\
& & &1 & && &1 &&&&1
\end{pmatrix}$

Since $yA=0$ implies $y=0$, $C$ is pointed.Hence $C$ is finitely generated by extreme rays, or $C=\{x: x=\lambda_1 r_1+.

Probability of reaching target after n tries with regression on failure.

The canonical-form transition matrix for this process is thus $$P=\left[\begin{array}{cccccc|c}0&p_0&0&0&0 & \cdots & 0 \\ q_1&0&p_1&0&0 & \cdots & 0 \\ 0&q_2&0&p_2&0 & \cdots & 0\\ 0&0&q_3&0&p_3 & \cdots & 0 \\ \vdots&\ddots&\ddots&\ddots&\ddots&\ddots&\vdots \\ 0&0&0&0&0& \cdots &p_8 \\ \hline 0&0&0&0&0 & \cdots & 1\end{array}\right].Consider the matrix for this Markov chain: $$P=\left[\begin{array}{cccccccccc}
0&1&&&&&&&&\\
1-p_{1}&0&p_{1}&&&\ddots&&&&\\
&1-p_{2}&0&p_{2}&&&0&&&\\
&&1-p_{3}&0&p_{3}&&&\ddots&&\\
&&&1-p_{4}&0&p_{4}&&&&\\
&&&&1-p_{5}&0&p_{5}&&&\\
&&\ddots&&&1-p_{6}&0&p_{6}&&\\
&&&0&&&1-p_{7}&0&p_{7}&\\
&&&&\ddots&&&1-p_{8}&0&p_{8}\\
&&&&&&&&0&1\end{array}\right],$$ where the transition probability of going from state $i$ to state $j$ is $P_{i,j}$ for each $0\leq i,j\leq 9.

Deserialize SOAP XML Response With No Enumerator

vedaadvantage/dp3/connectors"><enquiryReport><primaryMatch><bureauReference>805917662</bureauReference><individual><individualName><familyName>MOHAMMADINEJAD</familyName><firstGivenName>ALI</firstGivenName><createDate>2014-07-15</createDate></individualName><gender>male</gender><dateOfBirth>1982-01-06</dateOfBirth><driversLicenceNumber><countryCodes>AU</countryCodes><value/></driversLicenceNumber><b:address><b:unitNumber/><b:streetNumber>43</b:streetNumber><b:property>43</b:property><b:streetName>KING EDWARD</b:streetName><b:streetType>AVE</b:streetType><b:suburb>ALBION</b:suburb><b:city/><b:state>VIC</b:state><b:postcode>3020</b:postcode><b:countryCode>AU</b:countryCode><b:addressType>residentialCurrent</b:addressType><b:createDate>2015-09-04</b:createDate></b:address></individual><individualConsumerCreditFile><creditEnquiry><accountType><accountType>UA</accountType><value>Utilities</value></accountType><role><consumerRoleTypeCodesResponse>principal</consumerRoleTypeCodesResponse></role><enquiryAmount><currencyCodeType/><value>0</value></enquiryAmount><coBorrower/><creditEnquirer>AGL ENGY SALES & MKTG LTD</creditEnquirer><clientReference/><consumerCreditEnquiryTypeResponse>creditApplication</consumerCreditEnquiryTypeResponse><enquiryDate>2015-09-04</enquiryDate></creditEnquiry><creditEnquiry><accountType><accountType>TC</accountType><value>Telecommunication Service</value></accountType><role><consumerRoleTypeCodesResponse>principal</consumerRoleTypeCodesResponse></role><enquiryAmount><currencyCodeType/><value>0</value></enquiryAmount><coBorrower/><creditEnquirer>VODAFONE DECISION POINT</creditEnquirer><clientReference>1-DCQJWZG</clientReference><consumerCreditEnquiryTypeResponse>creditApplication</consumerCreditEnquiryTypeResponse><enquiryDate>2014-07-15</enquiryDate></creditEnquiry></individualConsumerCreditFile><individualCommercialCreditFile><creditEnquiry><accountType><commercialAccountTypeCodesResponse>CR</commercialAccountTypeCodesResponse><value>Commercial Rental</value></accountType><enquiryAmount><currencyCodeType/><value>25000</value></enquiryAmount><role><commercialRoleTypeCodesResponse>principal</commercialRoleTypeCodesResponse></role><coBorrower/><creditEnquirer>GOGETTA EQUIPMENT FUNDING</creditEnquirer><clientReference/><commercialCreditEnquiryTypeResponse>creditEnquiry</commercialCreditEnquiryTypeResponse><enquiryDate>2016-04-04</enquiryDate></creditEnquiry></individualCommercialCreditFile><matchType>strong</matchType></primaryMatch><summaryData><summary><name>enquiry-amount</name><summaryType>amount</summaryType><currencyCode>AUD</currencyCode><value>25000</value></summary><summary><name>age-of-file</name><summaryType>months</summaryType><currencyCode/><value>20</value></summary><summary><name>age-of-subject</name><summaryType>years</summaryType><currencyCode/><value>34</value></summary><summary><name>time-at-address</name><summaryType>months</summaryType><currencyCode/><value>7</value></summary><summary><name>time-at-employer</name><summaryType>months</summaryType><currencyCode/><value/></summary><summary><name>defaults</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>total-value-of-outstanding-defaults</name><summaryType>amount</summaryType><currencyCode>AUD</currencyCode><value>0</value></summary><summary><name>defaults-paid</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>defaults-12</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>defaults-12-paid</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>defaults-12-unpaid</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>defaults-24-paid</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>defaults-24-unpaid</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>defaults-36-paid</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>defaults-36-unpaid</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>time-since-last-default</name><summaryType>months</summaryType><currencyCode/><value/></summary><summary><name>total-credit-enquiries</name><summaryType>count</summaryType><currencyCode/><value>3</value></summary><summary><name>credit-enquiries-1</name><summaryType>count</summaryType><currencyCode/><value>1</value></summary><summary><name>credit-enquiries-3</name><summaryType>count</summaryType><currencyCode/><value>1</value></summary><summary><name>credit-enquiries-6</name><summaryType>count</summaryType><currencyCode/><value>1</value></summary><summary><name>credit-enquiries-12</name><summaryType>count</summaryType><currencyCode/><value>2</value></summary><summary><name>credit-enquiries-60</name><summaryType>count</summaryType><currencyCode/><value>3</value></summary><summary><name>time-since-last-enquiry</name><summaryType>months</summaryType><currencyCode/><value>7</value></summary><summary><name>telco-and-utility-defaults</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>telco-and-utility-defaults-12</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>telco-and-utility-enquiries</name><summaryType>count</summaryType><currencyCode/><value>2</value></summary><summary><name>telco-and-utility-enquiries-6</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>telco-and-utility-enquiries-12</name><summaryType>count</summaryType><currencyCode/><value>1</value></summary><summary><name>authorised-agents-enquiries-12</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>authorised-agents-enquiries-60</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>directorships-current</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>directorships-previous</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>judgements</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>proprietorships</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>adverse-on-file</name><summaryType/><currencyCode/><value>No</value></summary><summary><name>file-notes</name><summaryType/><currencyCode/><value>No</value></summary><summary><name>known-identities</name><summaryType>count</summaryType><currencyCode/><value>1</value></summary><summary><name>bankruptcies</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>writs-and-summons</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary><summary><name>external-administration-director</name><summaryType>count</summaryType><currencyCode/><value>0</value></summary></summaryData><scoreData><score><scorecardModel>0303</scorecardModel><relativeRisk>2.9</applicantOdds><contributingFactor><impact>Greatly Decreases Risk</impact><value>Lack of Consumer Adverse Information</value></contributingFactor><contributingFactor><impact>Moderately Decreases Risk</impact><value>Number of Consumer Credit Applications</value></contributingFactor><contributingFactor><impact>Marginally Decreases Risk</impact><value>Individual Shopping Pattern</value></contributingFactor><contributingFactor><impact>Marginally Decreases Risk</impact><value>Current and Historic Credit Type Sought</value></contributingFactor><population><populationOdds>11.