text:
Talk:Conlon

On 21 Jan 2005, this article was nominated for deletion. See Votes for deletion/Conlon for a record of the discussion. Rossami (talk) 02:14, 3 Feb 2005 (UTC)

This article has subsequently been turned into a disambiguation page. This resolves the disposition of the Wikipedia version article.

In a separate matter, I note that most of the names shown on this disambiguation page are currently redlinks with very few inbound links. In three cases, there were no inbound links except from this disambiguation page. Disambiguation pages are not really the appropriate place to enter the request for an article on that topic. I am removing the redlinked lines from the page. Please do not add them back until and unless a verifiable, non-stub article is created on this person. You can periodically check this version of the history to see if a redlink is now a bluelink. Thanks. Rossami (talk) 5 July 2005 23:11 (UTC)

Every one of those redlinks is a person mentioned in an existing Wikipedia article. It seems to me most unlikely that the creator of the redlinked articles will think to update this list. I do not understand the harm done by having them as redlinks until they are populated. —Theo (Talk) 6 July 2005 09:25 (UTC)
 * Answered at length on your Talk page. Apologies for the very long post.  Rossami (talk) 6 July 2005 15:36 (UTC)

Etymology
From the page: "″The name may be derived from two Irish Gaelic words 'Con' (the genitive case of Cú, meaning 'hound') and 'Lón' meaning lion - thereby implying a person who has the characteristics of a lion born of a hound - strength and speed." Would love to see this cited, not least as proof of lions in 13th C. Ireland, but also as "lón" means "lunch" in Irish, whereupon this name would more closely translate as 'hotdog'. More likely, it's neither lion from a dog nor lunch from a dog, but rather is speculative and should be removed. — Preceding unsigned comment added by 143.239.200.154 (talk) 15:45, 16 April 2018 (UTC)

title: Talk:Conlon


text: Template:New York City Subway

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Template:New York City Subway


text:
M-108 (Michigan highway)

M-108 was a state trunkline highway in the US state of Michigan. The highway followed Nicolet Street, although some maps also labeled it as Mackinaw Highway. The road was on the boundary between Emmet and Cheboygan counties.

The original M-108 designation dated back to 1928. This version was transferred to local control in 1957, but revived later under a similar routing in 1960. On April 29, 2010, the Petoskey News-Review reported that the Michigan Department of Transportation (MDOT) would rebuild the roadway in preparation to transfer it back to local control once again. MDOT and local officials signed memoranda of understanding, completing the transfer of the roadway on December 9, 2010.

Route description
The 1.069 mi trunkline connected two interchanges off Interstate 75 (I-75) on the south side of Mackinaw City with a tourist welcome center. The southern terminus was at a partial interchange with I-75 (exit 337) just south of Mackinaw City on the boundary between Emmet and Cheboygan counties. This interchange is about 2 mi north of the northern terminus of US Highway 31 (US 31). M-108 followed Nicolet Street north from I-75 into the Village of Mackinaw City past the Thunder Falls Water Park and some local motels to an intersection with US 23. North of the US 23 intersection is the Michigan Welcome Center and other tourist amenities on the west side of the street. State maintenance ended at the intersection with the off-ramp from northbound I-75 exit 338.

History
In 1928, the first M-108 designation was commissioned along a rare three-legged route connecting the State Highway Ferry Docks with the Fort Michilimackinac State Historic Park and US 31. At one point while traveling westbound on M-108, motorists could turn right onto northbound M-108 or left onto southbound M-108. In preparation for the opening of the Mackinac Bridge, the Michigan State Highway Department transferred all of M-108 to local control in late 1957, decommissioning the designation at the same time. In 1960, the current M-108 was commissioned along the final routing.

On April 29, 2010, MDOT announced plans to transfer M-108 in its entirety to the Village of Mackinaw City and Emmet County. In preparation for this transfer, MDOT repaved, widened and reconstructed the roadway. While rebuilding the section of the highway between US 23 and the northern terminus, the welcome center was closed. Plans had this section to be completed, and the center to be reopened, for Memorial Day weekend, with the remainder of construction to be completed in August. Following the transfer to local control, M-108 ceased to be a state highway and the designation was decommissioned. Previous news reports stated that the roadway was too small to merit highway status under federal guidelines. The transfer was completed on December 9, 2010, when MDOT and local officials signed memoranda of understanding to finalize the transfer. The section within the Village of Mackinaw City was transferred to the village, and the remainder to Emmet County.

Major intersections
The entire highway was on the Emmet–Cheboygan county line.

title: M-108 (Michigan highway)


text:
Talk:Collatz conjecture

Semi-protected edit request on 16 March 2024
BEFORE: Eliahou (1993) proved that the period p of any non-trivial cycle is of the form AFTER: Eliahou (1993) proved that the period p of the next candidate for a non-trivial cycle is of the form

Idk, im not a mathematician, but i read the paper cited and the p that is used here seems to be only the current (1993) best candidate for a loop above m=2**39, but below 2**48. As it is earlier mentioned, this region has already been investigated, so not only the original statements "any" false, but the big letter equation is also irrelevant. 89.223.151.22 (talk) 07:55, 16 March 2024 (UTC)
 * Red information icon with gradient background.svg Not done: From what I understand, the paper states that all non-trivial cycles (if any exist) have a cardinality of the form $$301994a + 17087915b + 85137581c$$. Your proposed change would imply that a non-trivial cycle that is not the first one to be found might not have a cardinality of that form, which contradicts the theorem proved by the paper. Saucy[talk – contribs] 10:43, 25 April 2024 (UTC)

Semi-protected edit request on 8 April 2024
Explaining Convergence

While a mathematical formula or explanation-based proof may yet be difficult, it is possible to explain the underlying mechanism responsible for convergence by transforming the problem statement as followsCollatz Conjecture - Explaining the Convergence: a) For an odd number N, (3N+1) is always an even number, therefore the next step will always be a division by 2. Both these steps can be considered as a single operation, i.e. (3N+1)/2.

b) Sequential multiplication steps (3N+1)/2 may be considered as a single operation until an even number is obtained.

c) Sequential division (N/2) may be considered as a single operation until an odd number is obtained.

With the help of these transformations, it can be observed that for a starting odd number series, (2i-1)*2n-1,

a) Multiplication steps result in the even series (2i-1)*3n-1

b) The resulting superset of even values is represented by either {(6i-4), i ∈ ℕ} or by {(6i-1)*3n-1 and (6i-5)*3n-1, i & n ∈ ℕ}

c) The next set of odd numbers obtained through division steps is represented by {(6i-5)*22n-1]/3 and (6i-1)*22n+1-1]/3, i & n ∈ ℕ}

While mathematical traceability between the starting odd number and the next odd number obtained in step (c) above is difficult to maintain, this approach still helps understand the underlying mechanism leading to convergence.

To explain this, one may begin from the other end of the problem and perform (2N-1)/3 operations on an even series (instead of (3N+1)/2 on a starting odd series). The starting even series E1=1*22n-1, results in a set of odd numbers which can be multiplied by 2n or 2n-1 if the odd number belongs to series {6i-5} or {6i-1} respectively. Sequential performance of these inverse operations results in a hierarchy of even series as shown in this exhibit Hierarchy of Even Series. Rakesh Vajpai (talk) 06:22, 8 April 2024 (UTC)
 * We cannot use this material without a published reliable source. Personal blogs are not reliable sources for this purpose. —David Eppstein (talk) 07:15, 8 April 2024 (UTC)
 * Thanks David. I am not a mathematician and have no idea what it takes for such articles to be published.  I may not even be interested in doing so as my focus is on making these aspects known to people who may be attempting to solve this problem.  I have no interest in claiming any credit for the insights.  Therefore, if it cannot be published here, I will understand and will leave it at that.  Thanks once again.  Cheers Rakesh Vajpai (talk) 12:49, 10 April 2024 (UTC)

Collatz function for some known megaprimes
The project math101.guru/en/category/collatz/ contains the logs of the Collatz function for some of the top known megaprimes and their vicinities (can not add link due to spam filter). The data currently cover 15 out of Top 17 known megaprimes (except for #7 and #8 discovered in 2023). There are also some interesting graphs with numerical data available that may be added to other graphs in the article. As far as I could say, such big numbers (>45 in total) have never been tested for the validity of the Collatz conjecture. Re2000 (talk) 07:06, 14 April 2024 (UTC)

 * You may be interested in this thread. --DaBler (talk) 14:22, 15 April 2024 (UTC)
 * The numbers they discuss there are infinitesimal compared with the tested numbers in the project above. E.g., they discuss 26,000,000 -1, whereas the largest known megaprime tested in the project was 282,589,933 − 1. There is nothing of value in the discussion you mention, though it is definitely asking a valid question - "what is the largest number tested for the validity of the Collatz conjecture?" Re2000 (talk) 14:33, 18 April 2024 (UTC)

 * They calculated 210,000,000 + 1 in 48 minutes. --DaBler (talk) 18:57, 18 April 2024 (UTC)
 * This is still 272,589,033 smaller than the largest tested number. 87.236.191.246 (talk) 06:06, 19 April 2024 (UTC)

Collatz 2nd loop proven impossible in 5 steps of easy logic.
SIMPLIFIED PROOF A LOOP IS IMPOSSIBLE IN THE 3x+1 PROBLEM USING LOGICAL DEDUCTION WITH EASY TO FOLLOW IMAGES AND VOICEOVER IN A 4 MINUTE VIDEO ON YOUTUBE https://youtu dot be/_uugKBK1-l0?si=jq0PO8q_kJLLdNdd

Sean A Gilligan April 2023 refined and revised most recently on 22 May 2024

Abstract Prove the function x×3+1/2^n when repeated will always go to 1. The origin of the function is attributed to being proposed by German mathematician Lothar Collatz in 1937 [1] Take any odd number multiply it by 3 and add one then divide by 2 until one arrives at the next odd number, repeat as many times as possible, so far every number goes to one and loops between 1421. The task is to prove it always will, 2 possible exceptions have been hypothesised, one where a sequence returns to the same value of x and loops forever or where it rises eternally higher towards infinity. In this paper I prove such a hypothesised loop is impossible.

Introduction In order to have a loop in the 3x+1 problem the value of all rises VR must equal the value of all falls VF between the 1st and final  X(capital X) so that VR-VF=0 We can deduce whether that is possible by working backwards and using only full values of x's in 5 simple steps of logical deduction.

Where any 3x+1=y y is always even.

1. the 1st rise we cancel 2X between X and y-1 (which is 3X leaving X from 0 to X and 0 from X to 3X) with 2X in the final fall between the final y(fy) and X. This leaves fy-3X in the final fall between fy and X.  y is always even x is always odd so fy-3x is always odd

2. So we know we must get a net rise (between all y to x to y-1's) between the 1st y and the final y-1(fy-1) to cancel to 0

3)a) Between X and X, where any x is greater than the previous x then y=2x so we cancel 1x in the descent from y to x with 1x in the rise from x to 3x this leaves a net rise (NR) of 1x from x to 3x (or y-1) (and one value of x between 0 and x). 1x is always odd.

3. b) Where x is less than the previous x y=x×2^n(n greater than 1) in the fall we can cancel 2x in the rise from x to 2x with 2x in the fall from y to x leave a net fall (NF)=y-3x always odd (plus 1x between 0 and x). Add up all NR to a total net rise TNR of all values between x to y's and y to x's, add up all NF(not including fy-3X) to a total net fall TNF. Subtract one from the other to leave an overall net ascent ONA (from all y to x to y-1's). If ONA=fy-3X we could cancel one from the other to leave a final value of 0 between all x's and y's.

4. This would need an odd number of x's between the starting X and yf because we need an odd TNR minus an even TNF or an even TNR minus an odd TNF to leave an odd number equal to fy-3X. So when one is cancelled from the other we are left with 0 for all values between x and y's between Xand X.

5. However here arises an inescapable inequality. For a loop to happen every value of x must be linked with no breaks in the chain so calculating from the lowest odd value of x in the loop as the starting X (Xn) we know the next odd value of x must be higher so the difference between X (Xn) and the next 3x or ((Xn+1)×3) must be an even number (Eg:between 31 and 47×3 we have 110) so if we cancel this value ((Xn+1)×3) from the final y instead of 3X we are still left with an odd number in the descent from the final y. However now we have an even number of odd x's between the 2nd y ((Xn+1)×3)+1 and the final y-1, this would be either an odd number of descents subtracted from an odd number of ascents or an even number of descents subtracted from an even number of ascents, which either would leave a net rise of an even number which can't cancel with the final y(fy) and X(n+1)×3 which is an odd number, so we can't get a net rise of 0.

So a 2nd loop is impossible in the 3x+1 problem, regardless of any value for X in any sequence within infinity.. This part of the conjecture is now ruled out as being impossible.

Having no address, no contacts in academic institutions and no bank account the peer review system is inaccessible. So it is in the public domain since May 2024. 83.137.6.162 (talk) 08:12, 8 June 2024 (UTC)

 * Sorry, Wikipedia is not the right place for Original Research.
 * Suggestion: team up with someone who does have access to the peer review system. Success! Uwappa (talk) 09:47, 8 June 2024 (UTC)
 * Thanks, that sounds easy and in theory should be, the comment no doubt from someone inside the academic system. That has been tried many times, as stated having no bank account means payment is not accessible, an endorsement requires someone willing to take time to read and think through of which there has been none found willing to do so without payment despite multiple requests. Even getting a meeting with busy people has been difficult, getting them to focus and read, listen without bias for 5 minutes impossible, requests for an endorsement for arxiv the same, people are clearly very busy and getting their time without money, bias or a "who knows who" is not as easy as it sounds, quite the opposite. Correction to your comment, it is not research it is absolute proof which you would see if you or anyone else would focus and read without bias for 5 minutes. It also begs the question... Why should a simple mathematical proof be held back from the public because the author(or his work) does not/cannot pay money to or become controlled by a hierarchical system? We saw this before with scientists like Galileo, Aristarchus and likely Tesla too. The lesson should be learned by now. If you don't understand the proof I suggest you focus and watch the video and follow the images for 5 minutes. The best we can hope is that the editors of the wiki page have scientific integrity enough to go with science and not bow down to a hierarchical monetary system which controls what or when truth reaches the public and discriminates in favour of richer people/nations, and against those with little or no money. Whatever such control is, it is not science.
 * If this is held back by such a hierarchical system that amounts to a colonial, anti science mindset, like it or not that's what it would be. Let's hope science is upheld over control. 185.114.163.227 (talk) 11:29, 8 June 2024 (UTC)
 * Sorry. Wikipedians will remove even the most brilliant absolute proof if not backed by a reliable secondary source. Wikipedia is not on the cutting edge, is not leading science. It trails science.
 * Your BREAKING PHYSICS youtube channel looks like a platform that suits you better. How about making more of the last 'A' (action) in AIDA_(marketing)? You do ask to share the video with anyone interested in mathematics and science. Why not take it one step further? Ask interested scientists to contact you so you can team up. Good luck! Uwappa (talk) 14:04, 8 June 2024 (UTC)
 * Thanks again, it's the easiest thing in the world to say something can't or won't be done and as for asking scientists to cooperate, you really have no idea how hard it is to get people to listen when you're not in the club. At the end of the day the essence of the proof is that 2 odd numbers added together cannot equate to an odd number. When something that simple needs someone with money to endorse it I guess it says a lot about the system and the people running it. It's sad for science, sad for humanity, I live in hope that common sense prevails somehow regardless. Thanks anyway for your interaction, even that is better than the wall of silence so often prevalent when the academic boat gets rocked. 83.137.6.166 (talk) 23:18, 8 June 2024 (UTC)

Please feel welcome to join 'this club'. No money or other people required to create a Wikipedia account. Still, face reality: Don't let these words deter you. Feel welcome. Join this club. Enjoy your own user page, your own talk page. Alternative: talk to local math students. They will understand you, adjudicate your proof and, once convinced, rub their hands with glee to take it up the hierarchy and rock a boat. Uwappa (talk) 12:31, 9 June 2024 (UTC)
 * 1) The top 25 of most popular Wikipedia pages contains very little, if any science. People mainly visit Wikipedia for sport results, news, movies, TV shows, artist fancruft, ...
 * 2) Original Research remains a big no no at Wikipedia. This is the wrong place to publish new proof, no matter how simple, true, brilliant, revolutionary...
 * 3) The academic use of Wikipedia is low. Wikipedia is not the right tool to rock an academic boat.

Different formulations as rewriting systems
Under the section "Other formulations of the conjecture", include some formulations of the Collatz conjecture as termination problems for rewriting systems. These formulations enable automated approaches to the Collatz conjecture by using methods that are developed for automatically proving termination of rewriting.

For this change, please add the following after the section "As a tag system" under "Other formulations of the conjecture".

As string rewriting systems
For this section, assume that the Collatz function is defined in the slightly modified form:

$$f(n) = \begin{cases} \frac{n}{2} &\text{if } n \equiv 0 \\[4px] \frac{3n+1}{2} & \text{if } n \equiv 1 \end{cases} \pmod{2}$$

The termination of the following string rewriting system is equivalent to the Collatz conjecture:

$$\begin{array}[t]{rcl} \mathtt{h} \mathtt{1} \mathtt{1} & \to & \mathtt{1} \mathtt{h} \end{array} \qquad \begin{array}{rcl} \mathtt{1} \mathtt{1} \mathtt{h} \mathtt{b} & \to & \mathtt{1} \mathtt{1} \mathtt{s} \mathtt{b} \\ \mathtt{1} \mathtt{s} & \to & \mathtt{s} \mathtt{1} \\ \mathtt{b} \mathtt{s} & \to & \mathtt{b} \mathtt{h} \end{array} \qquad \begin{array}{rcl} \mathtt{h} \mathtt{1} \mathtt{b} & \to & \mathtt{t} \mathtt{1} \mathtt{1} \mathtt{b} \\ \mathtt{1} \mathtt{t} & \to & \mathtt{t} \mathtt{1} \mathtt{1} \mathtt{1} \\ \mathtt{b} \mathtt{t} & \to & \mathtt{b} \mathtt{h} \end{array}$$

The above rewriting system represents each number in unary, and applications of its rules in any order to such a representation simulates the iterated applications of the Collatz function. Roughly speaking, this system simulates the execution of a Turing machine with cells that can be contracted or expanded, where $$\mathtt{h}$$, $$\mathtt{s}$$, $$\mathtt{t}$$ indicate the position of the head along with the state, $$\mathtt{b}$$ stands for the blank characters on the tape, and the symbol $$\mathtt{1}$$ is the unary digit.

An alternative string rewriting system that uses mixed binary–ternary representations of numbers is as follows:

$$\begin{array}{rcl} \mathtt{f} \triangleright & \to & \triangleright \\ \mathtt{t} \triangleright & \to & \mathtt{2} \triangleright \end{array} \qquad \begin{array}{rcl} \mathtt{f} \mathtt{0} & \to & \mathtt{0} \mathtt{f} \\ \mathtt{f} \mathtt{1} & \to & \mathtt{0} \mathtt{t} \\ \mathtt{f} \mathtt{2} & \to & \mathtt{1} \mathtt{f} \end{array} \qquad \begin{array}{rcl} \mathtt{t} \mathtt{0} & \to & \mathtt{1} \mathtt{t} \\ \mathtt{t} \mathtt{1} & \to & \mathtt{2} \mathtt{f} \\ \mathtt{t} \mathtt{2} & \to & \mathtt{2} \mathtt{t} \end{array} \qquad \begin{array}{rcl} \triangleleft \mathtt{0} & \to & \triangleleft \mathtt{t} \\ \triangleleft \mathtt{1} & \to & \triangleleft \mathtt{f} \mathtt{f} \\ \triangleleft \mathtt{2} & \to & \triangleleft \mathtt{f} \mathtt{t} \end{array}$$

In the above system, the symbols $$\mathtt{f}$$ and $$\mathtt{t}$$ represent the binary digits (0 and 1), while the symbols $$\mathtt{0}$$, $$\mathtt{1}$$, $$\mathtt{2}$$ represent the ternary digits. The symbols $$\triangleleft$$ and $$\triangleright$$ act as delimiters. The rules in the first column apply the Collatz function to a number represented in mixed base as long as the rightmost digit is binary. The remaining rules rewrite the representation (while preserving the value it represents) such that the rightmost digit is binary.

Rephrasing the Collatz conjecture as termination of string rewriting enables, at least in principle, using automated approaches to try to prove the conjecture thanks to the methods developed for automatically proving termination of rewriting.

46.196.80.203 (talk) 13:49, 17 June 2024 (UTC)

Not done: This seems a bit WP:TOOSOON to me. It's based on a paper that's less than a year old with few citations. PianoDan (talk) 22:32, 18 June 2024 (UTC)

 * The paper by Zantema is from 2005, so it is ~19 years old. The other paper by Yolcu, Aaronson, and Heule is actually ~3 years old; the conference version of their paper is here: https://doi.org/10.1007/978-3-030-79876-5_27. The latter work was also featured in 2021 in popular science magazines, for instance: https://www.technologyreview.com/2021/07/02/1027475/computers-ready-solve-this-notorious-math-problem. 46.196.80.203 (talk) 09:52, 24 June 2024 (UTC)
 * Red information icon with gradient background.svg Not done for now: please establish a consensus for this alteration before using the template. I still don't think it's warranted based on the level of citations it has received.  Given that there is disagreement from at least one editor that this material should be included in the article, the "Edit request template" procedure no longer applies, since it's only for non-controversial edits.  Instead, you can attempt to build a consensus on this page that the material should be included. PianoDan (talk) 16:29, 24 June 2024 (UTC)
 * I fail to see why the citation count of the source material should be a significant basis for the decision of whether to include some content on the page, but let's assume it should be: Arguably the most similar content currently visible on the page is Liesbeth De Mol's 2-tag system from the 2008 paper. According to Google Scholar, that paper has 36 citations since 2008. Zantema's paper has 64 citations since 2005, and YAH's (conference) paper has 12 citations since 2021. To my understanding, the edit decision should be made based on the significance of the content and whether it is interesting enough. I think those rewriting systems are somewhat more interesting than the tag system since they enable an entirely new approach (at least in principle) towards a proof of the conjecture. 46.196.80.203 (talk) 11:09, 25 June 2024 (UTC)

Binary number of trailing ones equals number of following increases
The chapter Collatz_conjecture Example:
 * 1) already states that the number of trailing binary zeroes equals the number of next repeated divisions (/2). That is obvious.
 * 2) but it does not yet state that the number of trailing binary ones equals the next number of increments, (*3+1)/2, as the number of trailing ones decreases by one with each increment.
 * 19: 10011 (2 next increments)
 * 29 : 11101 (1 next increment)
 * 44: 101100 (no immediate increment) The trailing 1100 indicates: after two decrements (22, 11), two increments will follow (17, 26).

The source (BOM - Beauty Of Mathematics) claims at https://www.youtube.com/watch?v=UZH3P8Ey_C8 Any mathematician known to have picked this up? Any secondary source known?
 * not to be a mathematician just working on it as a hobby, so a primary source.
 * this does not proof the conjecture, but it might lead to one.

The graph already shows the total number of binary ones in brackets.

Is there any graph available that shows the number of trailing ones? Uwappa (talk) 07:46, 25 June 2024 (UTC)

 * There does not seem to be a graph yet that shows how a Collatz sequence impacts trailing bits of binary numbers.
 * Created a graph for Collatz_conjecture showing how the Collatz conjecture 'nibbles' on trailing bits, binary ones and zeroes:
 * Collatz conjecture sequence for 27 with decreasing binary trailing bits.png Uwappa (talk) 13:28, 14 July 2024 (UTC)

title: Talk:Collatz conjecture


text:
Common gate

In electronics, a common-gate amplifier is one of three basic single-stage field-effect transistor (FET) amplifier topologies, typically used as a current buffer or voltage amplifier. In this circuit, the source terminal of the transistor serves as the input, the drain is the output, and the gate is connected to some DC biasing voltage (i.e. an AC ground), or "common," hence its name. The analogous bipolar junction transistor circuit is the common-base amplifier.

Applications
This configuration is used less often than the common source or source follower. However, it can be combined with common source amplifiers to create cascode configurations. It is useful in, for example, CMOS RF receivers, especially when operating near the frequency limitations of the FETs; it is desirable because of the ease of impedance matching and potentially has lower noise. Gray and Meyer provide a general reference for this circuit.

Low-frequency characteristics

At low frequencies and under small-signal conditions, the circuit in Figure 1 can be represented by that in Figure 2, where the hybrid-pi model for the MOSFET has been employed.

The amplifier characteristics are summarized below in Table 1. The approximate expressions use the assumptions (usually accurate) rO >> RL and gmrO >> 1.

In general, the overall voltage/current gain may be substantially less than the open/short circuit gains listed above (depending on the source and load resistances) due to the loading effect.

Closed circuit voltage gain
Taking input and output loading into consideration, the closed circuit voltage gain (that is, the gain with load RL and source with resistance RS both attached) of the common gate can be written as:

{A_\mathrm{v}} \approx \begin{matrix} \frac {g_m R_\mathrm{L}} {1+g_mR_S} \end{matrix}$$ , which has the simple limiting forms
 * $$A_\mathrm{v} = \begin{matrix} \frac {R_L}{R_S}\end{matrix} \ \ \mathrm{ or } \ \ A_\mathrm{v} = g_m R_L $$,

depending upon whether gmRS is much larger or much smaller than one.

In the first case the circuit acts as a current follower, as understood as follows: for RS >> 1/gm the voltage source can be replaced by its Norton equivalent with Norton current vThév / RS and parallel Norton resistance RS. Because the amplifier input resistance is small, the driver delivers by current division a current vThév / RS to the amplifier. The current gain is unity, so the same current is delivered to the output load RL, producing by Ohm's law an output voltage vout = vThévRL / RS, that is, the first form of the voltage gain above.

In the second case RS << 1/gm and the Thévenin representation of the source is useful, producing the second form for the gain, typical of voltage amplifiers.

Because the input impedance of the common-gate amplifier is very low, the cascode amplifier often is used instead. The cascode places a common-source amplifier between the voltage driver and the common-gate circuit to permit voltage amplification using a driver with RS >> 1/gm.

title: Common gate


text:
Common source

In electronics, a common-source amplifier is one of three basic single-stage field-effect transistor (FET) amplifier topologies, typically used as a voltage or transconductance amplifier. The easiest way to tell if a FET is common source, common drain, or common gate is to examine where the signal enters and leaves. The remaining terminal is what is known as "common". In this example, the signal enters the gate, and exits the drain. The only terminal remaining is the source. This is a common-source FET circuit. The analogous bipolar junction transistor circuit may be viewed as a transconductance amplifier or as a voltage amplifier. (See classification of amplifiers). As a transconductance amplifier, the input voltage is seen as modulating the current going to the load. As a voltage amplifier, input voltage modulates the current flowing through the FET, changing the voltage across the output resistance according to Ohm's law. However, the FET device's output resistance typically is not high enough for a reasonable transconductance amplifier (ideally infinite), nor low enough for a decent voltage amplifier (ideally zero). As seen below in the formula, the voltage gain depends on the load resistance, so it cannot be applied to drive low-resistance devices, such as a speaker (having a resistance of 8 ohms). Another major drawback is the amplifier's limited high-frequency response. Therefore, in practice the output often is routed through either a voltage follower (common-drain or CD stage), or a current follower (common-gate or CG stage), to obtain more favorable output and frequency characteristics. The CS–CG combination is called a cascode amplifier.

Characteristics
At low frequencies and using a simplified hybrid-pi model (where the output resistance due to channel length modulation is not considered), the following closed-loop small-signal characteristics can be derived.

Bandwidth
Bandwidth of common-source amplifier tends to be low, due to high capacitance resulting from the Miller effect. The gate-drain capacitance is effectively multiplied by the factor $$1+|A_\text{v}|\,$$, thus increasing the total input capacitance and lowering the overall bandwidth.

Figure 3 shows a MOSFET common-source amplifier with an active load. Figure 4 shows the corresponding small-signal circuit when a load resistor RL is added at the output node and a Thévenin driver of applied voltage VA and series resistance RA is added at the input node. The limitation on bandwidth in this circuit stems from the coupling of parasitic transistor capacitance Cgd between gate and drain and the series resistance of the source RA. (There are other parasitic capacitances, but they are neglected here as they have only a secondary effect on bandwidth.)

Using Miller's theorem, the circuit of Figure 4 is transformed to that of Figure 5, which shows the Miller capacitance CM on the input side of the circuit. The size of CM is decided by equating the current in the input circuit of Figure 5 through the Miller capacitance, say iM, which is:

 * $$\ i_\mathrm{M} = j \omega C_\mathrm{M} v_\mathrm{GS} = j \omega C_\mathrm{M} v_\mathrm{G}$$ ,

to the current drawn from the input by capacitor Cgd in Figure 4, namely jωCgd vGD. These two currents are the same, making the two circuits have the same input behavior, provided the Miller capacitance is given by:

 * $$ C_\mathrm{M} = C_\mathrm{gd} \frac {v_\mathrm{GD}} {v_\mathrm{GS}} = C_\mathrm{gd} \left( 1 - \frac {v_\mathrm{D}} {v_\mathrm{G}} \right)$$.

Usually the frequency dependence of the gain vD / vG is unimportant for frequencies even somewhat above the corner frequency of the amplifier, which means a low-frequency hybrid-pi model is accurate for determining vD / vG. This evaluation is Miller's approximation and provides the estimate (just set the capacitances to zero in Figure 5):

 * $$ \frac {v_\mathrm{D}} {v_\mathrm{G}} \approx -g_\mathrm{m} (r_\mathrm{O} \parallel R_\mathrm{L})$$ ,

so the Miller capacitance is

 * $$ C_\mathrm{M} = C_\mathrm{gd} \left( 1+g_\mathrm{m} (r_\mathrm{O} \parallel R_\mathrm{L})\right) $$.

The gain gm (rO || RL) is large for large RL, so even a small parasitic capacitance Cgd can become a large influence in the frequency response of the amplifier, and many circuit tricks are used to counteract this effect. One trick is to add a common-gate (current-follower) stage to make a cascode circuit. The current-follower stage presents a load to the common-source stage that is very small, namely the input resistance of the current follower (RL ≈ 1 / gm ≈ Vov / (2ID) ; see common gate). Small RL reduces CM. The article on the common-emitter amplifier discusses other solutions to this problem.

Returning to Figure 5, the gate voltage is related to the input signal by voltage division as:

 * $$ v_\mathrm{G} = V_\mathrm{A}\frac {1/(j \omega C_\mathrm{M}) } {1/(j \omega C_\mathrm{M}) +R_\mathrm{A}} = V_\mathrm{A}\frac {1} {1+j \omega C_\mathrm{M} R_\mathrm{A}} $$.

The bandwidth (also called the 3 dB frequency) is the frequency where the signal drops to 1/ $\sqrt{2}$ of its low-frequency value. (In decibels, dB($\sqrt{2}$) = 3.01 dB). A reduction to 1/ $\sqrt{2}$ occurs when ωCM RA = 1, making the input signal at this value of ω (call this value ω3 dB, say) vG = VA / (1+j). The magnitude of (1+j) = $\sqrt{2}$. As a result, the 3 dB frequency f3 dB = ω3 dB / (2π) is:

 * $$ f_\mathrm{3dB}=\frac {1}{2\pi R_\mathrm{A} C_\mathrm{M}}= \frac {1}{2\pi R_\mathrm{A} [ C_\mathrm{gd}(1+g_\mathrm{m} (r_\mathrm{O} \parallel R_\mathrm{L})]}$$.

If the parasitic gate-to-source capacitance Cgs is included in the analysis, it simply is parallel with CM, so
 * $$ f_\mathrm{3dB}=\frac {1}{2\pi R_\mathrm{A} (C_\mathrm{M}+C_\mathrm{gs})} =\frac {1}{2\pi R_\mathrm{A} [C_\mathrm{gs} + C_\mathrm{gd}(1+g_\mathrm{m} (r_\mathrm{O} \parallel R_\mathrm{L}))]}$$.

Notice that f3 dB becomes large if the source resistance RA is small, so the Miller amplification of the capacitance has little effect upon the bandwidth for small RA. This observation suggests another circuit trick to increase bandwidth: add a common-drain (voltage-follower) stage between the driver and the common-source stage so the Thévenin resistance of the combined driver plus voltage follower is less than the RA of the original driver.

Examination of the output side of the circuit in Figure 2 enables the frequency dependence of the gain vD / vG to be found, providing a check that the low-frequency evaluation of the Miller capacitance is adequate for frequencies f even larger than f3 dB. (See article on pole splitting to see how the output side of the circuit is handled.)

title: Common source


text:
Common drain

In electronics, a common-drain amplifier, also known as a source follower, is one of three basic single-stage field-effect transistor (FET) amplifier topologies, typically used as a voltage buffer. In this circuit (NMOS) the gate terminal of the transistor serves as the signal input, the source is the output, and the drain is common to both (input and output), hence its name. Because of its low dependence on the load resistor on the voltage gain, it can be used to drive low resistance loads, such as a speaker. The analogous bipolar junction transistor circuit is the common-collector amplifier. This circuit is also commonly called a "stabilizer".

In addition, this circuit is used to transform impedances. For example, the Thévenin resistance of a combination of a voltage follower driven by a voltage source with high Thévenin resistance is reduced to only the output resistance of the voltage follower (a small resistance). That resistance reduction makes the combination a more ideal voltage source. Conversely, a voltage follower inserted between a driving stage and a high load (i.e. a low resistance) presents an infinite resistance (low load) to the driving stage—an advantage in coupling a voltage signal to a large load.

Characteristics
At low frequencies, the source follower pictured at right has the following small-signal characteristics.

The variable gm that is not listed in the schematic is the transconductance of the device (usually given in units of siemens).

title: Common drain


text:
Split-quaternion

In abstract algebra, the split-quaternions or coquaternions form an algebraic structure introduced by James Cockle in 1849 under the latter name. They form an associative algebra of dimension four over the real numbers.

After introduction in the 20th century of coordinate-free definitions of rings and algebras, it was proved that the algebra of split-quaternions is isomorphic to the ring of the $2×2$ real matrices. So the study of split-quaternions can be reduced to the study of real matrices, and this may explain why there are few mentions of split-quaternions in the mathematical literature of the 20th and 21st centuries.

Definition
The split-quaternions are the linear combinations (with real coefficients) of four basis elements $1, i, j, k$ that satisfy the following product rules:

By associativity, these relations imply

and also $i^{2} = −1$.

So, the split-quaternions form a real vector space of dimension four with $j^{2} = 1$ as a basis. They form also a noncommutative ring, by extending the above product rules by distributivity to all split-quaternions.

Let consider the square matrices
 * $$\begin{align}

\boldsymbol{1} =\begin{pmatrix}1&0\\0&1\end{pmatrix},\qquad&\boldsymbol{i} =\begin{pmatrix}0&1\\-1&0\end{pmatrix},\\ \boldsymbol{j} =\begin{pmatrix}0&1\\1&0\end{pmatrix},\qquad&\boldsymbol{k} =\begin{pmatrix}1&0\\0&-1\end{pmatrix}. \end{align}$$ They satisfy the same multiplication table as the corresponding split-quaternions. As these matrices form a basis of the two-by-two matrices, the unique linear function that maps $k^{2} = 1$ to $$\boldsymbol{1}, \boldsymbol{i}, \boldsymbol{j}, \boldsymbol{k}$$ (respectively) induces an algebra isomorphism from the split-quaternions to the two-by-two real matrices.

The above multiplication rules imply that the eight elements $ij = k = −ji$ form a group under this multiplication, which is isomorphic to the dihedral group D4, the symmetry group of a square. In fact, if one considers a square whose vertices are the points whose coordinates are $jk = −i = −kj$ or $ki = j = −ik$, the matrix $$\boldsymbol{i}$$ is the clockwise rotation of the quarter of a turn, $$\boldsymbol{j}$$ is the symmetry around the first diagonal, and $$\boldsymbol{k}$$ is the symmetry around the $x$ axis.

Properties
Like the quaternions introduced by Hamilton in 1843, they form a four dimensional real associative algebra. But like the real algebra of 2×2 matrices – and unlike the real algebra of quaternions – the split-quaternions contain nontrivial zero divisors, nilpotent elements, and idempotents. (For example, $1⁄2$(1 + j) is an idempotent zero-divisor, and i − j is nilpotent.) As an algebra over the real numbers, the algebra of split-quaternions is isomorphic to the algebra of 2×2 real matrices by the above defined isomorphism.

This isomorphism allows identifying each split-quaternion with a 2×2 matrix. So every property of split-quaternions corresponds to a similar property of matrices, which is often named differently.

The conjugate of a split-quaternion $ijk = 1$, is $\{1, i, j, k\}$. In term of matrices, the conjugate is the cofactor matrix obtained by exchanging the diagonal entries and changing the sign of the other two entries.

The product of a split-quaternion with its conjugate is the isotropic quadratic form:
 * $$N(q) = q q^* = w^2 + x^2 - y^2 - z^2,$$

which is called the norm of the split-quaternion or the determinant of the associated matrix.

The real part of a split-quaternion $1, i, j, k$ is $1, i, j, k, −1, −i, −j, −k$. It equals the trace of associated matrix.

The norm of a product of two split-quaternions is the product of their norms. Equivalently, the determinant of a product of matrices is the product of their determinants. This property means that split-quaternions form a composition algebra. As there are nonzero split-quaternions having a zero norm, split-quaternions form a "split composition algebra" – hence their name.

A split-quaternion with a nonzero norm has a multiplicative inverse, namely $0$. In terms of matrices, this is equivalent to the Cramer rule that asserts that a matrix is invertible if and only its determinant is nonzero, and, in this case, the inverse of the matrix is the quotient of the cofactor matrix by the determinant.

The isomorphism between split-quaternions and 2×2 real matrices shows that the multiplicative group of split-quaternions with a nonzero norm is isomorphic with $$\operatorname{GL}(2, \mathbb R),$$ and the group of split quaternions of norm $1$ is isomorphic with $$\operatorname{SL}(2, \mathbb R).$$

Geometrically, the split-quaternions can be compared to Hamilton's quaternions as pencils of planes. In both cases the real numbers form the axis of a pencil. In Hamilton quaternions there is a sphere of imaginary units, and any pair of antipodal imaginary units generates a complex plane with the real line. For split-quaternions there are hyperboloids of hyperbolic and imaginary units that generate split-complex or ordinary complex planes, as described below in § Stratification.

Representation as complex matrices
There is a representation of the split-quaternions as a unital associative subalgebra of the $q = w + xi + yj + zk$ matrices with complex entries. This representation can be defined by the algebra homomorphism that maps a split-quaternion $q^{∗} = w − xi − yj − zk$ to the matrix
 * $$\begin{pmatrix}w+xi& y+zi\\y-zi&w-xi\end{pmatrix}.$$

Here, $i$ (italic) is the imaginary unit, not to be confused with the split quaternion basis element $q = w + xi + yj + zk$ (upright roman).

The image of this homomorphism is the matrix ring formed by the matrices of the form
 * $$\begin{pmatrix}u & v \\ v^* & u^* \end{pmatrix},$$

where the superscript $$^*$$ denotes a complex conjugate.

This homomorphism maps respectively the split-quaternions $w = (q^{∗} + q)/2$ on the matrices
 * $$\begin{pmatrix}i & 0 \\0 &-i \end{pmatrix}, \quad\begin{pmatrix}0 & 1 \\1 &0 \end{pmatrix},\quad \begin{pmatrix}0 & i \\-i &0 \end{pmatrix}.$$

The proof that this representation is an algebra homomorphism is straightforward but requires some boring computations, which can be avoided by starting from the expression of split-quaternions as $q^{∗}/N(q)$ real matrices, and using matrix similarity. Let $S$ be the matrix
 * $$S=\begin{pmatrix}1 & i \\i &1 \end{pmatrix}.$$

Then, applied to the representation of split-quaternions as $1$ real matrices, the above algebra homomorphism is the matrix similarity.
 * $$M\mapsto S^{-1}MS.$$

It follows almost immediately that for a split quaternion represented as a complex matrix, the conjugate is the matrix of the cofactors, and the norm is the determinant.

With the representation of split quaternions as complex matrices. the matrices of quaternions of norm $2×2$ are exactly the elements of the special unitary group SU(1,1). This is used for in hyperbolic geometry for describing hyperbolic motions of the Poincaré disk model.

Generation from split-complex numbers
Split-quaternions may be generated by modified Cayley–Dickson construction similar to the method of L. E. Dickson and Adrian Albert. for the division algebras C, H, and O. The multiplication rule $$(a,b)(c,d)\ = \ (ac + d^* b, \ da + bc^* )$$ is used when producing the doubled product in the real-split cases. The doubled conjugate $$(a,b)^* = (a^*, - b), $$ so that $$N(a,b) \ = \ (a,b)(a,b)^* \ = \ (a a^* - b b^*, 0).$$ If a and b are split-complex numbers and split-quaternion $$q = (a,b) = ((w + z j), (y + xj)), $$

then $$N(q) = a a^* - b b^* = w^2 - z^2 - (y^2 - x^2) = w^2 + x^2 - y^2 - z^2 .$$

Stratification
In this section, the real subalgebras generated by a single split-quaternion are studied and classified.

Let $w + xi + yj + zk$ be a split-quaternion. Its real part is $i$. Let $i, j, k$ be its nonreal part. One has $2×2$, and therefore $$p^2=w^2+2wq-N(q).$$ It follows that $2×2$ is a real number if and only $1$ is either a real number ($p = w + xi + yj + zk$ and $w = 1⁄2(p + p*)$) or a purely nonreal split quaternion ($q = p – w = 1⁄2(p – p*)$ and $q* = –q$).

The structure of the subalgebra $$\mathbb R[p]$$ generated by $p$ follows straightforwardly. One has
 * $$\mathbb R[p]=\mathbb R[q]=\{a+bq\mid a,b\in\mathbb R\},$$

and this is a commutative algebra. Its dimension is two except if $p$ is real (in this case, the subalgebra is simply $$\mathbb R$$).

The nonreal elements of $$\mathbb R[p]$$ whose square is real have the form $p^{2}$ with $$a\in \mathbb R.$$

Three cases have to be considered, which are detailed in the next subsections.

Nilpotent case
With above notation, if $$q^2=0,$$ (that is, if $p$ is nilpotent), then $q = 0$, that is, $$x^2-y^2-z^2=0.$$ This implies that there exist $w$ and $t$ in $$\mathbb R$$ such that $p = w$ and
 * $$p=w+a\mathrm i + a\cos(t)\mathrm j + a\sin(t)\mathrm k.$$

This is a parametrization of all split-quaternions whose nonreal part is nilpotent.

This is also a parameterization of these subalgebras by the points of a circle: the split-quaternions of the form $$\mathrm i + \cos(t)\mathrm j + \sin(t)\mathrm k$$ form a circle; a subalgebra generated by a nilpotent element contains exactly one point of the circle; and the circle does not contain any other point.

The algebra generated by a nilpotent element is isomorphic to $$\mathbb R[X]/\langle X^2\rangle$$ and to the plane of dual numbers.

Imaginary units
This is the case where $w = 0$. Letting $n=\sqrt{N(q)},$  one has
 * $$q^2 =-q^*q=N(q)=n^2=x^2-y^2-z^2.$$

It follows that $p = q$ belongs to the hyperboloid of two sheets of equation $$x^2-y^2-z^2=1.$$ Therefore, there are real numbers $aq$ such that $q$ and
 * $$p=w+n\cosh(u)\mathrm i + n\sinh(u)\cos(t)\mathrm j + n\sinh(u)\sin(t)\mathrm k.$$

This is a parametrization of all split-quaternions whose nonreal part has a positive norm.

This is also a parameterization of the corresponding subalgebras by the pairs of opposite points of a hyperboloid of two sheets: the split-quaternions of the form $$\cosh(u)\mathrm i + \sinh(u)\cos(t)\mathrm j + \sinh(u)\sin(t)\mathrm k$$ form a hyperboloid of two sheets; a subalgebra generated by a split-quaternion with a nonreal part of positive norm contains exactly two opposite points on this hyperboloid, one on each sheet; and the hyperboloid does not contain any other point.

The algebra generated by a split-quaternion with a nonreal part of positive norm is isomorphic to $$\mathbb R[X]/\langle X^2+1\rangle$$ and to the field $$\Complex$$ of complex numbers.

Hyperbolic units
This is the case where $N(q) = 0$. Letting $n=\sqrt{-N(q)},$  one has
 * $$q^2 = -q^*q=N(q)=-n^2=x^2-y^2-z^2.$$

It follows that $0 ≤ t < 2\pi$ belongs to the hyperboloid of one sheet of equation $N(q) > 0$. Therefore, there are real numbers $1⁄n q$ such that $n, t, u$ and
 * $$p=w+n\sinh(u)\mathrm i + n\cosh(u)\cos(t)\mathrm j + n\cosh(u)\sin(t)\mathrm k.$$

This is a parametrization of all split-quaternions whose nonreal part has a negative norm.

This is also a parameterization of the corresponding subalgebras by the pairs of opposite points of a hyperboloid of one sheet: the split-quaternions of the form $$\sinh(u)\mathrm i + \cosh(u)\cos(t)\mathrm j + \cosh(u)\sin(t)\mathrm k$$ form a hyperboloid of one sheet; a subalgebra generated by a split-quaternion with a nonreal part of negative norm contains exactly two opposite points on this hyperboloid; and the hyperboloid does not contain any other point.

The algebra generated by a split-quaternion with a nonreal part of negative norm is isomorphic to $$\mathbb R[X]/\langle X^2-1\rangle$$ and to the ring of split-complex numbers. It is also isomorphic (as an algebra) to $$\mathbb R^2$$ by the mapping defined by $(1,0)\mapsto \frac{1+X}2, \quad (0,1)\mapsto \frac{1-X}2. $

Stratification by the norm
As seen above, the purely nonreal split-quaternions of norm $0 ≤ t < 2\pi$ and $N(q) < 0$ form respectively a hyperboloid of one sheet, a hyperboloid of two sheets and a circular cone in the space of non real quaternions.

These surfaces are pairwise asymptote and do not intersect. Their complement consist of six connected regions:
 * the two regions located on the concave side of the hyperboloid of two sheets, where $$N(q)>1$$
 * the two regions between the hyperboloid of two sheets and the cone, where $$0<N(q)<1$$
 * the region between the cone and the hyperboloid of one sheet where $$-1<N(q)<0$$
 * the region outside the hyperboloid of one sheet, where $$N(q)<-1$$

This stratification can be refined by considering split-quaternions of a fixed norm: for every real number $1⁄n q$ the purely nonreal split-quaternions of norm $y^{2} + z^{2} − x^{2} = 1$ form an hyperboloid. All these hyperboloids are asymptote to the above cone, and none of these surfaces intersect any other. As the set of the purely nonreal split-quaternions is the disjoint union of these surfaces, this provides the desired stratification.

Colour space
Split quaternions have been applied to colour balance The model refers to the Jordan algebra of symmetric matrices representing the algebra. The model reconciles trichromacy with Hering's opponency and uses the Cayley–Klein model of hyperbolic geometry for chromatic distances.

Historical notes
The coquaternions were initially introduced (under that name) in 1849 by James Cockle in the London–Edinburgh–Dublin Philosophical Magazine. The introductory papers by Cockle were recalled in the 1904 Bibliography of the Quaternion Society.

Alexander Macfarlane called the structure of split-quaternion vectors an exspherical system when he was speaking at the International Congress of Mathematicians in Paris in 1900. Macfarlane considered the "hyperboloidal counterpart to spherical analysis" in a 1910 article "Unification and Development of the Principles of the Algebra of Space" in the Bulletin of the Quaternion Society.

The unit sphere was considered in 1910 by Hans Beck. For example, the dihedral group appears on page 419. The split-quaternion structure has also been mentioned briefly in the Annals of Mathematics.

Synonyms

 * Para-quaternions (Ivanov and Zamkovoy 2005, Mohaupt 2006) Manifolds with para-quaternionic structures are studied in differential geometry and string theory. In the para-quaternionic literature, $n, t, u$ is replaced with $0 ≤ t < 2\pi$.
 * Exspherical system (Macfarlane 1900)
 * Split-quaternions (Rosenfeld 1988)
 * Antiquaternions (Rosenfeld 1988)
 * Pseudoquaternions (Yaglom 1968 Rosenfeld 1988)

title: Split-quaternion


text:
Category:Donkey Kong video games

Category for video games featuring Donkey Kong or related characters.

title: Category:Donkey Kong video games


text:
Miguel Ángel de Quevedo metro station

Miguel Ángel de Quevedo (also spelt M. A. de Quevedo) is a station along Line 3 of the Mexico City Metro. It is located in Mexico City's southern Coyoacán borough, at the junction of Avenida Miguel Ángel de Quevedo and Avenida Universidad.

General information
The station logo represents a tree. Its name comes from the nearby avenue, which was named in honor of Miguel Ángel de Quevedo, an engineer who founded the nearby Viveros de Coyoacán arboretum and nursery (parts of which are a publicly accessible park and a popular area for recreation). Apparently, this station was initially designed to have a third platform between the other two, but it was never made operational, the design was changed, and today it is used by workers and for access to an electrical substation. The station serves the Colonia Chimalistac, Santa Catarina, and Romero de Terreros districts. It was opened on 30 August 1983.

This station transfers to trolleybus Line "K1", which runs between Ciudad Universitaria, the main campus of the Universidad Nacional Autónoma de México, and the San Lorenzo Tezonco campus of Universidad Autónoma de la Ciudad de México.

It also serves as a terminal for bus lines 41 and 66 which connect the station to several locations in the Contreras area.

Exits

 * Northeast: Avenida Universidad and Miguel Ángel de Quevedo, Romero de Terreros
 * Southwest: Avenida Universidad, Chimalistac
 * West: Avenida Universidad, Chimalistac

title: Miguel Ángel de Quevedo metro station


text:
Wikipedia:Articles for deletion/Carmella DeCesare

 This page is an archive of the discussion about the proposed deletion of the article below. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was KEEP. dbenbenn | talk 19:58, 14 Feb 2005 (UTC)

Carmella DeCesare
I strongly believe that this page is non-encyclopedic. Why do Playboy playmates get their own articles? For this example, there isn't anything "newsworthy" about CD except for the fact that she posed for an adult magazine and was involved with some charges. She doesnt have any other items noteworthy of mention such as being an actress/singer/etc. Markl222 07:57, 5 Feb 2005 (UTC)

 * I believe that if someone took the time to write up a page, and it contains factual information, it should be kept. There's no reason to remove it, it isn't harming anything/anywone, it informs, just like most other pages.
 * Unsigned keep vote by 68.102.219.124. Samaritan
 * if someone took the time to write up a page, and it contains factual information, it should be kept — No. That's not how an encyclopaedia works.  An encyclopaedia is not a bin into which one can throw any random facts that one can come up with about any random thing in the universe.  Read WP:WIN. Uncle G 18:00, 2005 Feb 5 (UTC)
 * Fwiw, there's only one Playmate of the Year per year, and every one of them since 1960 is red or blue linked at Playmate. Among the top of the 74k+ hits for "Playmate of the Year" are reports from major news organizations about Ms. DeCesare's troubles. I'm personally not too keen on the extent of porn-related content on Wikipedia, but that is no reason not to keep. Samaritan 14:14, 5 Feb 2005 (UTC)
 * I think that there's a distinction to be drawn between what is gossip-worthy and what is notable. Most of this article is the sort of "She had a fight with another woman over her boyfriend." factual information that makes someone gossip-worthy but almost never encyclopaedia-worthy.  (I'm sure that thousands of millions of women down the ages have had tussles with other women over their boyfriends.  There's nothing at all special about this particular case.)  The sole claim to notability here is the Playmate of The Year title.  And that, because of the status of the magazine and the notability of the title itself, raises this woman above the notability bar, if only barely.  Merge to Playmate or Weak Keep. Uncle G 18:00, 2005 Feb 5 (UTC)
 * Delete, this is tabloid content, not encyclopedic. Wyss 21:51, 5 Feb 2005 (UTC)
 * Keep. Random nudie models are non-notable, but the Playboy Playmate of the Year is notable.  -Sean Curtin 00:23, Feb 6, 2005 (UTC)
 * Delete. Playboy is notable. The young women that they get to pose for them generally aren't, even if the magazine does hype its sales, and one of the models, by having a "Playmate of the Year" issue. A few of these models, who are mostly amateurs, have parlayed their, ahem, exposure into notable careers.  Those few might merit articles in a general encyclopedia; but most, including this young woman so far, would not. --BM 00:43, 6 Feb 2005 (UTC)
 * Keep, Playmate of the Year title is notable, article needs expansion. Megan1967 02:48, 6 Feb 2005 (UTC)
 * Comment. It is just manufactured pseudo-notability.   Every year, Playboy declares one of the models to be the "Playmate of the Year".  This gets their core readership all abuzz, I suppose, as to whether Miss April was really better-looking than Miss October, etc, and they all run out and buy the PotY issue.   A year or two later, the PotY ends up getting publicity for being involved in a fight in a bar, which kind of tells you something if you are paying attention.  It's just marketing, and the fact that you think the person who is selected by this pseudo-process is notable just makes you a victim of mass marketing.  Nothing personal.   On the other hand, Wikipedia doesn't need to let itself be a victim of mass marketing.  --BM 00:47, 7 Feb 2005 (UTC)
 * Notability in a way is a product of mass marketing - you cant be notable unless you have a product that can sell to the masses (eg. books, records, films, theories etc). Being PotY is no different than earning a Pulitzer Prize in that respect. Megan1967 05:43, 7 Feb 2005 (UTC)
 * Not really. If you want to be considered current in American Literature or Journalism, you can't really remain ignorant about the winners of the Pulitzer Prize.   It is conceivable that there are circles where you have to be up on who won PotY three years ago, but I doubt it. If there are such circles, those people are probably not going to expect to get the information from an encyclopedia.  If they do -- well, I don't mind if they are disappointed.  --BM 15:33, 7 Feb 2005 (UTC)
 * An encyclopaedia will live or fall on its usefulness. If someone finds the article useful thats fine with me. Btw why do you regard a Blogger award as notable yet PotY as not? PotY has been around decades longer than blogs (and PotY more widely known for that matter). Megan1967 08:53, 8 Feb 2005 (UTC)
 * Keep, Although the part about her fight with another girl should be deleted, the rest should be kept. She's not only a figure in Playboy history but was also part of a major sports company. -NormalChick
 * Keep, quite interesting. Grue 10:36, 6 Feb 2005 (UTC)
 * Keep. I created this page, so of course I'd vote that way.  Perhaps every Playmate of the Month is not notable, but Miss DeCesare is in a select company.  Two, she has done a few things outside the realm of Playboy.  Three, most of the sites that will come up on Google for her name I suspect will be pornographic and here's a short article with facts about her that is not.  PedanticallySpeaking 16:59, Feb 7, 2005 (UTC)
 * I'd disagree that the fight is "gossip". Gossip would be so and so is dating someone.  She was arrested and put on trial for assault--which elevates it out of the realm of gossip.  PedanticallySpeaking 20:08, Feb 8, 2005 (UTC)

 * If we get a picture in here, I'd vote to keep. Just joking.  Delete -- we are an encyclopedia, not Hello! magazine or the gossip page in a tabloid.  I know lots of pole dancers who I could write up if that's the way we want to go......  HowardB 07:21, 8 Feb 2005 (UTC)
 * Yes but she is Playmate of the Year, not a poll dancer in a pub downtown. I agree not every model or dancer should be included in Wikipedia, but PotY is notable. Megan1967 08:55, 8 Feb 2005 (UTC)
 * I'm sorry, but am I missing something here? Some writers are saying/implying she is special in some way.  But the only facts in the article are 1. She was PotY.  2. She wrestled on WWE 3. She was arrested in a bar scuffle.  As for "article needs expansion" -- like how?  Maybe we wait for her next arrest or her agent's next publicity stunt.  C'mom, guys, she is a very minor celeb.  Not encyclopedic. HowardB 14:18, 8 Feb 2005 (UTC)
 * I eliminated the "stub" reference because, admittedly, there is not much more to say. I did add some details about how she became a Playmate and am going to check the newspapers once again to see if I can add more.  PedanticallySpeaking 20:34, Feb 8, 2005 (UTC)
 * Keep. Other Playmates of the Year are already in Wikipedia. -- Old Right 23:21, 8 Feb 2005 (UTC)
 * Keep for same reason as Old Right. Dismas 18:33, 9 Feb 2005 (UTC)
 * Keep Despite the fact that she is not that famous, i agree withPedanticallySpeaking that the web needs a non-porn biographical page. Dumboy 00:06, 10 Feb 2005 (UTC)
 * Duh, keep. —RaD Man (talk) 00:28, 10 Feb 2005 (UTC)

This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion, or the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.


text:
Talk:Baghdad (EP)

Fair use rationale for Image:TheOffspringBaghdad.jpg
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title: Talk:Baghdad (EP)


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Office of Information and Regulatory Affairs

The Office of Information and Regulatory Affairs (OIRA ) is a Division within the Office of Management and Budget (OMB), which in turn, is within the Executive Office of the President. OIRA oversees the implementation of government-wide policies in, and reviews draft regulations under, Executive Order 12866, the Paperwork Reduction Act, and the Information Quality Act.

Tasks
OIRA reviews draft rules that it receives from federal agencies under the three laws noted in the preamble to this article, and develops and oversees the implementation of government-wide policies in the areas of information technology, information policy, privacy, and statistical policy.

As one step in the entire rulemaking process (as explained in more detail in United States administrative law), OIRA reviews draft rules and regulations under 12866 from 1993. Executive Order 12866 describes OIRA's role in the rulemaking process and directs agencies to follow certain principles, such as consideration of alternatives and analysis of impacts, both benefits and costs. OIRA reviews draft regulations to ensure agency compliance with this executive order.

Cost/benefit analysis—Executive Order 12866 and its predecessors
Presidential regulatory principles and the centralized review of draft regulations had been part of U.S. regulatory development for decades. President Nixon's "Quality of Life" program involved such review, and President Ford's in 1974 required agencies to prepare inflation/economic impact statements.

A predecessor office had existed at Office of Management and Budget, OMB, an agency within the Executive Office of the President for many years; from 1977 to 1981, it was briefly at the Department of Commerce. It continued with President Jimmy Carter's on "Improving Government Regulations."

Today, about 20% of all regulations flow through OIRA for cost-benefit regulatory review under Executive Order 12866.

Paperwork Reduction Act, 1981
Congress passed the Paperwork Reduction Act of 1980 and its successor, the Paperwork Reduction Act of 1995, that established OIRA in the OMB.

The OMB review process became more formalized in 1981 with President Ronald Reagan's. During his administration, the White House had reviewed 2,000 to 3,000 regulations per year. It continued during the George H. W. Bush Administration and the first nine months of the Clinton administration.

In September 1993, President Bill Clinton issued, and the total dropped to between 500 and 700 annually. The executive order states OIRA should focus on "economically significant" rules. Of the 500 to 700 rules reviewed by OIRA annually, about 100 have been classified as "economically significant". In 1995, the Paperwork Reduction Act was updated.

In January 2007, President George W. Bush signed, which changed the rules as of July 24, 2007. The Executive Order covers federal agencies' "guidance documents", in addition to regulations. Its stated purpose was to ensure that agencies comply with the regulatory principles stated in Executive Order 12866 and that the President's policies are reflected in agency rules. It also specified procedures for the resolution of conflicts between or among agencies. In July 2007, controversy arose in the U.S. Congress over this order giving the OIRA additional powers. The House of Representatives voted to prohibit OIRA from spending federal money on Executive Order 13422.

In January 2011, President Barack Obama issued Executive Order 13563 to improve regulation and regulatory review.

OIRA guides and coordinates agencies with respect to Circular A4, Information Quality Guidelines, and the Bulletin for Agency Good Guidance Practices.

Organization
The office has five branches:
 * 1) Food, Health, and Labor Branch
 * 2) Information Policy Branch
 * 3) Natural Resources and Environment Branch
 * 4) Statistical & Science Policy Branch
 * 5) Transportation and Security Branch

Criticism
ProPublica released an investigation into the division as one that has since its creation had significant but little-known power to alter regulations. It has been controversial since its inception in the 1980s. It has been given significant authority over administrative agencies through executive orders signed by presidents of both parties. It also conducts much of its business in secret and is exempt from most Freedom of Information Act requests. It also "routinely declines to release the changes it has proposed, the evidence it has relied upon to make them, or the identities and affiliations of White House advisers and other agencies' staff it has consulted". It has also been successfully used by lobbyists to alter draft regulations, with a 2003 GAO report stating "'regulated parties,' typically corporations or their lobbyists, frequently get what they want after meetings with OIRA."

A 2011 report from the Center on Progressive Reform stated that in 10 years, OIRA altered 84 percent of EPA rule submissions (as well as 65 percent of proposed rules from other agencies). The EPA's new rules on ozone pollution developed since September 2009, rolled out as tougher draft standards in January 2010, were repeatedly delayed.


text: User talk:65.94.207.166

title: User talk:65.94.207.166


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User:Jengod/List of U.S. counties named for railroad people

 * Sanborn County, South Dakota: Sanborn is named for Milwaukee Railroad superintendent George W. Sanborn.
 * Flagler County, Florida: Flagler County was named for Henry Morrison Flagler, a famous railroad builder who built the Florida East Coast Railway.


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Jerry Tarkanian

Jerry Esther Tarkanian (August 8, 1930 – February 11, 2015) was an American basketball coach. He coached college basketball for 31 seasons over five decades at three schools. He spent the majority of his career coaching with the UNLV Runnin' Rebels, leading them four times to the Final Four of the NCAA Division I men's basketball tournament, winning the national championship in 1990. Tarkanian revolutionized the college game at UNLV, utilizing a pressing defense to fuel its fast-paced offense. Overall, he won over 700 games in his college coaching career, only twice failing to win 20 games, while never having a losing season. Tarkanian was inducted into the Naismith Memorial Basketball Hall of Fame in 2013.

Tarkanian studied at Pasadena City College and later Fresno State, earning a bachelor's degree while playing basketball. He was a head coach at the high school level before becoming a successful junior college coach at Riverside City College winning three state championships, and returned to Pasadena City College and led them to a state championship. In 1968, he moved to a four-year college at Long Beach State College. Tarkanian established a successful program built on former junior college players, who were typically considered second-rate by other four-year programs. He was also the rare coach who dared to start a predominantly black lineup. He compiled a 122–20 record over five years at Long Beach before moving to the University of Nevada, Las Vegas (UNLV). He transformed the small program into a national powerhouse while granting his players the freedom to express themselves. Known for his colorful behavior and affectionately referred to as "Tark the Shark", Tarkanian became a celebrity in Las Vegas. He left the Runnin' Rebels for a brief stint coaching professionally with the San Antonio Spurs in the National Basketball Association (NBA) before finishing his career at his alma mater, Fresno State.

Throughout his career, he battled accusations of rules violations from the National Collegiate Athletic Association (NCAA), with each of his three universities suffering penalties. Tarkanian responded by challenging the organization to also investigate larger and more powerful universities. The NCAA ordered UNLV to suspend him in 1977, but he sued the NCAA and continued coaching while the case was pending. The Supreme Court ruled against him in 1988, but he remained UNLV's coach after a settlement with the NCAA. Tarkanian sued them again in 1992, and the case was settled when he received $2.5 million in 1998.

Early life
Jerry Esther Tarkanian (ձեռյ եստհեր տարկանիան) was born in 1930 to Armenian immigrants in Euclid, Ohio. His mother, Rose, was a survivor of the Armenian genocide. Tarkanian's maternal grandfather, Mickael, was an Ottoman government official who was beheaded by Turkish authorities. Mickael's son was also decapitated by the same authorities. Fearing for their lives, Rose and the rest of her siblings eventually escaped the Ottoman Empire and settled in Lebanon, where Rose met George Tarkanian. The couple married and moved to the United States. However, Jerry's father died when he was 13. By this time, Jerry showed his interest in sports, but his stepfather disapproved of his involvement with sports, while his mother encouraged him to pursue it. A graduate of Pasadena High School, he initially attended Pasadena City College in California and played basketball at the college in the 1950–51 season. Tarkanian then transferred to Fresno State College, where he played basketball for the Bulldogs in the 1954–55 season as a backup guard. After graduating from Fresno State College in 1955, he earned a master's degree in educational management from the University of Redlands.

Early coaching career
He began his coaching career with five years of California high school basketball, starting with San Joaquin Memorial High School in Fresno. He then moved to Antelope Valley High School in Lancaster (1958) and Redlands High School (1959–1960). He then moved on to the junior college level at Riverside City College from 1961 to 1966 and Pasadena City College from 1966 to 1968. He coached teams to a record four straight California junior college championships — three at Riverside, one at Pasadena.

Long Beach State (1968–1973)
Tarkanian moved to Division I basketball as coach at Long Beach State from 1968 to 1973, where he was among the first coaches to shun an unwritten rule that at least three of the five starting players had to be white. He also pioneered the use of junior college athletes. University of Nevada, Reno history professor Richard O. Davies wrote in his book, The Maverick Spirit, that Tarkanian's recruiting practice drew complaints that he was running a "'renegade' program built upon less than stellar students." When the 49ers made the 1970 NCAA Division I men's basketball tournament led by All-America Ed Ratliff, Tarkanian boasted that his team consisted almost entirely of junior college transfers. Long Beach State reached four straight NCAA tournaments, and established itself as a regional power. Though the schools were separated by just 30 mi, John Wooden of UCLA refused to schedule a regular season game with them. At the peak of Wooden's dynasty, the schools met in the 1971 West Regional final. Long Beach led at the half by 12, but UCLA prevailed 57–55 en route to their fifth straight national championship. Wary of continuing in UCLA's shadow, Tarkanian accepted an offer to coach at the University of Nevada, Las Vegas in 1973.

University of Nevada, Las Vegas (1973–1992)
Prior to his arrival, UNLV was dubbed "Tumbleweed Tech" by locals, and their basketball program had no winning track record and minimal fan support. However, he achieved much success there, coaching the Runnin' Rebels from 1973 to 1992. In fact, it was Tarkanian's idea to call the team the "Runnin' Rebels". His teams were known for run-and-gun offense, stifling defense, and going on long runs that turned close games into blowouts. They hit their peak after joining the Pacific Coast Athletic Association (now the Big West Conference) in 1982, winning or sharing 10 straight regular-season titles and winning seven tournament titles.

He took his UNLV teams to four Final Fours. In the first, in 1977 (only seven years after the program joined Division I), the Rebels lost to North Carolina in the semifinals. The Rebels averaged 109 points per game that season in an era before the shot clock or the three-point shot. However, North Carolina controlled the tempo with coach Dean Smith's famous four corners offense, and the Rebels lost 84–83. Ten years later, UNLV was defeated by eventual national champion Indiana. Finally, in the 1990 NCAA Division I men's basketball tournament Tarkanian led UNLV to the championship, prevailing 103–73 against Duke, the largest margin of victory for a championship game in tournament history. That season, the team was heavily monitored by the NCAA, which visited their campus 11 times, and suspended 10 players at various times. The 1990–91 team appeared poised to repeat as champions after running their record to 34–0 while winning by an average margin of 27.3 points. However, a rematch against Duke in the national semifinals saw the Blue Devils prevail 79–77 after the Rebels' Anderson Hunt missed a 22-foot shot at the buzzer.

Tarkanian had been under more or less constant scrutiny from the NCAA for most of his career, but managed to weather the pressure until he signed Lloyd Daniels, a talented, but troubled shooting guard from New York City. In 1987 — just months before he was due to come to campus — Daniels was caught buying crack cocaine from an undercover policeman. While Tarkanian had been known for taking in troubled players, this was too much even for him, and he announced shortly afterward that Daniels would never play for UNLV. Not long after Daniels' arrest, it emerged he'd been led to UNLV by Richard Perry, a prominent gambler who had been convicted twice for sports bribery.

Perry's involvement triggered yet another NCAA investigation, which resulted in the NCAA initially banning the Rebels from the 1991 NCAA Tournament, only months after they won the 1990 title. However, the NCAA later agreed to a compromise which deferred the sanctions until 1992, allowing UNLV to defend its title. Months after UNLV's 1991 semifinal loss to Duke, the Las Vegas Review-Journal published a picture showing three of Tarkanian's players in a hot tub with Perry. The picture had been taken in 1989, only months after Tarkanian claimed that he had warned his players to stay away from Perry. On June 7, 1991, Tarkanian announced he would resign after coaching one more season. Already banned from any postseason play, Tarkanian guided the 1991–92 team to a 26–2 season. He won his final game 65–53 over Utah State.

San Antonio Spurs (1992)
Tarkanian was offered the Los Angeles Lakers head coaching job in 1979, but declined, continuing to coach college basketball. Tarkanian was hired to coach the San Antonio Spurs in 1992, not long after leaving UNLV. However, he disagreed with Spurs owner Red McCombs over the need for experience at point guard. During the offseason, the Spurs had lost Rod Strickland to free agency, when he signed with Portland, leaving the Spurs without a point guard with significant NBA experience. The Spurs had signed Vinny Del Negro, a combo-guard from the Italian League, to replace Strickland. They also signed NBA journeyman Avery Johnson, formerly of the Houston Rockets, to a one-year contract. Tarkanian felt that the Spurs wouldn't be competitive without an experienced point guard, but McCombs disagreed. As a result, Tarkanian was fired after only 20 games with a 9–11 record. He received a $1.3 million settlement, which he used to fund a lawsuit against the NCAA.

Fresno State (1995–2002)
He returned to college coaching at his alma mater, California State University, Fresno, from 1995 to 2002 and led them to six consecutive 20-win seasons. Tarkanian led the Bulldogs to five NIT tournaments and two NCAA appearances. He retired from coaching in 2002 with 778 career Division I wins. Following his retirement, Fresno State was placed on probation by the NCAA for violations committed by its men's basketball team under Tarkanian's watch. The Fresno Bee reported in 2003 that some Fresno State basketball players had coursework completed for them during the years 1999 to 2001.

Tarkanian and the NCAA
Tarkanian spent most of his career as a Division I coach in a battle with the NCAA. While at Long Beach, he wrote a newspaper column charging that the NCAA ignored improprieties at powerful schools while it pursued smaller, more defenseless institutions. After he left Long Beach State, its basketball program was slapped with probation for recruiting violations which occurred under his watch.

Just months before the 1976–1977 season, the NCAA placed UNLV on two years' probation for "questionable practices". Although the alleged violations dated back to 1971—before Tarkanian became coach—the NCAA pressured UNLV into suspending Tarkanian as coach for two years. Tarkanian sued, claiming the suspension violated his right to due process. In October 1977, a Nevada judge issued an injunction that reinstated Tarkanian as coach. The case eventually made it all the way to the Supreme Court of the United States, which ruled in 1988 that the NCAA had the right to discipline its member schools, reversing the 1977 injunction.

In the decade between the original suspension and the Supreme Court ruling, it was revealed that the NCAA's enforcement process was stacked heavily in the NCAA's favor — so heavily, in fact, that it created a perception that there was no due process. The enforcement staff was allowed to build cases on hearsay, and shared few of their findings with the targeted school. The resulting negative publicity led the NCAA to institute a clearer separation between the enforcement staff and the infractions committee, as well as a system for appeals. Also, hearsay evidence was no longer admissible in infractions cases.

NCAA executive director Walter Byers famously disliked Tarkanian, and said "Tark's black players play a fast city-lot basketball without much style. Grab ball and run like hell, not lots of passing to set up the shots." Byers described UNLV's style as "ghetto run-and-shoot basketball" with little concern for defense.

After being fired from the Spurs, Tarkanian sued the NCAA, claiming it had harassed him for over two decades. The harassment, Tarkanian claimed, started when he wrote a newspaper column alleging that the NCAA was more willing to punish less-prominent schools than big-name schools. Although the NCAA did not admit harassing Tarkanian, it settled out of court in 1998, paying him $2.5 million.

Legacy
Tarkanian was inducted into the Naismith Memorial Basketball Hall of Fame in 2013, an honor that fellow coaches had been saying was overdue. "Time has a way of healing things. And in this case, time worked in his favor," said Hall of Fame chairman Jerry Colangelo. The controversy from his NCAA dealings was widely believed to have contributed to the delay. ESPN wrote that Tarkanian "helped revolutionize the way the college game was played". Hall of Fame coach Larry Brown said he "influenced a lot of coaches", and coach Mike Krzyzewski added that he "taught pressure man-to-man defense as well as anyone has ever done." Upon Tarkanian's retirement, future Hall of Fame coach Jim Calhoun proclaimed him "one of the best teachers of defense in the last 25 to 30 years of basketball." In 31 years of coaching over five decades at three Division I schools, he compiled a career record of 729–201. At UNLV, 39 of his players were selected in the NBA draft; Larry Johnson was the first overall pick in 1991, and Armen Gilliam was No. 2 overall in 1987.

Tarkanian was an innovator who had his teams play a pressing defense that forced turnovers to trigger its run-and-gun offense. He was one of the few early coaches to effectively use the three-point shot, which was added by the NCAA in 1986. Tarkanian recruited players that his peers often passed over, taking chances on junior college students or those with a troubled past. His players hailed predominately from urban areas, and he allowed his team the freedom to express themselves. While some of those players were high-maintenance, he was the rare coach who was able to blend multiple personalities together into a team, and they played with a unique swagger. Tarkanian's teams changed the style and image of college basketball in a way that predated the impact the Fab Five of Michigan had in the 1990s. "He made the players more important than him. He made the players the show. It was about the players first," said former UNLV assistant Mark Warkentien. According to Fab Five member Jalen Rose, "We were considered rough-and-tumble at Michigan, but it started with UNLV."

UNLV was transformed by Tarkanian from a small commuter college into a national powerhouse. Demand for UNLV sweatshirts grew across the nation. He became a celebrity, and tickets to UNLV games became hot items with regulars, including Vegas headliners Frank Sinatra, Bill Cosby and Don Rickles. With no professional teams in the city, the Rebels became the town's center of attention, and their pregame ceremonies included light shows and fireworks during player introductions. His success at UNLV paved the way for other successful mid-majors.

The floor of UNLV's home arena at the Thomas & Mack Center was named "Jerry Tarkanian Court" in 2005. A bronze life-size statue of Tarkanian was added outside the arena in 2013. Since 2012, Bishop Gorman High School in Las Vegas has held the Tarkanian Classic, a high school tournament featuring some of the top teams in the country. In 2014, Fresno State retired Tarkanian's No. 2 jersey from his college playing days.

Tarkanian also has a middle school located in Southern Highlands, NV named after him and his wife Lois.

Other biographical details
He had small roles in the 1979 film, The Fish That Saved Pittsburgh as the LA Team Coach, in the 1992 film, Honeymoon in Vegas as a poker player, and in the 1994 film, Blue Chips as a basketball coach.

Jerry Tarkanian was married to Las Vegas city councilwoman Lois Tarkanian. They had four children and ten grandchildren. One of their sons, Danny Tarkanian, was an All-American Honorable Mention college basketball player while playing for Jerry Tarkanian at UNLV and has since run several political campaigns in Nevada.

Tarkanian was a good friend of college basketball coach Bob Knight. Tarkanian and Knight matched wits in the national semifinals of the 1987 NCAA Division I men's basketball tournament in New Orleans, with Knight's Indiana Hoosiers defeating UNLV, 97–93.

He also started a basketball school in Las Vegas, named The Tarkanian Basketball Academy.

His granddaughter Dannielle Diamant played for Northwestern University women's basketball team for three years (2009-2012).

On February 11, 2015, Tarkanian died at the age of 84 at Valley Hospital Medical Center in Las Vegas, where he had been hospitalized days earlier after having difficulty breathing. In a tribute to him, the city of Las Vegas lowered its flags at City Hall to half-staff on that day. On February 18, the casinos along the Las Vegas Strip dimmed their lights for roughly three minutes in Tarkanian's honor.

College
Note: The record of 784–202 includes six NCAA tournament games vacated by the NCAA while at Long Beach State and 49 games vacated while at Fresno State. Excluding these games, the record would be 729–201.

title: Jerry Tarkanian


text:
Dirichlet–Jordan test

In mathematics, the Dirichlet–Jordan test gives sufficient conditions for a real-valued, periodic function f to be equal to the sum of its Fourier series at a point of continuity. Moreover, the behavior of the Fourier series at points of discontinuity is determined as well (it is the midpoint of the values of the discontinuity). It is one of many conditions for the convergence of Fourier series.

The original test was established by Peter Gustav Lejeune Dirichlet in 1829, for piecewise monotone functions. It was extended in the late 19th century by Camille Jordan to functions of bounded variation (any function of bounded variation is the difference of two increasing functions).

Dirichlet–Jordan test for Fourier series
The Dirichlet–Jordan test states that if a periodic function $$f(x)$$ is of bounded variation on a period, then the Fourier series $$S_nf(x)$$ converges, as $$n\to\infty$$, at each point of the domain to $$\lim_{\varepsilon\to 0}\frac{f(x+\varepsilon)+f(x-\varepsilon)}{2}.$$ In particular, if $$f$$ is continuous at $$x$$, then the Fourier series converges to $$f(x)$$. Moreover, if $$f$$ is continuous everywhere, then the convergence is uniform.

Stated in terms of a periodic function of period 2π, the Fourier series coefficients are defined as $$ a_k = \frac{1}{2\pi} \int_{-\pi}^\pi f(x) e^{-ikx}\, dx,$$ and the partial sums of the Fourier series are $$S_nf(x) = \sum_{k=-n}^na_k e^{ikx}$$

The analogous statement holds irrespective of what the period of f is, or which version of the Fourier series is chosen.

There is also a pointwise version of the test: if $$f$$ is a periodic function in $$L^1$$, and is of bounded variation in a neighborhood of $$x$$, then the Fourier series at $$x$$ converges to the limit as above $$\lim_{\varepsilon\to 0}\frac{f(x+\varepsilon)+f(x-\varepsilon)}{2}.$$

Jordan test for Fourier integrals
For the Fourier transform on the real line, there is a version of the test as well. Suppose that $$f(x)$$ is in $$L^1(-\infty,\infty)$$ and of bounded variation in a neighborhood of the point $$x$$. Then $$\frac1\pi\lim_{M\to\infty}\int_0^{M}du\int_{-\infty}^\infty f(t)\cos u(x-t)\,dt = \lim_{\varepsilon\to 0}\frac{f(x+\varepsilon)+f(x-\varepsilon)}{2}.$$ If $$f$$ is continuous in an open interval, then the integral on the left-hand side converges uniformly in the interval, and the limit on the right-hand side is $$f(x)$$.

This version of the test (although not satisfying modern demands for rigor) is historically prior to Dirichlet, being due to Joseph Fourier.

Dirichlet conditions in signal processing
In signal processing, the test is often retained in the original form due to Dirichlet: a piecewise monotone bounded periodic function $$f$$ has a convergent Fourier series whose value at each point is the arithmetic mean of the left and right limits of the function. The condition of piecewise monotonicity is equivalent to having only finitely many local extrema, i.e., that the function changes its variation only finitely many times. (Dirichlet required in addition that the function have only finitely many discontinuities, but this constraint is unnecessarily stringent. ) Any signal that can be physically produced in a laboratory satisfies these conditions.

As in the pointwise case of the Jordan test, the condition of boundedness can be relaxed if the function is assumed to be absolutely integrable (i.e., $$L^1$$) over a period, provided it satisfies the other conditions of the test in a neighborhood of the point $$x$$ where the limit is taken.

title: Dirichlet–Jordan test


text:
Peter H. Gilmore

Peter Howard Gilmore (born May 24, 1958) is an American writer and LaVeyan Satanist. He is the current High Priest of the Church of Satan. As a representative of the Church of Satan, Gilmore has been interviewed on numerous television and radio programs dealing with the topic of Satanism, including appearances on History, the BBC, Syfy, Point of Inquiry, and Bob Larson's Christian radio show.

Biography
Gilmore was raised in upstate New York. He read The Satanic Bible at age thirteen and has described The Church of Satan as "the motivating philosophical force in my life" ever since.

He and his wife Peggy Nadramia published a Satanic journal, The Black Flame, from 1989 to 2005. In 2005, Gilmore wrote the new introduction to Anton LaVey's The Satanic Bible, and his essay on Satanism was published in The Encyclopedia of Religion and Nature.

The Satanic Scriptures
A hard cover edition of The Satanic Scriptures, a collection essays and other writings by Gilmore was released on Walpurgis Night 2007, with a subsequent paperback edition (ISBN 0976403595) released on October 13, 2007. The book includes rituals that were previously not public, such as marriages and Satanic burials.

Interviews

 * Alas, Babylon, article on the gentrification of New York City by Jim Knipfel in New York Press
 * Halloween special (4:46-8:14) (October 29, 2010), video interview with George Stroumboulopoulos on George Stroumboulopoulos Tonight (CBC Television)
 * Science and Satanism (August 10, 2007), audio interview on Point of Inquiry

title: Peter H. Gilmore