A.J. Styles Return to the independent circuit (2003-2005)
When did he return to the independent circuit?
When did A.J. Styles return to the independent circuit?
On March 14, Styles returned to International Wrestling Cartel (IWC) and successfully challenged IWC Super Indy Champion Super Hentai for the title. On April 13, Styles defended the title in a rematch against Hentai, but the match ended in a no contest, meaning Styles retained the title. On May 10, Styles vacated the title. On August 23, Styles unsuccessfully challenged new Super Indy Champion Colt Cabana after the match ended at a twenty-minute time limit draw, meaning Cabana retained the title. On December 12 at IWC: Call to Arms, Styles would once again challenge Cabana for the title, but again was unsuccessful. On April 12, Styles debuted in Combat Zone Wrestling (CZW), competing at the promotions 3rd Best of the Best event. Styles teamed with Jason Cross to face Jay Briscoe and Jimmy Rave, in a losing effort. On July 20, at CZW: Deja Vu II, Styles successfully defended the NWA World Heavyweight Championship against Rave.  On September 12, Styles debuted in Maximum Pro Wrestling (MXPW), successfully challenging MXPW Television Champion Chris Sabin and Christopher Daniels in a three-way match for the title. On October 4, Styles debuted in Pro Wrestling Guerrilla (PWG), unsuccessfully challenging PWG Champion Frankie Kazarian and Christopher Daniels for the title. On November 7, Styles returned to IWA: Mid-South to take part in the promotions annual Ted Petty Invitational, which saw Styles defeating Todd Sexton is his first round match. The following night, he defeated Jerry Lynn in the quarter-finals, but later that night would be eliminated by Danny Daniels in the semi-finals. On March 20, 2004, Styles returned to IWC, entering the promotions Super Indy Survivor Showdown tournament. Styles' first match in the tournament was in the semi-finals due to unknown reasons, in which he defeated CM Punk. Later that night, Styles faced IWC Super Indy Champion Colt Cabana in the final in a winning effort, capturing the title. On April 17, Styles successfully defended the title against Homicide, and on May 8 he did so again against Christopher Daniels.  On September 17, Styles returned to IWA: Mid-South, entering the promotions 2004 Ted Petty Invitational. Styles defeated Jimmy Rave in his first round match. The following night, Styles defeated Matt Sydal in the quarter finals. Later that night, Styles defeated Arik Cannon in the semi-finals, as well as defeating Bryan Danielson and Samoa Joe in the final to win the 2004 Ted Petty Invitational. On October 21, Styles won the vacant IWA: Mid-South Heavyweight Championship, defeating Chris Sabin, Christopher Daniels and Petey Williams in a four-way dance match. Two days later on October 23, Styles lost the title to CM Punk.  On April 1, 2005, Styles returned to PWG, defeating Samoa Joe in a PWG Championship number one contender match at the promotion's All-Star Weekend - Day 1. The following night on Day 2 of All-Star Weekend, Styles successfully challenged Super Dragon for the title. Styles defended the title until August 6 at Zombies Shouldn't Run, where he lost it to Kevin Steen. On September 3, Styles entered the 2005 Battle of Los Angeles tournament, but was defeated in the finals by Chris Bosh. CANNOTANSWER
On March 14, Styles returned to International Wrestling Cartel (IWC)
The return ratio of a dependent source in a linear electrical circuit is the negative of the ratio of the current (voltage) returned to the site of the dependent source to the current (voltage) of a replacement independent source. The terms loop gain and return ratio are often used interchangeably; however, they are necessarily equivalent only in the case of a single feedback loop system with unilateral blocks.

Calculating the return ratio

The steps for calculating the return ratio of a source are as follows:
  Set all independent sources to zero.
  Select the dependent source for which the return ratio is sought.
  Place an independent source of the same type (voltage or current) and polarity in parallel with the selected dependent source.
  Move the dependent source to the side of the inserted source and cut the two leads joining the dependent source to the independent source. 
  For a voltage source the return ratio is minus the ratio of the voltage across the dependent source divided by the voltage of the independent replacement source. 
  For a current source, short-circuit the broken leads of the dependent source. The return ratio is minus the ratio of the resulting short-circuit current to the current of the independent replacement source.

Other Methods 

These steps may not be feasible when the dependent sources inside the devices are not directly accessible, for example when using built-in "black box" SPICE models or when measuring the return ratio experimentally.
For SPICE simulations, one potential workaround is to manually replace non-linear devices by their small-signal equivalent model, with exposed dependent sources. However this will have to be redone if the bias point changes.

A result by Rosenstark shows that return ratio can be calculated by breaking the loop at any unilateral point in the circuit. The problem is now finding how to break the loop without affecting the bias point and altering the results. Middlebrook and Rosenstark have proposed several methods for experimental evaluation of return ratio (loosely referred to by these authors as simply loop gain), and similar methods have been adapted for use in SPICE by Hurst. See Spectrum user note or Roberts, or Sedra, and especially Tuinenga.

Example: Collector-to-base biased bipolar amplifier

Figure 1 (top right) shows a bipolar amplifier with feedback bias resistor Rf driven by a Norton signal source. Figure 2 (left panel) shows the corresponding small-signal circuit obtained by replacing the transistor with its hybrid-pi model. The objective is to find the return ratio of the dependent current source in this amplifier. To reach the objective, the steps outlined above are followed. Figure 2 (center panel) shows the application of these steps up to Step 4, with the dependent source moved to the left of the inserted source of value it, and the leads targeted for cutting marked with an x. Figure 2 (right panel) shows the circuit set up for calculation of the return ratio T, which is

The return current is

The feedback current in Rf is found by current division to be:

The base-emitter voltage vπ is then, from Ohm's law:

Consequently,

Application in asymptotic gain model 
The overall transresistance gain of this amplifier can be shown to be:

with R1 = RS || rπ and R2 = RD || rO.

This expression can be rewritten in the form used by the asymptotic gain model, which expresses the overall gain of a feedback amplifier in terms of several independent factors that are often more easily derived separately than the overall gain itself, and that often provide insight into the circuit. This form is:

where the so-called asymptotic gain G∞ is the gain at infinite gm, namely:

and the so-called feed forward or direct feedthrough G0 is the gain for zero gm, namely:

For additional applications of this method, see asymptotic gain model and Blackman's theorem.

References

See also
Asymptotic gain model
Blackman's theorem
Extra element theorem

Control theory
Signal processing
Electronic feedback The Big South League was an independent baseball league that operated from 1996 to 1997 in the states of Arkansas, Mississippi and Tennessee. The BSL sought to establish baseball clubs in a number of rapidly expanding urban areas without professional sports entertainment. The circuit featured six franchises represented on its inaugural season. At the time, none of the cities represented had hosted professional baseball for 40 years.

In its second season, the three teams from Tennessee left the BSL to join the Heartland League, while the team from Arkansas did not return. New teams from Mississippi and Tennessee joined the league to complete a four-team circuit, but the BSL failed when attendance fell drastically, from over 200,000 to under 100,000, and folded at the end of the season.

List of teams
Clarksville Coyotes, Clarksville, TN (1996)
Columbia Mules, Columbia, TN (1996)
Greenville Bluesmen, Greenville, MS (1996–1997)
Meridian Brakemen. Meridian, MS (1996–1997)
Pine Bluff Locomotives, Pine Bluff, AR (1996)
Tennessee Tomahawks, Winchester, TN, Tullahoma, TN (1996)
Tennessee Walkers, Tullahoma, TN (1997)
Tupelo Tornado, Tupelo, MS (1997)

Championships
Greenville Bluesmen (1996–1997)

Sources
Stott, Jon C. (2001) Leagues of Their Own: Independent Professional Baseball, 1993-1999. McFarland & Company. 
Big South League (Independent) Encyclopedia and History. Baseball Reference. Retrieved on April 10, 2016.
Big South League. Baseball Reference Bullpen. Retrieved on April 10, 2016.

Defunct minor baseball leagues in the United States
Defunct independent baseball leagues in the United States
Baseball leagues in Arkansas
Baseball leagues in Mississippi
Baseball leagues in Tennessee Samuel Locke Sawyer (November 27, 1813 – March 29, 1890) was a U.S. Representative from Missouri.

Born in Mont Vernon, New Hampshire, Sawyer was graduated from Dartmouth College, Hanover, New Hampshire, in 1833. He studied law, and was admitted to the bar in Amherst, New Hampshire, in 1836. He moved to Lexington, Missouri, in 1838 and continued his law practice.

Sawyer was elected circuit attorney of the sixth judicial circuit of Missouri in 1848 and reelected in 1852. He served as delegate to the Missouri constitutional convention in 1861. He served as delegate to the Democratic National Convention in 1868. Sawyer was elected judge of the twenty-fourth judicial circuit and served from 1871 until February 15, 1876, when he resigned.

Sawyer was elected as an Independent Democrat to the Forty-sixth Congress (March 4, 1879 – March 3, 1881). He did not seek renomination in 1880, and returned to the practice of law and engaged in banking. He died in Independence, Missouri, March 29, 1890, and was interred in Woodlawn Cemetery.

References

1813 births
1890 deaths
People from Mont Vernon, New Hampshire
Members of the United States House of Representatives from Missouri
Dartmouth College alumni
Missouri Independents
Missouri Democrats
Independent Democrat members of the United States House of Representatives
19th-century American politicians