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The State of Arkansas has a total of eight metropolitan statistical areas that are or located in the state. Twenty of the state's 75 counties are classified by the United States Census Bureau as metropolitan. Among these is one of the fastest growing MSAs in the United States, Fayetteville Springdale-Rogers; the following table lists population figures for the metropolitan areas with their Arkansas counties, in rank of population. Population figures are from the 2016 U. S. Census estimate. There are three combined statistical areas in the state; the Little Rock-North Little Rock, AR Combined Statistical Area includes the Little Rock and Pine Bluff metropolitan areas and the Searcy micropolitan area. The Jonesboro-Paragould combined statistical area was created by the Census Bureau in 2005 and includes the Jonesboro metropolitan area and Paragould micropolitan area; the Hot Springs-Malvern Combined statistical area was created in 2013 which includes the Hot Springs metropolitan area and the Malvern micropolitan area.

The three Combined Statistical Areas in the state are listed in the table below with their populations from the 2016 U. S. Census estimate

A projective vector field is a smooth vector field on a semi Riemannian manifold M whose flow preserves the geodesic structure of M without preserving the affine parameter of any geodesic. More intuitively, the flow of the projective maps geodesics smoothly into geodesics without preserving the affine parameter. In dealing with a vector field X on a semi Riemannian manifold, it is useful to decompose the covariant derivative into its symmetric and skew-symmetric parts: X a. Here a projective vector field is uniquely determined by specifying the values of X, ∇ X and ∇ ∇ X at any point of M. Projectives satisfy the properties: L X R a b c d = δ a d ψ b; these subalgebras are useful, for example, in classifying spacetimes in general relativity. Affine vector fields satisfy ∇ h = 0 and hence every affine is a projective. Affines preserve the geodesic structure of the semi Riem. Manifold whilst preserving the affine parameter; the set of all affines on M forms a Lie subalgebra of P denoted by A and satisfies for connected M, dim ⁡ A ≤ n.

An affine vector is uniquely determined by specifying the values of the vector field and its first covariant derivative at any point of M. Affines preserve the Riemann and Weyl tensors, i.e. L X R a b c d = 0, L

Cristian Machado is the vocalist for the nu metal band Ill Niño and was a lead singer for Roadrunner United. He has played in Headclamp and La Familia, in addition to making numerous guest appearances on albums such as Sepultura's Nation, Soulfly's 3 and 40 Below Summer's The Mourning After. Cristian Machado was born as the son of a Brazilian musician, but soon moved to Venezuela with his mother. In 1986 they moved to New Jersey, he only knew Marcello Machado, halfway through his teenage years. His mother told him his stepfather was his father, he found out only when his father called him, told him he was his real father. Cristian Machado told his father. Today, however, he communicates with his father through phone. Most of Cristian Machado's music influence is from his childhood without a father and growing up realizing that; when touring he would meet people that he felt left an impact on his life and he would show in his music how that person helped or ruined his life. The songs "Unframed" and "How Can I Live" are both about his father.

Cristian Machado uses Dave Williams of Drowning Pool's microphone. They were good friends and both bands created a bond and friendship while doing the Jägermeister tour. After Williams died, Drowning Pool and Dave's family gave him the mic in respect. Cristian is divorced and has a daughter

Apple PowerCD is a CD player sold by Apple Computer in 1993 and discontinued several years later. It was a re-badged Philips-designed product, sold in addition to Apple's speakers and included a remote control; the PowerCD was capable of reading data CDs and audio CDs. It can connect to Apple Macintosh personal computers through SCSI and to stereo systems and televisions. With the success of the Apple Newton, in mid-1992 Apple Industrial Design Group created a division called Mac Like Things, to focus on what they saw as a whole new market for Apple in consumer electronic devices; the PowerCD marked Apple's first stand-alone consumer-oriented product brought to market, which did not require a computer for use. It was analogous to Sony's Discman portable CD players of the time, unlike Sony's and most others, Apple's could be used as computer peripheral as well, and while most desktop Macs at the time included built-in CD-ROMs, the PowerCD was designed to match the PowerBook series which would not include a built-in CD-ROM for several more years.

Its ability to be operated under battery power alone made it not only a portable drive for computers, but gave it the added ability to be marketed as a stand-alone portable CD player. However, Mac Like Things was short-lived and by September 1992, it was folded into Apple's New Media Group having only brought to market the PowerCD and AppleDesign Powered Speakers series. Along with the PowerCD, Apple released two versions of their desktop speakers: the AppleDesign Powered Speakers and the redesigned AppleDesign Powered Speakers II a year later; the original speakers came in Platinum gray to match Apple's desktop line, while the second generation were curvier and came in a darker gray color designed to match the PowerBook line and PowerCD. Both were powered with an AC adapter and could be attached to any audio output source, with two separate inputs for the computer and an external CD player. Both had a headphone jack in the front of one speaker along with the volume control and an optional subwoofer connection port on some models.

Products on this timeline indicate introduction dates only and not discontinued dates, as new products begin on a contiguous product line. IPod Apple QuickTake Apple Interactive Television Box Bandai Pippin Mac Guides popcorn.cx - Apple PowerCD & AppleDesign Powered Speakers Apple PowerCD Apple/PHILIPS CDP/PowerCD

Neustria was, according to the early medieval geographical classification, the western portion of Langobardia Major, the north-central part of the Lombard Kingdom, extended from the Adda to the Western Alps and opposed to Austria. The bipartition, emerged during the 7th century, was not only in territorial area, but implies significant cultural and political differences; the Neustria included the duchies of the north-western Lombard Kingdom, among them a prominent role was played by Duchy of Pavia Duchy of Asti Duchy of Turin The duchies of Neustria were long the most loyal to the Bavarian dynasty, accepting both the pro-Catholic inspiration and the consequent policy of appeasement of Italy, without further attempts to expand against the Byzantines and the pope. In the 8th century, the widespread conversion of the Lombards to Catholicism smoothed the opposition between Austria and Neustria, thanks to a revived expansion at the expense of the Byzantine Empire with the Catholic and Neustrian Liutprand.

After the fall of the Lombard kingdom in 774, the Langobardia Maior fell under the dominion of the Franks. Its political-administrative structure was not disrupted, instead of the dukes, Frank but Lombard counts were settled. Origo gentis Langobardorum, ed. Georg Waitz in Monumenta Germaniae Historica SS rer. Lang. Paul Deacon, Historia Langobardorum. Lidia Capo. Comment to Deacon, Paul. Storia dei Longobardi. Curator: Lidia Capo. Milan: Lorenzo Valla/Mondadori. ISBN 88-04-33010-4. Jarnut, Jörg. Storia dei Longobardi. Torino: Einaudi. ISBN 88-464-4085-4. Rovagnati, Sergio. I Longobardi. Milano: Xenia. ISBN 88-7273-484-3. Langobardia Major Langobardia Minor Austria Lombard Kingdom

The horse-collar tackle is an American football maneuver in which a defender tackles another player by grabbing the back collar or the back-inside of an opponent's shoulder pads and pulling the ball carrier directly downward violently in order to pull his feet from underneath him. The technique is most associated with Pro Bowl safety Roy Williams. After being blamed for a series of major injuries in the 2004 season, the horse-collar tackle was banned from the NFL during the 2005 off-season; the rule forbidding it is referred to in the press as "The Roy Williams Rule". The rule, with modifications, was adopted in college football in 2008 and high school football in 2009. In the 1981 NFC Championship Game where the Dallas Cowboys visited the San Francisco 49ers, while the 49ers took the lead 28-27 due to "The Catch", the Cowboys had a chance to win the game when Drew Pearson caught a long pass from Danny White that would've gone for a touchdown. However, 49ers cornerback Eric Wright made a horse-collar tackle that stopped Pearson just outside field-goal range.

Roy Williams was well known for horse-collaring players while playing at Oklahoma, continued to use the tackle after moving to the NFL in 2002. The horse-collar tackle rose to infamy during the 2004 NFL season, in which it was implicated in six major injuries, four of which were caused by Williams, including two in one game; the injuries that season included broken legs for Philadelphia Eagles wide receiver Terrell Owens, Eagles quarterback Donovan McNabb, Carolina Panthers wide receiver Steve Smith Sr. Baltimore Ravens running back Musa Smith, Tennessee Titans wide out Tyrone Calico. On May 23, 2005, NFL owners voted 27–5 to ban the tackle, with the Dallas Cowboys, Detroit Lions, New England Patriots, New Orleans Saints, San Francisco 49ers voting against; the first year of the ban, only two penalties were called by referees for the horse-collar tackle. Owners voted 25–7 in 2006 to expand the rule to include tackles by the back of the jersey in addition to tackles by the shoulder pads; the horse-collar is dangerous due to the awkward position of the player being tackled, who will fall backward in a twisting motion with one or both legs trapped under the weight of his body.

This is exacerbated if the player's foot gets caught in the turf and by the additional weight of the defender. Potential injuries include sprains or tears to ligaments in the knees and ankles, fractures of the tibia and fibula. Smith, for instance, was sidelined for two seasons after a horse-collar tackle by Williams broke his right tibia; the ban states that a horse-collar tackle is an open-field tackle in which a defender uses the shoulder pads or jersey to bring a ball carrier down. The term "open field" means that horse-collar tackles committed near the line of scrimmage will be allowed. In the NFL, the horse-collar tackle results in a 15-yard major foul penalty and an automatic first down if committed by the defense, the penalty is assessed as if it were a dead ball, after the play foul, if the opposing offense gains yards, it will also result in a league-imposed fine on the player. Roy Williams was the first player suspended for repeated violations of the rule; the one-game suspension was given following a horse-collar tackle on Philadelphia Eagles quarterback Donovan McNabb that occurred on December 16, 2007, it was Williams' third violation of the rule of the 2007 season.

The tackle was made illegal in the CFL for the 2007 season. The horse collar tackle was legal through the 2007–2008 season in college football but was banned by the NCAA after criticism from pundits and coaches for the 2008–2009 season as part of a package that adopted several NFL rules into the college game; the National Federation of State High School Associations added a penalty for horse-collar tackles for the 2009 season