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Inverse limit

In mathematics, the inverse limit is a construction that allows one to "glue together" several related objects, the precise manner of the gluing process being specified by morphisms between the objects. Inverse limits can be defined in any category, they are a special case of the concept of a limit in category theory. We start with the definition of an inverse system of homomorphisms. Let be a directed poset. Let i∈I be a family of groups and suppose we have a family of homomorphisms fij: Aj → Ai for all i ≤ j, called bonding maps, with the following properties: fii is the identity on Ai, fik = fij ∘ fjk for all i ≤ j ≤ k; the pair is called an inverse system of groups and morphisms over I, the morphisms fij are called the transition morphisms of the system. We define the inverse limit of the inverse system as a particular subgroup of the direct product of the Ai's: A = lim ← i ∈ I ⁡ A i =; the inverse limit A comes equipped with natural projections πi: A → Ai which pick out the ith component of the direct product for each i in I.

The inverse limit and the natural projections satisfy a universal property described in the next section. This same construction may be carried out if the Ai's are sets, topological spaces, modules, etc. and the homomorphisms are morphisms in the corresponding category. The inverse limit will belong to that category; the inverse limit can be defined abstractly in an arbitrary category by means of a universal property. Let be an inverse system of objects and morphisms in a category C; the inverse limit of this system is an object X in C together with morphisms πi: X → Xi satisfying πi = fij ∘ πj for all i ≤ j. The pair must be universal in the sense that for any other such pair there exists a unique morphism u: Y → X such that the diagram commutes for all i ≤ j, for which it suffices to show that ψi = πi ∘ u for all i; the inverse limit is denoted X = lim ← ⁡ X i with the inverse system being understood. In some categories, the inverse limit of certain inverse systems does not exist. If it does, however, it is unique in a strong sense: given any two inverse limits X and X' of an inverse system, there exists a unique isomorphism X′ → X commuting with the projection maps.

We note that an inverse system in a category C admits an alternative description in terms of functors. Any ordered set I can be considered as a small category where the morphisms consist of arrows i → j if and only if i ≤ j. An inverse system is just a contravariant functor I → C, the inverse limit functor lim ←: C I o p → C is a covariant functor; the ring of p-adic integers is the inverse limit of the rings Z / p n Z with the index set being the natural numbers with the usual order, the morphisms being "take remainder". That is, one considers sequences of integers such that each element of the sequence "projects" down to the previous ones, that n i ≡ n j mod p i + 1 whenever i < j. The natural topology on the p-adic integers is the one implied here, namely the product topology with cylinder sets as the open sets. Let p be a prime number. Consider the direct system composed of the factor groups Z / p n Z and the homomorphisms Z / p n Z → Z / p n + 1 Z induced by multiplication by p; the inverse limit of this system is the circle group T = R / Z, expressed in a positional number system of base p.

This is similar to the construction of the real numbers by Cauchy sequences, using

North Carolina–Moldova National Guard Partnership

The North Carolina–Moldova National Guard Partnership is one of 22 European partnerships that make-up the U. S. European Command State Partnership Program and one of 65 worldwide partnerships that make-up the National Guard State Partnership Program; the Partnership was formalized on April 22, 1999. It has since evolved into a partnership that includes the efforts of many more organizations and individuals such as private firms, civic organizations and non-profit agencies; the partnership is a bi-lateral association with planning committees in both North Carolina and the Republic of Moldova who work together in a cooperative effort to improve and enrich the lives of everyone it touches. Overview Republic of Moldova declared its independence in 1991 Established the partnership on 22 April 1999 Moldova Participated in joint exercises Moldovan National Army consists of Land Forces with a small Air Force element 6 Moldovan Contingents participated in demining missions in Iraq between 2003-2008 Mil-to Civ events focused on dental treatments to children from orphanages and on disaster response and preparedness The Mil-to-Mil events focused on assisting the Moldovan military with developing its organic capabilities in the following areas: peacekeeping, SF, logistics etc.

In 1995, North Carolina had been partnered with Moldova as part of a program of military-to-military contact between the United States and emerging democracies of the former Soviet Union. It wasn't until 1999, that the program began to take off. Led by a North Carolina National Guard officer, what was the Military Liaison Team began overseeing contact between the National Army of Moldova and the various services of the United States military. Like elsewhere in the former Soviet Union and Eastern Bloc, the aim was simple – engage the Moldovan military, enlarge America's circle of friends and provide a secure platform for freedom and peace where the soldier is subordinate to civilian authority. Using a grass-roots organization like the National Guard with its base of citizen soldiers and airmen was seen as the best way to connect. Before military contact began, North Carolina citizens had laid the groundwork for non-military cooperation with this poorest nation in Europe as early as 1995. In 1999 Governor James B. Hunt Jr. signed the formal bilateral cooperation agreement with Moldovan President Petru Lucinschi, an agreement, renewed in 2004 by Governor Michael F. Easley.

The Agreement was renewed in 2010, signed by Vlad Filat, Republic of Moldova Prime-Minister, Elaine Marshall, North Carolina Secretary of State. Secretary Marshall is the head of the NC-Moldova Bilateral Committee and she has been part of it for over 10 years, she has visited MDA on committee business in support of the partnership on several occasions and has hosted several MDA GOV delegations to NC. She has been invited to MDA by the NCNG and private NC NGOs on different occasions. While she has no role in the NCNG, she has traveled with the current and former TAG's and has been supportive of the BAO mission in MDA. On the civilian side of the partnership, North Carolina had more than 60 projects accomplished or ongoing; the projects include engagement in secondary and higher education, exchanges of medical and dental students and practitioners to the arts, business, government reform and simple humanitarian aid in the form of donated medical equipment and computers. In 2000 NCNG engineers have teamed up with USMC Seabees to build a much-needed medical out-patient clinic at the country's largest orphanage/boarding school in Straseni.

The NCNG has conducted well digging projects in Straseni, while the civilians from NC have paid for the pumps to operate them. North Carolinians have adopted Moldovan children, paid for reconstructive surgery, both in Moldova and in the United States, funded private dental missions and Moldovan students have benefited from internships in offices at the highest levels of North Carolina state government. In 2003, a NCARNG training term provided instruction to Moldovan Carabinerii and civil police on counter-terrorism. Other Mil-to-Civ projects included – building a playground, facilitating the donation of two dental chairs to boarding schools, encouraging a series of virtual classes between UNC and Moldova State Medical University. Military and civilian medical professionals have teamed up to provide dental treatment and immunizations against hepatitis A, hepatitis B and chickenpox to nearly 25,000 Moldovan children in boarding schools. In 2013, the North Carolina-Moldova State Partnership Program will support a new mission which will focus on developing the nursing capabilities within the Moldovan Army and civilian institutions.

North Carolinians have privately funded dozens of humanitarian trips to Moldova to treat children's dental needs free-of-charge. Several NC organizations have donated humanitarian aid in the form of medical equipment, water distillers, books and computers worth over US$750,000. In the summer of 2013 a contingent from the Air National Guard of different states are going to contribute with personnel to the construction of a Medical and Rehabilitation Center in Marculesti town, Floresti district; the military will be working on a two-week rotation schedule as part of their training to help enhance medical capabilities in the area. During the period of 2008-2012 various contingents of the North Carolina National Guard worked side-by-side with the Moldovan Peacekeeping Force to assist them in their efforts of getting certified within the NATO Operations Capability Concept eva

Jeff Harris (baseball)

Jeffrey Austin Harris is a former Major League Baseball relief pitcher, a professional scout for the Philadelphia Phillies. He threw right-handed; when Harris debuted with the Seattle Mariners on April 2, 2005, he was 31 years of age. This was unusually old for a major league rookie, was due to his meandering career. Harris, who has done construction jobs and landscaping during offseasons, spent six years in the Minnesota Twins organization before being released in 2000 played three years for the Chico Heat of California in the independent Western Baseball League. From there, Harris tried, but failed to make a team in Taiwan, bounced to China in 2003, when the SARS epidemic forced him to leave and go back to North America where he played for the Quebec Capitales of the Canadian-American Association of Professional Baseball; the Mariners found Harris playing for the Capitales and signed him in June 2005. Harris made three long-relief appearances in the 2005 season, he posted a 2-5 record with a 4.19 ERA in 54.2 innings.

In 2006, Harris pitched in only 3 games early in season. In December 2006, the Cleveland Indians signed Harris to a minor league contract, he retired. He was named the pitching coach of the Arizona League Indians for the 2009 season, he was the pitching coach for the Lake County Captains in the Cleveland Indians organization. Baseball Reference ESPN updates NY Times Minor League Splits and Situational Stats

Michael Rudroff

Michael Rudroff is a German former professional Grand Prix motorcycle road racer. Rudolf competed in his first Grand Prix in 1987, made one podium, his career ranged from 1987 until 1996, where he started in 53 races, though he never started from pole position. Rudroff, riding a Honda bike, appeared in two Grand Prix in 1987, the West Germany Grand Prix and the Austrian Grand Prix where he qualified in positions 38 and 26 but did not compete in the final race, he raced in the West German, Dutch TT and Yugoslavian Grand Prix in 1988, completing 28 laps in the first and coming in at 15th having started at 24th, completing 20 laps and coming in at 19th having started in 31st, failing to qualify for the race in Yugoslavia.1989 saw regular appearances for Rudroff, racing in the Australian Grand Prix where he came 15th from a starting position of 21, followed by the United States Grand Prix where he came 15th one more having started again at 21. Following the Spanish Grand Prix, where he came 20th having begun at 23, he raced in the Nations Grand Prix.

He began at 24, finished 3rd in 59 minutes, 53.630 seconds over 33 laps. This was the only podium in his career, he raced in West Germany, Yugoslavia and the Czechoslovakian Grand Prix that year. He ended the season with 18 championship points. Rudolf competed in three rounds of the 1990 Superbike World Championship aboard a Bimota, he returned to Grand Prix competition in 1991, where he competed in 10 races, one other race in which he was not classified. This included a season-best 11th in the Australian Grand Prix, he enjoyed a career-best 26 championship points, he made 13 more starts in 1992, now on a Harris Yamaha, but only returned three points despite coming 8th at the British Grand Prix. In 1993 he made 14 appearances again on the Yamaha, returning 17 points despite falling out of the Australian Grand Prix and of the Japanese Grand Prix in the first lap, he was not seen again on the race track until 1996, where he raced once in the German Grand Prix on a Suzuki bike and fell at the first lap.

Michael Rudroff from World Superbike Rider Profile

Ali Brustofski

Ali Brustofski is an American singer-songwriter from Oakland, New Jersey. She was a finalist on The CW television network's singing show, The Next: Fame Is at Your Doorstep in 2012, the 2011 winner of New York's Z100 radio station's "Hometown Hero" competition, in which around 400 up-and-coming musicians participated; as a songwriter, Brustofski won the 2009 NYC Songwriters Circle's "Young Songwriter Award". On television, her original song "Rewind" was featured in two episodes of NBC's The Voice. Brustofski is a successful YouTuber who performs cover versions of well-known artists like Katy Perry and David Guetta; as of October 2015, her YouTube channel had nearly 100 million total video views and more than a half a million subscribers. She released her first original EP Dream Big independently in 2013. After spending several years performing in musical theater and recording voiceovers, Ali Brustofski uploaded her 1st video to YouTube in December, 2008. Up to June 2014, she has uploaded including over 120 music videos.

In November 2009, Brustofski won the NY Songwriters Circle "Young Songwriter Award" for her original song "Rewind" over 4,000 other entries. In April, 2011, Ali Brustofski was chosen to be a contestant on the MSG Varsity Talent Show from hundreds of submissions; the television show was broadcast on Cablevision's MSG Varsity Network, she reached the semi-finals. In December, 2011 Ali Brustofski won the Z100/State Farm Hometown Hero Competition, she was voted into the top 25 artists, selected to be a top 5 finalist by a music industry A-List panel of judges. Brustofski performed at the 2011 Z100 Jingle Ball Coca-Cola All-Access Lounge in the Hammerstein Ballroom on 12/09/2011 along with The Script, Gym Class Heroes, Hot Chelle Rae, Karmin. In August, 2012 Ali Brustofski was selected to appear on The Next: Fame Is at Your Doorstep, a nationally broadcast TV singing competition show which aired on The CW Network, she was mentored by Gloria Estefan, performed at The Paramount Theater, won the New York episode of the show.

Brustofski worked with all four of the shows mentors: Gloria Estefan, Joe Jonas and John Rich to prepare to perform in the semi-finals and finals episodes, broadcast from The Orpheum Theatre in Los Angeles. Ali Brustofski has recorded over 80 individual cover songs independently, which have been distributed by, Keep Your Soul Records, more. They include collaborations with Sabrina Carpenter, Katherine Hughes, Peter Hollens and Savannah Outen. Brustofski has released two full albums of her cover songs: Cover to Cover, Vol. 1 and Cover to Cover, Vol. 2. Brustofski recorded five studio versions of the cover songs she performed on the television show The Next: Fame Is at Your Doorstep, all of which were released by Atlantic Records in 2012. Singles On January 1, 2009, Ali Brustofski released her first original single, "Up, Up, Up!" which reached No. 2 on the Tween Pop Radio Top 40. Her second single, "Rewind" was released on April 4, 2011. Brustofski's recent single "Boys Like U" was made with the band "Like The Movies".

Dream Big EP Ali Brustofski's first EP, Dream Big, was realized through a successful Crowdfunding campaign on RocketHub. The EP was released on July 10, 2013; the first single was "Green Light" and the music video. "You Are", the second single from the EP received its music video premiere on on January 17, 2014. "Goodbye To The Rain" is the final single from the Dream Big EP. It premiered on Brustofski began performing at the age of three, with the first of many competition dance programs, she acted in several New Jersey musical theater productions, including "Annie" at the Darress Theatre in Boonton, NJ. At 10 years old, Brustofski performed as “Brigitta” in her first professional musical, The Sound of Music, at New Jersey's Paper Mill Playhouse.) Brustofski performed Off-Broadway in the role of Nicki in "Dear Maudie" at the 78th St. Theatre. In 2003, Brustofski was hired by Nickelodeon to be the voice for Piper O'Possum, the mascot of Nick Jr. after Face, from October 11, 2004, to September 7, 2007.

She has continued to do voiceover work. Official website

Road to Hell (film)

Road to Hell is a 2008 action-fantasy film directed by Albert Pyun. It was inspired by Walter Hill's Streets of Fire and began shooting that same year in June at Los Angeles. Pyun states that the genesis of Road to Hell began when he and Paré attended a film festival in Spain. Michael Paré as Cody Deborah Van Valkenburgh as Sister Clare Kramer as Caitlin Courtney Peldon as Ashley Anita Leeman as Ellen Lauren Sutherland as Mc Coy Joei Fulco as Gabriel Roxy Gunn as Ellen Dream Chris Reject as DJ Dante The film had its world premiere at the Alamo Drafthouse Cinema in Austin, Texas, in October 2008; the Chicago premiere of Road to Hell was at the Patio Theater on March 9, 2013. In November 2013, additional shooting was done with singer Joei Fulco from ABC's reality television show Wife Swap. 2012 PollyGrind Film Festival: Best Fantasy Movie Best Actor: Michael Paré Best Actress: Clare Kramer Newcomer Award: Roxy Gunn Best Supporting Actress In A Fantasy Film: Deborah Van Valkenburgh Best Writer: Cynthia Curnan, Ph.

D. Best Visual Effects: Daniel Ray Gutierrez Best Song: Streets of Fire Best Use Of Music: Albert Pyun2012 Yellow Fever Independent Film Festival: Best Film Official site Road to Hell on IMDb