Trace operator

In mathematics, the concept of trace operator plays an important role in studying the existence and uniqueness of solutions to boundary value problems, that is, to partial differential equations with prescribed boundary conditions. The trace operator makes it possible to extend the notion of restriction of a function to the boundary of its domain to "generalized" functions in a Sobolev space.

Informal discussion

Let be a bounded open set in the Euclidean space with C¹ boundary If is a function that is (or even just continuous) on the closure of its function restriction is well-defined and continuous on If however, is the solution to some partial differential equation, it is in general a weak solution, so it belongs to some Sobolev space. Such functions are defined only up to a set of measure zero, and since the boundary does have measure zero, any function in a Sobolev space can be completely redefined on the boundary without changing the function as an element in that space. It follows that simple function restriction cannot be used to meaningfully define what it means for a general solution to a partial differential equation to behave in a prescribed way on the boundary of

Trace (Died Pretty album)

Trace is the fifth album by Australian rock band Died Pretty. It was released in 1993. The album was the most commercially successful of the band's career, peaking at No.11 on the ARIA album charts, while a single, "Harness Up" (August 1993), peaked at No.35. A four-track EP, "Caressing Swine" (June), and two other singles, "Headaround" (November) and "A State of Graceful Mourning" (December), failed to chart.

Despite its commercial success, singer and songwriter Ron Peno has expressed disappointment with it. In a 1995 interview he said: "There were some nice moments on Trace, and there were some moments that fell short of the mark. Some songs that just didn't quite get there. It was a valiant attempt, but it didn't make it. Out of all the songs that came from Trace, we only perform one with any regularity, and that's 'Harness Up'. Occasionally we have been doing 'State of Graceful Mourning'—to me, they're the two highlights of the album." Peno acknowledged the production of Trace might have been too polished. "I think we're were getting a bit soft in the sound department. We were losing that hard edge."

TRACE (computer program)

TRACE is a high-precision orbit determination and orbit propagation program. It was developed by The Aerospace Corporation in El Segundo, California. An early version is known to have run on the IBM 7090 computer in 1964. The Fortran source code can be compiled for any platform with a Fortran compiler.

When Satellite Tool Kit's high-precision orbit propagator and parameter and coordinate frame transformations underwent an Independent Verification and Validation effort in 2000, TRACE v2.4.9 was the standard against which STK was compared.

As of 2013, TRACE is still used by the U.S. Government and some of its technical contractors.

References

Angel (Angel album)

Angel is the first album by the rock band Angel. "Tower", the keyboard-heavy opening track, was used widely during the late 1970s and early 1980s by album rock radio stations in the USA for various advertising purposes. The track is also on K-SHE radio's Classic List. This album can be seen as representing the band's early progressive roots, with Helluva Band seeing the group starting to move towards an increasingly hard rock-oriented sound. Tracks 6-8 segue to form a 10-minute mini suite.

Track listing

Personnel

References

Angel (season 5)

The fifth and final season of the television series Angel, the spin-off of Buffy the Vampire Slayer, premiered on October 1, 2003 on The WB and concluded its 22-episode season and its television run on May 19, 2004. The season aired on Wednesdays at 9:00 pm ET. This was the first and only season of Angel to air following the finale of Buffy the Vampire Slayer.

Season synopsis

List of The Wonder Years episodes

The following is an episode list for the ABC comedy-drama series The Wonder Years. The series premiered on January 31, 1988 and ran for a total of 115 episodes spanning 6 seasons ending on May 12, 1993.

Originally, none of the seasons were available on DVD as official season box sets due to the cost of securing the music rights. (See The Wonder Years article for more detailed information.) Time Life released the complete series on DVD Friday October 10th 2014.

Series overview

Season 1 (1988)

Season 2 (1988–1989)

Season 3 (1989–1990)

Season 4 (1990–1991)

Season 5 (1991–1992)

Season 6 (1992–1993)

References

External links

Fall (Clay Walker song)

"Fall", written by Clay Mills, Sonny LeMaire, and Shane Minor, is a song which has been recorded by both country music singer Clay Walker and pop music singer Kimberley Locke, both of whom are signed to Curb Records. Both versions were released within weeks of each other in mid-2007; while Walker's version was released to country radio, Locke's was released to the adult contemporary radio format. Walker's reached number 5 on the U.S. country singles charts, and Locke's reached Number One on the U.S. Dance charts. Go West front man Peter Cox has recorded a version of "Fall" on his 2010 CD "The S1 Sessions".

Content

"Fall" is a mid-tempo ballad in which the narrator addresses a lover who has had a bad day. The narrator then offers moral support to the lover: "Fall, go on and lose it all / Every doubt, every fear / Every worry, every tear".

Clay Walker version

Walker's version, the first version of the song to be released, was the second single from his 2007 album, which was also titled Fall. A music video was issued on October 17, 2007.