In physics, a frame of reference consists of an abstract coordinate system and the set of physical reference points that uniquely fix the coordinate system and standardize measurements within that frame. In n dimensions, n + 1 reference points are sufficient to define a reference frame. Using rectangular coordinates, a reference frame may be defined with a reference point at the origin and a reference point at one unit distance along each of the n coordinate axes. In Einsteinian relativity, reference frames are used to specify the relationship between a moving observer and the phenomenon or phenomena under observation. In this context, the phrase becomes "observational frame of reference", which implies that the observer is at rest in the frame, although not located at its origin. A relativistic reference frame includes the coordinate time, which does not correspond across different frames moving to each other; the situation thus differs from Galilean relativity, where all possible coordinate times are equivalent.

The need to distinguish between the various meanings of "frame of reference" has led to a variety of terms. For example, sometimes the type of coordinate system is attached as a modifier, as in Cartesian frame of reference. Sometimes the state of motion is emphasized, as in rotating frame of reference. Sometimes the way it transforms to frames considered as related is emphasized as in Galilean frame of reference. Sometimes frames are distinguished by the scale of their observations, as in macroscopic and microscopic frames of reference. In this article, the term observational frame of reference is used when emphasis is upon the state of motion rather than upon the coordinate choice or the character of the observations or observational apparatus. In this sense, an observational frame of reference allows study of the effect of motion upon an entire family of coordinate systems that could be attached to this frame. On the other hand, a coordinate system may be employed for many purposes where the state of motion is not the primary concern.

For example, a coordinate system may be adopted to take advantage of the symmetry of a system. In a still broader perspective, the formulation of many problems in physics employs generalized coordinates, normal modes or eigenvectors, which are only indirectly related to space and time, it seems useful to divorce the various aspects of a reference frame for the discussion below. We therefore take observational frames of reference, coordinate systems, observational equipment as independent concepts, separated as below: An observational frame is a physical concept related to state of motion. A coordinate system is a mathematical concept, amounting to a choice of language used to describe observations. An observer in an observational frame of reference can choose to employ any coordinate system to describe observations made from that frame of reference. A change in the choice of this coordinate system does not change an observer's state of motion, so does not entail a change in the observer's observational frame of reference.

This viewpoint can be found elsewhere as well. Which is not to dispute that some coordinate systems may be a better choice for some observations than are others. Choice of what to measure and with what observational apparatus is a matter separate from the observer's state of motion and choice of coordinate system. Here is a quotation applicable to moving observational frames R and various associated Euclidean three-space coordinate systems: and this on the utility of separating the notions of R and: and this on the distinction between R and: and from J. D. Norton: The discussion is taken beyond simple space-time coordinate systems by Brading and Castellani. Extension to coordinate systems using generalized coordinates underlies the Hamiltonian and Lagrangian formulations of quantum field theory, classical relativistic mechanics, quantum gravity. Although the term "coordinate system" is used in a nontechnical sense, the term "coordinate system" does have a precise meaning in mathematics, sometimes, what the physicist means as well.

A coordinate system in mathematics is a facet of geometry or of algebra, in particular, a property of manifolds. The coordinates of a point r in an n-dimensional space are an ordered set of n numbers: r =. In a general Banach space, these numbers could be coefficients in a functional expansion like a Fourier series. In a physical problem, they could be spacetime normal mode amplitudes. In a robot design, they could be angles of relative rotations, linear displacements, or deformations of joints. Here we will suppose these coordinates can be related to a Cartesian coordinate system by a set of functions: x j = x j, j = 1, …, n, where x, y, z, etc. are the n Car

Dúlamán, is an Irish folk song. The text of the song relates to the Irish practice of gathering seaweed, done for various purposes, including as fertiliser and food. There are many contemporary versions of the song's melody. Among the best known settings is that of Clannad, who recorded it for their 1976 album Dúlamán. A slower melody was recorded by Altan on their 1993 album Island Angel. A contemporary musical setting of the song for choir was made by composer Michael McGlynn, featured in Endless Ocean: Blue World; the song title was used in 2016 as name of an Irish music & dance show called Dúlamán - Voice of the Celts. 1976 - Clannad - Dúlamán 1993 - Altan - Island Angel 1994 - Pádraigín Ní Uallacháin - A Stór Is A Stóirín 1995 - Anúna - Omnis Michael McGlynn composition. 1997 - Chanticleer - Wondrous Love Michael McGlynn composition. 1999 - Dónal Lunny - TV Programme on the privatisation of Telecom Éireann". 2001 - Cantus - Let Your Voice Be Heard 2007 - Celtic Woman - A New Journey — 2003 - Omnia - 3 2009 - Omnia - World of Omnia 2012 - Celtic Thunder - Voyage Michael McGlynn composition.

2012 - Celtic Woman - Believe — 2012 - The Vocal Consort - Incantations Michael McGlynn composition. 2014 - Celtic Woman - Emerald: Musical Gems — 2014 - Song of the Sea 2016 - Celtic Woman - Voices of Angels — 2019 - Ajeet Kaur - Indigo Sea — 1976 Clannad lyrics 1993 Altan lyrics 1993 Lyrics with phonetic spellings. Review and history of the song

The Dictionary of Virginia Biography is a multivolume biographical reference work published by the Library of Virginia that covers aspects of Virginia's history and culture since 1607. The work was intended to run for a projected fourteen volumes, but as of 2015 only three have been published; because for two and a half centuries of its history Virginia encompassed a much larger territory than it does today, the DVB defines Virginia as the current state boundaries plus Kentucky before its separate statehood in 1792 and West Virginia before its separate statehood in 1863. Content from the Dictionary of Virginia Biography, including content not published in print, is being published online through a partnership with Encyclopedia Virginia; the first volume was published in 1998 and covered individuals with surnames from Aaroe through Blanchfield. A second volume was released in 2001 and covered Bland through Cannon, volume 3 covered Caperton through Daniels. Virginians covered in the DVB were chosen because they made significant contributions or achieved particular distinction in their professions or chosen fields.

No persons living at the time of publication are included. Kneebone, John T.. Dictionary of Virginia Biography. Vol. 1 Aaroe - Blanchfield. Richmond: Library of Virginia. ISBN 9780884901891. Bearss, Sara B.. Dictionary of Virginia Biography. Vol. 2 Bland-Cannon. Richmond: Library of Virginia. ISBN 9780884901990. Bearss, Sara B.. Dictionary of Virginia Biography. Vol. 3 Caperton-Daniels. Richmond: Library of Virginia. ISBN 9780884902065. Dictionary of Virginia Biography home page Dictionary of Virginia Biography entries published on Encyclopedia Virginia to date

Bare Fists is a 1919 American Western film directed by John Ford and featuring Harry Carey. It is considered to be a lost film. John Ford and actor Harry Carey collaborated on at least 25 films in the years of 1917-1921. During these collaborations, Carey made more per film than Ford. By 1919 Ford was making 300 dollars a week, Carey was making 1,250; this differential in pay led to tension between the two. The film takes place in a lawless town in southwestern Kansas during the era of cowboys. After the marshal is killed while breaking up a saloon fight, his son, Cheyenne Harry avenges his father’s death by killing two of the men involved, his mother pleads with him to never carry a gun again and Cheyenne Harry agrees. Harry is wooing the beautiful Conchita. Conchita is being wooed by the devious Boone Travis. In order to eliminate his rival, Travis murders frames Harry. Harry is allowed one last visit to see his mother. During this trip he is told that his brother Bud was branded by cattle thieves.

Harry punishes the men who attacked his brother. He is cleared of the charge of murder. Harry Carey as Cheyenne Harry Betty Schade as Conchita Joe Harris as Boone Travis Vester Pegg as Lopez Mollie McConnell as Conchita's Mother Anna Mae Walthall as Ruby Howard Enstedt as Bud Joseph W. Girard as Harry's Father List of American films of 1919 Harry Carey filmography John Ford filmography List of lost films Bare Fists on IMDb

The Erlenmeyer–Plöchl azlactone and amino acid synthesis, named after Friedrich Gustav Carl Emil Erlenmeyer who discovered the reaction, is a series of chemical reactions which transform an N-acyl glycine to various other amino acids via an oxazolone. Hippuric acid, the benzamide derivative of glycine, cyclizes in the presence of acetic anhydride, condensing to give 2-phenyl-oxazolone; this intermediate has two acidic protons and reacts with benzaldehyde, acetic anhydride and sodium acetate to a so-called azlactone. This compound on reduction gives access to phenylalanine. Variants of the azlactone synthesis in which analogues of azlactones are used are sometimes advantageous. Hydantoin and rhodanine have each been employed as the enolate-forming component of the condensation. 2,5-Diketopiperazine can be used as a methylene component as well. In one study the Erlenmeyer amino acid synthesis was used in the heart of an L-m-tyrosine synthesis Dakin-West reaction Perkin reaction

Mental is a television series produced by Fox's subsidiary Fox Telecolombia, which aired in the summer and fall of 2009 on FOX international channels for Latin America and Asia, starring Chris Vance and Annabella Sciorra. Mental was executive-produced by Deborah Joy LeVine – creator of the successful drama series Lois & Clark: The New Adventures of Superman and the Lifetime series The Division, executive producer of Any Day Now, Dawson's Creek and the CBS series Early Edition – and her brother and writing/producing partner, Dan LeVine. Following its U. S. debut, it aired in 35 additional countries. Fox Latin America aired the first episode as a "Worldwide Premiere" on June 2, 2009. Fox aired the pilot episode on May 2009, for the American market. Fox TV Studios ordered 13 episodes, it began production on June 2, 2008, at the Fox Telecolombia production facilities in Bogotá. Although the series was filmed in the city of Bogotá in Colombia representing Los Angeles, no Colombian actor was cast as a regular character and few were cast for occasional roles, because of the strict American nature of the series.

According to TVWeek, Jacqueline McKenzie, Derek Webster, Nicholas Gonzalez, Marisa Ramirez were added to the cast of Mental, "probably as recurrent characters."Due to declining ratings, Fox cancelled the show following its first season. Dr. Jack Gallagher The protagonist of the show, Jack is an Australian man living in America, for what seems like much of his life as his step-father of many years is American, he uses rather unorthodox methods to get inside the patient's head to help cure them. He enjoys riding his bike and has a mentally unstable sister whom he is trying to find, has been for four years. At the end of the episode entitled, Do Over, he finds Becky and she is put into the hospital with schizophrenia. Jack's mother and stepfather come and try to convince him to let them take Becky to Florida for treatment. Jack is skeptical. In the season finale, Jack is seen talking to an anonymous therapist, admits that he has an irrational fear of developing schizophrenia, why he is afraid of commitment.

It is revealed that he, most is dealing with clinical depression at this point. In the final scene, he punches Carl, is subsequently fired. Jack leaves and the season, as well as the series, ends; the last shot of the series shows us Dr. Gallagher now "vagrant" and without direction, in opposition to his vagrant sister, who has chosen to return home with her family; the season ends in direct opposition to the season opening—an ironic ending. Nora Skoff She is a hospital administrator. Nora has a conservative style, she battled cancer and is divorced with two daughters. Dr. Carl Belle Dr. Belle is a master politician, dedicated to Jack's downfall secretly black-mailing Arturo to spy on Jack. Dr. Veronica Hayden-Jones Dr. Hayden-Jones is a dedicated psychiatrist, upset that she wasn't given Jack's job, she was cheating on him with one of the doctors in the hospital. This doctor has subsequently resigned. Dr. Chloë Artis Dr. Artis is a gorgeous doctor, passing the time in a residency she feels is beneath her until Jack opens her mind to the inspirational benefits of psychiatry.

She is pursued by Arturo before she reveals to him that she is a lesbian. Dr. Arturo Suarez Dr. Suarez is a first-year resident, he is young and cocky looking for love, won't seem to give up on Chloe knowing her sexual orientation. Arturo falsified his transcripts so that he could become a doctor and that information is being held against him by Carl, blackmailing Arturo into spying on Jack. Margo Stroud Jack and Becky's mother, whose the father of her children, died, she is married to James. James Stroud Jack and Becky's Margo's second husband. James is a retired Navy Vice Admiral - Jack bitterly states that James raised them as though they were soldiers. Jack holds a grudge on James for sticking Becky in the first institution he could find, twenty years ago, when Becky was diagnosed with schizophrenia, he is American. Becky Gallagher Becky is Jack's twin sister, diagnosed with schizophrenia twenty years ago, she has been missing for four years, showed up on Jack's doorstep near the end of the first season.

Jack is protective over her and they both share a strong loving bond. She is haunted by hallucinations of a young man named Gabe; the series features performances by actors from the United States or other countries who have traveled to Bogotá, Colombia, to film the episode where they have their respective appearance in the next table special performances that stand out: Metacritic gave season 1 a score of 40% based on reviews by 18 critics. The series premiere of Mental on FOX improved on its lead-in and averaged a 3.6/6, to go with just under 5.8 million viewers. A DVD of the complete series titled Mental - The Complete 1st Season was announced on September 2, 2009; the DVD was released on December 1, 2009. The DVD includes all 13 episodes on a 4-disc set, plus an unrated alternate pilot. Mental Official Site at FOX.com Mental on IMDb