In special relativity , electromagnetism and Wave wave theory , the d Alembert operator represented by a box math scriptstyle Box math , also called the d Alembertian or the wave operator , is the Laplace operator of Minkowski space . The operator is named for French mathematician and physicist Jean le Rond d Alembert . In Minkowski space in standard coordinates t , x , y , z it has the form math begin align Box & partial mu partial mu g mu nu partial nu partial mu frac 1 c 2 frac partial 2 partial t 2 frac partial 2 partial x 2 frac partial 2 partial y 2 frac partial 2 partial z 2 & frac 1 c 2 partial 2 over partial t 2 nabla 2 frac 1 c 2 partial 2 over partial t 2 Delta. end align math Here math scriptstyle g mu nu math is the inverse Minkowski metric with math scriptstyle g 00 , , 1 math , math scriptstyle g 11 , , g 22 , , g 33 , , 1 math , math scriptstyle g mu nu , , 0 math for math scriptstyle mu , neq , nu math . Note that the and summation indices range from 0 to 3 see Einstein notation . We have assumed units such that the speed of light math scriptstyle c , , 1 math . Some authors also use the negative metric signature of with math scriptstyle eta 00 , , 1, eta 11 , , eta 22 , , eta 33 , , 1 math . Lorentz transformation s leave the Minkowski metric invariant, so the d Alembertian is a Lorentz scalar . The above coordinate expressions remain valid for the standard coordinates in every inertial frame. Alternate notations There are a variety of notations for the d Alembertian. The most common is the symbol math scriptstyle Box math the four sides of the box representing the four dimensions of space time and the math scriptstyle Box 2 math which emphasizes the scalar property through the squared term much like the Laplacian . This symbol is sometimes called the quabla cf . nabla symbol . In keeping with the triangular notation for the Laplacian ... he nl D Alembertiaan ja pl Operator d Alemberta pt Operador de d Alembert ru ... more details
D Alembert may refer to Jean le Rond d Alembert the D Alembert operator , named after the former D Alembert crater a lunar crater , also named after the above disambig ... more details
Infobox Planet minorplanet yes width 25em bgcolour FFFFC0 apsis name d Alembert symbol image caption discovery yes discovery ref discoverer Elst, E. W. discovery site La Silla discovered February 13, 1988 designations yes mp name 5956 alt names 1988 CF5 named after Jean le Rond d Alembert mp category orbit ref epoch May 14, 2008 aphelion 3.5002561 perihelion 1.9294561 semimajor eccentricity 0.2892971 period 1633.8742804 avg speed inclination 8.94352 asc node 188.82445 mean anomaly 306.39073 arg peri 182.63918 satellites physical characteristics yes dimensions mass density surface grav escape velocity sidereal day axial tilt pole ecliptic lat pole ecliptic lon albedo temperatures temp name1 mean temp 1 max temp 1 temp name2 max temp 2 spectral type abs magnitude 12.7 5956 d Alembert 1988 CF5 is a Asteroid belt main belt asteroid discovered on February 13, 1988 by Elst, E. W. at La Silla . External links http ssd.jpl.nasa.gov sbdb.cgi?sstr 5956 d 27Alembert JPL Small Body Database Browser on 5956 d Alembert MinorPlanets Navigator 5955 Khromchenko 5957 Irina MinorPlanets Footer DEFAULTSORT d Alembert Category Main Belt asteroids Category Asteroids named for people Category Discoveries by Eric Walter Elst Category Astronomical objects discovered in 1988 beltasteroid stub fa it 5956 d Alembert la 5956 d Alembert hu 5956 d Alembert pl 5956 d Alembert pt 5956 d Alembert uk 5956 vi 5956 d Alembert yo 5956 d Alembert ... more details
lunar crater data latitude 50.8 N or S N longitude 163.9 E or W E diameter 248 km depth Unknown colong 201 eponym Jean le Rond d Alembert Jean d Alembert D Alembert is a large Moon lunar impact crater located in the northern hemisphere on the Far side Moon far side of the Moon , to the northeast of the somewhat smaller walled plain Campbell lunar crater Campbell . Astride the southwest rim of D Alembert is Slipher lunar crater Slipher . To the north is the crater Yamamoto crater Yamamoto , and to the south southwest lies Langevin crater Langevin . This walled plain has the same diameter as Clavius crater Clavius on the near side, making it one of the largest such formations on the Moon. As with many lunar walled plains of comparable dimensions, the outer rim of this formation has been worn and battered by subsequent impacts. Besides Slipher, the most notable of these craters is D Alembert Z intruding into the northern rim. There is also a small crater on the northwest inner wall that has a wide cleft in its eastern side, and a smaller crater along the southeastern inner wall. As eroded as the rim may be, its form can still be readily discerned as a roughly circular ridge line in the lunar terrain. The interior floor of D Alembert is a relatively level surface, at least in comparison with the rough terrain that surrounds the crater rim. It is marked with a number of small crater impacts, the largest being D Alembert G and D Alembert E toward the eastern rim. In the southwest, the floor is more irregular due to the outer wikt rampart rampart and layers of ejecta from Slipher. A pair of shallow clefts in the floor surface radiate away from this crater, beginning near the mid point of D Alembert and reaching half way toward the inner wall. Satellite craters By convention these features are identified on lunar maps by placing the letter on the side of the crater mid point that is closest to D Alembert. class wikitable width 25 style background eeeeee D Alembert width 25 ... more details
The Family D Alembert series is a set of science fiction novels by Stephen Goldin , the first of which was expanded from a novella by E E Doc Smith E. E. Doc Smith . Plot Jules and Yvette D Alembert are a brother and sister team of aerialists in the D Alembert family Circus of the Empire and also work as agents in SOTE, The Service of The Empire , the imperial intelligence agency. Series The series comprises the following books Imperial Stars 1976 Stranglers Moon 1976 The Clockwork Traitor 1976 Getaway World 1977 Appointment at Bloodstar , also known as The Bloodstar Conspiracy 1978 The Purity Plot 1978 Planet of Treachery 1981 Eclipsing Binaries 1983 The Omicron Invasion 1984 Revolt of the Galaxy 1985 Category Science fiction book series ... more details
Classical mechanics cTopic Fundamental concepts Image Alembert.jpg thumb right Jean d Alembert D Alembert s principle , also known as the Lagrange d Alembert principle , is a statement of the fundamental classical physics classical laws of motion. It is named after its discoverer, the France French physicist and mathematician Jean le Rond d Alembert . The principle states that the sum of the differences between the force s acting on a system and the time derivative s of the momentum momenta of the system itself along any virtual displacement consistent with the constraints of the system, is zero. Thus, in symbols d Alembert s principle is written as following, math sum i mathbf F i m i mathbf a i cdot delta mathbf r i 0, math where math i math is an integer used to indicate via subscript a variable corresponding to a particular particle in the system, math mathbf F i math is the total applied force excluding constraint forces on the math i math th particle, math m i scriptstyle math is the mass of the math i math th particle, math mathbf a i math is the acceleration of the math i math th particle, math m i mathbf a i math together as product represents the time derivative of the momentum of the math i math th particle, and math delta mathbf r i math is the virtual displacement of the math i math th particle, consistent with the constraints. It is the dynamic analogue to the principle of virtual work for applied forces in a static system and in fact is more general than Hamilton s principle , avoiding restriction to holonomic systems. ref name Lanczos cite book title The variational principles of mechanics author Cornelius Lanczos page 92 edition 4rth Edition publisher Dover Publications Inc. location New York isbn 0 486 65067 7 year 1970 url http books.google.com books?id ZWoYYr8wk2IC&pg PA92&dq 22d 27Alembert 27s principle 22 ref A holonomic constraint depends only on the coordinates and time. It does not depend on the velocities. If the negative terms in acc ... more details
wiktionary Operatoroperator operators Operator may refer to tocright Music Operator band , an American hard rock band Operator Motown song Operator Motown song , a 1965 song recorded by Mary Wells and Brenda Holloway Operator That s Not the Way It Feels , a 1972 song by Jim Croce from You Don t Mess Around with Jim Operator Midnight Star song Operator Midnight Star song 1984 Operator A Girl Like Me , a 2008 song by Shiloh Operator , a 1970 song by the Grateful Dead from American Beauty album American Beauty Operator , a 1975 song by the Manhattan Transfer from The Manhattan Transfer album The Manhattan Transfer Operator , a 1993 song by Blue System from Backstreet Dreams album Backstreet Dreams Operator , a 1995 song by Real McCoy from Another Night Real McCoy album Another Night Computers Computer operatorOperator programming , a type of computer program function Operator extension , an extension for the Firefox web browser, for reading microformats Operator YAPO or OperaTor, a portable implementation of the Opera web browser Science and mathematics Operator mathematics , a function between vector spaces Operator biology , a segment of DNA regulating the activity of genes Operator linguistics , a special category including wh interrogatives Operator physics , mathematical operators in quantum physics Fiction Operator Ghost in the Shell Operator Ghost in the Shell , a fictional group in the Ghost in the Shell series Operator The Matrix Operator The Matrix , a crew position in The Matrix franchise Other uses Operator profession Telephone operator , person or company offering telephone services Operator military , a soldier in a special operations force Network operator , a phone carrier Operator sternwheeler Operator sternwheeler , an early 20th century ship on the Skeena River Operator Grammar , a theory of human language See also Operation disambiguation Operator precedence grammar , a grammar for formal languages Operator No. 5 , a pulp fiction hero from the 1930s ... more details
Infobox Single See Wikipedia WikiProject Songs Name Operator, Operator Cover Artist Eddy Raven Album Love and Other Hard Times B side Just for the Sake of the Thrill ref name raven Released 1985 Format 7 single Recorded Genre Country music Country Length 3 04 Label RCA Records RCA Writer Larry Willoughby , Janet Willoughby Producer Paul Worley , Eddy Raven Last single She s Gonna Win Your Heart br 1984 This single Operator, Operator br 1985 Next single I Wanna Hear It from You br 1985 Misc Operator, Operator originally titled Heart on the Line Operator, Operator is a country music song co written and recorded by Larry Willoughby , a cousin of country music singer Rodney Crowell , and Janet Willoughby. He released the song in 1983 from the album Building Bridges , and took it to number 65 on the Hot Country Songs charts. ref name whitburn cite book last Whitburn first Joel title Hot Country Songs 1944 to 2008 publisher Record Research, Inc date 2008 page 469 isbn 0 89820 177 2 ref The Oak Ridge Boys also recorded it under the original title, as the b side to their 1983 single Love Song The Oak Ridge Boys song Love Song . ref Whitburn, p. 303 ref A 1985 recording by Eddy Raven , under the title Operator, Operator , appeared on his album Love and Other Hard Times . This version went to number 9 on the same chart. ref name raven Whitburn, p. 340 ref Chart performance Larry Willoughby class wikitable sortable align left Chart 1983 align center Peak br position align left U.S. Billboard Hot Country Singles align center 65 Eddy Raven class wikitable sortable align left Chart 1985 align center Peak br position align left U.S. Billboard Hot Country Singles align center 9 align left Canadian RPM Country Tracks align center 8 References reflist Category 1983 singles Category 1985 singles Category Eddy Raven songs Category Larry Willoughby songs Category Songs produced by Paul Worley 1980s country song stub ... more details
lowercase d Alembert Euler condition In mathematics and physics , especially the study of mechanics and fluid dynamics , the d Alembert Euler condition is a requirement that the Streamlines, streaklines and pathlines streaklines of a flow are irrotational . Let x x X , t be the coordinates of the point x into which X is carried at time t by a fluid flow. Let math ddot mathbf x frac D 2 mathbf x Dt math be the second material derivative of x . Then the d Alembert Euler condition is math mathrm curl mathbf x mathbf 0 . , math The d Alembert Euler condition is named for Jean le Rond d Alembert and Leonhard Euler who independently first described its use in the mid 18th century. It is not to be confused with the Cauchy Riemann equations Cauchy Riemann conditions . References cite book last Truesdell first Clifford A. authorlink Clifford Truesdell title The Kinematics of Vorticity year 1954 publisher Indiana University Press location Bloomington, IN See sections 45 48. http eom.springer.de c c020970.htm d Alembert Euler conditions on the Springer Encyclopedia of Mathematics DEFAULTSORT D alembert Euler Condition Category Fluid mechanics Category Mechanical engineering Category Vector calculus bs D Alembert Eulerov uslov ... more details
Unreferenced date November 2011 infobox Book See Wikipedia WikiProject Novels or Wikipedia WikiProject Books name D Alembert s Dream title orig Le R ve de d Alembert translator image prefer 1st edition image caption author Denis Diderot illustrator cover artist country France language French language French series genre publisher release date 1830 english release date media type pages isbn D Alembert s Dream lang fr Le R ve de d Alembert is an ensemble of three philosophical dialogues authored by Denis Diderot in 1769 and published in 1830 Conversation between d Alembert and Diderot D Alembert s Dream Continuation of the Conversation between d Alembert and Diderot In this work, Diderot is at the zenith of his development of materialism materialist theories. It is here that he introduces his theory on life and nature, indicating that matter is not fixed but that, on the contrary, subject to evolution . Each species in existence transforms itself and gives birth to a new species. He would later create a special version for his patroness, Catherine the Great Catherine II of Russia, replacing the certain character names. Both Julie de Lespinasse and D Alembert took poorly to being used as protagonists of the conversations. External links http records.viu.ca johnstoi diderot revedalembert tofc.htm Denis Diderot R ve d Alembert French and English texts Denis Diderot DEFAULTSORT Reve De Dalembert Category 1769 novels Category 1830 novels Category Novels by Denis Diderot 19thC novel stub fr Le R ve de D Alembert ... more details
Letter to D Alembert on the Theatre 1758 Lettre a M. d Alembert sur les Spectacles is an essay written by Jean Jacques Rousseau in opposition to an article published in the Encyclop die by Jean d Alembert , that proposed the establishment of a theatre in Geneva . More generally, it is a critical analysis of the effects of culture on morals, that clarifies the links between politics and social life. ref name fermon cite book title Domesticating Passions Rousseau, Woman, and Nation last Fermon first Nicole year 1997 publisher Wesleyan University Press location Hanover isbn 9780819563057 ref Rousseau relates the issue of a theatre in Geneva to the broader social context, warning of the potential the theatre has to corrupt the morality in society. ref name dent cite book title A Rousseau Dictionary last Dent first Nicholas year 1992 publisher Blackwell Publishers location Oxford isbn 9780631175698 ref The Letter is considered to be highly personally relevant to Rousseau, whose patriotism and affinity for Geneva shows through as he writes to defend his country from moral decay. By focusing on his belief in the natural order and harmony of traditional sex roles and community, Rousseau writes to convince d Alembert , and the public of Geneva , that a theatre is a threat to an ideal, natural way of life. ref name grimsley cite book title Jean Jacques Rousseau last Grimsley first Ronald year 1983 publisher The Harvester Press location Sussex isbn 9780389203780 ref Historical context Rousseau generally opposed the Age of Enlightenment Enlightenment thrust that was occurring during his lifetime. He sought to distance himself philosophically from the views that the universal use of reason, science, uninhibited freedom of thought, and increasing appreciation for the fine arts would make society a better place. Rousseau is often characterized as the Father of Romanticism , as he opposed Modernity and the Age of Enlightenment Enlightenment and glorified the heroic ethos of ancient ... more details
Hilbert operator may refer to The epsilon operator in David Hilbert Hilbert s epsilon calculus . The Hilbert Schmidt operator s on a Hilbert space . The Hilbert Schmidt integral operator s. Generally, any operator on a Hilbert space . disambig ... more details
Hello Operator may refer to Hello Operator band , a Canadian band Hello Operator single , by White Stripes Miss Susie , a children s song sometimes referred to as hello operator. disambig Long comment to avoid being listed on short pages it Hello Operator sh Hello Operator ... more details
other uses operator disambiguation Image Avenue of Stars boom operator.JPG thumb 200px Statue of a Boom operator media boom operator on the Avenue of Stars, Hong Kong Avenue of Stars in Hong Kong . An operator is a professional designation used in various industries , including broadcast ing in television and radio , computing , customer service , physics , and construction . Operators are day to day end user s of systems, that may or may not be mission critical , but are typically managed and maintained by technician s or engineer s. They might also work on a 24 hour rotating shift work shift schedule. cn date September 2011 Types of operators Broadcasting Technical operator, transmission controller or broadcast operator Network operations center NOC operator Master control MCR operator Production control room PCR operator Transmission control room TCR operator Video tape operator VTO Certified Television Operator CTO by Society of Broadcast Engineers SBE ref http www.sbe.org Society of Broadcast Engineers ref Certified Radio Operator CRO operator by SBE Television studio Studio technical operator gallery operator Vision mixer operator technical director TD Sound and communications comms talkback recording talkback studio operator Image KC 135Boom operator 521.jpg thumb 210px KC 135 Stratotanker KC 135 Boom operator military Boom operator Camera operator Jib camera operator Boom operator media Boom operator Dolly grip operator Other Computer operator Crane machine Crane operator Radio operator Satellite controller Telephone operator Winch operator Nuclear power plant operator Gallery gallery Image Hg winch operator.jpg Operator of a stationary winch, launching a hang glider . Image Telegraphone with operator.png Valdemar Poulsen Telegraphone with operator gallery References reflist Category Occupations included for non broadcast occupations Category Broadcasting occupations Job stub cs Oper tor profese ru uk ... more details
The translation operator can refer to these things A shift operator , which effects a geometric translation. See also Translation geometry . An alternative name for the displacement operator in quantum optics. Disambig ... more details
In mathematics , especially operator theory , a convexoid operator is a bounded operator bounded linear operator T on a complex Hilbert space H such that the closure of the numerical range coincides with the convex hull of its spectrum. An example of such an operator is a normal operator or some of its generalization . It is not known whether a paranormal operator is a convexoid or not, I think. Taku. A closely related operator is a spectraloid operator an operator whose spectral radius coincides with its numerical radius . In fact, an operator T is convexoid if and only if math T lambda math is spectraloid for every complex number math lambda math . This result is due to Furuta, I believe Taku See also Aluthge transform References T. Furuta. http www.projecteuclid.org DPubS?service UI&version 1.0&verb Display&handle euclid.pja 1195526397 Certain convexoid operators Category Operator theory mathanalysis stub ... more details
In mathematics , operator theory is the branch of functional analysis that focuses on bounded linear operator s, but which includes closed operator s and nonlinear operator s. Operator theory also includes the study of linear algebra algebra s of operators. Single operator theory Single operator theory deals with the properties and classification of single operators. For example, the classification of normal operator s in terms of their spectrum of an operator spectra falls into this category. Operator algebras The theory of operator algebra s brings algebra over a field algebra s of operators such as C algebra s to the fore. See also Invariant subspace Functional calculus Spectral theory Resolvent formalism Compact operator Fredholm theory of integral equation s Integral operator Fredholm operator Self adjoint operator Unbounded operator Differential operator Umbral calculus Contraction mapping Positive operator on a Hilbert space Perron Frobenius theorem Generalizations Nonnegative operator on a ordered vector space partially ordered vector space External links http www.mathphysics.com opthy OpHistory.html History of Operator Theory Mathanalysis stub Category Operator theory de Operatorenrechnung fa ko kk nl Operatorentheorie pt Teoria dos operadores ru tt uk vi L thuy t to n t ... more details
Unreferenced stub auto yes date December 2009 Disputed date March 2008 In theoretical physics , a disorder operator is an Operator mathematics operator that creates a discontinuity of the ordinary order operator s or a monodromy for their values. For example, a t Hooft operator is a disorder operator. So is the Jordan Wigner transformation . DEFAULTSORT Disorder Operator Category Quantum field theory Category Statistical mechanics Phys stub ... more details
The term boom operator may refer to Boom operator military , a member of the crew aboard an aerial refueling tanker, responsible for flying the boom Boom operator media , a member of the crew of a film or radio project, responsible for operating a microphone and sound boom disambig ... more details
see also inversion In the mathematics , inversion operator can refer to the Operator mathematics operator which assigns the inverse element to an element of a group mathematics group Inversion in a point Chromosomal inversion , reordering of genes in a DNA sequence. mathdab ... more details
In mathematics , especially operator theory , a hyponormal operator is a generalization of a normal operator . In general, a bounded linear operator T on a complex Hilbert space H is said to be p hyponormal math 0 p le 1 math if math T T p ge TT p math That is to say, math T T p TT p math is a positive operator. If math p 1 math , then T is called a hyponormal operator. If math p 1 2 math , then T is called a semi hyponormal operator. Moreoever, T is said to be log hyponormal if it is invertible and math log T T ge log TT . math An invertible p hyponormal operator is log hyponormal. On the other hand, not every log hyponormal is p hyponormal. The class of semi hyponormal operators was introduced by Xia, and the class of p hyponormal operators was studied by Aluthge, who used what is today called the Aluthge transformation . Every subnormal operator in particular, a normal operator is hyponormal, and every hyponormal operator is a paranormal operator paranormal convexoid operator . Not every paranormal operator is, however, hyponormal. Let T be a hyponormal operator. If math T T TT math is compact, then T is normal. Maybe the statement isn t quite accurately stated. See also Putnam s inequality References http www.jstor.org pss 2162263 Category Operator theory mathanalysis stub ... more details
Unreferenced date December 2009 In operator theory , a multiplication operator is a linear operator T defined on some function space vector space of functions and whose value at a function is given by multiplication by a fixed function f . That is, math T varphi x f x varphi x quad math for all in the function space and all x in the domain mathematics domain of which is the same as the domain of f . This type of operators is often contrasted with composition operator s. Multiplication operators generalize the notion of operator given by a diagonal matrix . More precisely, one of the results of operator theory is a spectral theorem , which states that every self adjoint operator on a Hilbert space is unitarily equivalent to a multiplication operator on an Lp space L sup 2 sup space . Example Consider the Hilbert space X L sup 2 sup &minus 1, 3 of complex number complex valued square integrable functions on the interval mathematics interval &minus 1, 3 . Define the operator math T varphi x x 2 varphi x quad math for any function in X . This will be a self adjoint operator self adjoint bounded linear operator with operator norm norm 9. Its spectrum of an operator spectrum will be the interval 0, 9 the range mathematics range of the function x x sup 2 sup defined on &minus 1, 3 . Indeed, for any complex number , the operator T is given by math T lambda varphi x x 2 lambda varphi x . quad math It is invertible function invertible if and only if is not in 0, 9 , and then its inverse is math T lambda 1 varphi x frac 1 x 2 lambda varphi x quad math which is another multiplication operator. This can be easily generalized to characterizing the norm and spectrum of a multiplication operator on any Lp space . See also translation operator shift operator Decomposition of spectrum functional analysis DEFAULTSORT Multiplication Operator Category Functional analysis ... more details
In mathematics , especially operator theory , a paranormal operator is a generalization of a normal operator . More precisely, a bounded linear operator T on a complex Hilbert space H is said to be paranormal if math T 2x ge Tx 2 , math for every unit vector x in H . The class of paranormal operators was introduced by V. Istratescu in 1960s, though the term paranormal is probably due to Furuta. ref V. Istratescu. http projecteuclid.org DPubS Repository 1.0 Disseminate?view body&id pdf 1&handle euclid.pjm 1102992095 On some hyponormal operators ref ref name Furuta Every hyponormal operator in particular, a subnormal operator , a quasinormal operator and a normal operator is paranormal. If T is a paranormal, then T sup n sup is paranormal. ref name Furuta Furuta, Takayuki. http projecteuclid.org DPubS Repository 1.0 Disseminate?view body&id pdf 1&handle euclid.pja 1195521514 On the Class of Paranormal Operators ref On the other hand, Paul Halmos Halmos gave an example of a hyponormal operator T such that T sup 2 sup isn t hyponormal. Consequently, not every paranormal operator is hyponormal. ref P.R.Halmos, A Hilbert Space Problem Book 2nd edition, Springer Verlag, New York, 1982. ref A Compact operator compact paranormal operator is normal. ref Furuta, Takayuki. http www.journalarchive.jst.go.jp jnlpdf.php?cdjournal pjab1945&cdvol 47&noissue SupplementI&startpage 888&lang en&from jnlabstract Certain Convexoid Operators ref References reflist Category Operator theory mathanalysis stub ... more details
Encyclopedia
top
