In atomic physics , the principalquantum symbolized as n is the first of a set of quantumnumber s which includes the principalquantumnumber, the azimuthal quantumnumber , the magnetic quantumnumber , and the spin quantumnumber of an atomic orbital . The principalquantumnumber can only have positive ... are all interrelated. The principalquantumnumber arose in the solution of the radial part of the wave ... on the principalquantumnumber. The principalquantumnumber is related to the radial quantumnumber, n sub r sub , by math n n r ell 1 , math where is the azimuthal quantumnumber and n sub r ... less tightly bound to the nucleus. This is the only quantumnumber introduced by the Bohr ... hbar n cdot h over 2 pi math where n 1, 2, 3, &hellip and is called the principalquantumnumber, and h is Planck s constant . This formula is not correct in quantum mechanics as the angular momentum magnitude is described by the azimuthal quantumnumber , but the energy levels are accurate ... quantumnumber n represents the relative overall energy of each orbital, and the energy ... momentum quantumnumber Basic quantum mechanics Schr dinger equation External references http www.colorado.edu physics 2000 applets a2.html Periodic Table Applet showing principal and azimuthal quantumnumber for each element Category Quantum chemistry Category Atomic physics ar bg ... has an integral number of floors, and a well functioning elevator can only stop at a particular floor. Furthermore the elevator can only travel an integer number of levels. As with the principalquantumnumber, higher numbers are associated with higher potential energy. Of course beyond this point the analogy breaks down. In the case of elevators the potential energy is gravitational but with the quantumnumber it is electromagnetic. The gains and losses in energy are approximate with the elevator, but precise with quantum state. The elevator ride from floor to floor is continuous whereas ... more details
class wikitable name symbol orbital meaning range of values value example principalquantumnumber n shell 1 n n 1, 2, 3, azimuthal quantumnumber angular momentum ell subshell s orbital is listed as 0, p orbital as 1 etc. 0 ell n &minus 1 for n 3 br ell 0, 1, 2 s, p, d magnetic quantumnumber , projection ... requires at least one quantumnumber. The dynamics of any quantum system are described by a quantum Hamiltonian quantum mechanics Hamiltonian , H . There is one quantumnumber of the system corresponding to the energy, i.e., the eigenvalue of the Hamiltonian. There is also one quantumnumber for each ... quantumnumber. The second, ell , describes the electron shell Subshells subshell 0 s orbital ... ell 2 appears in the third shell n 3 , and so on. A quantumnumber beginning in 3, 0, describes an electron ... m sub ell sub ell for ell 2 br m sub ell sub &minus 2, &minus 1, 0, 1, 2 spin quantumnumber spin projection quantumnumber m sub s sub spin of the electron &minus counter clockwise, clockwise &minus ... quantumnumber n 1, 2, 3, 4, denotes the eigenvalue of Hamiltonian H , i.e. the energy, with the contribution ... coordinate, r . The average distance increases with n , and hence quantum states with different principalquantum numbers are said to belong to different shells. The azimuthal quantumnumber ell 0, 1, , n &minus 1 also known as the angular quantumnumber or orbital quantumnumber gives the orbital ... orbital, ell 2 a d orbital, and ell 3 an f orbital. The magnetic quantumnumber m sub ell sub &minus ... along a specified axis. L sub z sub m sub ell sub . spin quantumnumber The spin projection quantum ... exclusion principle . A fourth quantumnumber with two possible values was added as an ad hoc ... coefficients See also Azimuthal quantumnumber Total angular momentum of an electron in the atom When ... angular momentum quantumnumber ell s gives the total angular momentum through the relation nowrap J sup 2 sup sup 2 sup j j 1 . The Azimuthal quantumnumber Example total angular momentum in the atom ... more details
number Azimuthal quantumnumberPrincipalquantumnumber Spin quantumnumber Total angular momentum ...Unreferenced date August 2009 In atomic physics , the magnetic quantumnumber is the third of a set of quantumnumber s the principalquantumnumber , the azimuthal quantumnumber , the magnetic quantumnumber, and the spin quantumnumber which describe the unique quantum state of an electron and is designated by the letter m . The magnetic quantumnumber denotes the energy levels available within ... interrelated. The magnetic quantumnumber arose in the solution of the azimuthal part of the wave equation as shown below. The magnetic quantumnumber associated with the quantum state is designated as m . The quantumnumber m refers, loosely, to the direction of the angular momentum Vector geometric vector . The magnetic quantumnumber m does not affect the electron s energy, but it does affect ... from up to . More precisely, for a given orbital momentum quantumnumber representing the azimuthal quantumnumber associated with angular momentum , there are 2 1 integral magnetic quantum numbers ... quantumnumber m you begin with an atomic electron s angular momentum, L, which is related to its quantumnumber by the following equation math mathbf L hbar sqrt ell ell 1 math where math hbar h ... . To show each of the quantum numbers in the quantum state, the formulae for each quantumnumber include .... The quantumnumber m refers to the projection of the angular momentum for any given direction, conventionally ... quantumnumber math m l ell, ell 1,..., 0, ..., ell 1, ell math is the eigenvalue , J sub z sub m sub sub h 2 . Where the quantumnumber is the subshell, the magnetic number m represents .... class wikitable colspan 3 Relationship between Quantum Numbers Orbital Values Number of Values ..., 4 math 9 The magnetic quantumnumber determines the energy shift of an atomic orbital due to an external magnetic field, hence the name magnetic quantumnumber Zeeman effect . However, the actual magnetic ... more details
orbital wavefunctions of a hydrogen atom . The principalquantumnumber is at the right of each row and the azimuthal quantumnumber is denoted by letter at top of each column. Atomic orbitals have distinctive .... For a given value of the principalquantumnumber n , the possible values of range from 0 ... Quantumnumber Magnetic quantumnumberPrincipalquantumnumber Spin quantumnumber Total angular ...The azimuthal quantumnumber is a quantumnumber for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital. The azimuthal quantumnumber is the second of a set of quantum numbers which describe the unique quantum state of an electron the others being the principalquantumnumber , following spectroscopic notation , the magnetic quantumnumber , and the spin quantumnumber . It is also known as the orbital angular momentum quantumnumber or second quantum ... for the first three quantum numbers are all interrelated. The azimuthal quantumnumber arose in the solution ... momentum , L , is related to its quantumnumber by the following equation math mathbf L 2 Psi hbar ... use the quantumnumber . The energy of any wave is the frequency multiplied by Planck s constant ... each of the quantum numbers in the quantum state, the formulae for each quantumnumber include Planck ... angular momentum states can take 2 2 1 electrons. This is because the third quantumnumber m ... spins given by the quantumnumber m sub s sub , giving 2 2 1 electrons overall. Orbitals with higher ... of electrons in the n th energy level is 2 n sup 2 sup . The angular momentum quantumnumber, , governs ..., no nodes go through the nucleus, therefore the corresponding azimuthal quantumnumber takes the value ... has the value . Depending on the value of n , there is an angular momentum quantumnumber and the following ... vec ell 2 math , math vec jmath vec ell 1 vec ell 2 math the quantumnumber math j math associated ... , J sub y sub , and J sub z sub . The quantumnumber s describing the system, which are constant over ... more details
nofootnotes date February 2010 In quantum field theory , multiplicative quantum numbers are conserved quantumnumber s of a special kind. A given quantumnumber q is said to be additive if in a particle reaction the sum of the q values of the interacting particles is the same before and after the reaction. Most conserved quantum numbers are additive in this sense the electric charge is one example. A multiplicative quantumnumber q is one for which the corresponding product, rather than the sum, is preserved. Any conserved quantumnumber is a symmetry of the Hamiltonian quantum theory Hamiltonian of the system see Noether s theorem . Symmetry group mathematics groups which are examples of the abstract group called Z sub 2 sub give rise to multiplicative quantum numbers. This group consists of an operation, P , whose square is the identity, P sup 2 sup 1 . Thus, all symmetries which are mathematically similar to parity physics give rise to multiplicative quantum numbers. In principle, multiplicative quantum numbers can be defined for any Abelian group. An example would be to trade the electric charge , Q , related to the Abelian group U 1 of electromagnetism , for the new quantumnumber exp 2 i &pi Q . Then this becomes a multiplicative quantumnumber by virtue of the charge being an additive quantumnumber. However, this route is usually followed only for discrete subgroups of U 1 , of which Z sub 2 sub finds the widest possible use. See also Parity physics Parity , C symmetry , T symmetry and G parity References Group theory and its applications to physical problems, by M. Hamermesh Dover publications, 1990 ISBN 0 486 66181 4 Category Quantum field theory Category Particle physics Category Nuclear physics sl Multiplikativno kvantno tevilo ... more details
inline citations date August 2011 In atomic physics , the spin quantumnumber is a quantumnumber that Parameterization ... spin physics spin of a given Elementary particle particle . The spin quantumnumber is the fourth of a set of quantumnumber s the principalquantumnumber , the azimuthal quantumnumber , the magnetic quantumnumber , and the spin quantumnumber , which describe the unique quantum state of an electron ... momentum quantumnumber it holds that math Vert mathbf s Vert sqrt s , s 1 , hbar math where math mathbf ... of the spin vector math s math is the spin quantumnumber associated with the spin angular momentum ... is the secondary spin quantumnumber , ranging from &minus s to s in steps of one. This generates ... quantum numbers , n , l , and m . These were identified as, respectively, the electron shell number, n , the orbital number, l , and the orbital angular momentum number m . Angular momentum is a so ... numbers l and m . The spin angular momentum is characterized by a quantumnumber spin s 1 2 specifically ... give rise to magnetic moment , which was a requisite for the fourth quantumnumber. The electron ... magnetic field, what depends on the value of the magnetic spin quantumnumber. When the spin of the electron ... equation all four quantum numbers including the additional quantumnumber, s arose naturally during its solution. See also Total angular momentum quantumnumber Basic quantum mechanics External ... copy of the Angular momentum Angular momentum in quantum mechanics Angular momentum in quantum ... numbers start at 1 and increase indefinitely. Each shell of number n contains n orbitals. Each orbital is characterized by its number l , where l takes integer values from 0 to n 1, and its angular momentum number m , where m takes integer values from l to l . By means of a variety of approximations ... quantum leap jumping from one state to another, where a state is represented by values of n , l ... in the electromagnetic dipole of the atom. However, it was recognized in the early years of quantum ... more details
Unreferenced auto yes date December 2009 Flavour quantum numbers Charm symbol C is a flavour physics flavour flavour quantumnumberquantumnumber representing the difference between the number of charm quark charm quark s SubatomicParticle charm quark and charm antiquarks SubatomicParticle Charm antiquark that are present in a particle math C n text c n mathrm overline c . math By convention, the sign of flavour quantum numbers agree with the sign of the electric charge carried by the quark of corresponding flavour. The charm quark, which carries an electric charge Q of Frac 2 3 , therefore carries a charm of 1. The charm antiquarks have the opposite charge physics charge Nowrap Q &minus Frac 2 3 , and flavour quantum numbers Nowrap C &minus 1 . As with any flavour related quantum numbers, charm is preserved under strong interaction strong and electromagnetic interaction , but not under weak interaction see CKM matrix . For first order weak decays, that is processes involving only one quark decay, charm can only vary by 1 Nowrap C 1 . Since first order processes are more common than second order processes involving two quark decays , this can be used as an approximate selection rule for weak decays. See also Isospin Strangeness particle physics Strangeness Bottomness Topness Hypercharge Further reading http arxiv.org PS cache arxiv pdf 0906 0906.1271v2.pdf Lessons in Particle Physics Luis Anchordoqui and Francis Halzen, University of Wisconsin, 18th Dec. 2009 DEFAULTSORT Charm QuantumNumber Category Particle physics Category Quarks Category Particle physics flavour quantumnumber Physics stub de Flavour Quark Flavours it Charm numero quantico ja sl ar fizika uk ... more details
Expert verify date February 2010 In physics , a topological quantumnumber also called topological charge is any quantity, in a physical theory, that takes on only one of a discrete set of values, due to topology topological considerations. Most commonly, topological quantum numbers are topological invariant s associated with topological defect s or soliton type solutions of some set of differential equation s modeling a physical system, as the solitons themselves owe their stability to topological ... group that is preserved by the differential equations. The topological quantumnumber of a solution is sometimes called the winding number of the solution, or, more precisely, it is the degree of a continuous ... is given by the Skyrmion , for which the baryon number is a topological quantumnumber. The origin ... there is math pi 1 S 1 mathbb Z math and so is literally a winding number a circle can be wrapped around a circle an integer number of times. Quantum sine Gordon model is equivalent to massive Thirring model . Fundamental excitations are fermions topological quantumnumber math mathbb Z math is the number ... that topological quantum numbers, and their associated solitons, can be created or destroyed during ... group of the three sphere is math pi 3 S 3 mathbb Z math and so the baryon number can only take on integer ... . Consistent consideration of ultraviolet renormalization shows that a fractional number of fermions ... number depending on Plank constant. Solid state physics In solid state physics , certain types of crystalline ... transform Central charge Quantum topology Topological defect Topological entropy in physics Topological order Topological quantum field theory Topological string theory References cite book title Topological Quantum Numbers in Nonrelativistic Physics first D. J. last Thouless publisher World Scientific year 1998 isbn 9810229003 DEFAULTSORT Topological QuantumNumber Category Solitons Category Exactly solvable models Category Quantum mechanics Category Quantum field theory it carica topologica ... more details
In quantum mechanics , given a particular Hamiltonian quantum mechanics Hamiltonian math H math and an Operator mathematics operator math O math with corresponding eigenvalues and eigenvectors given by math O q j rangle q j q j rangle math then the physical quantities math q j math are said to be good quantum numbers if every eigenvector math q j rangle math remains an eigenvector of math O math with the same eigenvalue as time evolves. Hence, if math O q j rangle O sum k c k 0 e k rangle q j q j rangle math then we require math O sum k c k 0 exp i e k t hbar , e k rangle q j sum k c k 0 exp i e k t hbar , e k rangle math for all eigenvectors math q j rangle math in order to call math q math a good quantumnumber. A necessary and sufficient condition for q to be good is that math O math Commutativity commute with the Hamiltonian math H math . Proof Assume math O, ,H 0 math . If math psi 0 rangle math is an eigenvector of math O math , then we have by definition that math O psi 0 rangle q j psi 0 rangle math , and so math O psi t rangle O ,T t , psi 0 rangle math math O e itH hbar psi 0 rangle math math O sum n 0 infty frac 1 n i H t hbar n psi 0 rangle math math sum n 0 infty frac 1 n i H t hbar n O psi 0 rangle math math q j psi t rangle math It can be said that a good classical analogue is that good quantum numbers are the equivalent of conserved quantities in classical mechanics, as their values do not change over time.In non relativistic treatment,l and s are good quantum numbers but in relativistic quantum mechanics they are no longer good quantum numbers as L and S do not commute with H in Dirac theory . J L S is a good q.no. in relativistic quantum mechanics as J commutes with H. Category Quantum mechanics quantum stub ... more details
see Azimuthal quantumnumber Addition of quantized angular momenta In quantum mechanics , the total angular quantum momentum numbers parameterize the total angular momentum of a given Subatomic particle particle , by combining its angular momentum operator orbital angular momentum and its intrinsic angular momentum i.e., its spin physics spin . If s is the particle s spin angular momentum and its orbital angular momentum vector, the total angular momentum j is math mathbf j mathbf s boldsymbol ell math The associated quantumnumber is the main total angular momentum quantumnumber j . It can take the following range of values, jumping only in integer steps math ell s le j le ell s math where is the azimuthal quantumnumber parameterizing the orbital angular momentum and s is the spin quantumnumber parameterizing the spin . The relation between the total angular momentum vector j and the total angular momentum quantumnumber j is given by the usual relation see angular momentum quantumnumber math Vert mathbf j Vert sqrt j , j 1 , hbar math the vector s z projection is given by math j z m j , hbar math where m sub j sub is the secondary total angular momentum quantumnumber . It ranges from &minus j to j in steps of one. This generates 2 j 1 different values of m sub j sub . The total angular momentum corresponds to the Casimir invariant of the Lie algebra infinitesimal rotation so 3 of the three dimensional rotation group . See also principalquantumnumber azimuthal quantumnumber orbital angular momentum quantumnumber magnetic quantumnumber spin quantumnumber angular momentum coupling Clebsch Gordan coefficients References cite book author Griffiths, David J. title Introduction to Quantum Mechanics 2nd ed. publisher Prentice Hall year 2004 isbn 0 13 805326 X External links http hyperphysics.phy astr.gsu.edu hbase quantum vecmod.html Vector model of angular momentum http hyperphysics.phy astr.gsu.edu hbase atomic lcoup.html c1 LS and jj coupling Category Atomic ... more details
distinguish principle wiktionary principalPrincipal may refer to TOC right Education Principal school , a head of a primary or secondary school Principal academia , a chief executive of a university or college Law Principal commercial law , a person who authorises an agent Principal criminal law , a primary actor in a criminal offense Science Principal Investigator , a lead scientist or engineer for a field Principal value , a value along a chosen branch of a multivalued function Principal branch , a special selected branch of a multivalued function Principal ideal , an ideal with a single generator, and the related concept of principal ideal domains Cauchy principal value , a way of assigning a finite value to improper integrals that seem to diverge Performing arts Principal dancer , a high ranked dancer in a ballet company The Principal, or Diapason, an List of pipe organ stops organ stop on a pipe organ Principal, the lead of a section of an Orchestra Organization orchestra Places Principal, Cape Verde , a village Principal, Ecuador , a parish in Azuay Province , Ecuador linked only in template for parishes of Azuay province Other uses Principal architecture Principal computer security , an entity that can be identified and verified Principal sum , the original amount of a debt or investment on which interest is calculated The Principal , a 1987 action film Principal Financial Group , a life insurance company traded on the NYSE Dean Christianity or principal, the head of a cathedral or collegiate church Principal civil service or principal officer, a senior management grade in Her Majesty s Civil Service People with the surname Victoria Principal , American actress See also lookfrom Principal intitle Principal Disambiguation surname cs Princip l de Principal es Principal fr Principal ro Principal ru ... more details
Infobox Film name The Principal image Principalposter1987.jpg caption Theatrical release poster director Christopher Cain producer Thomas H. Brodek writer Frank Deese starring James Belushi br Louis Gossett, Jr. br Rae Dawn Chong br Kelly Jo Minter Kelly Minter music Jay Gruska cinematography Arthur Albert editing Jack Hofstra distributor TriStar Pictures released September 18, 1987 in film 1987 runtime 109 minutes country Cinema of the United States United States language English language English gross 19,734,940 USA ref cite web url http www.imdb.com title tt0093780 business title Box office business for The Principal accessdate 2009 08 01 publisher Internet Movie Database ref The Principal is a 1987 in film 1987 action film , starring James Belushi and Louis Gossett, Jr. It was written by Frank Deese and directed by Christopher Cain , and filmed in Oakland, California . Plot Rick Latimer Belushi is a high school teacher with a drinking problem. Spotting his ex wife in a bar one night, Rick gets into a fight with the man she s with, culminating in his beating the hapless man s car with a baseball bat. The board of education finds that Rick s behavior is reflecting poorly on the school district s image. They unanimously decide to transfer him to another school, in another district Brandel High, a crime ridden and gang dominated institution, where he is made the new principal. Believing he can repair his image by cleaning up the school, Rick attempts to have an assembly to declare ... are? , Rick responds I m the principal, man and rides away on his motorcycle. Cast James Belushi as Principal ... title The Principal Amg movie 139226 The Principal Christopher Cain Category 1987 films Principal, The Category American comedy drama films Principal,The Category TriStar Pictures films Principal Category English language films Principal, The Category Films about school violence Principal, The Category Films about educators de Der Prinzipal Einer gegen alle fr Le Proviseur pt The Principal ru ... more details
certain discrete values. There is a related term of quantumnumber . An example of an entity that is quantized ...Other uses Quantum disambiguation pp move indef In physics , a quantum plural quanta is the minimum amount ... quantization . ref Wiener, N. 1966 . Differential Space, Quantum Systems, and Prediction . Cambridge ... quantum of light, and is referred to as a light quantum . The energy of an electron bound to an atom .... As incorporated into the theory of quantum mechanics , this is regarded by physicists as part of the fundamental .... Etymology and discovery The word quantum comes from the Latin quantus, for how much. Quanta .... However, the word quantum in general was well known before 1900. ref E. Cobham Brewer 1810 ... by physicians , such as the term quantum satis . Both Helmholtz and Julius von Mayer were physicians as well as physicists. Helmholtz used quantum with reference to heat in his article ref E. Helmholtz ... R Mayer.pdf de icon ref on Mayer s work, and indeed, the word quantum can be found in the formulation ... cite journal last1 Klein first1 Martin J. title Max Planck and the beginnings of the quantum theory ... constant , and could also report a more precise value for the Avogadro s number Avogadro Loschmidt number , the number of real molecules in a mole unit mole and the unit of electrical charge , to the German ... trunc sys.shtml Real World Quantum Effects Demonstrated ref In the attempt to bring experiment into agreement ... also colbegin 3 Basic concepts of quantum mechanics Elementary particle Introduction to quantum mechanics Magnetic flux quantum Photon polarization Quantization physics Quantum cellular automata Quantum channel Quantum coherence Quantum chromodynamics Quantum computer Quantum cryptography Quantum dot Quantum electronics Quantum entanglement Quantum immortality Quantum lithography Quantum mechanics QuantumnumberQuantum sensor Quantum state Subatomic particle colend References reflist 2 Further reading B. Hoffmann, The Strange Story of the Quantum , Pelican 1963. Lucretius, On the Nature of the Universe ... more details
previously assumed solely by the principal. The number of assistant principals that a school employs may vary, depending on the number of students. blockquote from http www.bls.gov oco ocos007.htm ...In larger school systems, a Head teacher principal is often assisted by someone known as a vice principal Republic of Ireland deputy principal or assistant principal . Unlike the principal, the vice principal does not have quite the decision making authority that the principal carries. Although they still carry nearly the same authority among students, vice principals do not have the same power on the board. Experience as an assistant principal is often a prerequisite for advancement to a principalship. Job Description blockquote Assistant principals aid the principal in the overall administration of the school. Some assistant principals hold this position for several years to prepare for advancement to principal jobs others are career assistant principals. They are primarily responsible for scheduling student classes, ordering textbooks and supplies, and coordinating transportation, custodial, cafeteria, and other support services. They usually handle student discipline and attendance problems, social and recreational programs, and health and safety matters. They also may counsel students ..., in the event that something happens to the principal, such as an extended leave of absence, the assistant principal would act as the interim principal. Because of this, many see this position as a stepping stone to the larger role of principal and is often used as such. In most schools, the vice principal forgoes all teaching duties in order to address broader educational issues. See also Head teacher Principal school References reflist External Links http www.ascd.org portal site ascd menuitem.beab42d78ce93287572011d3e3108a0c ..., Assistant Principal http www.bls.gov oco ocos007.htm US Department of Labor Bureau of Labor Statistics ... Association Drive, Reston, VA 20191 1537 Category Vice offices Principal Category Educational leadership ... more details
principal part g bor a i , I ate . Strong verbs Icelandic Germanic strong verb strong verbs have the following principal parts class wikitable First principal part Second principal part Third principal part Fourth principal part Infinitive Grammatical person First person Grammatical number singular ... principal part Fourth principal part Infinitive Grammatical person First person Grammatical number singular ... to be are simply irregular. A number of verbs have less than four principal parts deponent verb ...about the grammar term the mathematical meaning Principal part unreferenced date July 2011 In language learning, the principal parts of a verb are those forms that a student must memorize in order to be able to grammatical conjugation conjugate the verb through all its forms. By language English The principal ... . For example the verb to take has the principal parts take took taken . The verb to do has do ... of the principal parts. For example the verb love derives all its forms systematically love, loves ..., or lexicographic form, which in English is the bare infinitive , no other principal parts have to be learned ... be deduced, so the learner of English must memorize three principal parts, sing sang sung . From ... language English that are so irregular that the principal parts are not enough to grammatical conjugation conjugate them fully. For example the verb to be has the principal parts be was were been ... principal part be . See also English verbs , English irregular verbs , English as an additional language . Icelandic There are four types of principal parts in the Icelandic language , determined by the type of verb Weak verbs Icelandic Germanic weak verb weak verbs have the following principal parts class wikitable First principal part Second principal part Third principal part Infinitive Grammatical person First person Grammatical number singular past tense Realis mood indicative mood Participle ... mood tt g bor i , though I eat from the first principal part a bor a , to eat . It s also ... more details
number complex coefficients. The ideal x , y generated by x and y , which consists of all the polynomials in C x , y that have 0 number zero for the constant term , is not principal. To see this, suppose ...In ring theory , a branch of abstract algebra , a principal ideal is an ideal ring theory ideal I in a ring mathematics ring R that is generated by a single element a of R . More specifically a left principal ideal of R is a subset of R of the form Ra ra r in R a right principal ideal is a subset of the form aR ar r in R a two sided principal ideal is a subset of the form RaR r sub 1 sub as sub 1 sub ... to write the ideal generated by a as a . Not all ideals are principal. For example, consider the commutative ... . A ring in which every ideal is principal is called principal , or a principal ideal ring . A principal ideal domain PID is an integral domain that is principal. Any PID must be a unique factorization ... principal ideals in a commutative ring have a greatest common divisor in the sense of ideal multiplication. In principal ideal domains, this allows us to calculate greatest common divisors of elements ... of the ideal a , b . For a Dedekind domain R , we may also ask, given a non principal ideal I of R , whether there is some extension S of R such that the ideal of S generated by I is principal said more loosely, I becomes principal in S . This question arose in connection with the study of rings of algebraic integer s which are examples of Dedekind domains in number theory , and led to the development of class field theory by Teiji Takagi , Emil Artin , David Hilbert , and many others. The principal ideal theorem principal ideal theorem of class field theory states that every integer ring R i.e. the ring of integers of some number field is contained in a larger integer ring S which has the property that every ideal of R becomes a principal ideal of S . In this theorem we may take S to be the ring ... of the fraction field of R , and this is uniquely determined by R . Krull s principal ideal theorem ... more details
orphan date July 2010 A principal teacher PT , in Scotland is a promoted post that usually refers to being head of a particular department within a secondary school, in charge of running the department and ensuring it is performing to school standard, but can also refer to a guidance position with responsibility for the pastoral care of a cohort of pupils. Increasingly, principal teacher posts are being introduced into schools where they involve specific management responsibilities in a school e.g. assessment, ICT . A PT is not a headteacher or even a Principal school School Principal and is not responsible for running a school. Recently, most local authorities have been following a policy of reducing the number of principal teachers in secondary schools by combining departments and having PT s titled curriculum leaders or faculty heads , who essentially carry out the same responsibilities but over more than one department. ref http www.snct.org.uk library 25 Aberdeenshire LNCT Piloting Alternative Management Struc.pdf Aberdeenshire Council Arrangements for piloting alternative management structures in secondary schools 2002 ref For example, History , Geography and Modern Studies are all separate departments and may have their own Principal Teacher however in a Curriculum Leader system these three departments would form the Social Sciences Faculty, headed by one person. Since principal ... concern that the drive towards replacing groups of departmental Principal Teachers with fewer Faculty Principal Teachers is being driven by the desire to cut costs rather than about improving the management ... teacher , one to six Deputy Deputy head teachers, one to ten Pastoral principal teachers guidance staff , and one Principal teacher for each subject area i.e. Maths, English, Modern Languages, Physics etc. . Principal teachers in Primary Schools in Scotland refer to a classroom teacher who also ... for development and managerial duties. Principal teachers tend to work under both head teachers and Depute ... more details
Principal axis may refer to Principal axis mechanics Aircraft principal axes Principal axis theorem Spectral theorem Principal axes of a Matrix Principal axis crystallography Optical axis disambig es Direcci n principal pt Dire o principal ... more details
diminution in the number of sheriffs principal. The final amalgamation occurred in 1975 when Scotland was divided into six sheriffdoms, with each one presided over by a full time sheriff principal. That remains the position at the present time. Duties The work of a sheriff principal is partly .... An appeal lies from the sheriff principal to the Inner House of the Court of Session . In terms of the Sheriff Courts Scotland Act 1971 sheriffs principal are charged with a number of duties in respect ...Unreferenced date November 2007 CourtsScotland The office of sheriff principal is unique within the judicial structure of Scotland , and it cannot therefore readily be compared with any other judicial office. It is one of great antiquity, having existed continuously since around the 11th century. It has gradually developed over the centuries, and is still developing, into an office of some complexity and considerable weight. Numbers and amalgamation Until about the middle of the 19th century there were 30 sheriffs principal or sheriff s, as they were then known . Of those sheriffs principal two Glasgow and Edinburgh were effectively full time appointments while the remainder were part time appointments ... under various statutes administrative functions in relation to the courts within a sheriff principal ... statutory and other appointments and functions by virtue of holding office as sheriff principal ... Shipping Act 1995 all of the sheriffs principal are Commissioners of Northern Lighthouses and serve on the Northern Lighthouse Board . Judicial functions A sheriff principal sometimes sits in criminal courts or conducts major fatal accident inquiries. However, a sheriff principal is primarily an appellate ... Kingdom Edward VII a sheriff principal, in his own sheriffdom, ranks in precedence immediately after the Royal family and the Lord Lieutenant of the County. For that reason sheriffs principal ... Judicial Appointments Board description of post of Sheriff Principal Stair Memorial Encyclopaedia of the Laws ... more details
The Principal Secretary is a senior government official in various Commonwealth countries. Principal Secretary Canada Principal Secretary India disambig ... more details
For a complex number math z r e phi i , math the principal value of the square root is math mathrm ... functions The principal value of Arg mathematics complex number argument measured in radian s can be defined ...For the use of the term principal value in describing improper integrals Cauchy principal value Unreferenced date December 2009 In considering complex multiple valued function s in complex analysis , the principal values of a function are the values along one chosen branch mathematics branch of that function, so it is Single valued function single valued . Motivation Consider the complex logarithm function log z . It is defined as the complex number w such that math e w z , math Now, for example ... ln z i left mathrm Arg z 2 pi k right math for an integer k , where Arg z is the principal argument .... The branch corresponding to k 0 is known as the principal branch , and along this branch, the values the function takes are known as the principal values . General case In general, if f z is multiple valued, the principal branch of f is denoted math mathrm pv f z math such that for z in the domain of f , pv f z is single valued. Principal values of standard functions Complex valued List of mathematical functions elementary functions can be multiple valued over some domains. Determining the principal ... whereby the principal value of the simple functions are straightforward to obtain. Logarithm function ... Now, arg z is intrinsically multivalued. One often defines the argument of some complex number to be between exclusive and inclusive , so we take this to be the principal value of the argument ... instead of arg z , we obtain the principal value of the logarithm, and we write math mathrm pv log z ... sup log z sup is multiple valued since we are using log as opposed to Log. Using Log we obtain the principal ... functions atan2 with principal value in the range , Inverse trigonometric functions atan with principal value in the range 2, 2 See also Principal branch Branch point DEFAULTSORT Principal Value ... more details
In mathematics , a principal branch is a function which selects one branch, or slice , of a multi valued function . Most often, this applies to functions defined on the complex plane see branch cut . One way to view a principal branch is to look specifically at the exponential function , and the logarithm , as it is defined in complex analysis . The exponential function is single valued, where math e z math is defined as math e z e a cos b i e a sin b math where math z a bi math . However, the periodic nature of the trigonometric functions involved makes it clear that the logarithm is not so uniquely determined. One way to see this is to look at the following math operatorname Re log z log sqrt a 2 b 2 math and math operatorname Im log z arctan b a 2 pi k math where k is any integer. Any number log z defined by such criteria has the property that e sup log z sup z . In this manner log function is a multi valued function often referred to as a multifunction in the context of complex analysis . A branch cut, usually along the negative real axis, can limit the imaginary part so it lies between &minus and . These are the chosen principal value s. This is the principal branch of the log function. Often it is defined using a capital letter, Log z . A more familiar principal branch function, limited to real numbers, is that of a positive real number raised to the power of 1 2. For example, take the relation y x sup 1 2 sup , where x is any positive real number. This relation can be satisfied by any value of y equal to a square root of x either positive or negative . When y is taken to be the positive square root, we write math y sqrt x math . In this instance, the positive square root function is taken as the principal branch of the multi valued relation x sup 1 2 sup . Principal branches are also used in the definition of many inverse trigonometry trigonometric ... PrincipalBranch title Principal Branch http math.fullerton.edu mathews c2003 ComplexFunBranchMod.html ... more details
A principal direction can be one of the following Principal curvature Principal directions In differential geometry, one of the directions of principal curvature. List of gear nomenclature Principal directions Principal directions a term used in gear nomenclature. In stress analysis, a set of axes where the normal stress vector is maximized. See Stress mechanics Principal stresses and stress invariants Stress mechanics disambig ... more details
For the other Simpsons character of the same name The Principal and the Pauper Simpsons character name Seymour Skinner image Image Seymour Skinner.png 200px gender Male job Principal education Principal ... Skinner Agnes Skinner appearance Simpsons Roasting on an Open Fire voiceactor Harry Shearer Principal W. Seymour Skinner born The Principal and the Pauper Armin Tamzarian ref IMDb title 701257 The Principal and the Pauper ref ref cite web url http www.thesimpsons.com episode guide 0902.htm title The Principal ... The Simpsons . He is voiced by Harry Shearer . Born in Capitol City, he is the Principal education principal of Springfield Elementary School . He struggles to control the crumbling school and is constantly ..., Josh Anderson, Bob network Fox airdate 1994 04 28 season 5 number 19 ref In an accident involving ... The Simpsons credits Cohen, Joel H. Nastuk, Matthew network Fox airdate 2008 03 02 season 19 number ... and Selma Bouvier Patty Bouvier , ref cite episode title Principal Charming episodelink Principal ... Fox airdate 1991 02 14 season 2 number 14 ref Skinner s love life has focused on Edna Krabappel ... Fox airdate 2003 01 05 season 14 number 7 ref but later cancelled the wedding. ref cite episode ... credits Curran, Kevin Kirkland, Mark network Fox airdate 2004 04 18 season 15 number 17 ref ..., Lance network Fox airdate 2000 12 17 season 12 number 8 ref The controversial season nine episode The Principal and the Pauper revolutionises Skinner s back story, revealing that Skinner is an imposter ... of becoming a school principal. The real Seymour Skinner voiced by Martin Sheen , had been alive after ... Principal, but had proved hopelessly unpopular and the Springfielders ran him out of town on the railroad ... s increasingly gimmicky and nonsensical plots . Character Creation Principal Skinner first appeared ... . ref name Reiss1 Reiss, Mike. 2002 . Commentary for Principal Charming , in The Simpsons The Complete .... ref name Groening1 Groening, Matt. 2002 . Commentary for Principal Charming , in The Simpsons The Complete ... more details
In linear algebra mathematics , the principal angles , also called canonical angles , provide information about the relative position of two subspaces of a Euclidean space . The concept was first introduced by Camille Jordan Jordan in 1875. Definition Let math mathcal E math be a Euclidean vector space with inner product math langle cdot , cdot rangle math and given two subspaces math mathcal U , mathcal W math with math operatorname dim mathcal U k leq operatorname dim mathcal W l math . There exists then a set of math k math angles math theta 1, ldots theta k math called the principal angles, the first one being defined as math theta 1 min arccos left frac langle U,W rangle U cdot W right U in mathcal U , W in mathcal W angle U 1,W 1 math where math . math is the induced Norm mathematics norm of the inner product. The vectors math U 1 math and math W 1 math are called principal vectors. The other principal angles and vectors are then defined recursively via math theta i min arccos left frac langle U,W rangle U cdot W right U in mathcal U , U perp U j, W in mathcal W , W perp W j forall j in 1, ldots,i 1 . math This means that the principal angles form a set of minimized angles, where every two principal vectors of one subspace defining two different principal angles are orthogonal to each other. Examples Geometric Example Geometrically, subspaces are planes that cross the origin, thus any two subspaces intersect at least in the origin. Two two dimensional subspaces math mathcal ..., the pair of principal vectors corresponding to the angle math theta 1 math with math cos theta 1 a sqrt 1 a 2 math , and math U 2 math and math W 2 math are the principal vectors corresponding ... angle is zero, the subspaces intersect at least in a line. The number of angles equal to zero ... www.haverford.edu math cshonkwi research notes PrincipalAngles.pdf Principal angles in terms of inner product Downloadable note on the construction of principal angles, Shonkwiler, Haverford Category ... more details
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