Every physical quantity has a Hermitian linear operator associated to it, and the states where the value of this physical quantity is definite are the eigenstates of this linear operator.

Every spin network is an eigenstate of each such operator, and the area eigenvalue equals

Every generalized eigenvalue of a normal operator is thus genuine.

Every operator also received 80 hours of medical training.

Every delta operator ' has a unique sequence of " basic polynomials ", a polynomial sequence defined by three conditions:

Every motion of the lock is derived from movement of the hands rather than elements beyond the operator ’ s control, such as dirt, rust, or memory.

* Every first time purchaser of an automobile deprived the streetcars operator of income whilst simultaneously created additional traffic congestion which often reduced service speeds and thereby increased their operational costs and making the services less attractive to the remaining users.

Is fundamental for the many-body theory that Every operator can be expressed in terms of annihilation and creation operators.

Every closure operator on a poset has many fixed points ; these are the " closed elements " with respect to the closure operator, and they are the main reason the closure operator was defined in the first place.

Every self-adjoint operator is normal.

Every symmetric operator is closable.

Every self-adjoint operator is maximal symmetric.

Every self-adjoint operator is densely defined, closed and symmetric.

Every operator in the unit is cross-trained in a variety of " low-visibility " skills such as weapons, survival, sniping, medic, small boat handling, driving, tracking, air ops etc.

where the rank refers to the rank of the linear operator F. Every nonsimple bivector can be written as a sum of at most two simple ones.

Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.

** Well-ordering theorem: Every set can be well-ordered.

Every information exchange between living organisms — i. e. transmission of signals that involve a living sender and receiver can be considered a form of communication ; and even primitive creatures such as corals are competent to communicate.

Every context-sensitive grammar which does not generate the empty string can be transformed into an equivalent one in Kuroda normal form.

* Every regular language is context-free because it can be described by a context-free grammar.

Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed into an equivalent one which is in Chomsky normal form.

Every real number has a ( possibly infinite ) decimal representation ; i. e., it can be written as

Every module over a division ring has a basis ; linear maps between finite-dimensional modules over a division ring can be described by matrices, and the Gaussian elimination algorithm remains applicable.

Every entire function can be represented as a power series that converges uniformly on compact sets.

Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.

Every positive integer n > 1 can be represented in exactly one way as a product of prime powers:

Every sequence can, thus, be read in three reading frames, each of which will produce a different amino acid sequence ( in the given example, Gly-Lys-Pro, Gly-Asn, or Glu-Thr, respectively ).

Every hyperbola is congruent to the origin-centered East-West opening hyperbola sharing its same eccentricity ε ( its shape, or degree of " spread "), and is also congruent to the origin-centered North-South opening hyperbola with identical eccentricity ε — that is, it can be rotated so that it opens in the desired direction and can be translated ( rigidly moved in the plane ) so that it is centered at the origin.

Every holomorphic function can be separated into its real and imaginary parts, and each of these is a solution of Laplace's equation on R < sup > 2 </ sup >.

Every species can be given a unique ( and, one hopes, stable ) name, as compared with common names that are often neither unique nor consistent from place to place and language to language.

Every vector v in determines a linear map from R to taking 1 to v, which can be thought of as a Lie algebra homomorphism.

Every morpheme can be classified as either free or bound.

Every use of modus tollens can be converted to a use of modus ponens and one use of transposition to the premise which is a material implication.

Every document window is an object with which the user can work.

Every adult, healthy, sane Muslim who has the financial and physical capacity to travel to Mecca and can make arrangements for the care of his / her dependants during the trip, must perform the Hajj once in a lifetime.

Every ordered field can be embedded into the surreal numbers.

* Every finite topological space gives rise to a preorder on its points, in which x ≤ y if and only if x belongs to every neighborhood of y, and every finite preorder can be formed as the specialization preorder of a topological space in this way.

* Every preorder can be given a topology, the Alexandrov topology ; and indeed, every preorder on a set is in one-to-one correspondence with an Alexandrov topology on that set.

Every binary relation R on a set S can be extended to a preorder on S by taking the transitive closure and reflexive closure, R < sup >+=</ sup >.

Every so often the diminishing sound of a car came under the trailer as it slowed down for the wreck then speeded up again as it got clear.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

Every member of the future protectionist cabinet then in parliament ( except Disraeli ) voted against the measure.

Disraeli wrote a personal letter to Gladstone, asking him to place the good of the party above personal animosity: " Every man performs his office, and there is a Power, greater than ourselves, that disposes of all this ..." In responding to Disraeli Gladstone denied that personal feelings played any role in his decision then and previously to accept office, while acknowledging that there were differences between him and Derby " broader than you may have supposed.

Every decision made by German or opposing forces required time to gather information, make a decision, disseminate orders to subordinates, and then implement this decision through action.

Every sequence that ran off to infinity in the real line will then converge to ∞ in this compactification.

Every now and then an atom is replaced by a completely different atom ( and this could be as few as one in a million atoms ).

Every URL consists of some of the following: the scheme name ( commonly called protocol ), followed by a colon, two slashes, then, depending on scheme, a server name ( exp.

Every member of both gangs was always a potential killer even then.

She appeared in the 1975 screen adaptation of the Hans Fallada novel, Every Man Dies Alone directed by Alfred Vohrer, released in English as Everyone Dies Alone in 1976 and for which she won an award for best actress at the International Film Festival in Carlsbad, then in Czechoslovakia.

The gag originated in a sketch in which Scott Thompson played a homophobic man who took offense at another man's ( McKinney ) attempt to seduce him by taking him to a Maple Leafs game: " Every time I come to this city, some guy picks me up at the bus station, takes me to a Leaf game, gets me pissed, then tries to blow me.

Every finite-dimensional vector space is isomorphic to its dual space, but this isomorphism relies on an arbitrary choice of isomorphism ( for example, via choosing a basis and then taking the isomorphism sending this basis to the corresponding dual basis ).

Every Baronet of Ruddigore since then had fallen under the curse's influence, and died in agony once he could no longer bring himself to continue a life of crime.

Every morphism in a concrete category whose underlying function is injective is a monomorphism ; in other words, if morphisms are actually functions between sets, then any morphism which is a one-to-one function will necessarily be a monomorphism in the categorical sense.

Every now and then we then one thing hard-for example one week we were mad on Cat's cradle – at least Rivers, Ray and I were-McDougall soon fell victim and even Myers eventually succumbed.

Every man that came would fall in love with Hildr, and then Signy would have to kill them, until one man is not afraid.

" Ogni volta " (" Every Time ") was sung by Anka during the Festival di San Remo of 1964 and then sold more than one million copies in Italy alone ; it was also awarded a gold disc.

Every game financed is, then, a large gamble, and pressure to succeed is high.

Every summer thousands would arrive by train at Landing Station, and then travel by water taxi across Lake Hopatcong to the area's many large resort hotels to escape the city heat and enjoy the famous " Mount Arlington breeze " which always cooled the summer evenings.

Every year a Mayor of Ock Street is elected by the inhabitants of Ock Street ; he then parades through the town preceded by the famous Horns of Ock St, a symbol of Abingdon's Morris Dance troupe.

Every packet which is sent requires a token, and if there are no tokens, then it cannot be sent.

He was a successful songwriter ; one of his most famous compositions is " Every Beat of My Heart ", first recorded by The Royals in 1952 on Federal Records but which became a hit for Gladys Knight and the Pips then just ' Pips ' in 1961.

Every month, SPU's food lab plays host to a Community Kitchen ; a time for homeless people to come and assist with cooking meals that they then all eat together.