* Goma-Noriko Tsukase → Chie Satō

*« Je les ai pris » (" I took them ") → « Je ne les ai pas pris » (" I did not take them ")

After ascending to the throne in December 1722, Yinzhen took the era name " Harmonious Justice " ( → yōngzhèng ) in 1723 from his peerage title " harmonious " ( → yōng ) and " just, correct, upright " ( → zhèng ).

In 11th century a border castle was established by Duke Bretislaus I which took his name ( in Czech Břetislav → Břeclav ).

If X and Y are Banach spaces over the same ground field K, the set of all continuous K-linear maps T: X → Y is denoted by B ( X, Y ).

A Banach *- algebra A is a Banach algebra over the field of complex numbers, together with a map *: A → A called involution which has the following properties:

A C *- algebra, A, is a Banach algebra over the field of complex numbers, together with a map *: A → A.

* Given any set X, there is an equivalence relation over the set of all possible functions X → X.

A differential field F is a field F < sub > 0 </ sub > ( rational functions over the rationals Q for example ) together with a derivation map u → ∂ u.

Tensor products: If C denotes the category of vector spaces over a fixed field, with linear maps as morphisms, then the tensor product defines a functor C × C → C which is covariant in both arguments.

* Formally, when working over the reals, as here, this is accomplished by considering the limit as ε → 0 ; but the " infinitesimal " language generalizes directly to Lie groups over general rings.

Let V and W be vector spaces over the same field K. A function f: V → W is said to be a linear map if for any two vectors x and y in V and any scalar α in K, the following two conditions are satisfied:

In this approach a model of a theory is replaced by an object called a superstructure V ( S ) over a set S. Starting from a superstructure V ( S ) one constructs another object * V ( S ) using the ultrapower construction together with a mapping V ( S ) → * V ( S )

It is the inverse limit of the finite groups Z / p < sup > n </ sup > Z where n ranges over all natural numbers and the natural maps Z / p < sup > n </ sup > Z → Z / p < sup > m </ sup > Z ( n ≥ m ) are used for the limit process.

Let M and N be ( left or right ) modules over the same ring, and let f: M → N be a module homomorphism.

* The free functor F: Set → Grp ( which assigns to every set S the free group over S ) is left adjoint to forgetful functor U and is, therefore, cocontinuous.

If C and D are preadditive categories, then a functor F: C → D is additive if it too is enriched over the category Ab.

When specializing to the preadditive categories of abelian groups or modules over a ring, this notion of kernel coincides with the ordinary notion of a kernel of a homomorphism, if one identifies the ordinary kernel K of f: A → B with its embedding K → A.

If S is a commutative associative algebra over R, if I is an ideal of S such that the I-adic topology on S is complete, and if x is an element of I, then there is a unique Φ: R < nowiki ></ nowiki > X < nowiki ></ nowiki > → S with the following properties:

If S is a commutative associative algebra over R, if I is an ideal of S such that the I-adic topology on S is complete, and if x < sub > 1 </ sub >, ..., x < sub > r </ sub > are elements of I, then there is a unique Φ: R < nowiki ></ nowiki > X < sub > 1 </ sub >, ..., X < sub > n </ sub >< nowiki ></ nowiki > → S with the following properties:

The distance d ( p, q ) between two points p and q of M is defined as the infimum of the length taken over all continuous, piecewise continuously differentiable curves γ: → M such that γ ( a ) = p and γ ( b ) = q.

If V is a vector space over the field F, the general linear group of V, written GL ( V ) or Aut ( V ), is the group of all automorphisms of V, i. e. the set of all bijective linear transformations V → V, together with functional composition as group operation.

Let U, V, and W be vector spaces over the same field with given bases, S: V → W and T: U → V be linear transformations and ST: U → W be their composition.

The group GL ( n, F ) splits over its determinant ( we use F < sup >×</ sup > ≅ GL ( 1, F ) → GL ( n, F ) as the monomorphism from F < sup >×</ sup > to GL ( n, F ), see semidirect product ), and therefore GL ( n, F ) can be written as a semidirect product of SL ( n, F ) by F < sup >×</ sup >:

For this reason, it makes sense to call a pair ( C, U ) where C is a category and U a faithful functor C → X a concrete category over X.

The typical example of the latter kind of correspondence is the graph of a function f: X → Y Correspondences also play an important role in the construction of motives.

They also play the same role for the modal logic wK4 = K + p ∧□ p → □□ p that Boolean algebras play for ordinary propositional logic.

The key role of RBMT systems is that they help fill the gap left in the translation process of s-p → p-t, in the sense that these parallels are included in the SMT model for s-t.

This thesis is supported by the Royal Asiatic Society of Great Britain and Ireland, explaining that the Turko-Mongol name Timur underwent a similar evolution, from the Sanskrit word cimara (" iron ") via a modified version * čimr to the final Turkicized version timür, with-ür replacing-r due to the Turkish vowel harmony ( hence babr → babür ).

Despite its rare use, Italian orthography allows the circumflex accent ( î ) too, in two cases: it can be found in old literary context ( roughly up to 19th century ) to signal a syncope ( fêro → fecero, they did ), or in modern Italian to signal the contraction of ″- ii ″ due to the plural ending-i whereas the root ends with another-i ; e. g., s. demonio, p. demonii → demonî ; in this case the circumflex also signals that the word intended is not demoni, plural of " demone " by shifting the accent ( demònî, " devils "; dèmoni, " demons ").

This remarkably systematic correspondence is due to the identity of the commutators of the umbral quantities to their continuum analogs ( h → 0 limits ),

E. coli were treated with Ethyl methanesulfonate ( EMS ), known to induce G: C → A: T transitions due to generation of abnormal base O-6-ethylguanine, which is further misrecognized during DNA replication and paired with T instead of C. The sequenced DNA from individual colonies of EMS-mutagenized bacteria exhibited long stretches of solely G → A or C → T transitions, which in some cases were spanning entire bacterial genome.

Finally, im q is isomorphic to A due to the exactness of 0 → A → B ; so B is isomorphic to the direct sum of A and C, which proves ( 3 ).

The transparency of the scintillator to the emitted photon is due to the fact that the energy of the photon is less than that required for a S < sup >*</ sup > → S < sub > 0 </ sub > transition ( the transition is usually being to a vibrational level above S < sub > 0 </ sub >).

Multiple outcomes for MC initials ( e. g. MC / g / → Pinyin g, j, k, q ) are primarily due to two reasons:

NNOs in CCCs or topoi are sometimes defined in the following equivalent way ( due to Lawvere ): for every pair of arrows g: A → B and f: B → B, there is a unique h: N × A → B such that the squares in the following diagram commute.

Membrane 1 now contains: " dd " and, due to the out rule e → e < sub > out </ sub >, the environment contains: " eeee.

→ Assuming for simplicity no technological progress or labor force growth, diminishing returns implies that at some point the amount of new capital produced is only just enough to make up for the amount of existing capital lost due to depreciation.

For example, the most intense features of a K-edge are due to 1s → np transitions, while the most intense features of the L < sub > 3 </ sub >- edge are due to 2p → nd transitions.

* World Welterweight Championship – Paddy Duffy → title vacant following death of Paddy Duffy

* Historical Situation → The historical situation goes through three stages: in chapters 1 – 39 the prophet speaks of a judgment which will befall the wicked Israelites ; in chapters 40 – 55 the destruction of Jerusalem and the Temple ( 587 BCE ) is treated as an accomplished fact and the fall of Babylon as an imminent threat ; and in chapters 56 – 66 the fall of Babylon is already in the past.

In a breeder reactor, uranium-238 can also be converted into plutonium through the following reaction: < sup > 238 </ sup > U ( n, gamma ) → < sup > 239 </ sup > U -( beta ) → < sup > 239 </ sup > Np -( beta ) → < sup > 239 </ sup > Pu.

Such uses typically arise through ellipsis or metonymy: a car made by Toyota → a Toyota car → a Toyota.

During an action potential, most channels of this type go through a cycle deactivated → activated → inactivated → deactivated.

In the terminology of the International Color Consortium, a translation between two color spaces can go through a profile connection space ( PCS ): Color Space 1 → PCS ( CIELAB or CIEXYZ ) → Color space 2 ; conversions into and out of the PCS are each specified by a profile.

Many languages, including all living Germanic languages, French, Welsh and some Berber and Arabic dialects, have gone through a process known as Jespersen's cycle, where an original negative particle is replaced by another, passing through an intermediate stage employing two particles ( e. g. Old French jeo ne dis → Modern Standard French je ne dis pas → Modern Colloquial French je dis pas " I don't say ").

Any transformation of the plane leaving this pattern invariant can be decomposed into a translation, ( x, y ) → ( n + x, y ), optionally followed by a reflection in either the horizontal axis, ( x, y ) → ( x ,− y ), or the vertical axis, ( x, y ) → (− x, y ), provided that this axis is chosen through or midway between two dots, or a rotation by 180 °, ( x, y ) → (− x ,− y ) ( ditto ).

Linehan and others combined a commitment to the core conditions of acceptance and change through the Hegelian principle of dialectical progress ( in which thesis + antithesis → synthesis ) and assembled an array of skills for emotional self-regulation drawn from Western psychological traditions, such as cognitive behavioral therapy and an interpersonal variant, " assertiveness training ", and Eastern meditative traditions, such as Buddhist mindfulness meditation.

In terms of universal properties, the perfect closure of a ring A of characteristic p is a perfect ring A < sub > p </ sub > of characteristic p together with a ring homomorphism u: A → A < sub > p </ sub > such that for any other perfect ring B of characteristic p with a homomorphism v: A → B there is a unique homomorphism f: A < sub > p </ sub > → B such that v factors through u ( i. e. v

In other words, the perfection R ( A ) of A is a perfect ring of characteristic p together with a map θ: R ( A ) → A such that for any perfect ring B of characteristic p equipped with a map φ: B → A, there is a unique map f: B → R ( A ) such that φ factors through θ ( i. e. φ =