Similarly, given any element y of Y, there is a function f < sub > y </ sub >, or f (·, y ), from X to Z, given by f < sub > y </ sub >( x ) := f ( x, y ).

Similarly, as an infinite-dimensional example, the Lebesgue space L < sup > p </ sup > is always a Banach space but is only a Hilbert space when p = 2.

Similarly, relatively little energy is used in producing and combining the raw materials ( although large amounts of CO < sub > 2 </ sub > are produced by the chemical reactions in cement manufacture ).

Similarly, the pentafluoride, DbF < sub > 5 </ sub >, should be even more volatile.

Similarly, the variation in the concentration of gas B is-dC < sub > B </ sub >/ dx.

Similarly, the partial pressure of B changes dP < sub > B </ sub >.

Similarly, for any a in F other than 0, there exists an element a < sup >− 1 </ sup > in F, such that a · a < sup >− 1 </ sup > = 1.

Similarly, < tt >( λx. y ) s → y := s = y </ tt >, demonstrating that < tt > λx. y </ tt > really is a constant function.

Similarly, methyl iodide and methyl triflate are viewed as the equivalent of the methyl cation because they readily undergo S < sub > N </ sub > 2 reactions by weak nucleophiles.

Similarly, for a given vacuum wavelength λ < sub > 0 </ sub >, the wavelength

Similarly, p < sup >-</ sup > would indicate a very lightly doped p-type material.

* Similarly the even-graded element γ = − σ < sub > 1 </ sub > σ < sub > 2 </ sub > corresponds to a vector rotation of 180 °:

Similarly the number for " P " in some countries is actually the weight of an equivalent quantity of P < sub > 2 </ sub > O < sub > 5 </ sub > whereas in others ( including Australia ) it refers to elemental phosphorus.

Similarly, given points ( x < sub > 1 </ sub >, y < sub > 1 </ sub >, z < sub > 1 </ sub >) and ( x < sub > 2 </ sub >, y < sub > 2 </ sub >, z < sub > 2 </ sub >) in three-space, the distance between them is:

Similarly, products of the gammas such as γ < sub > μ </ sub > γ < sub > ν </ sub > represent oriented surface elements, and so on.

Similarly, teams might use a Serving Specialist to sub out a poor server situationally.

Similarly, if g: A → B ⊗ C is a morphism of representations, dualizing it will give another morphism of representations g ′: A ⊗ C < sup >*</ sup > → B.

Similarly, a fold F < sub > 2 </ sub >( s ) perpendicular to m < sub > 2 </ sub > through its midpoint will place p < sub > 1 </ sub > on the line at location d < sub > 2 </ sub >.

Similarly, the quantum group U < sub > q </ sub >( G ) can be regarded as an algebra over the field Q ( q ), the field of all rational functions of an indeterminate q over Q ( see below in the section on quantum groups at q

Similarly, a right R-module M is flat if and only if Tor < sub > n </ sub >< sup > R </ sup >( M, X ) = 0 for all and all left R-modules X.

Similarly, if f is a smooth function on an open set U in N, then the same formula defines a smooth function on the open set φ < sup >- 1 </ sup >( U ) in M. ( In the language of sheaves, pullback defines a morphism from the sheaf of smooth functions on N to the direct image by φ of the sheaf of smooth functions on M .)

Similarly for continuous random variables, the marginal probability density function can be written as p < sub > X </ sub >( x ).

Similarly, K < sub > 1 </ sub >( R ) is a modification of the group of units in a ring, using elementary matrix theory.

Similarly for continuous random variables, the joint probability density function can be written as f < sub > X, Y </ sub >( x, y ) and this is

Similarly the split categories over E form a 2-category Scin ( E ) ( from French catégorie scindée ), where the category of morphisms between two split categories F and G is the full sub-category Scin < sub > E </ sub >( F, G ) of E-functors from F to G consisting of those functors that transform each transport morphism of F into a transport morphism of G. Each such morphism of split E-categories is also a morphism of E-fibred categories, i. e., Scin < sub > E </ sub >( F, G ) ⊂ Cart < sub > E </ sub >( F, G ).

Similarly in Illinois there is Lincoln country to be seen -- his tomb and other landmarks.

Similarly, at the opposite end of the market cycle, towards the end of an intermediate or major decline, usually while the bottom is being formed on the price chart, it is characteristic that an increase is noticed in odd-lot selling again alerting the chartist that a bottom is becoming a greater likelihood.

Similarly, the American Cancer Society ( ACS ), the Arthritis and Rheumatism Foundation, and the BBB have each stated lately that medical quackery is at a new high.

Similarly, a girl who graduates with a good working knowledge of stenography and the use of clerical machines and who is able to get a job at once may wish to improve her skill and knowledge by a year or two of further study in a community college or secretarial school.

Similarly, the Italian verb corresponding to ' spell ( out )', compitare, is unknown to many Italians because the act of spelling itself is rarely needed: Italian spelling is highly phonemic.

Similarly, Helen Keller stated that " Life is either a daring adventure or nothing.

Similarly, although a subset of the real numbers that is not Lebesgue measurable can be proven to exist using the axiom of choice, it is consistent that no such set is definable.

Similarly, all the statements listed below which require choice or some weaker version thereof for their proof are unprovable in ZF, but since each is provable in ZF plus the axiom of choice, there are models of ZF in which each statement is true.

Similarly in St Peter: " Christ .. Who verily was foreordained before the foundation of the world, but was manifest in these last times for you " ( 1 Peter 1: 20 ), and " But the end of all things is at hand " ( 1 Peter 4: 7 ).

Similarly, the subset order ⊆ on the subsets of any given set is antisymmetric: given two sets A and B, if every element in A also is in B and every element in B is also in A, then A and B must contain all the same elements and therefore be equal:

Similarly, in the Greek Magical Papyri, the term " Aion " is often used to denote the All, or the supreme aspect of God

Similarly, " suprarenal " is derived from supra-( Latin, " above ") and renes.

Similarly the freehold of a benefice, on the death of the incumbent, is said to be in abeyance until the next incumbent takes possession.

Similarly, the use of excessively high doses ( often the result of polypharmacy ) continues despite clinical guidelines and evidence indicating that it is usually no more effective but is usually more harmful.

Similarly, any set with 4 elements can be given two non-isomorphic group structures: one isomorphic to ; the other isomorphic to.

Similarly, in the second diagram the naturally isomorphic spaces C, C ⊗ K and K ⊗ C are identified.

Similarly, a group G and its dual group are not in general isomorphic, but their group algebras are: C ( G ) via the Fourier transform, though one must carefully define these algebras analytically.

Similarly, if Peggy knew in advance that Victor would ask to see the isomorphism then she could simply generate an isomorphic graph H ( in which she also does not know a Hamiltonian Cycle ).