Similarly, when W is an odd integer the formula for an ( authentic ) tensor density can be rewritten as

Similarly, a product of even tensor densities and odd tensor densities will be an even tensor density when an even number of the factors are odd tensor densities ; it will be an odd tensor density when an odd number of the factors are odd tensor densities.

Similarly, the partial differentiation of the displacement vector with respect to the spatial coordinates yields the spatial displacement gradient tensor.

Similarly experience itself can be conventionalized so that people react to certain preconceived clues for behavior without awareness of the vitality of their experiential field.

Similarly, the intensity of electromagnetic forces depends upon the strength ( electric charge ) of the electromagnetic field.

Similarly, the acceleration field is given by

Similarly, the Catholic Institute for International Relations ( CIIR, now known as " Progressio "), a human rights organization which identifies itself with liberation theology, had summarized Contra operating procedures in their 1987 human rights report: " The record of the contras in the field, as opposed to their official professions of democratic faith, is one of consistent and bloody abuse of human rights, of murder, torture, mutilation, rape, arson, destruction and kidnapping.

Similarly, if only the magnetic field () is non-zero and is constant in time, the field is said to be a magnetostatic field.

Similarly, the multiplicative group of the field is a cyclic group.

Similarly, in Thermal quantum field theory a compactification of the euclidean time dimension leads to the Matsubara frequencies and thus to a discretized thermal energy spectrum.

Similarly, the set of all solutions to Einstein's field equations is simpler than a specific solution.

Despite the nomenclature, the " field " under study is the gravitational potential, φ, rather than the gravitational field, g. Similarly, when classical field theory is used to study electromagnetism, the " field " of interest is the electromagnetic four-potential ( V / c, A ), rather than the electric and magnetic fields E and B.

Similarly, at a fixed temperature below the critical temperature, superconducting materials cease to superconduct when an external magnetic field is applied which is greater than the critical magnetic field.

Similarly, if the length scales are much longer than the wave ’ s wavelength, as is often the case for light in the field of optics, one can treat the waves as light rays which correspond locally to plane waves.

Similarly, the manual for the ORCA / M assembler refers to a field indicating the order of the bytes in a number field as, and the Mac OS X operating system refers to " byte sex " in its compiler tools .</ ref > The usual contrast is whether the most significant or least significant byte is ordered first — i. e., at the lowest byte address — within the larger data item.

Similarly, the manual for the ORCA / M assembler refers to a field indicating the order of the bytes in a number field as, and the Mac OS X operating system refers to " byte sex " in its compiler tools .</ ref > x86 computers do not have the same " byte sex ", as HC11 computers, for example.

Similarly, Barnum Brown claimed to have seen over 500 skulls in the field.

Similarly, autonomy has been and probably will continue to be considered an extension of the controls field.

Similarly, biproducts exist in the category of vector spaces over a field.

Similarly, the completeness property cannot be expected to carry over, because the reals are the unique complete ordered field up to isomorphism.

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, Hindi-Urdu speakers might unconsciously apply their native ' v-w ' allophony rules to English words, pronouncing war as var or advance as adwance, which can result in intelligibility problems with native English speakers.

Similarly IF A > B THEN A ← A − B.

Similarly the Sagnac effect, observed by G. Sagnac in 1913 was immediately seen to be fully consistent with special relativity.

Similarly, the intensity of the output on TV and computer display devices is not directly proportional to the R, G, and B applied electric signals ( or file data values which drive them through Digital-to-Analog Converters ).

Similarly, P. G.

The image of this function was called an automorphism of G. ( Similarly, a homomorphic function ( or homomorph ) was a function between groups which preserved the product while a homomorphism was the image of a homomorph.

Similarly, if g and h are elements of a finite cyclic group G then a solution x of the equation g < sup > x </ sup > = h is called a discrete logarithm to the base g of h in the group G.

* Similarly, the number of conjugates gHg < sup >− 1 </ sup > of a subgroup H in G is equal to the index of the normalizer of H in G.

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, in 2003 USAF Secretary James G. Roche authorized the POW Medal to all " U. S. Air Force personnel taken hostage anytime during the period of 4 November 1979 to 22 January 1981, at the U. S. Embassy in Tehran, Iran.

* Similarly, if is the finite cyclic group of order n and the set S consists of two elements, the standard generator of G and its inverse, then the Cayley graph is the cycle.

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, quarries at Glencullen provided stone for such buildings as the G. P. O. on O ' Connell Street and the Industry and Commerce building on Kildare Street in Dublin.

Similarly, the p ′- core is the largest normal subgroup of G whose order is coprime to p and is denoted.

Similarly, the result of Bayesian inference applied to a choice of single multinomial distribution for all rows of the contingency table taken together versus the more general alternative of a separate multinomial per row produces results very similar to the G statistic.

Similarly, the identity path component of a topological group G is the path component of G that contains the identity element of the group.

Then, for each integer n define n ( G ) to be the number of subgroups U of index n in G. Similarly, if G is a topological group, s_n ( G ) denotes the number of open subgroups U of index n in G. One similarly defines ' m_n ( G ) and to denote the number of maximal and normal subgroups of index n, respectively.