More generally, suppose that an experiment consists of a number of independent trials, that each trial results in either a `` success '' or a `` non-success '' ( `` failure '' ), and that the probability of success remains constant from trial to trial.

More generally, in a k-dimensional array, the address of an element with indices i < sub > 1 </ sub >, i < sub > 2 </ sub >, …, i < sub > k </ sub > is

More recently, an abettor is generally known as an accomplice.

More expensive pigments are generally replicated by hues.

More generally, one curve is a curvilinear asymptote of another ( as opposed to a linear asymptote ) if the distance between the two curves tends to zero as they tend to infinity, although usually the term asymptote by itself is reserved for linear asymptotes.

More generally, as noted by A. W.

More generally, a binary relation between two sets A and B is a subset of.

More generally, a new component is said to be backward compatible if it provides all of the functionality of the old component.

More generally, an n-piece cubic Bézier curve can approximate a circle, when each inner control point is the distance from an outer control point on a unit circle, where t is 360 / n degrees, and n > 2.

More generally, every C *- algebra is a Banach algebra.

More generally, a series

More generally, if ƒ has a branch-point near the origin of such a nature that then

More generally, calculus ( plural calculi ) refers to any method or system of calculation guided by the symbolic manipulation of expressions.

More generally, many philosophers and scientists have been unhappy about the difficulty of producing a definition that does not involve circularity or fuzziness.

More broadly, philosophers who do not accept the possibility of zombies generally believe that consciousness is reflected in behavior ( including verbal behavior ), and that we attribute consciousness on the basis of behavior.

Among the teachings of Jesus Christ in the Gospel of Luke and the Gospel of Matthew, the message to his followers that one should " Turn the other cheek " and his example in the story Pericope Adulterae, in which Jesus intervenes in the stoning of an adulteress, are generally accepted as his condemnation of physical retaliation ( though most scholars agree that the latter passage was " certainly not part of the original text of St John's Gospel ") More militant Christians consider Romans 13: 3 – 4 to support the death penalty.

* More generally, compact groups such as an orthogonal group are compact, while groups such as a general linear group are not.

More generally, compact sets can be separated by open sets: if K < sub > 1 </ sub > and K < sub > 2 </ sub > are compact and disjoint, there exist disjoint open sets U < sub > 1 </ sub > and U < sub > 2 </ sub > such that and.

More generally, electric current can be represented as the rate at which charge flows through a given surface as:

More generally, the idea of a contractive mapping can be defined for maps between metric spaces.

More generally, unspecific coercion may be the form taken by disciplinary coercion, and this appears to be in fact the case within the most effective command systems of the modern world.

More generally, judges look at the difficulty and execution of jumps, stunts and tumbling, synchronization, creativity, the sharpness of the motions, showmanship, and overall routine execution.

More generally among Baptists, a variety of parachurch agencies and evangelical educational institutions may be supported generously or not at all, depending entirely upon the local congregation's customs and predilections.

More generally, one can consider finite direct sums of matrix algebras.

More generally, inheritance now is quite different than those in the past.

* More generally, the kernel in algebra is the set of elements that map to the neutral element.

After a basis for the vector space is chosen, this ring is naturally identified with the ring of n-by-n matrices with entries in K. More generally, the endomorphism algebra of the free module is naturally n-by-n matrices with entries in R.

* The Laurent polynomial ring RX < sup >− 1 </ sup > is isomorphic to the group ring of the group Z of integers over R. More generally, the Laurent polynomial ring in n variables is isomorphic to the group ring of the free abelian group of rank n. It follows that the Laurent polynomial ring can be endowed with a structure of a commutative, cocommutative Hopf algebra.

More generally in n-dimensional geometric algebra pseudovectors are the elements of the algebra with dimension, written Λ < sup > n − 1 </ sup > R < sup > n </ sup >.

More generally, the Cayley – Dickson construction takes any algebra with involution to another algebra with involution of twice the dimension.

More advanced computer algebra systems will return an infinity as a result for division by zero ; for instance, Microsoft Math and Mathematica will show a ComplexInfinity result.

* More generally, the conjugation involution in any Cayley – Dickson algebra such as the complex numbers, quaternions and octonions, if a blind eye is turned on the nonassociativity of the latter.

More specifically, in topology, compact Hausdorff topological spaces can be reconstructed from the Banach algebra of functions on the space ( Gel ' fand-Neimark ).

More formally, a skein relation can be thought of as defining the kernel of a quotient map from the planar algebra of tangles.

More generally, one can consider the image, kernel, coimage, and cokernel, which are related by the fundamental theorem of linear algebra.

More generally, the Chevalley – Shephard – Todd theorem characterizes finite groups whose algebra of invariants is a polynomial ring.

More generally, any division algebra is a domain, since all its non-zero elements are invertible.

More refined information is available, for larger values of g, but in these cases canonical curves are not generally complete intersections, and the description requires more consideration of commutative algebra.

More formally, the group algebra of the Heisenberg group has center so rather than simply thinking of the group algebra as an algebra over the field of scalars K, one may think of it as an algebra over the commutative algebra As the center of a matrix algebra or operator algebra is the scalar matrices, a-structure on the matrix algebra is a choice of scalar matrix – a choice of scale.

More sophisticated theories are valence bond theory which includes orbital hybridization and resonance, and the linear combination of atomic orbitals molecular orbital method which includes ligand field theory.

More generally, functional analysis includes the study of Fréchet spaces and other topological vector spaces not endowed with a norm.

More importantly, it includes details of more than 150 single and compound formulations of both herbal and animal origin.

This group includes Jan Baptist van Helmont ( 1618-1699 ), Robert Fludd ( 1574-1637 ), John Pordage ( 1608-1681 ), Jane Leade ( 1623-1704 ), Henry More ( 1614-1687 ), Pierre Poiret ( 1646-1719 ), and Antoinette Bourignon ( 1616-1680 ).

More than 200 factories operate at the Jebel Ali complex in Dubai, which includes a deep-water port and a free trade zone for manufacturing and distribution in which all goods for re-export or transshipment enjoy a 100 % duty exemption.

More rigorously, an interpretation of quantum mechanics satisfies CFD if it includes in the statistical population of measurement results, those measurements which are counterfactual by virtue of their being excluded by the quantum mechanical prohibition on simultaneous measurement of certain pairs of properties.

More recent statements of the theorem are sometimes careful to exclude the equality condition ; that is, the condition is if x ( t ) contains no frequencies higher than or equal to B ; this condition is equivalent to Shannon's except when the function includes a steady sinusoidal component at exactly frequency B.

More typically the Fertile Crescent includes also the Levantine coast of the Mediterranean Sea, with Syria, Jordan, Israel, Lebanon and the West Bank.

More generally, optimization includes finding " best available " values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains.

More than one-fifth of the island is protected as Quttinirpaaq National Park ( formerly Ellesmere Island National Park Reserve ), which includes seven fjords and a variety of glaciers, as well as Lake Hazen, North America's largest lake north of the Arctic Circle.

Source music in portions of the film includes instrumental versions of " Again " by Lionel Newman and Dorcas Cochran, " You Make Me Feel So Young " by Josef Myrow and Mack Gordon, and " The More I See You " by Harry Warren and Mack Gordon.

More recent developments includes the BBC's iPlayer, which was released for open beta testing in July 2007.

More than just finding a vessel's present location, safe navigation includes predicting future location, route planning and collision avoidance.

To coincide with the band's reunion tour, Rhino released the sixth Faith No More compilation, The Very Best Definitive Ultimate Greatest Hits Collection, a double album that includes their hit singles and b sides & rarities, in the UK on June 8, 2009.

More specifically, one includes additional first-order properties, such as the existence of a root for every odd-degree polynomial.

More sophisticated analysis includes the use of differential equations, as detailed below.

One Stone-penned demo called " Coming Back for More " appears to be autobiographical and includes the verse: " Been so high, I touched the sky and the sky says ' Sly, why you tryin ' to get by?

More recent scholarship includes V. Saunier's two-volume Sorbonne dissertation on the poet ( Paris, 1948 ), as well as three excellent critical editions by Eugène Parturier ( Paris, 1916, reissued 2001 with an introduction and bibliography by C. Alduy ), I. D McFarlane ( Cambridge, 1966 ) and Gérard Defaux ( Geneva, 2004 ).

The album includes the hit singles " Walk Idiot Walk ," which debuted at No. 13 on the UK singles charts, " Two-Timing Touch and Broken Bones ," another top 50 hit, and " A Little More for Little You.

More than 80 % of the park is designated as the Pinnacles Wilderness (), which provides even higher protection for the rock spires that give Pinnacles its name, as well as Chalone Peak, the highest peak in the Gabilan Range, and includes the creeks and canyons that are habitat for the endangered red-legged frog.

More obvious folk etymologies include the story that the coffin of St Cuthbert was dropped near Pity Me on the way to Durham, at which point the saint implored the monks carrying him to take pity on him and be more careful ; or that coming to the location during a flight from a Viking raid, a group of monks sang the 51st Psalm, the Latin version of which includes the words " Miserere mei, Deus ", which may be rendered in English as " Pity me, O God ".

More generally, the Ricci tensor can be defined in broader class of metric geometries ( by means of the direct geometric interpretation, below ) that includes Finsler geometry.

More than 90 percent of the population live in the eastern half of the district, which includes the suburbs of Munich.