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 technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.

More rigorously, the divergence of a vector field F at a point p is defined as the limit of the net flow of F across the smooth boundary of a three dimensional region V divided by the volume of V as V shrinks to p. Formally,

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

More generally, if a linear operator on a vector space ( possibly infinite-dimensional ) has finite-dimensional range ( e. g., a finite-rank operator ), then the rank of the operator is defined as the dimension of the range.

More generally yet, the additive groups of all topological vector spaces, such as Banach spaces or Hilbert spaces, are topological groups.

More formally, a multivariate random variable is a column vector X = ( X < sub > 1 </ sub >, ..., X < sub > n </ sub >)< sup > T </ sup > ( or its transpose, which is a row vector ) whose components are scalar-valued random variables on the same probability space ( Ω,, P ), where Ω is the sample space, is the sigma-algebra ( the collection of all events ), and P is the probability measure ( a function returning every event's probability ).

More generally, a norm on a vector space is Lipschitz continuous with respect to the associated metric, with the Lipschitz constant equal to 1.

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.

More generally, every module category over a ring is additive, and so in particular, the category of vector spaces over a field is additive.

Given a differentiable manifold M, a vector field on M is an assignment of a tangent vector to each point in M. More precisely, a vector field F is a mapping from M into the tangent bundle TM so that is the identity mapping

More formally, a support vector machine constructs a hyperplane or set of hyperplanes in a high-or infinite-dimensional space, which can be used for classification, regression, or other tasks.

More precisely, in order to define the covariant derivative of it is necessary first to extend to a continuously differentiable vector field in an open set.

More generally, the same construction allows one to construct a vector field for any Ehresmann connection on the tangent bundle.

More generally, let V be a vector space over a field K, and let

More generally still, the general linear group of a vector space GL ( V ) is the abstract automorphism group, not necessarily written as matrices.

More detailed discussion of wave functions as elements of vector spaces is below, following further definitions.

More precisely, the divergence theorem states that the outward flux of a vector field through a closed surface is equal to the volume integral of the divergence of the region inside the surface.

More precisely, if V is a vector space over &# x211D ;, the inner product is a function

More recently, a number of loop-free distance vector protocols have been developed — notable examples are EIGRP, DSDV and Babel.

More precisely, the vorticity of a flow is a vector field, equal to the curl ( rotational ) of its velocity field v. It can be expressed by the vector analysis formula, where is the nabla operator.