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For and one-dimensional
For one-dimensional problems, a unique median exists for practical continuous problems.
For example, the simple traversal of elements in a one-dimensional array, from the base address to the highest element would exploit the sequential locality of the array in memory.
For many simple applications, Fourier's law is used in its one-dimensional form.
For along with his steady diet of giggles and unconditional love, Barney offers our children a one-dimensional world where everyone must be happy and everything must be resolved right away.
For an electron, the one-dimensional Schrödinger equation can be written in the form
For the one-dimensional harmonic oscillator
For example, when Σ is a 2-sphere, this Hilbert space is one-dimensional and so there is only one state.
For example, if is a figure eight, then it has two holes, which in this context count as being one-dimensional.
For simplicity, we will consider the one-dimensional case.
For one-dimensional integration, quadrature methods such as the trapezoidal rule, Simpson's rule, or Newton – Cotes formulas are known to be efficient if the function is smooth.
For a complex vector space V, it means for any x in C, C contains the circle through x, centred on the origin, in the one-dimensional complex subspace generated by x.
For a complex vector space V, it means for any x in C, C contains the disk with x on its boundary, centred on the origin, in the one-dimensional complex subspace generated by x. Equivalently, a balanced set is a circled cone.
For instance, the LAPACK Fortran package stores an unsymmetric tridiagonal matrix of order n in three one-dimensional arrays, one of length n containing the diagonal elements, and two of length n − 1 containing the subdiagonal and superdiagonal elements.
For instance, in 1971, Charles Fefferman was able to use the Besicovitch set construction to show that in dimensions greater than 1, truncated Fourier integrals taken over balls centered at the origin with radii tending to infinity need not converge in L < sup > p </ sup > norm when p ≠ 2 ( this is in contrast to the one-dimensional case where such truncated integrals do converge ).
For " one-dimensional " ( single-indexed ) arrays — vectors, sequence, strings etc.
For a real-valued continuous function f, defined on an interval b ⊂ ℝ, its total variation on the interval of definition is a measure of the one-dimensional arclength of the curve with parametric equation x ↦ f ( x ), for x ∈ b.
For the one-dimensional case, the new patterns are introduced by solving an auxiliary optimization problem called the knapsack problem, using dual variable information from the linear program.
For example, observations distributed according to a mixture of one-dimensional Gaussian distributions will have a mean and variance for each component.
For n = 3, 4 there are two additional one-dimensional irreducible representations, corresponding to maps to the cyclic group of order 3: and
* For n = 3 the obvious analogue of the ( n − 1 )- dimensional representation is reducible – the permutation representation coincides with the regular representation, and thus breaks up into the three one-dimensional representations, as is abelian ; see the discrete Fourier transform for representation theory of cyclic groups.
For the graph of a one-dimensional function, this corresponds to a point on the graph where the tangent is parallel to the x-axis.
For performance and architectural reasons, traditional router-based queueing schemes are limited to a small number of classes and only allow one-dimensional classification.
For example, the one-dimensional, abelian Lie algebra R is obviously reductive, and is the Lie algebra of both a reductive algebraic group G < sub > m </ sub > ( the multiplicative group of nonzero real numbers ) and also a unipotent ( non-reductive ) algebraic group G < sub > a </ sub > ( the additive group of real numbers ).
In practice, this is usually the maximally-localized set, in which the Wannier function is localized around the point R and rapidly goes to zero away from R. For the one-dimensional case, it has been proved by Kohn that there is always a unique choice that gives these properties ( subject to certain symmetries ).

For and simple
For better or worse we cannot regard `` imitation '' in the arts in the simple mode of classical rationalism or detached realism.
For examples of simple addition algorithms specified in the detailed manner described in Algorithm characterizations, see Algorithm examples.
: For an example of the simple algorithm " Add m + n " described in all three levels see Algorithm examples.
For Lamprias had said that the first articulate sound made is " alpha ", because it is very plain and simplethe air coming off the mouth does not require any motion of the tongue — and therefore this is the first sound that children make.
For a simple substance, during an adiabatic process in which the volume increases, the internal energy of the working substance must decrease
For a simple model, with two alleles:
For the simple case where the direction of the light beam along the line SE is perpendicular to the motion of the observer then only light emitted at an angle equal to the arc cosine of the ratio of the observer's speed to the speed of light will reach the telescope.
For example, eliminating dependence on the electrical grid is relatively simple but growing all necessary food is a more demanding and time-consuming proposition.
For a Gaussian response system ( or a simple RC roll off ), the rise time is approximated by:
For a finite-dimensional vector space, the outer product can be understood as simple matrix multiplication:
For example, the rules of the Hebrew calendar depend on the seven-day week cycle ( a very simple calendar ), so the week is one of the cycles of the Hebrew calendar.
For example, industrial farming could not have been invented before simple farming, and metallurgy could not have developed without previous non-smelting processes involving metals ( such as simple ground collection or mining ).
For example, simple hydrogen gas combined with simple oxygen gas can produce a more complex substance, such as water.
For example, endosperm cell walls in the seeds of cereal grasses, nasturtium, and other species, are rich in glucans and other polysaccharides that are readily digested by enzymes during seed germination to form simple sugars that nourish the growing embryo.
For I am not as simple as I may seem.
For example, the Cyrillic letter Р is usually written as R in the Latin script, although in many cases it is not as simple as a one-for-one equivalence.
For about a decade, every student taking the 6. 004 class at MIT was part of a team — each team had one semester to design and build a simple 8 bit CPU out of 7400 series integrated circuits.
For effective utilization and handling it is desired that a data model is relatively simple and intuitive.
For the simple electric dipole given above, the electric dipole moment points from the negative charge towards the positive charge, and has a magnitude equal to the strength of each charge times the separation between the charges.
For simple dynamical systems, knowing the trajectory is often sufficient, but most dynamical systems are too complicated to be understood in terms of individual trajectories.
For low-frequency radiation ( radio waves to visible light ) the best-understood effects are those due to radiation power alone, acting through the effect of simple heating when the radiation is absorbed by the cell.
* A simple explanation of Euler's Conjecture at Maths Is Good For You!
For example, just by applying a simple rule that constrains each queen to a single column ( or row ), though still considered brute force, it is possible to reduce the number of possibilities to just 16, 777, 216 ( that is, 8 < sup > 8 </ sup >) possible combinations.

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