For example, the security available with a 1024-bit key using asymmetric RSA is considered approximately equal in security to an 80-bit key in a symmetric algorithm ( Source: RSA Security ).

For a symmetric distribution ( where the median equals the midhinge, the average of the first and third quartiles ), half the IQR equals the median absolute deviation ( MAD ).

For example, we must always use symmetric states when describing photons or helium-4 atoms, and antisymmetric states when describing electrons or protons.

For example, a single electron in an unexcited atom is pictured classically as a particle moving in a circular trajectory around the atomic nucleus, whereas in quantum mechanics it is described by a static, spherically symmetric wavefunction surrounding the nucleus ( Fig.

For simplicity, we will first discuss second quantization for bosons, which form perfectly symmetric quantum states.

For a radially symmetric scattering potential, as in the case of the Coulombic potential,, yielding the expression for the scattering cross section

For the remainder of this article, " symmetric group " will mean a symmetric group on a finite set.

For a lightly damped linear oscillator with a resonance frequency Ω, the intensity of oscillations I when the system is driven with a driving frequency ω is typically approximated by a formula that is symmetric about the resonance frequency:

For example, S < sub > 5 </ sub >, the symmetric group in 5 elements, is not solvable which implies that the general quintic equation cannot be solved by radicals in the way equations of lower degree can.

For n = 2 the theorem claims that a convex figure in the plane symmetric about the origin and with area greater than 4 encloses at least one lattice point in addition to the origin.

For the simple Metropolis algorithm described here, this proposal density must be symmetric in that.

For large astronomical bodies which are near-spherical due to self-gravitation, the tidal distortion produces a slightly prolate spheroid-i. e., an axially symmetric ellipsoid that is elongated along its major axis.

For example, the gravitational field vectors for a spherically symmetric body would all point towards the sphere's center with the magnitude of the vectors reducing as radial distance from the body increases.

For example, Skype uses a proprietary protocol to route calls through other Skype peers on the network, allowing it to traverse symmetric NATs and firewalls.

For quantum systems which are invariant under time reversal the Hamiltonian can be made real and symmetric, so that the action of time-reversal on the wave-function is just complex conjugation.

More explicitly: For every symmetric real matrix A there exists a real orthogonal matrix Q such that D = Q < sup > T </ sup > AQ is a diagonal matrix.

) For a symmetric airfoil, as angle of attack and lift coefficient change, the center of pressure does not move.

For illustration, consider a Lagrangian that does not depend on time, i. e., that is invariant ( symmetric ) under changes t → t + δt, without any change in the coordinates q.

In mathematics, and in particular linear algebra, a skew-symmetric ( or antisymmetric or antimetric ) matrix is a square matrix A whose transpose is also its negative ; that is, it satisfies the equation If the entry in the and is a < sub > ij </ sub >, i. e. then the skew symmetric condition is For example, the following matrix is skew-symmetric:

For a symmetric operator A, the domain of the operator A * contains the domain of the operator A, and the restriction of the operator A * on the domain of A coincides with the operator A, i. e., in other words A * is extension of A.

* For symmetric cases.

For these lenses the field produced for the lens must be radially symmetric, as deviation from the radial symmetry of the magnetic lens causes aberrations such as astigmatism, and worsens spherical and chromatic aberration.

For the symmetric difference of two distinct index 2 subgroups ( which are necessarily normal ) gives the third point on the projective line containing these subgroups, and a group must contain index 2 subgroups – it cannot contain exactly 2 or 4 index 2 subgroups, for instance.

For relations, a symmetric relation is analogous to a commutative operation, in that if a relation R is symmetric, then.

For a few details of the system the lines are 1-1/4'' '' X-Tru-Coat, a product of Republic Steel Corp., and all lines are welded.

For the lines of any plane, **yp, meeting Q in a conic C, are transformed into the congruence of secants of the curve C' into which C is transformed in the point involution on Q.

For if such were the case, either the plane of the two lines would meet **zg in more than K points or, alternatively, the order of the image regulus of the pencil determined by the two lines would be too high.

For any pencil in a plane containing a Af-fold secant of **zg has an image regulus which meets the plane of the pencil in Af lines, namely the images of the lines of the pencil which pass through the intersection of **zg and the multiple secant, plus an additional component to account for the intersections of the images of the general lines of the pencil.

For each of these lines meets Q in three points, namely two points on **zg and one point on one of the multiple secants.

* 732: 958 For Verizon land lines.

For example, the well-known lines from Kipling's Song of the Dead:

For curves given by the graph of a function, horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to Vertical asymptotes are vertical lines near which the function grows without bound.

For instance, relatively new biostatistics departments have been founded with a focus on bioinformatics and computational biology, whereas older departments, typically affiliated with schools of public health, will have more traditional lines of research involving epidemiological studies and clinical trials as well as bioinformatics.

For example, Baldrick is reduced to making coffee from mud and cooking rats, while General Melchett hatches a plan for the troops to walk very slowly toward the German lines, because " it'll be the last thing Fritz will expect.

For artists whose interests necessitate precision line-work, ballpoints are an obvious attraction ; ballpoint pens allow for sharp lines not as effectively executed using a brush.

For a time, the combined company retained the Burroughs processors as the A and V systems lines.

For the Sun and stars with low temperatures, the prominence of the H and K lines can be an indication of strong magnetic activity in the chromosphere.

For example, Philip K. Dick's works contain recurring themes of social decay, artificial intelligence, paranoia, and blurred lines between objective and subjective realities, and the influential cyberpunk movie Blade Runner is based on one of his books.

For example, in AC power lines, the waves of electromagnetic energy propagate through the space between the wires, moving from a source to a distant load, even though the electrons in the wires only move back and forth over a tiny distance.

For example, Australian left-wing " true believers " levelled it at supporters of the failed republic referendum of 1999 ( where the vote was split not along conventional party lines but very much along socio-economic divides, with the rich overwhelmingly supporting the change while the less well-off were opposed – a superficially bizarre pattern for a non-economic issue ).

For instance, Microsoft Word files are normally created and modified by the Microsoft Word program in response to user commands, but the user can also move, rename, or delete these files directly by using a file manager program such as Windows Explorer ( on Windows computers ) or by command lines ( CLI ).

For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is defined to be the smallest such distance.

For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance.

For best results the lines in a sketch are typically drawn to follow the contour curves of the surface, thus producing a depth effect.