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 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 small angles a symmetrical airfoil will generate a lift force roughly proportional to the angle of attack.

For any airfoil generating lift, there must be a pressure imbalance, i. e. lower average air pressure on the top than on the bottom.

For instance, Bernoulli's equation can be used to determine the pressure at each point on the airfoil from the speed of the velocity field.

For a conventionally cambered airfoil, the center of pressure lies a little behind the quarter-chord point at maximum lift coefficient ( large angle of attack ), but as lift coefficient reduces ( angle of attack reduces ) the center of pressure moves toward the rear.

For a reflex-cambered airfoil, the center of pressure lies a little ahead of the quarter-chord point at maximum lift coefficient ( large angle of attack ), but as lift coefficient reduces ( angle of attack reduces ) the center of pressure moves forward.

For full size and flying model aircraft wing structures that are usually made of wood, ribs can either be in one piece ( forming the airfoil at that rib's " station " in the wing ), or be in a three-piece format, with the rib web being the part that the one-piece rib consisted of, with capstrips for the upper and lower edging of the rib, running from the leading edge to the trailing edge, being the other two component parts.

For airfoil designations, most traditional NACA 4 -, 5 -, and 6-airfoils can be specified in Digital DATCOM.

For vertical take-off, hovering, low-speed flight, and vertical landing, the main airfoil is spun like a helicopter's rotor by directing the exhaust from a jet engine through thrust nozzles in the wingtips.

For high-speed flight, the exhaust is redirected through an ordinary jet nozzle and the airfoil is held in a fixed position, as in a conventional airplane.

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, the C-C-C bond angle in propylene is 123. 9 °.

For example, when a woman lies on her back, the angle of the breast apex becomes a flat, obtuse angle ( less than 180 degrees ) while the base-to-length ratio of the breast ranges from 0. 5 to 1. 0.

For example, water is a compound containing hydrogen and oxygen in the ratio of two to one, with the oxygen atom between the two hydrogen atoms, and an angle of 104. 5 ° between them.

For example, a lamp that emits 590 cd with a radiation angle of 40 ° emits about 223 lumens.

For example, a point on the unit circle in the plane can be specified by two Cartesian coordinates, but one can make do with a single coordinate ( the polar coordinate angle ), so the circle is 1-dimensional even though it exists in the 2-dimensional plane.

For example, the problem of trisecting an angle with a compass and straightedge is one that naturally occurs within the theory, since the axioms refer to constructive operations that can be carried out with those tools.

Rail fins evolved into being and surged into popularity as riders ( Simon Anderson, most famously ) sought a solution to two major performance issues of a central " single " fin-both related to engagement of the foil: For one, a centrally-mounted fin is tilted up out of the water as the board is leaned over, and thus it loses more and more of its lift as the lean angle increases-if the lean angle is acute enough, the fin's tip can be the only area left in the water ; the tip may then rapidly stall and, having lost its lift, become disengaged from the water, leaving the board's bottom as the only control surface still operating.

For local detail surveys, tacheometers are commonly employed although the old-fashioned rectangular technique using angle prism and steel tape is still an inexpensive alternative.

For example, as the amphiboles are double-chain silicates and the pyroxenes are single-chain silicates, the angle between their cleavage planes is different.

For example, the phenomenon of flutter in aerodynamics occurs when an arbitrarily small displacement of an aircraft wing ( from its equilibrium ) results in an increase in the angle of attack of the wing on the air flow and a consequential increase in lift coefficient, leading to a still greater displacement.

For example, the center segments return the ball a 90 ° angle in relation to the paddle, while the outer segments return the ball at smaller angles.

For example, an angle of 1. 2 radians would be written as " 1. 2 rad " or " 1. 2 < sup > c </ sup >" ( the second symbol is often mistaken for a degree: " 1. 2 °").

For a brief while it was also implied that Skuld had a crush on Keiichi ; the second special episode of the first TV series ( where she's grown up for a day ) explored this angle by placing Skuld and Keiichi in situations where they appear as a couple.

For electromagnetic waves, this change in the angle of propagation is governed by Snell's law.

For a wing to produce " lift ", it must be oriented at a suitable angle of attack relative to the flow of air past the wing.

For instance, at Mach 1. 3 the angle of the Mach cone formed off the body of the aircraft will be at about μ

For example, the task of describing mathematically the motion of a projectile is made easier by separating out the force of gravity, angle of projection and initial velocity.

For example, describing a transformation as a rotation by a certain angle with respect to a certain axis is easier to get an idea of the overall behavior of the transformation than describing it as a combination of a translation and a rotation.

For a given mirror ratio ( the maximum field strength divided by the minimum field strength ), particles with a pitch angle ( angle between the particle velocity and the magnetic field ) greater than a critical value will be reflected, those with a smaller pitch angle will escape.