For, with a single exception, nothing had happened to them.

For the purposes of setting the product price, the industry behaves as a single entity.

For a single stage we may define Af where the maximization is by choice of Af.

For new galaxies to be created, Professor Bondi declares, it would only be necessary for a single hydrogen atom to be created in an area the size of your living room once every few million years.

For single factor ( one way ) ANOVA,

For general computer use access technology such as screen readers, screen magnifiers and refreshable Braille displays has been widely taken up along with standalone reading aids that integrate a scanner, optical character recognition ( OCR ) software, and speech software in a single machine.

For example, if we abbreviate by BP the claim that every set of real numbers has the property of Baire, then BP is stronger than ¬ AC, which asserts the nonexistence of any choice function on perhaps only a single set of nonempty sets.

For example, if a single photon strikes the electrons, only a single electron changes states in response to the photon.

For example, the allotropes of carbon include diamond ( where the carbon atoms are bonded together in a tetrahedral lattice arrangement ), graphite ( where the carbon atoms are bonded together in sheets of a hexagonal lattice ), graphene ( single sheets of graphite ), and fullerenes ( where the carbon atoms are bonded together in spherical, tubular, or ellipsoidal formations ).

For some applications, a single alpha channel is not sufficient: a stained-glass window, for instance, requires a separate transparency channel for each RGB channel to model the red transparency, green transparency, and blue transparency.

For example, if the numbers involved in a computation may be arbitrarily large, the time required by a single addition can no longer be assumed to be constant.

For example, if a program needs 20 hours using a single processor core, and a particular portion of 1 hour cannot be parallelized, while the remaining promising portion of 19 hours ( 95 %) can be parallelized, then regardless of how many processors we devote to a parallelized execution of this program, the minimum execution time cannot be less than that critical 1 hour.

For example if a runner on first base reached third base on a single, it would count as a steal.

For example, the three-domain system separates Archaea and Bacteria, previously grouped into the single kingdom Monera ( bacteria ).

For case of single stranded DNA / RNA units of nucleotides are used, abbreviated nt ( or knt, Mnt, Gnt ), as they are not paired.

For example, an IBM PC might have either a monochrome or a color display adapter ( using different display memory addresses and hardware ), but a single, standard, BIOS system call may be invoked to display a character at a specified position on the screen in text mode.

For a single year in 1949, the team performed in an all-yellow scheme with blue markings.

For example, if a game is played by wagering on the number that would result from the roll of one die, true odds would be 5 times the amount wagered since there is a 1 in 6 chance of any single number appearing, assuming that you get the original amount wagered back.

For example, he or she cannot veto the legislative budget, and thus Congress is sovereign over the year's single most important piece of legislation.

For example, carbon can be found as diamond, which has a tetrahedral structure around each carbon atom ; graphite, which has layers of carbon atoms with a hexagonal structure stacked on top of each other ; graphene, which is a single layer of graphite that is incredibly strong ; fullerenes, which have nearly spherical shapes ; and carbon nanotubes, which are tubes with a hexagonal structure ( even these may differ from each other in electrical properties ).

For him, celibacy is the single life, free from such distraction, not a life of saintly denial.

For F that are universal, such a p can generally be seen both as the concatenation of a program part and a data part, and as a single program for the function F.

For example up to 200, 000 different small molecules might be made in plants, although not all these will be present in the same species, or in a single cell.

For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point.

For more details of this early work, see Alpha particle # History of discovery and use.

For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is

( For one particle, J = L + S.

For example, it also predicts the variation of the particle density in a gravitational field with height, if.

For example, the probability that an alpha particle striking a beryllium target will produce a neutron can be expressed as the equivalent cross section of beryllium for this type of reaction.

For example, if we suppose at t = 0 the extension is a unit distance ( x = 1 ), and the particle is not moving ( dx / dt = 0 ).

For mathematical purposes, elementary particles are normally treated as point particles, although some particle theories such as string theory posit a physical dimension.

: For an elementary introduction to how Lie algebras are related to particle physics, see the article Particle physics and representation theory.

The red dot overtakes two green dots when moving from the left to the right of the figure. New waves seem to emerge at the back of a wave group, grow in amplitude until they are at the center of the group, and vanish at the wave group front. For surface gravity waves, the water particle velocities are much smaller than the phase velocity, in most cases.

For a free non-relativistic particle it follows that

For non-interacting particles, i. e. particles which do not interact mutually and move independently, the potential of the system is the sum of the separate potential energy for each particle, that is

For instance, if a particle is in a state | ψ ⟩, the probability of finding it in a region of volume d < sup > 3 </ sup > x surrounding some position x is

For example, in a collision of two particles a reference frame can be chosen where one particle begins at rest.

For example, one can talk about motion of a wave or a quantum particle ( or any other field ) where the configuration consists of probabilities of occupying specific positions.

For example, mā ( high level pitch ) means " mom ", má ( rising pitch ) means " hemp ", mǎ ( falling then rising ) means " horse ", mà ( falling ) means " scold ", and ma ( neutral tone ) is an interrogative particle.

For example, a single photon may be refracted by a lens or exhibit wave interference with itself, but also act as a particle giving a definite result when its position is measured.

The red dot overtakes two green dots when moving from the left to the right of the figure. New waves seem to emerge at the back of a wave group, grow in amplitude until they are at the center of the group, and vanish at the wave group front. For surface gravity waves, the water particle velocities are much smaller than the phase velocity, in most cases.

For example, the free particle in the previous example will usually have a wavefunction that is a wave packet centered around some mean position x < sub > 0 </ sub > ( neither an eigenstate of position nor of momentum ).

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 example, consider a free particle.

For instance, the fundamental observables associated with the motion of a single quantum mechanical particle are the position and momentum operators and.

For example, the 3-particle state with one particle in state and two in state is

For the case of light alpha particles scattering off heavy nuclei, as in the experiment performed by Rutherford, the reduced mass is essentially the mass of the alpha particle and the nucleus off of which it scatters is essentially stationary in the lab frame.

For head on collisions between alpha particles and the nucleus, all the kinetic energy of the alpha particle is turned into potential energy and the particle is at rest.