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constant and N
For N to be constant for all values of w, a ' tan w '/ a tan w must also be constant.
where is the Boltzmann constant, T is temperature ( assumed to be a well-defined quantity ), is the degeneracy ( meaning, the number of levels having energy ; sometimes, the more general ' states ' are used instead of levels, to avoid using degeneracy in the equation ), N is the total number of particles and Z ( T ) is the partition function.
For each specific consistent effectively represented axiomatic system for the natural numbers, such as Peano arithmetic, there exists a constant N such that no bit of Ω after the Nth can be proven to be one or zero within that system.
Thus, if ( M, d ) and ( N, d ) are two metric spaces, and, then there is a constant k such that
The machine can only add the value of a column n + 1 to column n to produce the new value of n. Column N can only store a constant, column 1 displays ( and possibly prints ) the value of the calculation on the current iteration.
* The atomic mass unit ( u ) is defined so that a single carbon-12 atom has a mass of 12 u ; 1 u is approximately .< ref group =" note "> Since the Avogadro constant N < sub > A </ sub > is defined as the number of atoms in 12 g of carbon-12, it follows that 1 u is exactly 1 /( 10 < sup > 3 </ sup > N < sub > A </ sub >) kg .</ ref > The atomic mass unit is convenient for expressing the masses of atoms and molecules.
Also the molar mass comes into comparison with the number of particles contained within the structure by multiplying the number of moles by Avogadro's constant: N < sub > A </ sub >= 6. 022 · 10 < sup > 23 </ sup > mol < sup >− 1 </ sup >.
The Peano axioms define the arithmetical properties of natural numbers, usually represented as a set N or The signature ( a formal language's non-logical symbols ) for the axioms includes a constant symbol 0 and a unary function symbol S.
The equation is most conveniently expressed in terms of the measured quantity N ( t ) rather than the constant initial value N < sub > o </ sub >.
where N < sup > 2 </ sup > is a constant.
where F is the restoring elastic force exerted by the spring ( in SI units: N ), k is the spring constant ( N · m < sup >− 1 </ sup >), and x is the displacement from the equilibrium position ( in m ).
is the functor that maps each object N in C to the constant functor Δ ( N ): J → C to N ( i. e. Δ ( N )( X )
N m, and the total spring constant of the array K
He also introduced the concept of the chemical potential of a given chemical species, defined to be the rate of the increase in U associated with the increase in the number N of molecules of that species ( at constant entropy and volume ).
where N < sup >+</ sup > is the nucleophile dependent parameter and k < sub > 0 </ sub > the reaction rate constant for water.
The second order reaction rate constant k at 20 ° C for a reaction is related to a nucleophilicity parameter N, an electrophilicity parameter E, and a nucleophile-dependent slope parameter s. The constant s is defined as 1 with 2-methyl-1-pentene as the nucleophile.

constant and depends
) In a mobile society, congregational health depends on a constant process of recruitment ; ;
For an ideal gas, the temperature remains constant because the internal energy only depends on temperature in that case.
Theorem: If K < sub > 1 </ sub > and K < sub > 2 </ sub > are the complexity functions relative to description languages L < sub > 1 </ sub > and L < sub > 2 </ sub >, then there is a constant c – which depends only on the languages L < sub > 1 </ sub > and L < sub > 2 </ sub > chosen – such that
This algorithm, for all strings, allows codes as short as allowed by any other algorithm up to an additive constant that depends on the algorithms, but not on the strings themselves.
where A < sub > α </ sub > and B < sub > α </ sub > are any two solutions of Bessel's equation, and C < sub > α </ sub > is a constant independent of x ( which depends on α and on the particular Bessel functions considered ).
Because Ω depends on the program encoding used, it is sometimes called Chaitin's construction instead of Chaitin's constant when not referring to any specific encoding.
If the diffusion coefficient is not a constant, but depends upon the coordinate and / or concentration, Fick's Second Law yields
It consists of a mass m, which experiences a single force, F, which pulls the mass in the direction of the point x = 0 and depends only on the mass's position x and a constant k. Newton's second law for the system is
The duration of state 1 ( low output ) will be related to the time constant R < sub > 2 </ sub > C < sub > 1 </ sub > as it depends on the charging of C1, and the duration of state 2 ( high output ) will be related to the time constant R < sub > 3 </ sub > C < sub > 2 </ sub > as it depends on the charging of C2.
If the Euler-Lagrange equations are solved for this system, it is found that the motion depends on two constants and ( each related to a constant of motion ).
Second, he found that the orbital speed of each planet is not constant, as had previously been thought, but rather that the speed depends on the planet's distance from the Sun.
Even though some nuclides that decay by the process of electron capture, such as beryllium-7, strontium-85, and zirconium-89, are not fully suitable for radiometric dating because their decay rate may be slightly affected by local electron density, in general, the half-life of a nuclide depends solely on its nuclear properties and is essentially a constant.
: τ < sub > S </ sub > is the saturation time constant, which depends on the spontaneous emission lifetimes of the various transitions between the energy levels related to the amplification.
Note that the power injected by the torque depends only on the instantaneous angular speed – not on whether the angular speed increases, decreases, or remains constant while the torque is being applied ( this is equivalent to the linear case where the power injected by a force depends only on the instantaneous speed – not on the resulting acceleration, if any ).
This free-energy relationship relates the pseudo first order reaction rate constant ( in water at 25 ° C ), k, of a reaction, normalized to the reaction rate, k < sub > 0 </ sub >, of a standard reaction with water as the nucleophile, to a nucleophilic constant n for a given nucleophile and a substrate constant s that depends on the sensitivity of a substrate to nucleophilic attack ( defined as 1 for methyl bromide ).
These relationships are certainly not exact because the size of an atom is not constant but depends on its chemical environment.
This argument depends on a lack of a variation of the distribution ( spatial or otherwise ) in the vacuum energy density, as would be expected if the dark energy were the cosmological constant.
The total number of flux line s depends on the strength of the source and is constant with increasing distance.

constant and on
In any case, Miss Millay's sweet-throated bitterness, her variations on the theme that the world was not only well lost for love but even well lost for lost love, her constant and wonderfully tragic posture, so unlike that of Fitzgerald since it required no scenery or props, drew from the me that I was when I fell upon her verses an overwhelming yea.
The theory predicts a linear dependence of Af on Af, where J is the experimentally determined Curie-Weiss constant.
There remains a residue of total costs, or total `` revenue requirements '' which, since it is found to behave as if it were constant over substantial variations in traffic density, is strictly unallocable on a cost-finding basis.
A constant problem confronting Davis on any proposals for new taxes will be the charge by his foes that he has not tried to economize.
With the definitions used before 2012, the astronomical unit was dependent on the heliocentric gravitational constant, that is the product of the gravitational constant G and the solar mass M < sub >☉</ sub >.
In particular, time intervals measured on the surface of the Earth ( terrestrial time, TT ) are not constant when compared to the motions of the planets: the terrestrial second ( TT ) appears to be longer in Northern Hemisphere winter and shorter in Northern Hemisphere summer when compared to the " planetary second " ( conventionally measured in barycentric dynamical time, TDB ).
As the meter is defined in terms of the second, and the speed of light is constant for all observers, the terrestrial meter appears to change in length compared to the " planetary meter " on a periodic basis.
An adiabat is a curve of constant entropy on the P-V diagram.
# If adiabats and isotherms are graphed severally at regular changes of entropy and temperature, respectively ( like altitude on a contour map ), then as the eye moves towards the axes ( towards the south-west ), it sees the density of isotherms stay constant, but it sees the density of adiabats grow.
He is immediately at a loss, and knows not what to answer ... a Pyrrhonian cannot expect, that his philosophy will have any constant influence on the mind: or if it had, that its influence would be beneficial to society.
The principle it works on, the constant of simultaneity, is analogous in some ways to gravity ... One point has to be fixed, on a planet of certain mass, but the other end is portable.
When the effects of compressibility on the solution are small, the aerodynamicist may choose to assume that density is constant.
If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.
If the net force on some body is directed always toward some fixed point, the center, then there is no torque on the body with respect to the center, and so the angular momentum of the body about the center is constant.
For any system, the following restrictions on measurement results apply, where is the reduced Planck constant and is any direction vector such as x, y, or z:
Detailed analysis shows that the complexity class is unchanged by allowing error as high as 1 / 2 − n < sup >− c </ sup > on the one hand, or requiring error as small as 2 < sup >− n < sup > c </ sup ></ sup > on the other hand, where c is any positive constant, and n is the length of input.

0.157 seconds.