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where r = radius of gyration of cross-section which is equal to the square root of ( I / A ), K = ratio of the longest half sine wave to the actual column length, and KL
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where and r
On the plane the most common alternative is polar coordinates, where every point is represented by its radius r from the origin and its angle θ.
where r is the position vector of the particle relative to the origin, p is the linear momentum of the particle, and × denotes the cross product.
where θ < sub > r, p </ sub > is the angle between r and p measured from r to p ; an important distinction because without it, the sign of the cross product would be meaningless.
where is the component of p that is perpendicular to r. As above, the sign is decided based on the sense of rotation.
t < sub > r </ sub > * BW = 0. 35, where t < sub > r </ sub > is rise time in seconds and BW is bandwidth in Hz.
where n > 1 is an integer and p, q, and r are prime numbers, then 2 < sup > n </ sup >× p × q and 2 < sup > n </ sup >× r are a pair of amicable numbers.
where n > m > 0 are integers and p, q, and r are prime numbers, then 2 < sup > n </ sup >× p × q and 2 < sup > n </ sup >× r are a pair of amicable numbers.
In 1996, Serge Vaudenay found a known-plaintext attack requiring 2 < sup > 8r + 1 </ sup > known plaintexts to break, where r is the number of rounds.
Driven off by Roman forces, the coalition host moved overland into Thracia, where finally it was crushed by emperor Claudius II ( r. 268-70 ) at Naissus ( 269 ).
The Hilbert space of a spin-0 point particle is spanned by a " position basis ", where the label r extends over the set of all points in space.
: The 2br enzymes, with the letter " r " denoting reduced binding to clavulanic acid and sulbactam, are also called inhibitor-resistant TEM-derivative enzymes ; nevertheless, they are commonly still susceptible to tazobactam, except where an amino acid replacement exists at position met69.
where h ( 0 ) is the height of the water at r
where r is the radius from the axis of rotation.
where h ( 0 ) is the height at r = 0 ( the axis ).
( x ( s ), y ( s )) where s represents arc length and r is the position vector.
The tension at r is parallel to the curve at r and pulls the section to the right, so it may be written Tu =( Tcos φ, Tsin φ ), where T is the magnitude of the force and φ is the is the angle between the curve at r and the x-axis ( see tangential angle ).
Finally, weight of the chain is represented by ( 0, − λgs ) where λ is the mass per unit length, g is the acceleration of gravity and s is the length of chain between c and r.
where and =
where 144 =
In an adiabatic irreversible process, dQ = 0 is not equal to TdS ( TdS > 0 ) where Q is thermal energy, T is temperature, and S is entropy.
If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.
Thus, all the antiderivatives of x < sup > 2 </ sup > can be obtained by changing the value of C in F ( x ) = ( x < sup > 3 </ sup >/ 3 ) + C ; where C is an arbitrary constant known as the constant of integration.
Let ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.
Set-theoretically, one may represent a binary function as a subset of the Cartesian product X × Y × Z, where ( x, y, z ) belongs to the subset if and only if f ( x, y ) = z.
The Boltzmann distribution is often expressed in terms of β = 1 / kT where β is referred to as thermodynamic beta.
Self-adjoint operators, where A = A < sup >†</ sup >, play an important role in quantum mechanics ; for example, an observable is always described by a self-adjoint operator.
where e = 2. 718 ....
where the convention B < sub > 1 </ sub > = + 1 / 2 is used.
where a = 0. 246 nm.
* Place (< span lang = grc > pou </ span >, where ) — examples: in a marketplace, in the Lyceum
The open-chain form of a monosaccharide often coexists with a closed ring form where the aldehyde / ketone carbonyl group carbon ( C = O ) and hydroxyl group (- OH ) react forming a hemiacetal with a new C-O-C bridge.
A simple electric circuit, where current is represented by the letter i. The relationship between the voltage ( V ), resistance ( R ), and current ( I ) is V = IR ; this is known as Ohm's Law.
where E = elastic modulus of the material, I < sub > min </ sub >
P < sub > cr </ sub >/ A, where A = cross-sectional area of the column ), is greater than the proportional limit of the material, the column is experiencing inelastic buckling.
( Note: bandwidth is proportional to where = bit time ) Therefore, the bandwidth of the data signal is and the bandwidth of the spread spectrum signal is.
Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.
where | v | = Rω is the magnitude of the velocity ( the speed ).
where it already is established that α = ρ.
where and radius
The quantum number n first appeared in the Bohr model where it determines the radius of each circular electron orbit.
George Stokes had shown that the mobility for a spherical particle with radius is, where is the dynamic viscosity of the fluid.
The use of Stokes's law in Nernst's case, as well as in Einstein and Smoluchowski, is not strictly applicable since it does not apply to the case where the radius of the sphere is small in comparison with the mean free path.
This solution had a peculiar behaviour at what is now called the Schwarzschild radius, where it became singular, meaning that some of the terms in the Einstein equations became infinite.
Because of this property, the collapsed stars were called " frozen stars ," because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius.
where ρ is the radius of curvature.
where vertical bars |...| denote the vector magnitude, which in the case of r ( t ) is simply the radius R of the path.
If friction cannot do this ( that is, the coefficient of friction is exceeded ), the ball slides to a different radius where the balance can be realized.
where is the coordinate radius, and are the test-particle's conserved energy and angular momentum respectively ( constructed from the killing vectors ).
The equation of a circle is ( x − a )< sup > 2 </ sup > + ( y − b )< sup > 2 </ sup > = r < sup > 2 </ sup > where a and b are the coordinates of the center ( a, b ) and r is the radius.
In some cases where the radius of the substitutional atom ( ion ) is substantially smaller than that of the atom ( ion ) it is replacing, its equilibrium position can be shifted away from the lattice site.
where a is the radius of the circular aperture, k is equal to 2π / λ and J < sub > 1 </ sub > is a Bessel function.
where R < sub > s </ sub > is the radius of the star, R < sub > o </ sub > is the occulting object's radius, and r is the distance from the star to the occulting object.
The redshift is not defined for photons emitted inside the Scharzschild radius, the distance from the body where the escape velocity is greater than the speed of light.
where B < sub > r </ sub > is the disk of radius r and denotes the supremum norm of f ( z ) on B < sub > r </ sub >.
radius ) a and flattening f. The quantity f = ( a − b )/ a, where b is the semi-minor axis ( polar radius ), is a purely geometrical one.
There are also several implementations of the concept of an extended cell, where the cell radius could be double or even more, depending on the antenna system, the type of terrain and the timing advance.
where λ is the longitude from the central meridian in degrees, φ is the latitude, and R is the radius of the globe used as the model of the earth for projection.
where λ is the longitude from the central meridian ( in radians ), φ is the latitude, and R is the radius of the globe used as the model of the earth for projection.
0.152 seconds.