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where and M
We could, alternatively, choose an encoding for Turing machines, where an encoding is a function which associates to each Turing Machine M a bitstring < M >.
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.
He currently works at Texas A & M University, United States, as a Distinguished Professor where he holds the College of Engineering Endowed Chair in Computer Science.
For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies
The name originated from the Basic Input Output System used in the CP / M operating system ( released in 1976 ), where the BIOS was loaded from disk, with only a small boot loader program stored in read-only memory.
The unit MBtu was defined as one thousand Btu, presumably from the Roman numeral system where " M " stands for one thousand ( 1, 000 ).
In large churches where they were celebrated the services were usually grouped ; e. g. Matins and Lauds ( about 7. 30 A. M .); Prime, Terce ( High Mass ), Sext, and None ( about 10 A. M .); Vespers and Compline ( 4 P. M .); and from four to eight hours ( depending on the amount of music and the number of high masses ) are thus spent in choir.
He also often employed inanimate objects in his films, often transforming them into other objects in an almost surreal way, such as in The Pawnshop ( 1916 ) and One A. M. ( 1916 ), where Chaplin is the only actor aside Chester Conklin's brief appearance in the very first scene.
HTML (< u > H </ u > yper < u > t </ u > ext < u > M </ u > arkup < u > L </ u > anguage ) has been in use since 1991, but HTML 4. 0 ( December 1997 ) was the first standardized version where international characters were given reasonably complete treatment.
Let M be a smooth manifold and let x be a point in M. Let I < sub > x </ sub > be the ideal of all functions in C < sup >∞</ sup >( M ) vanishing at x, and let I < sub > x </ sub >< sup > 2 </ sup > be the set of functions of the form, where f < sub > i </ sub >, g < sub > i </ sub > ∈ I < sub > x </ sub >.
where θ ∈ T < sub > f ( x )</ sub >< sup >*</ sup > N and X < sub > x </ sub > ∈ T < sub > x </ sub > M.
In cells with a nucleus ( eukaryotes ), the cell cycle can be divided in two periods: interphase — during which the cell grows, accumulating nutrients needed for mitosis and duplicating its DNA — and the mitosis ( M ) phase, during which the cell splits itself into two distinct cells, often called " daughter cells " and the final phase, cytokinesis, where the new cell is completely divided.
The town behind the front where George spends much of his time is referred to as M ---.
For example an electrochemical cell, where two copper electrodes are submerged in two copper ( II ) sulfate solutions, whose concentrations are 0. 05 M and 2. 0 M, connected through a salt bridge.
where p is pressure, ρ is density, R < sub > u </ sub > is the gas constant, M is the molar mass and T is temperature.
Other games which feature graffiti include Bomb the World ( 2004 ), an online graffiti simulation created by graffiti artist Klark Kent where users can virtually paint trains at 20 locations worldwide, and Super Mario Sunshine ( 2002 ), in which the hero, Mario must clean the city of graffiti left by the villain, Bowser Jr. in a plotline which evokes the successes of the Anti-Graffiti Task Force of New York's Mayor Rudolph Giuliani ( a manifestation of " broken window theory ") or those of the " Graffiti Blasters " of Chicago's Mayor Richard M. Daley.
All Mersenne primes are in the form M < sub > q </ sub >, where q is the ( prime ) exponent.
where ' is the rest mass of the electron, and M is the mass of the atomic nucleus.

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.
t < sub > r </ sub > * BW = 0. 35, where t < sub > r </ sub > is rise time in seconds and BW is bandwidth in Hz.
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 h ( 0 ) is the height at r = 0 ( the axis ).
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 >
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
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 | =is the magnitude of the velocity ( the speed ).
where it already is established that α = ρ.

where and δ
where α > − 1, δ < sub > m, n </ sub > is the Kronecker delta, and u < sub > α, m </ sub > is the m-th zero of J < sub > α </ sub >( x ).
for α > − 1 / 2 and where δ is the Dirac delta function.
where E is the electric field and δ < sup > 3 </ sup > is the 3-dimensional delta function.
where δ is the Dirac delta function.
The Lindemann criterion states that melting occurs because of vibrational instability, e. g. crystals melt when the average amplitude of thermal vibrations of atoms is relatively high compared with interatomic distances, e. g. < δu < sup > 2 </ sup >> 1 / 2 > δ < sub > L </ sub > R < sub > s </ sub >, where δu is the atomic displacement, the Lindemann parameter δ < sub > L </ sub >0. 20 ... 0. 25 and R < sub > s </ sub > is a half of the inter-atomic distance.
The RNA fragments are then removed by DNA polymerase I for prokaryotes or DNA polymerase δ for eukaryotes ( different mechanisms are used in eukaryotes and prokaryotes ) and new deoxyribonucleotides are added to fill the gaps where the RNA was present.
In virus species with reverse transcriptase lacking DNA-dependent DNA polymerase activity, creation of double-stranded DNA can possibly be done by host-encoded DNA polymerase δ, mistaking the viral DNA-RNA for a primer and synthesizing a double-stranded DNA by similar mechanism as in primer removal, where the newly synthesized DNA displaces the original RNA template.
where δ ( E < sub > ψ </ sub >– E < sub > χ </ sub >) restricts tunneling to occur only between electron levels with the same energy.
where μ < sub > α </ sub > and μ < sub > δ </ sub > are the components of proper motion in the R. A. and Declination, respectively, and δ is the Declination.
where λ is the wavelength of the waves that are focused for imaging, D the entrance pupil diameter of the imaging system, in the same units, and the angular resolution δ is in radians.
The δ < sup > 18 </ sup > O of coraline red algae provides a useful proxy of sea surface temperature at high latitudes, where many traditional techniques are limited.
Generally, unless both the objective function and the feasible region are convex in a minimization problem, there may be several local minima, where a local minimum x < sup >*</ sup > is defined as a point for which there exists some δ > 0 so that for all x such that
Carbon from this type of clathrate is isotopically heavier ( δ < sup > 13 </ sup > C is-29 to-57 ‰) and is thought to have migrated upwards from deep sediments, where methane was formed by thermal decomposition of organic matter.
where δ equals Rasalgheti's angular diameter in arcseconds, d < sub > R </ sub > the star's diameter in AU, and D < sub > R </ sub > the Distance from Earth in parsecs.
( where δ < sub > mn </ sub > denotes the Kronecker delta, equal to 1 if m = n and to 0 otherwise ).
: An automaton is represented formally by a 5-tuple ( Q, Σ, δ, q < sub > 0 </ sub >, F ), where:
: A sequence of states q < sub > 0 </ sub >, q < sub > 1 </ sub >, q < sub > 2 </ sub >,...., q < sub > n </ sub >, where q < sub > i </ sub > ∈ Q such that q < sub > 0 </ sub > is the start state and q < sub > i </ sub > = δ ( q < sub > i-1 </ sub >, a < sub > i </ sub >) for 0 < i ≤ n, is a run of the automaton on an input word w
Since only the positions in space – time are being warped, not the fields, the Ψ are all zero and the X < sub > μ </ sub >< sup > ν </ sup > equal the Kronecker delta δ < sub > μ </ sub >< sup > ν </ sup >, where we have used μ instead of r for the index.
The EDM is defined through the shift in the energy of a state when it is put in an external electric field: Δe = d · E + E · δ · E, where d is called the EDM and δ, the induced dipole moment.
where Kronecker delta δ < sub > ij </ sub > is a piecewise function of variables and.
The associated charge density is( r ), where δ ( r ) is the Dirac delta function.
where δ ( Greek lower case delta ) means a small change.

0.164 seconds.