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If and Af
Note: If 1/2-inch panel board is used inside and out, or 5/8-inch one side and 3/8-inch the other, and 1/8-inch glass is used, stock lumber in Af, Af, and Af can be used in making the glass panels.
If the volume is the molal volume, then Af is obtained on a molal basis which is the customary terminology of the chemists.
If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.
If A is the major axis of an ellipsoid and B and C are the other two axes, the radius of curvature in the ab plane at the end of the axis Af, and the difference in pressure along the A and B axes is Af.
If it is assumed that the formula given by Lodge of cosec Af applies, the pressure difference along the major axes can be calculated from the angle of inclination of the major axis, and from this the interfacial tension can be calculated.
If the Af bond is linear then there are three reasonable positions for the hydrogen atoms: ( 1 ) The hydrogen atoms are centered and hence all lie on a sheet midway between the oxygen sheets ; ;
If such is the case, the particles within a distance of about Af of the Earth will have, relative to the Earth, a kinetic energy less than their potential energy and they will be captured into orbits about the Earth.
If the deficiency persists long enough, it is reasonable to suppose that the Af label will reflect the Af distribution in the thyroglobulin.
If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.
If the direct-sum decomposition ( A ) is valid, how can we get hold of the projections Af associated with the decomposition??
If Af, then Af is divisible by Af and so Af, i.e., Af.
If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.

If and denotes
If Af denotes the space of N times continuously differentiable functions, then the space V of solutions of this differential equation is a subspace of Af.
If D denotes the differentiation operator and P is the polynomial Af then V is the null space of the operator p (, ), because Af simply says Af.
If denotes the quantum state of a particle ( n ) with momentum p, spin J whose component in the z-direction is σ, then one has
* If M is some set and S denotes the set of all functions from M to M, then the operation of functional composition on S is associative:
Frege, however, did not conceive of objects as forming parts of senses: If a proper name denotes a non-existent object, it does not have a reference, hence concepts with no objects have no truth value in arguments.
Tensor products: If C denotes the category of vector spaces over a fixed field, with linear maps as morphisms, then the tensor product defines a functor C × C → C which is covariant in both arguments.
# If A is a cartesian product of intervals I < sub > 1 </ sub > × I < sub > 2 </ sub > × ... × I < sub > n </ sub >, then A is Lebesgue measurable and Here, | I | denotes the length of the interval I.
If denotes the state of the system at any one time t, the following Schrödinger equation holds:
* If R denotes the ring CY of polynomials in two variables with complex coefficients, then the ideal generated by the polynomial Y < sup > 2 </ sup > − X < sup > 3 </ sup > − X − 1 is a prime ideal ( see elliptic curve ).
* If the base field is C, then for all complex numbers λ, where denotes the complex conjugation of λ.
* If denotes the conjugate transpose of ( i. e., the adjoint of ), then
If the sender has nothing more to send, the line simply remains in the marking state ( as if a continuing series of stop bits ) until a later space denotes the start of the next character.
If the position was found to be r < sub > 0 </ sub > then in an interpretation satisfying CFD, the statistical population describing position and momentum would contain all pairs ( r < sub > 0 </ sub >, p ) for every possible momentum value p, whereas an interpretation that rejects counterfactual values completely would only have the pair ( r < sub > 0 </ sub >,⊥) where ⊥ denotes an undefined value.
If an origin is chosen, and denotes its image, then this means that for any vector:
If denotes the polarization vector of the wave exiting the waveplate, then this expression shows that the angle between and is − θ.
If the string is stretched between two points where x = 0 and x = L and u denotes the amplitude of the displacement of the string, then u satisfies the one-dimensional wave equation in the region where 0 < x < L and t is unlimited.
If the heuristic h satisfies the additional condition for every edge x, y of the graph ( where d denotes the length of that edge ), then h is called monotone, or consistent.
If A is n-by-n, B is m-by-m and denotes the k-by-k identity matrix then the Kronecker sum is defined by:
If Sym < sub > n </ sub > denotes the space of symmetric matrices and Skew < sub > n </ sub > the space of skew-symmetric matrices then since and
If the measures of correlation used are product-moment coefficients, the correlation matrix is the same as the covariance matrix of the standardized random variables X < sub > i </ sub > / σ ( X < sub > i </ sub >) for i = 1, ..., n. This applies to both the matrix of population correlations ( in which case " σ " is the population standard deviation ), and to the matrix of sample correlations ( in which case " σ " denotes the sample standard deviation ).
If denotes the total energy of a system, one may write
If Skew < sub > n </ sub > denotes the space of skew-symmetric matrices and Sym < sub > n </ sub > denotes the space of symmetric matrices and then since and
The conjecture is stated in terms of three positive integers, a, b and c ( whence comes the name ), which have no common factor and satisfy a + b = c. If d denotes the product of the distinct prime factors of abc, the conjecture essentially states that d cannot be much smaller than c.

If and net
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.
If a player does not lift, his only remaining option is to push the shuttlecock softly back to the net: in the forecourt this is called a netshot ; in the midcourt or rearcourt, it is often called a push or block.
If the rearcourt attacker plays a dropshot, his partner will move into the forecourt to threaten the net reply.
If the current account is in surplus, the country's net international asset position increases correspondingly.
If F ( r ) represents gravity, it is a negative term proportional to 1 / r < sup > 2 </ sup >, so the net acceleration in r in the rotating frame depends on a difference of reciprocal square and reciprocal cube terms, which are in balance in a circular orbit but otherwise typically not.
If these other charges and currents are comparable in size to the sources producing the above electromagnetic field, then a new net electromagnetic field will be produced.
If some of the magnetic ions subtract from the net magnetization ( if they are partially anti-aligned ), then the material is " ferrimagnetic ".
If the moments of the aligned and anti-aligned ions balance completely so as to have zero net magnetization, despite the magnetic ordering, then it is an antiferromagnet.
If necessary, a second net may be clasped to the back of the net on the inside.
If this rule is interpreted as saying that straight-line motion is an indication of zero net force, the rule does not identify inertial reference frames, because straight-line motion can be observed in a variety of frames.
If the rule is interpreted as defining an inertial frame, then we have to be able to determine when zero net force is applied.
If the net excitation received by a neuron over a short period of time is large enough, the neuron generates a brief pulse called an action potential, which originates at the soma and propagates rapidly along the axon, activating synapses onto other neurons as it goes.
If X is a topological space, a net in X is a function from some directed set A to X.
If A is a directed set, we often write a net from A to X in the form ( x < sub > α </ sub >), which expresses the fact that the element α in A is mapped to the element x < sub > α </ sub > in X.
If ( x < sub > α </ sub >) is a net from a directed set A into X, and if Y is a subset of X, then we say that ( x < sub > α </ sub >) is eventually in Y ( or residually in Y ) if there exists an α in A so that for every β in A with β ≥ α, the point x < sub > β </ sub > lies in Y.
If ( x < sub > α </ sub >) is a net in the topological space X, and x is an element of X, we say that the net converges towards x or has limit x and write
If the system is displaced from the equilibrium, there is a net restoring force on the mass, tending to bring it back to equilibrium.
If there was a net gain, one could in theory use a number of control nodes for which many hosts on the Internet form a distributed computing network completely unawares.
If the number of photons being amplified per unit time is greater than the number of photons being absorbed, then the net result is a continuously increasing number of photons being produced ; the laser medium is said to have a gain of greater than unity.
If the ground state has a higher population than the excited state ( N < sub > 1 </ sub > > N < sub > 2 </ sub >), the process of absorption dominates and there is a net attenuation of photons.
If the higher energy state has a greater population than the lower energy state ( N < sub > 1 </ sub > < N < sub > 2 </ sub >), then the emission process dominates, and light in the system undergoes a net increase in intensity.
If the rotor disk is to be tilted forward ( to gain forward velocity ), its rotation requires that the downward net force on the blade be applied roughly 90 degrees ( depending on blade configuration ) before, or when the blade is to one side of the pilot and rotating forward.

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