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If P is a d-dimensional unit hypercube whose vertices are the integer lattice points all of whose coordinates are 0 or 1, then the t-fold dilation of P is a cube with side length t, containing ( t + 1 )< sup > d </ sup > integer points.
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If and P
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 T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.
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 P, then Q.
If P is a program which outputs a string x, then P is a description of x.
* If the balance factor of P is-2 then the right subtree outweighs the left subtree of the given node, and the balance factor of the right child ( R ) must be checked.
* If the balance factor of R is-1, a single left rotation ( with P as the root ) is needed ( Right-Right case ).
* If the balance factor of P is 2, then the left subtree outweighs the right subtree of the given node, and the balance factor of the left child ( L ) must be checked.
* If the balance factor of L is + 1, a single right rotation ( with P as the root ) is needed ( Left-Left case ).
If we assume the controller C, the plant P, and the sensor F are linear and time-invariant ( i. e., elements of their transfer function C ( s ), P ( s ), and F ( s ) do not depend on time ), the systems above can be analysed using the Laplace transform on the variables.
If either P or Q is true and P is false, then Q is true.
If the partial pressure of A at x < sub > 1 </ sub > is P < sub > A < sub > 1 </ sub ></ sub > and x < sub > 2 </ sub > is P < sub > A < sub > 2 </ sub ></ sub >, integration of above equation,
If ~ is an equivalence relation on X, and P ( x ) is a property of elements of X, such that whenever x ~ y, P ( x ) is true if P ( y ) is true, then the property P is said to be well-defined or a class invariant under the relation ~.
The well-known historian of physics, C. P. Snow, says about him, " If Fermi had been born a few years earlier, one could well imagine him discovering Rutherford's atomic nucleus, and then developing Bohr's theory of the hydrogen atom.
If the cause of the crash is uncertain, this number is rendered as 48454C50, which stands for " HELP " in hexadecimal ASCII characters ( 48 = H, 45 = E, 4C = L, 50 = P ).
If the quantity of powder stored for personal use exceeds 75 kg, then a Propellant Magazine Licence ( Type P ) is required.
If one chooses a critical value of the test statistic D < sub > α </ sub > such that P ( D < sub > n </ sub > > D < sub > α </ sub >)
If the base manifold is four-dimensional, the Kaluza – Klein manifold P is five-dimensional.
If and is
If the circumstances are faced frankly it is not reasonable to expect this to be true.
If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.
If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.
If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;
If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.
If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.
If it is an honest feeling, then why should she not yield to it??
If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.
If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.
If he is good, he may not be legal ; ;
If the man on the sidewalk is surprised at this question, it has served as an exclamation.
If the existent form is to be retained new factors that reinforce it must be introduced into the situation.
If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
If he is a traditionalist, he is an eclectic traditionalist.
If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.
If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.
If and d-dimensional
In a flat d-dimensional space M, at any given time, the configuration of two identical particles can be specified as an element of M × M. If there is no overlap between the particles, so that they do not interact ( at the same time, we are not referring to time delayed interactions here, which are mediated at the speed of light or slower ), then we are dealing with the space
Varopoulos ' theorem: If G is a graph satisfying a d-dimensional isoperimetric inequality then
If a polytope is d-dimensional, its facets are its ( d − 1 )- dimensional faces, its vertices are its 0-dimensional faces, its edges are its 1-dimensional faces, and its ridges are its ( d − 2 )- dimensional faces.
If and unit
If you have a house which heat doesn't penetrate easily, your unit will have less heat to remove.
If the retailer and hotelman's downtown unit sales have been decreasing, however, his dollar volume continues to rise, and it is dollars which you put in the bank.
* Corollary If X is a Banach space, then X is reflexive if and only if X ′ is reflexive, which is the case if and only if its unit ball is compact in the weak topology.
* Indivisibility of certain goods: If a person wants to buy a certain amount of another's goods, but only has for payment one indivisible unit of another good which is worth more than what the person wants to obtain, a barter transaction cannot occur.
If a Banach algebra has unit 1, then 1 cannot be a commutator ; i. e., for any x, y ∈ A.
If, for instance, an addition operation was requested, the arithmetic logic unit ( ALU ) will be connected to a set of inputs and a set of outputs.
If a player bets 1 unit on red, his chance of winning 1 unit is therefore 18 / 38 and his chance of losing 1 unit ( or winning-1 ) is 20 / 38.
If one chooses an infinite number of distinct points in the unit interval, then there must be some accumulation point in that interval.
If is any unit vector, the projection of the curl of F onto is defined to be the limiting value of a closed line integral in a plane orthogonal to as the path used in the integral becomes infinitesimally close to the point, divided by the area enclosed.
If is an outward pointing in-plane normal, whereas is the unit vector perpendicular to the plane ( see caption at right ), then the orientation of C is chosen so that a tangent vector to C is positively oriented if and only if forms a positively oriented basis for R < sup > 3 </ sup > ( right-hand rule ).
If the weight of the roadway per unit length is w and the weight of the cable and the wire supporting the bridge is negligible in comparison, then the weight on the cable from c to r is wx where x is the horizontal distance between c to r. Proceeding as before gives the differential equation
If one member ran away or married into another household or died, the rest of family continued to be responsible for the tax obligation of the family unit.
If measured instead per unit wavelength, using Wien's law, the peak is at 1. 06 mm corresponding to a frequency of 283 GHz.
If there is more than one allograph of a unit of writing, and the choice between them depends on context or on the preference of the author, they now have to be treated as separate glyphs, because mechanical arrangements have to be available to differentiate between them and to print whichever of them is required.
If testing showed that the central processing unit was working but the FPU was defective, the FPU's power and bus connections were destroyed with a laser and the chip was sold cheaper as an SX ; if the FPU worked it was sold as a DX.
If the monopolist practiced price discrimination he would sell the first unit for $ 50 the second unit for $ 40 and so on.
If the firm lowers price P < MC then it will be losing money on every unit sold.
: If the temperature T of a body is quantified as 300 kelvin ( in which T is the quantity symbol, 300 the value, and K is the unit ), this is written
: If a person weighs 120 pounds, then " 120 " is the numerical value and " pound " is the unit.
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 original rhombicuboctahedron has unit edge length, its dual strombic icositetrahedron has edge lengths
0.282 seconds.