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If g is large and b is small so that the angle is not negligible one can write the integral for the on-axis case ( P < sub > 1 </ sub > is at the center of the shadow ) as ( see ):
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If and g
If the above errors be eliminated, the two astigmatic surfaces united, and a sharp image obtained with a wide aperture — there remains the necessity to correct the curvature of the image surface, especially when the image is to be received upon a plane surface, e. g. in photography.
If, in an unsharp image, a patch of light corresponds to an object point, the center of gravity of the patch may be regarded as the image point, this being the point where the plane receiving the image, e. g., a focusing screen, intersects the ray passing through the middle of the stop.
If the creditworthiness of the issuer deteriorates ( e. g. rating downgrade ) and its credit spread widens, the bond price tends to move lower, but, in many cases, the call option part of the convertible bond moves higher ( since credit spread correlates with volatility ).
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.
If there are g ( E ) dE states with energy E to E + dE, then the Boltzmann distribution predicts a probability distribution for the energy:
If BCG is accidentally given to an immunocompromised patient ( e. g., an infant with SCID ), it can cause disseminated or life-threatening infection.
* If G is a locally compact Hausdorff topological group and μ its Haar measure, then the Banach space L < sup > 1 </ sup >( G ) of all μ-integrable functions on G becomes a Banach algebra under the convolution xy ( g ) = ∫ x ( h ) y ( h < sup >− 1 </ sup > g ) dμ ( h ) for x, y in L < sup > 1 </ sup >( G ).
If we attempt to use the above formula to compute the derivative of f at zero, then we must evaluate 1 / g ′( f ( 0 )).
If k, m, and n are 1, so that and, then the Jacobian matrices of f and g are.
If matrix support is polar ( e. g. paper, silica etc.
If the disk was not otherwise prepared with a custom format, ( e. g. for data disks ), 664 blocks would be free after formatting, giving 664 × 254 = 168, 656 bytes ( or almost 165 kB ) for user data.
If G is a group, and g is a fixed element of G, then the conjugation map
If is a constant, the solution is particularly simple, and describes, e. g., if, the exponential decay of radioactive material at the macroscopic level.
If f is a surjection and a ~ b ↔ f ( a ) = f ( b ), then g is a bijection.
Many results about plane figures are proved, e. g., If a triangle has two equal angles, then the sides subtended by the angles are equal.
If the gain is not constant, e. g., by clipping the output signal at the limits of its capabilities, the output signal will be distorted.
If we allow also the system boundary to move ( e. g. due to moving pistons ) we get a rather general form of the first law for open systems.
If there is another functional group at a carbon, it may be named with the Greek letter, e. g., the gamma-amine in gamma-aminobutanoic acid is on the third carbon of the carbon chain attached to the carboxylic acid group.
If f: A < sub > 1 </ sub > → A < sub > 2 </ sub > and g: B < sub > 1 </ sub > → B < sub > 2 </ sub > are morphisms in Ab, then the group homomorphism Hom ( f, g ): Hom ( A < sub > 2 </ sub >, B < sub > 1 </ sub >) → Hom ( A < sub > 1 </ sub >, B < sub > 2 </ sub >) is given by φ g o φ o f. See Hom functor.
If f: X < sub > 1 </ sub > → X < sub > 2 </ sub > and g: Y < sub > 1 </ sub > → Y < sub > 2 </ sub > are morphisms in C, then the group homomorphism Hom ( f, g ): Hom ( X < sub > 2 </ sub >, Y < sub > 1 </ sub >) → Hom ( X < sub > 1 </ sub >, Y < sub > 2 </ sub >) is given by φ g o φ o f.
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 large
If we are to believe the list of titles printed in Malraux's latest book, La Metamorphose Des Dieux, Vol. 1 ( ( 1957 ), he is still engaged in writing a large novel under his original title.
If the Dominican Republic achieves free, democratic government, it will be due in large part to the U.S. show of force that enabled President Balaguer to prevent a threatened restoration of Trujillo dictatorship.
If a nation wished to get a head start in physical fitness over all other nations, it would start its kindergarten students on a program of gymnastics the day they entered and thus eliminate a large number of the problems that plague American schools.
If, in a certain part of the range, it starts life 1 foot longer than do any of the other ( relatively large ) giants, and reaches maturity at, let us guess, 18 inches longer than the others, a quadrupling of the maturity length would result in a maximum of ( nearly ) 40 feet.
If tyrosine and a system generating hydrogen peroxide are added to a cell-free homogenate of the thyroid, large quantities of free mono-iodotyrosine can be formed ( Alexander, 1959 ).
If we thus spent our very first day in the midst of a large number of your people honoring a new hero and a great national achievement, our last day, to us at least, was equally impressive and very moving, even though the crowds were absent and there was almost complete silence.
If the resulting four kilobyte table size is too large for a given target platform, the table lookup operation can be performed with a single 256-entry 32-bit ( i. e. 1 kilobyte ) table by the use of circular rotates.
If there is much current, or the vessel is moving while dropping the anchor, it may " kite " or " skate " over the bottom due to the large fluke area acting as a sail or wing.
If a king held sway over a large kingdom, such as when the Mercians dominated the East Anglians, the relationship would have been more equal than in the case the Mercian dominance of the Hwicce, which was a comparatively small kingdom.
If we look at this situation from far above, so that we cannot see the supporters, we see the large balloon as a small object animated by erratic movement.
If a mutual is large, or is expected to grow if it can raise capital by a conversion, its managers derive more value from a conversion but do not suffer much loss of perks than if the bank were small.
If the addition operation produces a result too large for the CPU to handle, an arithmetic overflow flag in a flags register may also be set.
If the condition number is large, then the matrix is said to be ill-conditioned.
If, i. e., it has a large norm with each value of s, and if, then Y ( s ) is approximately equal to R ( s ) and the output closely tracks the reference input.
If the depletion layer is large enough to catch the whole shower or to stop a heavy particle, a fairly accurate measurement of the particle ’ s energy can be made, simply by measuring the charge conducted and without the complexity of a magnetic spectrometer, etc.
If the difference in vapor pressure between the two components A and B is large ( generally expressed as the difference in boiling points ), the mixture in the beginning of the distillation is highly enriched in component A, and when component A has distilled off, the boiling liquid is enriched in component B.
If the viewing distance is large compared with the separation of the slits ( the far field ), the phase difference can be found using the geometry shown in the figure below right.
If all layers of an image change regularly but a large number of layer still need to be composited ( such as in distributed rendering ), the commutativity of a compositing operator can still be exploited to speed up computation through parallelism even when there is no gain from pre-computation.
If the cell is growing rapidly, each complex also needs to transport about 6 newly assembled large and small ribosomal subunits per minute from the nucleus to the cytosol, where they are used to synthesize proteins.
If implemented using remainders of Euclidean division rather than subtractions, Euclid's algorithm computes the GCD of large numbers efficiently: it never requires more division steps than five times the number of digits ( base 10 ) of the smaller integer.
If a player is " easy to read " he very seldom will win large pots even when holding a very good hand.
If the number of counts is not very large, it is more accurate to measure the time interval for a predetermined number of occurrences, rather than the number of occurrences within a specified time.
If this were the restriction, planar graphs would require arbitrarily large numbers of colors.
If the depletion region expands to completely close the channel, the resistance of the channel from source to drain becomes large, and the FET is effectively turned off like a switch.
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