* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

* 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 this limit exists, then it may be computed by taking the limit as h → 0 along the real axis or imaginary axis ; in either case it should give the same result.

If h is negative, then a + h is on the low part of the step, so the secant line from a to a + h is very steep, and as h tends to zero the slope tends to infinity.

If h is positive, then a + h is on the high part of the step, so the secant line from a to a + h has slope zero.

If K is a subset of ker ( f ) then there exists a unique homomorphism h: G / K → H such that f = h φ.

If G is a group and X is a set then a group action may be defined as a group homomorphism h from G to the symmetric group of X.

If the minibus exceeds 100 km / h, the beeping will turn into a sustained tone.

If a spatial extra dimension is of radius R, the invariant mass of such standing waves would be M < sub > n </ sub > = nh / Rc with n an integer, h being Planck's constant and c the speed of light.

If c, h, and e were all changed so that the values they have in metric ( or any other ) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our World.

If the areas of the two parallel faces are A < sub > 1 </ sub > and A < sub > 3 </ sub >, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A < sub > 2 </ sub >, and the height ( the distance between the two parallel faces ) is h, then the volume of the prismatoid is given by ( This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.

: If we are given h ( x )= g ( f < sub > 1 </ sub >( x ), ..., f < sub > m </ sub >( x ) )

⟨ H ⟩, be the group generated by H. Then the word problem in H < sup >*</ sup > is solvable: given two words h, k in the generators H of H < sup >*</ sup >, write them as words in X and compare them using the solution to the word problem in G. It is easy to think that this demonstrates a uniform solution the word problem for the class K ( say ) of finitely generated groups that can be embedded in G. If this were the case the non-existence of a universal solvable word problem group would follow easily from Boone-Rogers.

If h has a fixed ( non-zero ) value instead of approaching zero, then the right-hand side of the above equation would be written

If ~ is a unary operation, then h (~ x ) = ~ h ( x ).

If * is a binary operation, then h ( x * y ) = h ( x ) * h ( y ).

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 he is not told which of four or five readings was meant for him, he can more readily assess each item in a larger frame: `` Does that statement really sound as if it were for me, significant in my particular life??

If we look about the world today, we can see clearly that there are two especially significant factors shaping the future of our civilization: science and religion.

Naamani Tarkow has written: " If one is to make sweeping statements, one may say that, save Magna Carta ( more truly, its implications ), the Act of Settlement is probably the most significant statute in English history ".

If the rider plans a significant amount of hillclimbing, a triple-crank ( three chainrings ) front gear system may be preferred.

If the core becomes sufficiently dense, electron degeneracy pressure will play a significant part in stabilizing it against gravitational collapse.

If there is a significant ( greater than 10 %) difference between cylinders, that may be an indication that valves or cylinder head gaskets are leaking, piston rings are worn or that the block is cracked.

If the test was true, the value one is written to the least significant bit of the destination register to indicate the condition.

If a project plan contains a significant portion of LOE, and the LOE is intermixed with discrete effort, EVM results will be contaminated.

If high output powers are needed from a class-A circuit, the power waste ( and the accompanying heat ) will become significant.

If a significant amount of greens work is required in a film, then the Greens may be an identifiable sub-department, with its own team-often of a size numbering double figures-and hierarchy ( eg.

If this happens rapidly before significant decay to the organic tissue, very fine three-dimensional morphological detail can be preserved.

If drain-to-source voltage is increased, this creates a significant asymmetrical change in the shape of the channel due to a gradient of voltage potential from source to drain.

If the radix point is omitted then it is implicitly assumed to lie at the right ( least significant ) end of the string ( that is, the number is an integer ).

If an appropriate form of written text is made available before formal schooling begins, reading should be learned inductively, emerge naturally, and with no significant negative consequences.

If an orbit is about a planetary body with significant atmosphere, its orbit can decay because of drag.

If they had any significant level of non-organic parts then something as simple as an x-ray scan would show them not to be human ( unless their creators designed the non-organic parts to have almost exactly the same structure and density as the organic components they were replacing, which would be both infeasible and highly improbable but not completely out of the question ).

If a safety engineer then discovers significant safety problems late in the design process, correcting them can be very expensive.

If the thermistor is being used to measure the temperature of the environment, this electrical heating may introduce a significant error if a correction is not made.

If these limited provisions are significant, however, they may be printed as " notes " underneath related sections of the Code.

If water loss leads to a significant decline in turgor pressure, the cell will plasmolyze.

If the fuel is dense enough and hot enough, the fusion reaction rate will be high enough to burn a significant fraction of the fuel before it has dissipated.

* If the boat has an internal combustion engine anyway, then its alternator will provide significant charge when it is running.

If the most significant digit cannot take all values from 0 to 9 is often termed a fractional digit.

If this voltage is significant it can be reduced ( also reducing the inherent accuracy and precision of the measurement ) by using a higher current range.

If the beam does not fill more than a third of the beam profiler ’ s sensor area, then there will be a significant number of pixels at the edges of the sensor that register a small baseline value ( the background value ).