If we are to keep a right-handed coordinate system, into the page will be in the negative z direction.

* If ƒ ( z ) is locally integrable in an open domain Ω ⊂ C, and satisfies the Cauchy – Riemann equations weakly, then ƒ agrees almost everywhere with an analytic function in Ω.

If the axes are named x, y, and z, then the x coordinate is the distance from the plane defined by the y and z axes.

If the measurement result is + z, this means that immediately after measurement the system state undergoes an orthogonal projection of ψ onto the

* If V is a normed vector space with linear subspace U ( not necessarily closed ) and if z is an element of V not in the closure of U, then there exists a continuous linear map with ψ ( x ) = 0 for all x in U, ψ ( z ) = 1, and || ψ || = 1 / dist ( z, U ).

If the limit exists, we say that ƒ is complex-differentiable at the point z < sub > 0 </ sub >.

If ƒ is complex differentiable at every point z < sub > 0 </ sub > in an open set U, we say that ƒ is holomorphic on U. We say that ƒ is holomorphic at the point z < sub > 0 </ sub > if it is holomorphic on some neighborhood of z < sub > 0 </ sub >.

If two quarks have unaligned spins, the spin vectors add up to make a vector of length S = 0 and only one spin projection ( S < sub > z </ sub > = 0 ), called the spin-0 singlet.

Alice could send bits to Bob in the following way: If Alice wishes to transmit a " 0 ", she measures the spin of her electron in the z direction, collapsing Bob's state to either or.

* If x < y and y < z, then x < z.

* If x < y and z > 0, then xz < yz.

If λ represents wavelength and f represents frequency ( note, λf = c where c is the speed of light ), then z is defined by the equations:

If an electron of energy E is incident upon an energy barrier of height U ( z ), the electron wave function is a traveling wave solution,

:: If Alice wishes to transmit a ' 0 ', she measures the spin of her electron in the z direction, collapsing Bob's state to either | z +>< sub > B </ sub > or | z ->< sub > B </ sub >.

If the right-hand side is specified as a given function, f ( x, y, z ), i. e., if the whole equation is written as

If z is the vector, one has

If z is a complex number, written in polar form as

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 you use parking attendants, can they be replaced by automatic parking gates??

If you provide inter-plant transportation, can this be replaced by available public transportation??

If you have a full-time doctor now, can he be replaced with a part-time doctor or one who serves on a fee-per-case basis only??

If women replaced people, it would normally have dominant stress.

If the object point O is infinitely distant, u1 and u2 are to be replaced by h1 and h2, the perpendicular heights of incidence ; the sine condition then becomes sin u ' 1 / h1 = sin u ' 2 / h2.

If there is still a tie, each atom in each of the two lists is replaced with a sub-list of the other atoms bonded to it ( at distance 3 from the stereocenter ), the sub-lists are arranged in decreasing order of atomic number, and the entire structure is again compared atom by atom.

If this occurs, the oil will burn and has to be replaced.

If the toms are omitted completely, or the bass drum replaced by a pedal-operated beater on the bottom skin of a floor tom and the hanging toms omitted, in either case the result is a two-piece kit.

If the outcomes x < sub > i </ sub > are not equiprobable, then the simple average ought to be replaced with the weighted average, which takes into account the fact that some outcomes are more likely than the others.

If the plates are bolted to the comb, the reed plates can be replaced individually.

If just one plank has been replaced, will we say that the ship is a different ship?

If the circle is replaced by an ellipse, and rotated about the major axis, the shape becomes a prolate spheroid, rotated about the minor axis, an oblate spheroid.

If the object is present, any matched portion is replaced by the object via rules for replacement.

; Code factoring: If several sequences of code are identical, or can be parameterized or reordered to be identical, they can be replaced with calls to a shared subroutine.

:: If the repeaters in a network that is based upon the physical extended star topology are replaced with hubs or switches, then a hybrid network topology is created that is referred to as a physical hierarchical star topology, although some texts make no distinction between the two topologies.

* If lead-acid batteries are used, all cells in the formerly good parallel strings will begin to sulfate due to the inability for them to be fully recharged, resulting in the storage capacity of these cells being permanently damaged, even if the damaged cell in the one degraded string is eventually discovered and replaced with a new one.

If the Vikings had a great impact on Pictland and in Ireland, in Dál Riata, as in Northumbria, they appear to have entirely replaced the existing kingdom with a new entity.

If this path is shorter than the current shortest path recorded for < code >< var > v </ var ></ code >, that current path is replaced with this < code >< var > alt </ var ></ code > path.

If the news presenter wears blue clothes, his clothes will also be replaced with the background video.

If the color at a particular point on the screen matches ( either exactly, or in a range ), then the video at that point is replaced by the alternate background video.

If the order ≤ in the definition of monotonicity is replaced by the strict order <, then one obtains a stronger requirement.

If the printer's head cannot be removed, the printer itself will then need to be replaced.

If the sucrose ( or other sugar ) that is replaced has contributed to the texture of the product, then a bulking agent is often also needed.

If the load balancer is replaced or fails, this information may be lost, and assignments may need to be deleted after a timeout period or during periods of high load to avoid exceeding the space available for the assignment table.