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Page "Cauchy distribution" ¶ 74
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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 wrapped
If the visible spectrum is wrapped to form a color wheel, magenta ( additive secondary ) appears midway between red and violet:
If the way that DNA is wrapped around the histones changes, gene expression can change as well.
If the coil of wire is wrapped around a material with no special magnetic properties ( e. g., cardboard ), it will tend to generate a very weak field.
This identification is taken up by later writers such as Camões (" If in Summanus ' gloomy realm / Severest punishment you now endure …") and Milton, in a simile to describe Satan visiting Rome: " Just so Summanus, wrapped in a smoking whirlwind of blue flame, falls upon people and cities ".
If a datatype is recursive, the entire sum of products is wrapped in a recursive type, and each constructor also rolls the datatype into the recursive type.
If left supported only by rope or webbing wrapped around the waist, the diaphragm could be constricted and many climbers died as a result of asphyxiation.
If the bands become wrapped around the head or umbilical cord it can be life threatening for the fetus.
If a silver coin were to be soaked in that blood and wrapped in cloth, it would become an amulet offering permanent protection from any shtriga.

If and Cauchy
If is the Cauchy stress, then
If are independent and identically distributed random variables, each with a standard Cauchy distribution, then the sample mean has the same standard Cauchy distribution ( the sample median, which is not affected by extreme values, can be used as a measure of central tendency ).
If X is Cauchy distributed with median μ and scale parameter γ, then the complex variable
If φ is C < sup > k </ sup >, then the inhomogeneous equation is explicitly solvable in any bounded domain D, provided φ is continuous on the closure of D. Indeed, by the Cauchy integral formula,
If is continuous in an open set Ω and the partial derivatives of ƒ with respect to x and y exist in Ω, and satisfies the Cauchy – Riemann equations throughout Ω, then ƒ is holomorphic ( and thus analytic ).
* 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.
This is a Cauchy sequence of rational numbers, but it does not converge towards any rational limit: If the sequence did have a limit x, then necessarily x < sup > 2 </ sup > = 2, yet no rational number has this property.
If a complex function = is holomorphic, then u and v have first partial derivatives with respect to x and y, and satisfy the Cauchy – Riemann equations:
If f = u + iv, then the Cauchy – Riemann equations state that
If the Cauchy surface were noncompact, then the image has a boundary.
:: Loopholes: If closed timelike curves exist, then timelike curves don't have to intersect the partial Cauchy surface.
If the Cauchy surface were compact, i. e. space is compact, the null geodesic generators of the boundary can intersect everywhere because they can intersect on the other side of space.
If we have a space where Cauchy sequences are meaningful ( such as a ` rational ' metric space, i. e., a space in which distance is defined and takes rational values, or more generally a uniform space ), a standard procedure to force all Cauchy sequences to converge is adding new points to the space ( a process called completion ).
If the boundary has the form of a curve or surface that gives a value to the normal derivative and the problem itself then it is a Cauchy boundary condition.
If the integral were absolutely convergent we would have that its Cauchy principal value, that is, the limit
# If u and v are solutions of the Cauchy – Riemann equations, then u is a solution of the Laplace equation
If we can assume that the spacetime inside the Cauchy horizon violates AWEC, then the horizon becomes stable and frequency boosting effects would be canceled out by the tendency of the spacetime to act as a divergent lens.
* A field F is complete if there is no ordered field K properly containing F such that F is dense in K. If the cofinality of K is κ, this is equivalent to saying Cauchy sequences indexed by κ are convergent in F.
If F and f < sub > j </ sub > are analytic functions near 0, then the non-linear Cauchy problem
If there are no closed timelike curves, then given a partial Cauchy surface and if, the entire manifold, then is a Cauchy surface.

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