(" Frob " is a word in MIT slang, and appears as a prefix for invented words throughout many of Infocom's works.

To show the derivation clearly, we propose that the stress should be on the penultimate syllable, the second half of the word being pronounced like " ptosis " ( with the " p " silent ), which comes from the same root " to fall ", and is already used to describe the drooping of the upper eyelid.

( 2009, p. 189 ) Bliss complaints about his symbols “ being abused ” by the OCCC became so intense that the director of the OCCC told Bliss, on his 1974 visit, never to come back.

Since all probabilities p < sub > i </ sub > add up to one: p < sub > 1 </ sub > + p < sub > 2 </ sub > + ... + p < sub > k </ sub > = 1, the expected value can be viewed as the weighted average, with p < sub > i </ sub >’ s being the weights:

But when a man acts wrongly, nature is not to be blamed ; for what is wrong, takes place not according to nature, but contrary to nature, it being the work of choice, and not of nature ” ( The Christian Examiner, Volume One, published by James Miller, 1824 Edition, p. 66 )

The morphisms from the point p to the point q are equivalence classes of continuous paths from p to q, with two paths being equivalent if they are homotopic.

< p > In winter, the material has yang potency within it, so it remains active even after being kept from thirty to forty days.

* The ring of p-adic integers is the inverse limit of the rings Z / p < sup > n </ sup > Z ( see modular arithmetic ) with the index set being the natural numbers with the usual order, and the morphisms being " take remainder ".

#* Note: This fact provides a proof of the infinitude of primes distinct from Euclid's Theorem: if there were finitely many primes, with p being the largest, we reach an immediate contradiction since all primes dividing 2 < sup > p </ sup > − 1 must be larger than p .</ li >

He remains continuously optimistic ; even his being told to " p ** s off " by Victor is laughed off.

But across the country the term p. c., as it is commonly abbreviated, is being heard more and more in debates over what should be taught at the universities.

to call a user procedure ( n being the number of parameters, p the procedure's address ).

Frazer ( 2006: p. 106 ) in The Golden Bough tells us that, “ In modern Greece, when the foundation of a new building is being laid, it is the custom to kill a cock, a ram, or a lamb, and to let its blood flow on the foundation-stone ”.

My wife, after the absence of her terms for seven weeks, gave me hopes of her being with child, but on the last day of the year she hath them again .</ p >

Carol Christ used the term more substantially in " Laughter of Aphrodite " ( 1987 ), acknowledging that those who create thealogy cannot avoid being influenced by the categories and questions posed in Christian and Jewish theologies ( Christ 1987, p. xii ).

Medical activities involving the vagina, including examinations, administration of medicine, and inspection of discharges, are also referred to as being per vaginam ( or p. v.

Kittinger set unbeaten () world records for: high-altitude jump ; free-fall by falling 16. 0 miles ( 25. 7 kilometers ) before opening his parachute ; and the fastest speed attained by a human being without mechanical or chemical assistance, about 982 k. p. h ( 614 m. p. h .).

The finite fields are classified by size ; there is exactly one finite field up to isomorphism of size p < sup > k </ sup > for each prime p and positive integer k. Each finite field of size q is the splitting field of the polynomial x < sup > q </ sup > − x, and thus the fixed field of the Frobenius endomorphism which takes x to x < sup > q </ sup >.

Over the finite field with q = p < sup > r </ sup > elements, F < sub > q </ sub >, there is a unique quadratic extension field, F < sub > q² </ sub >, with order 2 automorphism ( the rth power of the Frobenius automorphism ).

In his first paper about characters ( 1896 ), Frobenius constructed the character table of the group of order ( 1 / 2 )( p < sup > 3 </ sup > − p ) for all odd primes p ( this group is simple provided p > 3 ).

Specifically, if K / Q is a finite Galois extension then to each ( positive ) prime p which does not ramify in K and to each prime ideal P lying over p in K there is a unique element g of Gal ( K / Q ) satisfying the condition g ( x ) = x < sup > p </ sup > ( mod P ) for all integers x of K. Varying P over p changes g into a conjugate ( and every conjugate of g occurs in this way ), so the conjugacy class of g in the Galois group is canonically associated to p. This is called the Frobenius conjugacy class of p and any element of

the conjugacy class is called a Frobenius element of p. If we take for K the mth cyclotomic field, whose Galois group over Q is the units modulo m ( and thus

is abelian, so conjugacy classes become elements ), then for p not dividing m the Frobenius class in the Galois group is p mod m. From this point of view,

Furthermore, if, and if the Frobenius endomorphism of F is an automorphism, g may be written as, and in particular, ; a contradiction of the irreducibility of f. Therefore, if F possesses an inseparable irreducible ( non-zero ) polynomial, then the Frobenius endomorphism of F cannot be an automorphism ( where F is assumed to have prime characteristic p ).

By the argument outlined in the above paragraphs, it follows that F is perfect if and only if F has characteristic zero, or F has ( non-zero ) prime characteristic p and the Frobenius endomorphism of F is an automorphism.

An alternative way to arrive at this conclusion is to use the identity which is valid in characteristic p ( and which is based on the same properties of binomial coefficients, and gives rise to the Frobenius endomorphism ), to compute the reduction modulo p of the quotient of polynomials:

The points of X that are defined over F < sub >< span > p < sup > n </ sup ></ span ></ sub > are those fixed by F < sup > n </ sup >, where F is the Frobenius automorphism in characteristic p.

* Either k has characteristic 0, or, when k has characteristic p > 0, the Frobenius endomorphism x → x < sup > p </ sup > is an automorphism of k

Since the early 20th century it has been commonly accepted that Old Irish Bel ( l ) taine is derived from a Common Celtic * belo-te ( p ) niâ, meaning " bright fire " ( where the element * belo-might be cognate with the English word bale in ' bale-fire ' meaning ' white ' or ' shining '; compare Anglo-Saxon bael, and Lithuanian / Latvian baltas / balts, found in the name of the Baltic ; in Slavic languages byelo or beloye also means ' white ', as in Беларусь ( White Russia or Belarus ) or Бе ́ лое мо ́ ре Sea ).

This ring is a field because it contains a multiplicative inverse for each element N other than zero ( an integer that, multiplied by the element modulo p yields 1 ), and it has a finite number of elements ( p ), making it a finite field.

In Z < sub >< var > p </ var ></ sub > for a prime number < var > p </ var >, one non-identity element can be replaced by any other, with corresponding changes in the other elements.

The smallest filter that contains a given element p is a principal filter and p is a principal element in this situation.

An element p of R is called prime element if it is neither zero nor a unit ( i. e., does not have a multiplicative inverse ) and satisfies the following requirement: given x and y in R such that p divides the product xy, then p divides x or y.

In mathematics, given a prime number p, a p-group is a periodic group in which each element has a power of p as its order: each element is of prime power order.

That is, for each element g of the group, there exists a nonnegative integer n such that g to the power p < sup > n </ sup > is equal to the identity element.

An element x in R is a unit if and only if all of its components are units, i. e. if and only if p < sub > i </ sub >( x ) is a unit in R < sub > i </ sub > for every i in I.

A product of more than one non-zero rings always has zero divisors: if x is an element of the product all of whose coordinates are zero except p < sub > i </ sub >( x ), and y is an element of the product with all coordinates zero except p < sub > j </ sub >( y ) ( with i ≠ j ), then xy

Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

Work-outs for the week are as follows: Plain Scotch, 3 ( by Scotch Victor ), Demon Law, 3 ( by Demon Hanover ), Coffee Royal, p ( by Royal Blackstone ) and Beauty Way, p, 3 ( by Demon Hanover ) in 25 ; ;

Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.

Note that we need not know the value of p, for the experiment to be binomial.

He also offers a conversion table ( see Cohen, 1988, p. 283 ) for eta squared ( η < sup > 2 </ sup >) where 0. 0099 constitutes a small effect, 0. 0588 a medium effect and 0. 1379 a large effect.

The natural allegiance and obedience is an incident inseparable to every subject, for as soon as they are born they owe by birthright allegiance and obedience to the Sovereign ( Ex p. Anderson ( 1861 ) 3 E & E 487 ).

::::::::::::- Christie wishing for an earlier exposure to Archaeology, a passage from An Autobiography ( 1984 ), p. 546

Since p ( x ) is irreducible, this means that p ( x ) = k ( x − a ), for some k ∈ F

In number theory, if P ( n ) is a property of positive integers, and if p ( N ) denotes the number of positive integers n less than N for which P ( n ) holds, and if

Under Ambrose's major influence, emperors Gratian, Valentinian II and Theodosius I carried on a persecution of Paganism .< ref name = " MacMullen1984p100 "> MacMullen ( 1984 ) p. 100: ‘ The law of June 391, issued by Theodosius [...] was issued from Milan and represented the will of its bishop, Ambrose ; for Theodosius — recently excommunicated by Ambrose, penitent, and very much under his influence < sup > 43 </ sup > — was no natural zealot.

Chinese languages treat these two phones differently ; for example in Mandarin, ( written b in Pinyin ) and ( written p ) contrast phonemically.

Then, p < sup > 2 </ sup > is the fraction of the population homozygous for the first allele, 2pq is the fraction of heterozygotes, and q < sup > 2 </ sup > is the fraction homozygous for the alternative allele.

His key contributions include topological tensor products of topological vector spaces, the theory of nuclear spaces as foundational for Schwartz distributions, and the application of L < sup > p </ sup > spaces in studying linear maps between topological vector spaces.

Since 1990, AIX has served as the primary operating system for the RS / 6000 series ( later renamed IBM eServer pSeries, then IBM System p, and now IBM Power Systems ).

Model theory generalizes the notion of algebraic extension to arbitrary theories: an embedding of M into N is called an algebraic extension if for every x in N there is a formula p with parameters in M, such that p ( x ) is true and the set

Ackermann's three-argument function,, is defined such that for p = 0, 1, 2, it reproduces the basic operations of addition, multiplication, and exponentiation as

and for p > 2 it extends these basic operations in a way that happens to be expressible in Knuth's up-arrow notation as

Ackermann's original three-argument function is defined recursively as follows for nonnegative integers m, n, and p:

Its spectral type is A0p ; the " p " stands for peculiar, as the spectrum of its light is characteristic of an Alpha2 Canum Venaticorum variable.

* For a finite field of prime order p, the algebraic closure is a countably infinite field which contains a copy of the field of order p < sup > n </ sup > for each positive integer n ( and is in fact the union of these copies ).