query: when was ai n 't i a woman given

pos: Ain't I a Woman? Ain't I a Woman? "Ain't I a Woman?" is the name given to a speech, delivered extemporaneously, by Sojourner Truth, (1797–1883), born into slavery in New York State. Some time after gaining her freedom in 1827, she became a well known anti-slavery speaker. Her speech was delivered at the Women's Convention in Akron, Ohio, on May 29, 1851, and did not originally have a title. The speech was briefly reported in two contemporary newspapers, and a transcript of the speech was published in the "Anti-Slavery Bugle" on June 21, 1851. It received wider publicity in 1863 during the American Civil

neg: Covering groups of the alternating and symmetric groups has order "n"! except when "n" is 6 or 7, in which case the Schur cover has order 3⋅"n"!. Schur covers can be described using finite presentations. The symmetric group "S" has a presentation on "n"−1 generators "t" for "i" = 1, 2, ..., n−1 and relations These relations can be used to describe two non-isomorphic covers of the symmetric group. One covering group formula_1 has generators "z", "t", ..., "t" and relations: The same group formula_1 can be given the following presentation using the generators "z" and "s" given by "t" or "t""z" according as "i" is odd or

neg: Ancient Greek phonology and shortened. Five are prefixable vowels: "a, e, ē, o, ō". They are called prefixable because they form a complete syllable when prefixed before "i" and "y": for instance, "ai au". Two are suffixable: "i" and "y". And "y" is sometimes prefixable before "i", as in "myia" and "harpyia". Six are diphthongs: "ai au ei eu oi ou". The remaining seventeen letters are consonants [pronounced-with]: "b, g, d, z, th, k, l, m, n, x, p, r, s, t, ph, kh, ps". They are called consonants because they do not have a sound on their own, but they form a

neg: Lillian M. N. Stevens Beecher Stowe. And I think the greatest service of any woman of this day and generation. She was a wonder of intellect, moral and physical strength." In 1917, "The Little Water Girl" temperance fountain was donated to the City of Portland by the W. C. T. U. Designed by British sculptor George Wade for the Columbia Exposition at Chicago, this bronze copy was given to honor Lillian M. N. Stevens, 55-year-long resident of the city, and president of the Maine W. C. T. U., the National W. C. T. U., and benefactor of Portland. Originally installed at Congress Square, since

neg: Rice's theorem property), and is given in general below. The claim is that we can convert our algorithm for identifying squaring programs into one that identifies functions that halt. We will describe an algorithm that takes inputs "a" and "i" and determines whether program "a" halts when given input "i". The algorithm for deciding this is conceptually simple: it constructs (the description of) a new program "t" taking an argument "n", which (1) first executes program "a" on input "i" (both "a" and "i" being hard-coded into the definition of "t"), and (2) then returns the square of "n". If "a"("i") runs

neg: Origin hypotheses of the Croats of the ethnonym from adjectives "*xar-va(n)t" (feminine, rich in women), which derives from the etymology of Sarmatians, the Indo-Aryan "*sar-ma(n)t" (feminine), in both Indo-Iran adjective suffix "-ma(n)t/wa(n)t", and Indo-Aryan and Indo-Iranian word "*sar-" (woman), which in Iranian gives "*har". Another interpretation was given by the scholar Jevgenij Paščenko; he considered that the Croats were a heterogeneous group of people belonging to the Chernyakhov culture, a poly-ethnic cultural mélange of mostly Slavs and Sarmatians, but also Goths, Getae and Dacians. There was happening an interrelation between Slavic and Iranian language and culture, seen for example in the toponymy. As such, under

neg: Mara language K, L, M, N, NG, O, Ô, P, R, S, T, U, V, Z Mara Alphabet (small letters):a, aw, y, b, ch, d, e, f, h, i, k, l, m, n, ng, o, ô, p, r, s, t, u, v, z Mara diphthongs:ao, yu, ai, ei, ia, ie, ua The plural form of a noun is formed by affixing one of the following terms to the end of the noun: Words inside bracket were how a foreign author N.E. Parry (1937) wrote according to his understanding of the sound. But now the Maras have their own alphabet and the correct

neg: Schwarzschild's equation for radiative transfer a medium, "dI" = 0. In that situation, Schwarzschild’s equation simplifies to Planck's law: When "I" > "B"(T), "dI" is negative and when "I" < "B"(T), "dI" is positive. As a consequence, the intensity of radiation traveling through any medium is always approaching the blackbody intensity given by Planck's law and the local temperature. The rate of approach depends on the density of absorbing/emitting molecules (n) and their absorption cross-section ("σ"). When the intensity of the incoming radiation, "I", is much greater than the intensity of blackbody radiation, "B"("T"), the emission term can be neglected. This is usually the case

neg: Bislama from pseudo-French "bêche de mer", which has taken the form "besdemea", has become more popular. Its alphabet uses A, B, D, E, F, G, H, I, J, K, L, M, N, digraph NG, O, P, R, S, T, U, V, W, and Y; along with the "AE" and "AO". Before 1995, an older orthography had an "É", (now written E); "AI" and "AU" instead of "AE" and "AO". For hiatus, "AÏ" and "AÜ" (now written "AI" and "AU") were used, and "M̄" was used for , and "P̄" for – the orthography after 1995 has no diacritics and writes these

neg: Absorbing Markov chain where "N" is the diagonal matrix with the same diagonal as "N" and "N" is the Hadamard product of "N" with itself (i.e. each entry of "N" is squared). The expected number of steps before being absorbed when starting in transient state "i" is the "i"th entry of the vector where 1 is a length-"t" column vector whose entries are all 1. The variance on the number of steps before being absorbed when starting in transient state "i" is the "i"th entry of the vector where t is the Hadamard product of t with itself (i.e. each entry of t

neg: Time-slot interchange from a higher-level system design of the switching fabric. Hence the technology yielding T determines n for a given t. T also limits t for a given n. Real switching fabrics have real requirements for n and t, and therefore since T must be an actual number set by a possible technology, real switches cannot be arbitrarily large n or small t. In higher-speed switches, the limit from T can be halved by using a more expensive, less reliable two-port RAM. In these designs, the read and write usually occur at the same time. The switch must still arbitrate when

neg: Covering groups of the alternating and symmetric groups even: The other covering group formula_3 has generators "z", "t", ..., "t" and relations: The same group formula_3 can be given the following presentation using the generators "z" and "s" given by "t" or "t""z" according as "i" is odd or even: Sometimes all of the relations of the symmetric group are expressed as ("t""t") = 1, where "m" are non-negative integers, namely "m" = 1, "m" = 3, and "m" = 2, for 1 ≤ "i" < "i"+2 ≤ "j" ≤ "n"−1. The presentation of formula_1 becomes particularly simple in this form: ("t""t") = "z", and "zz" = 1.

neg: Sentience (EP) Sentience (EP) Sentience (stylised as S E N T I E N C E) is the debut extended play by electronic music producer 1788-L. It was released by Canadian record label Deadbeats on August 24, 2018. Four songs were released with the album, including two singles, "Full / Burst" with Totto, and "Nu / Ver / Ka". On July 25, 2018, 1788-L launched a website where someone could ask any questions to an AI. If asked certain questions, several details surrounding the extended play would be revealed, including the title, tracklist, that it would be released in August and the

neg: Coupon collector's problem grows as formula_1. For example, when "n" = 50 it takes about 225 trials on average to collect all 50 coupons. Let "T" be the time to collect all "n" coupons, and let "t" be the time to collect the "i"-th coupon after "i" − 1 coupons have been collected. Think of "T" and "t" as random variables. Observe that the probability of collecting a coupon is "p" = ("n" − ("i" − 1))/"n". Therefore, "t" has geometric distribution with expectation 1/"p". By the linearity of expectations we have: Here "H" is the "n"-th harmonic number. Using the asymptotics of

neg: Time value of money the contributions of "FV", the value of cash flow at time "t": Note that this series can be summed for a given value of "n", or when "n" is ∞. This is a very general formula, which leads to several important special cases given below. In this case the cash flow values remain the same throughout the "n" periods. The present value of an annuity (PVA) formula has four variables, each of which can be solved for by numerical methods: To get the PV of an annuity due, multiply the above equation by (1 + "i"). In this case each

neg: Absorbing Markov chain "Q". Summing this for all "k" (from 0 to ∞) yields the fundamental matrix, denoted by "N". It can be proven that where "I" is the "t"-by-"t" identity matrix. The ("i", "j") entry of matrix "N" is the expected number of times the chain is in state "j", given that the chain started in state "i". With the matrix "N" in hand, other properties of the Markov chain are easy to obtain. The variance on the number of visits to a transient state "j" with starting at a transient state "i" (before being absorbed) is the ("i","j")-entry of the matrix

neg: Teochew dialect Initial consonants of Teochew, are represented in the Guangdong Romanization system as: B, BH, C, D, G, GH, H, K, L, M, N, NG, P, R, S, T, and Z. "Examples": Vowels and vowel combinations in the Teochew dialect include: A, E, Ê, I, O, U, AI, AO, IA, IAO, IO, IU, OI, OU, UA, UAI, UE, and UI. "Examples:" Many words in Teochew are nasalized. This is represented by the letter "n" in the Guangdong Pengim system. "Example (nasalized)": Ending consonants in Teochew include M and NG as well as the stops discussed below. "Examples": Teochew retains many consonant

neg: Division algorithm := N D := D « n -- R and D need twice the word width of N and Q for i := n − 1 .. 0 do -- For example 31..0 for 32 bits end -- Where: N = Numerator, D = Denominator, n = #bits, R = Partial remainder, q(i) = bit #i of quotient The above restoring division algorithm can avoid the restoring step by saving the shifted value 2"R" before the subtraction in an additional register "T" (i.e., "T" = "R" « 1) and copying register "T" to "R" when the result of the subtraction

neg: Yaghan language Chile is as follows: a, æ, ch, e, ö, f, h, i, j, k, l, m, n, o, p, r, rh, s, š, t, u, w, x. A simplified orthography is a variant of the old Bridges system, created for online use on the Waata Chis discussion list on Yahoo Groups and elsewhere. It has tense and lax vowels as well as voiced and voiceless consonants. In the system, tenseness is marked by colon (:) following the vowel sign: a, a:, ai, au, e, e:, i, i:, iu:, o, o:, oi, u, u:, v (pronounced as a schwa, not ),

neg: Fortran 95 language features not allowed. However, we can achieve the same effect by defining a derived data type with a pointer as its sole component: TYPE row END TYPE and then defining arrays of this data type TYPE(row) :: s(n), t(n) where the storage for the rows can be allocated by, for instance, DO i = 1, n END DO The array assignment s = tis then equivalent to the pointer assignments s(i)%r => t(i)%r for all components. Given an array REAL, TARGET :: table(100,100) that is frequently referenced with the fixed subscripts table(m:n, p:q) these references may be replaced by REAL, DIMENSION(:,

neg: Virtual work "δW" associated with this nearby path, known as the "virtual work", can be computed to be If there are no constraints on the motion of "P", then 6 parameters are needed to completely describe "Ps position at any time "t". If there are "k" ("k" ≤ 6) constraint forces, then "n" = (6 - "k") parameters are needed. Hence, we can define "n" generalized coordinates "q" ("t") ("i" = 1, 2, ..., "n"), and express r("t") and "δr="εh"'("t") in terms of the generalized coordinates. That is, Then, the derivative of the variation "δr="εh("t") is given by then we have The

neg: Bass–Serre theory represented as a product of the form where "e", ..., "e" is a closed edge-path in "A" with the vertex sequence "v", "v", ..., "v" = "v" (that is "v"="o"("e"), "v" = "t"("e") and "v" = "t"("e") = "o"("e") for 0 < "i" < "n") and where formula_16 for "i" = 0, ..., "n". Suppose that "g" = 1 in "G". Then The normal forms theorem immediately implies that the canonical homomorphisms "A" → π(A, "T") are injective, so that we can think of the vertex groups "A" as subgroups of "G". Higgins has given a nice version of the

neg: Chaka Khan "Drum ' n voice 3". In 2010, she contributed to vocals for Beverley Knight's "Soul Survivor", collaborated with Clay Aiken on a song for the kids show "Phineas and Ferb", and performed two songs with Japanese singer Ai on Ai's latest album "The Last Ai". Khan continues to perform to packed audiences both in her native United States and overseas. On May 19, 2011, Khan was given the 2,440th Hollywood Walk of Fame star plaque on a section of Hollywood Boulevard in Los Angeles. Her family was present when the singer accepted the honor, as was Stevie Wonder, who had

neg: Normal (geometry) formula_4. For a hyperplane in "n"+1 dimensions, given by the equation where a is a point on the hyperplane and a for "i" = 1, ..., "n" are non-parallel vectors lying on the hyperplane, a normal to the hyperplane is any vector in the null space of "A" where "A" is given by That is, any vector orthogonal to all in-plane vectors is by definition a surface normal. If a (possibly non-flat) surface "S" is parameterized by a system of curvilinear coordinates x("s", "t"), with "s" and "t" real variables, then a normal is given by the cross product of

neg: Superspace R, which contains one real direction "t" identified with time and "N" complex Grassmann directions which are spanned by Θ and Θ, where "i" runs from 1 to "N". Consider the special case "N" = 1. The superspace R is a 3-dimensional vector space. A given coordinate therefore may be written as a triple ("t", Θ, Θ). The coordinates form a Lie superalgebra, in which the gradation degree of "t" is even and that of Θ and Θ is odd. This means that a bracket may be defined between any two elements of this vector space, and that this bracket

neg: Orchard-planting problem "t"("n") to be the maximum number of 3-point lines attainable with a configuration of "n" points. For an arbitrary number of points, "n", "t"("n") was shown to be (1/6)"n" − O(n) in 1974. The first few values of "t"("n") are given in the following table . Since no two lines may share two distinct points, a trivial upper-bound for the number of 3-point lines determined by "n" points is Using the fact that the number of 2-point lines is at least 6"n"/13 , this upper bound can be lowered to Lower bounds for "t"("n") are given by constructions for sets

neg: Grille (cryptography) messages are filled with null letters (i.e., padding). Messages longer than 64 letters require another turn of the board and another sheet of paper. If the plaintext is too short, each square must be filled up entirely with nulls. J M T H H D L I S I Y P S L U I A O W A E T I E E N W A P D E N E N E L G O O N N A I T E E F N K E R L O O N D D N T T E

neg: Poincaré duality vertices of formula_13. Then formula_15 is defined to be the convex hull (in formula_13) of the barycentres of all subsets of the vertices of formula_13 that contain formula_18. One can check that if "S" is "i"-dimensional, then "DS" is an ("n" − "i")-dimensional cell. Moreover, the dual cells to "T" form a CW-decomposition of "M", and the only ("n" − i)-dimensional dual cell that intersects an "i"-cell "S" is "DS". Thus the pairing formula_19 given by taking intersections induces an isomorphism formula_20, where formula_21 is the cellular homology of the triangulation "T", and formula_22 and formula_23 are the cellular homologies

neg: Ethnographic film film, later housed in the National Museum at Victoria. In the 1930s, Gregory Bateson and Margaret Mead discovered that using film frame-by-frame was an essential component of documenting complex rituals in Bali and New Guinea. John Marshall made what is likely the most-viewed ethnographic film in American colleges ("The Hunters"), his filming of the Ju/'hoansi of the Kalahari (the !Kung-San) that spans from 1951 to 2000. His ethnographic film "N!ai, the Story of a !Kung Woman" is not only ethnography but also a biography of the central character, N!ai, incorporating footage from her childhood through adulthood. Marshall ended his career

neg: Dusun language E, F, Q, and X are not used except in loanwords): A B D G H I K L M N O P R S T U V W Y Z These characters together are called "Pimato". Semivowels /w j/ and rhotic /r/ only occur in most of the other dialects of the Dusun/Kadazan languages. Forschner (1978) and Antonissen (1958) list two fricatives /v z/ for the Rungus and Penampang Kadazan dialects. [x] is also listed as an allophone of /k/ in word-medial position. The vowels are divided into: Simple vowels: /i u a o/ Diphthongs: "aa ai" (sometimes pronounced

neg: K. N. Singh became legendary – so much so that on one occasion (in his own words) "Even off-screen I was a bad man. One day on my way back from shooting, I had to deliver an envelope at an address given to me by my friend. I pressed the doorbell and, from the moving curtains, I could see a woman hurrying to open the door. When she saw me standing in front of her, she screamed out in fright and ran inside leaving the door open." As an actor, Singh's thirst for learning was legendary. For example, he studied the style and

neg: Regular paperfolding sequence approaches the dragon curve fractal. For instance the following curve is given by folding a strip four times to the right and then unfolding to give right angles, this gives the first 15 terms of the sequence when 1 represents a right turn and 0 represents a left turn. Starting at "n" = 1, the first few terms of the regular paperfolding sequence are: The value of any given term "t" in the regular paperfolding sequence can be found recursively as follows. If "n" = "m"·2 where "m" is odd then Thus "t" = "t" = 0 but "t" =

neg: Hawaiian language in the following chart. This writing system was developed by American Protestant missionaries during 1820–1826. It was the first thing they ever printed in Hawaii, on January 7, 1822, and it originally included the consonants "B, D, R, T," and "V," in addition to the current ones ("H, K, L, M, N, P, W"), and it had "F, G, S, Y" and "Z" for "spelling foreign words". The initial printing also showed the five vowel letters ("A, E, I, O, U") and seven of the short diphthongs ("AE, AI, AO, AU, EI, EU, OU"). In 1826, the developers voted to

neg: Minimum mean square error recursive expression can be derived when at each "t"-th time instant the underlying linear observation process yields a scalar such that formula_183, where formula_184 is 1-by-"n" known row vector whose values can change with time, formula_185 is "n"-by-1 random column vector to be estimated, and formula_186 is scalar noise term with variance formula_187. After ("t"+1)-th observation, the direct use of above recursive equations give the expression for the estimate formula_188 as: where formula_190 is the new scalar observation and the gain factor formula_191 is "n"-by-1 column vector given by The formula_193 is "n"-by-"n" error covariance matrix given by Here, no

neg: Buzen's algorithm is a significant improvement and allows for computations to be performed with much larger networks. Consider a closed queueing network with "M" service facilities and "N" circulating customers. Write "n"("t") for the number of customers present at the "i"th facility at time "t", such that formula_2. We assume that the service time for a customer at the "i"th facility is given by an exponentially distributed random variable with parameter "μ" and that after completing service at the "i"th facility a customer will proceed to the "j"th facility with probability "p". It follows from the Gordon–Newell theorem that the equilibrium distribution

neg: Morane-Saulnier AI AI, formerly flown by Charles Nungesser is in the Old Rhinebeck Aerodrome collection, and was flown in the weekend airshows there. Morane-Saulnier AI The Morane-Saulnier AI (also Type AI) was a French parasol-wing fighter aircraft produced by Morane-Saulnier during World War I. The AI was developed as a refinement of the Morane-Saulnier Type N concept, and was intended to replace the Nieuport 17 and SPAD VII in French service, in competition with the SPAD XIII, which it was built as a back-up for. Its Gnome Monosoupape "9N" 160 CV rotary engine was mounted in a circular open-front cowling. The strut

neg: You Got to Move Vastine said, 'I see my name,' and she went down the list and she took the ruler from me and she said, 'That's Anna, that's my first name.' And then she went over on the other side up and down 'til she found Vastine and said, 'That's my name, V-A-S-T-I-N-E ,Vastine.' And goose pimples just came out all over me, because that woman couldn't read or write when she came in there. She was 65 years old." Bernice Johnson Reagon A college student who participated in challenging the legality of segregated public facilities in her hometown of Albany, Georgia—a student

neg: T. N. Sadalakshmi T. N. Sadalakshmi Takella. N. Sadalakshmi (1928–2004) was the first Dalit woman legislator of Telangana Sadalakshmi was born at Pensionpura in Hyderabad. She studied at Keyes High School and had begun a course in medicine in Madras when she heard B. R. Ambedkar deliver a speech at Jeera Compound. She decided then to abandon medicine in favour of politics. Sadalakshmi was first elected from the Peddapalli constituency and subsequently from that of Kamareddy. She rose to become deputy speaker of the Andhra Pradesh Legislative Assembly. In 1962, Sadalakshmi was elected to the state assembly from Yellareddy assembly constituency. She became

neg: Holomorphic functional calculus a square matrix with complex entries, a case which will be used to illustrate functional calculus and provide some heuristic insights for the assumptions involved in the general construction. In this section "T" will be assumed to be a "n" × "n" matrix with complex entries. If a given function "f" is of certain special type, there are natural ways of defining "f"("T"). For instance, if is a complex polynomial, one can simply substitute "T" for "z" and define where "T" = "I", the identity matrix. This is the polynomial functional calculus. It is a homomorphism from the ring of

neg: Work (physics) 1, ..., "n" are defined by the movement of the rigid body. This movement is given by the set of rotations ["A"("t")] and the trajectory d("t") of a reference point in the body. Let the coordinates x "i" = 1, ..., "n" define these points in the moving rigid body's reference frame "M", so that the trajectories traced in the fixed frame "F" are given by The velocity of the points X along their trajectories are where ω is the angular velocity vector obtained from the skew symmetric matrix known as the angular velocity matrix. The small amount of work

neg: Square root of a matrix finitely many terms will be non-zero and It suffices to check uniqueness for a Jordan block with λ = 1. The square constructed above has the form "S" = "I" + "L" where "L" is polynomial in "N" without constant term. Any other square root "T" with positive eigenvalues has the form "T" = "I" + "M" with nilpotent, commuting with "N" and hence "L". But then . Since "L" and commute, the matrix is nilpotent and is invertible with inverse given by a Neumann series. Hence "L" = . If is a matrix with positive eigenvalues and minimal polynomial

neg: Morane-Saulnier AI Morane-Saulnier AI The Morane-Saulnier AI (also Type AI) was a French parasol-wing fighter aircraft produced by Morane-Saulnier during World War I. The AI was developed as a refinement of the Morane-Saulnier Type N concept, and was intended to replace the Nieuport 17 and SPAD VII in French service, in competition with the SPAD XIII, which it was built as a back-up for. Its Gnome Monosoupape "9N" 160 CV rotary engine was mounted in a circular open-front cowling. The strut braced parasol wing was swept back. The spars and ribs of the circular section fuselage were wood, wire-braced and covered in

neg: Process management (computing) a computer was allocated to a single user, the processor was idle; when the user was entering information or debugging programs for example. Computer scientists observed that overall performance of the machine could be improved by letting a different process use the processor whenever one process was waiting for input/output. In a "uni-programming system", if "N" users were to execute programs with individual execution times of "t", "t", ..., "t", then the total time, "t", to service the "N" processes (consecutively) of all "N" users would be: However, because each process consumes both CPU cycles and I/O cycles, the time

neg: Hurrian language presence of; from "āyi" "face"). "N-fa etīta" or "N-fa etīfa" (for, because of; from "eti" "body, person"), "N-fenē etiyē" (concerning), "N-fa furīta" (in sight of; from "furi", "sight, look"), and only in Hattusha "N-fa āpita" (in front of; from "āpi", "front"). Besides these, there is "ištani" "space between," which is used with a plural possessive pronoun and the locative, for "between us/you/them", e.g. "ištaniffaša" (between us, under us). Only a few sentence-initial particles are attested. In contract with nouns, which also end in /i/, the final vowel of the conjunctions "ai" (when) and "anammi" (therefore) is not dropped before an

neg: Self-phase modulation amount of dispersion. For an ultrashort pulse with a Gaussian shape and constant phase, the intensity at time "t" is given by "I"("t")": where "I" is the peak intensity, and τ is half the pulse duration. If the pulse is travelling in a medium, the optical Kerr effect produces a refractive index change with intensity: where "n" is the linear refractive index, and "n" is the second-order nonlinear refractive index of the medium. As the pulse propagates, the intensity at any one point in the medium rises and then falls as the pulse goes past. This will produce a time-varying

neg: Lumpability for any states "n,n’" in subset "t", where "q"("i,j") is the transition rate from state "i" to state "j". Similarly, for a stochastic matrix "P", "P" is a lumpable matrix on a partition "T" if and only if, for any subsets "t" and "t" in the partition, and for any states "n,n’" in subset "t", where "p"("i,j") is the probability of moving from state "i" to state "j". Consider the matrix and notice it is lumpable on the partition "t" = {(1,2),(3,4)} so we write and call "P" the lumped matrix of "P" on "t". In 2012, Katehakis and Smit

neg: Chern class × "n" matrices whose entries are polynomials in "t" with coefficients in the commutative algebra of even complex differential forms on "M". The curvature form Ω of "V" is defined as with ω the connection form and "d" the exterior derivative, or via the same expression in which ω is a gauge form for the gauge group of "V". The scalar "t" is used here only as an indeterminate to generate the sum from the determinant, and "I" denotes the "n" × "n" identity matrix. To say that the expression given is a "representative" of the Chern class indicates that

neg: Polynomial identity ring it is a T-ideal. Conversely, if "I" is a T-ideal of "F" then "F"/"I" is a PI-ring satisfying all identities in "I". It is assumed that "I" contains monic polynomials when PI-rings are required to satisfy monic polynomial identities. [[Category:Ring theory]] Polynomial identity ring In mathematics, in the subfield of ring theory, a ring "R" is a polynomial identity ring if there is, for some "N" > 0, an element "P" other than 0 of the free algebra, Z, over the ring of integers in "N" variables "X", "X", ..., "X" such that for all "N"-tuples "r", "r", ..., "r"

neg: Radiocarbon dating the sample, the less will be left. The equation governing the decay of a radioactive isotope is: where "N" is the number of atoms of the isotope in the original sample (at time "t" = 0, when the organism from which the sample was taken died), and "N" is the number of atoms left after time "t". "λ" is a constant that depends on the particular isotope; for a given isotope it is equal to the reciprocal of the mean-life – i.e. the average or expected time a given atom will survive before undergoing radioactive decay. The mean-life, denoted by

neg: T. N. Sadalakshmi Telugu Desam Party in 1982 at N. T. Rama Rao's insistence and was appointed to be the party's vice-president. She later left Telugu Desam Party to work for the Telangana Congress Party. Sadalakshmi was married to T. Venkata Narayana, a prominent Scheduled Caste leader. They had a son and two daughters. She died on 24 July 2004 at CARE Hospital due to a cardiac problem. She was cremated at Bansilalpet. T. N. Sadalakshmi Takella. N. Sadalakshmi (1928–2004) was the first Dalit woman legislator of Telangana Sadalakshmi was born at Pensionpura in Hyderabad. She studied at Keyes High School and had

neg: Vietnamese language variation section for further elaboration. The analysis of syllable-final orthographic "ch" and "nh" in Hanoi Vietnamese has had different analyses. One analysis has final "ch", "nh" as being phonemes contrasting with syllable-final "t", "c" and "n", "ng" and identifies final "ch" with the syllable-initial "ch" . The other analysis has final "ch" and "nh" as predictable allophonic variants of the velar phonemes and that occur after the upper front vowels "i" and "ê" ; although they also occur after "a", but in such cases are believed to have resulted from an earlier "e" which diphthongized to "ai" (cf. "ach" from

neg: The Phonetic Journal t, d; ç, j; k, g; f, v; [th], [dh], s, z; ʃ, ʒ; m, n, ŋ; l, r; w, y; h. Vowels: a, ɐ; e, ɛ; i, [ee]; o, [o]; γ, σ; u, ɥ. Diphthongs: ei , iu , ou , ai , oi . The alphabet also included 9 "foreign sounds", 7 from French and 2 from German. Isaac Pitman, the founder of the journal published "Phonotypy" in 1844, his major work on spelling reform just three years after the founding of the journal. Pitman and Alexander John Ellis, an English mathematician and philologist jointly proposed in 1845

neg: Enggano language Malay 1sg "aku ~ ku", 1. "kami", 1. "kita", 2pl "kalian", 3sg/pl "dia", and suffixes 1sg "-ku", 2sg "-mu", 3sg "-nya", with *k, *t (d), *l, *m, *n having shifted to "’, k, r, b, d" in Enggano, and with final consonants and (where possible) vowels being lost. The possessive suffixes appear on nouns, and they are often preceded by a vowel. Few forms are attested, but this vowel is "i" or "ai" after (as with 'bag' in the phonology section), an echo vowel after several other consonants, and with several words not predictable on current evidence: "’eam – ’ami’"

neg: Hall–Littlewood polynomials Hall–Littlewood polynomials In mathematics, the Hall–Littlewood polynomials are symmetric functions depending on a parameter "t" and a partition λ. They are Schur functions when "t" is 0 and monomial symmetric functions when "t" is 1 and are special cases of Macdonald polynomials. They were first defined indirectly by Philip Hall using the Hall algebra, and later defined directly by . The Hall–Littlewood polynomial "P" is defined by where λ is a partition of at most "n" with elements λ, and "m"("i") elements equal to "i", and "S" is the symmetric group of order "n"!. As an example, We have that

neg: Verifiable secret sharing polynomial interpolation modulo "p", but any set of at most "t" share holders cannot. (In fact, at this point any set of at most "t" share holders has no information about "s".) So far, this is exactly Shamir's scheme. To make these shares verifiable, the dealer distributes commitments to the coefficients of "P". If "P"("x") = "s" + "a""x" + ... + "a""x", then the commitments that must be given are: Once these are given, any party can verify their share. For instance, to verify that "v" = "P"("i") modulo "q", party "i" can check that formula_1. Once "n" shares

neg: Vertex operator algebra vertex superalgebra attached to the odd lattice Z. This correspondence has been used by Date-Jimbo-Kashiwara-Miwa to construct soliton solutions to the KP hierarchy of nonlinear PDEs. The Virasoro algebra has some supersymmetric extensions that naturally appear in superconformal field theory and superstring theory. The "N"=1, 2, and 4 superconformal algebras are of particular importance. Infinitesimal holomorphic superconformal transformations of a supercurve (with one even local coordinate "z" and "N" odd local coordinates θ...,θ) are generated by the coefficients of a super-stress–energy tensor "T"(z,θ...,θ). When "N"=1, "T" has odd part given by a Virasoro field "L"("z"), and even part given by

neg: Bingo (folk song) dog leapt over the stile, his name was little Bingo. B with an I — I with an N, N with a G — G with an O; his name was little Bingo: B—I—N—G—O! His name was little Bingo. The farmer loved a cup of good ale, he called it rare good stingo, the farmer loved a cup of good ale, he called it rare good stingo. S—T with an I — I with an N, N with a G — G with an O; He called it rare good stingo: S—T—I—N—G—O! He called it rare good stingo And is

neg: Boolean algebras canonically defined call it "u". So first prove "s" = "u" and "t" = "u" as above, that is, evaluate "s" and "t" using A1, R1, and R3, and then invoke R2 to infer "s" = "t". In A1, if we view the number "n" as the function type "m"→"n", and "m" as the application "m"("n"), we can reinterpret the numbers "i", "j", "ĵ", and "i""ĵ" as functions of type "i": ("m"→2)→2, "j": "m"→(("n"→2)→2), "ĵ": ("n"→2)→("m"→2), and "i""ĵ": ("n"→2)→2. The definition ("i""ĵ") = "i" in A1 then translates to ("i""ĵ")("v") = "i"("ĵ"("v")), that is, "i""ĵ" is defined to be composition of "i"

neg: Kadu language into the Chindwin Valley (Matisoff 2013:13). Kadu vowels consist of eight monophthongs and a diphthong /ai/. Kadu has 20 consonants. The final consonants need to be nasals /m, n, ŋ/ or voiceless stops /p, t, k, ʔ/. Kadu has three tones; high, mid, and low. CCVVC C: Consonant V: Vowel C: necessary, this can be any Kadu consonant except unvoiced nasals. C: optional, this can be only /l, w, y/. V: necessary, this can be any Kadu vowel, however, /ɘ/ appears only in the form of CɘC. V: optional. C: optional, this can be only /p, t, m, n, ʔ,

neg: Equidissection area of "K" is denoted "t"("K"). If "K" has an "n"-equidissection, then "t"("K") = 1; otherwise it is less than 1. The authors show that for a quadrilateral "K", "t"("K") ≥ 4"n"/(4"n" + 1), with "t"("K") = 8/9 if and only if "K" is affinely congruent to the trapezoid "T"(2/3). For a pentagon, "t"("K") ≥ 2/3, "t"("K") ≥ 3/4, and "t"("K") ≥ 2"n"/(2"n" + 1) for "n" ≥ 5. Günter M. Ziegler asked the converse problem in 2003: Given a dissection of the whole of a polygon into "n" triangles, how close can the triangle areas be to equal? In

neg: Abadi language they are given a Christian name. Marriage Traditionally, when discussing a marriage, a man would be required to be at least over 25 years of age and the woman over 20. The man would inform his parents of the woman he has chosen to marry and his parents would then conversate with the woman’s parents. If all parties agree, a bride price would take place before the ceremony begins. Bride prices are no longer common though the bride may request one. Writing System and Sounds The Adabi alphabet includes a, b, d, e, g, i, k, m, n, o, p,

neg: Financial correlation are student-t, Fréchet, and Marshall-Olkin. For an overview of these copulas, see Nelsen (2006). Hence, from equations (7) and (8) we derive the Gaussian default time copula CGD, In equation (9) the terms formula_58 map the cumulative default probabilities Q of asset i for time t, formula_55, percentile to percentile to standard normal. The mapped standard normal marginal distributions formula_60 are then joined to a single n-variate distribution formula_61 by applying the correlation structure of the multivariate normal distribution with correlation matrix R. The probability of n correlated defaults at time t is given by formula_61. Numerous non-academic articles have

neg: Two-body problem be solved exactly, the corresponding two-body problem can also be solved. By contrast, the three-body problem (and, more generally, the "n"-body problem for "n" ≥ 3) cannot be solved in terms of first integrals, except in special cases. Let x and x be the vector positions of the two bodies, and "m" and "m" be their masses. The goal is to determine the trajectories x("t") and x("t") for all times "t", given the initial positions x("t" = 0) and x("t" = 0) and the initial velocities v("t" = 0) and v("t" = 0). When applied to the two masses, Newton's

neg: Hyam language Vowels (Vawella̱ Sha̱kuup) a a̱ e e̱ i i̱ o u Long Vowels aa ee ii oo uu (Khwikhwir Vawel) ai au a̱u ou CONSONANTS b c d dh dz f g gy gb gh ghy h hw hwy hyw j k ky kh khy kp l m n nh ng ny p r s sh t th thn ts v w y yw z zh Hayab (2016:66) pinpoints, stating that "available data in Hyam by Koelle (1854: appendix, 2-188) and Meek (1931:120) reveals that the Ham contest in virtually a dissimilar way from what is obtained today." He added

neg: Level ancestor problem with a preprocessing algorithm of complexity O("n" log "n"). The preprocessing time is improved to O("n") by an application of the Method of Four Russians. Level ancestor problem In graph theory and theoretical computer science, the level ancestor problem is the problem of preprocessing a given rooted tree "T" into a data structure that can determine the ancestor of a given node at a given distance from the root of the tree. More precisely, let "T" be a rooted tree with "n" nodes, and let "v" be an arbitrary node of "T". The level ancestor query LA("v","d") requests the ancestor

neg: 102 JAMZ SuperJam Yang Twins, Chingy, Petey Pablo, J-Kwon, Trillville, Elephant Man and Crime Family T. I., Ying Yang Twins, Trillville, Boyz n da Hood and Young Jeezy SuperJam X took place Friday night, June 30, 2006, featuring T. I., Three 6 Mafia, Dem Franchize Boyz, Remy Ma, T-Pain, Yung Joc and Paul Wall. Celebrating 102 JAMZ' tenth anniversary, $10,000 was given away to a single winner. On stage activity included air personality/audience interaction, Mix Squad sets and the 102 JAMZ Dancers. The 11th annual show took place Friday night, June 29, 2007, with Young Jeezy, Yung Joc, Crime Mob, Ricky Ruckus, Lloyd,

neg: Exterior algebra a graded vector space from that on T("V"). It carries an associative graded product formula_94 defined by Although this product differs from the tensor product, the kernel of "Alt" is precisely the ideal "I" (again, assuming that "K" has characteristic 0), and there is a canonical isomorphism Suppose that "V" has finite dimension "n", and that a basis of "V" is given. then any alternating tensor can be written in index notation as where "t" is completely antisymmetric in its indices. The exterior product of two alternating tensors "t" and "s" of ranks "r" and "p" is given by The

neg: Cheap talk messages are constant: for "t(N) < t < t(N), µ(t) = m". Actions. Since actions are functions of messages, actions are also constant over these intervals: for "t(N) < t < t(N)", "α(t) = α(m) = a". The action function is now indirectly characterized by the fact that each value "a" optimizes return for the "R", knowing that "t" is between "t" and "t". Mathematically (assuming that "t" is uniformly distributed over [0, 1]), formula_3 → "Quadratic utilities:" Given that "R" knows that "t"is between "t" and "t", and in the special case quadratic utility where "R" wants action "a"

neg: Lillian M. N. Stevens refugees in Portland. When Lillian M. N. Stevens died of kidney failure on April 6, 1914, Gov. William Thomas Haines of Maine promptly reflected the public's response. "I have ordered the flag at half staff in recognition of the respect in which I know this great woman was held by all the people of Maine." It is believed this was the first time the flag was so lowered for any woman in Maine. Gov. Haines summarized her significance. "Mrs. Stevens has rendered a greater service to mankind than any woman who ever lived in Maine, with possibly one exception, Harriet

neg: Light's associativity test For each "t" in "T", let "L"("t") be the "m" × "n" matrix of elements of "X" whose "i" - th row is and let "R"("t") be the "m" × "n" matrix of elements of "X", the elements of whose "j" - th column are According to the generalised test (due to Bednarek), that the property to be verified holds if and only if "L"("t") = "R"("t") for all "t" in "T". When "X" = "T", Bednarek's test reduces to Light's test. There is a randomized algorithm by Rajagopalan and Schulman to test associativity in time proportional to the input

neg: Boltzmann equation formula_29 is the local Maxwellian distribution function given the gas temperature at this point in space. For a mixture of chemical species labelled by indices "i" = 1, 2, 3, ..., "n" the equation for species "i" is where "f" = "f"(r, p, "t"), and the collision term is where "f′" = "f′"(p′, "t"), the magnitude of the relative momenta is and "I" is the differential cross-section, as before, between particles "i" and "j". The integration is over the momentum components in the integrand (which are labelled "i" and "j"). The sum of integrals describes the entry and exit of

neg: TeraChem 2010 I. S. Ufimtsev, N. Luehr and T. J. Martinez Journal of Physical Chemistry Letters, Vol. 2, 1789-1793 (2011) C. M. Isborn, N. Luehr, I. S. Ufimtsev and T. J. Martinez Journal of Chemical Theory and Computation, Vol. 7, 1814-1823 (2011) N. Luehr, I. S. Ufimtsev, and T. J. Martinez Journal of Chemical Theory and Computation, Vol. 7, 949-954 (2011) I. S. Ufimtsev and T. J. Martinez Journal of Chemical Theory and Computation, Vol. 5, 2619-2628 (2009) I. S. Ufimtsev and T. J. Martinez Journal of Chemical Theory and Computation, Vol. 5, 1004-1015 (2009) I. S. Ufimtsev and T. J.

neg: Proto-Germanic language these two effects created an alternation between -ā- and -ai- found in class 3 weak verbs, with -ā- < -aja- < -əja- and -ai- < -əi- < -əji-. I-mutation was the most important source of vowel alternation, and continued well into the history of the individual daughter languages (although it was either absent or not apparent in Gothic). In Proto-Germanic, only -e- was affected, which was raised by -i- or -j- in the following syllable. Examples are numerous: The system of nominal declensions was largely inherited from PIE. Primary nominal declensions were the stems in /a/, /ō/, /n/, /i/, and

neg: Name of Croatia the name of the Croats: From the Iranian theses the most widely accepted is the derivation by Oleg Trubachyov from "*xar-va(n)t" (feminine, rich in women, ruled by women), which derives from the etymology of Sarmatians name, the Indo-Aryan "*sar-ma(n)t" "feminine", in both Indo-Iranian adjective suffix "-ma(n)t/wa(n)t", and Indo-Aryan and the Indo-Iranian "*sar-" "woman", which in Iranian gives "*har-". According to Radoslav Katičić this thesis doesn't entirely fit with the Croatian ethnonym, as the original form was "Hrъvate" not "Hъrvate", and the vowel "a" in the Iranian "harvat-" is short, while in the Slavic "Hrъvate" it is long. Katičić concluded that

neg: Inner model model of "T" (in "M"). Usually "T" will equal (or subsume) "S", so that "N" is a model for "S" 'inside' the model "M". If only conditions 1 and 2 hold, "N" is called a standard model. A model "N" is called transitive when it is standard and condition 3 holds. If the axiom of foundation is not assumed (that is, is not in "S") all three of these concepts are given the additional condition that "N" be well-founded. Hence inner models are transitive, transitive models are standard, and standard models are well-founded. The assumption that there exists a standard

neg: Covering space of coverings. Proofs of these facts are given in the book 'Topology and Groupoids' referenced below. If "X" is a connected cell complex with homotopy groups for all , then the universal covering space "T" of "X" is contractible, as follows from applying the Whitehead theorem to "T". In this case "X" is a classifying space or for . Moreover, for every the group of cellular "n"-chains "C"("T") (that is, a free abelian group with basis given by "n"-cells in "T") also has a natural ZG"-module structure. Here for an "n"-cell "σ" in "T" and for "g" in "G" the

neg: Worst-case complexity its average-case complexity, which is an average measure of the amount of resources the algorithm uses on a random input. Since we usually are interested in the dependence of the time complexity on different input length, abusing terminology, the time complexity is sometimes referred to the mapping T:N→N, defined by T("n"):= max{t("x")}. Similar definitions can be given for space complexity, randomness complexity, etc. Consider performing insertion sort on "n" numbers on a random access machine. The best-case for the algorithm is when the numbers are already sorted, which takes O("n") steps to perform the task. However, the input in the

neg: Common knowledge (logic) Kripke structure is given by (i) a set of states (or possible worlds) "S", (ii) "n" "accessibility relations" formula_13, defined on formula_14, intuitively representing what states agent "i" considers possible from any given state, and (iii) a valuation function formula_15 assigning a truth value, in each state, to each primitive proposition in the language. The semantics for the knowledge operator is given by stipulating that formula_16 is true at state "s" iff formula_1 is true at "all" states "t" such that formula_18. The semantics for the common knowledge operator, then, is given by taking, for each group of agents "G",

neg: Convergent matrix T is semi-convergent. We call an "n" × "n" matrix T a convergent matrix if for each "i" = 1, 2, ..., "n" and "j" = 1, 2, ..., "n". Let Computing successive powers of T, we obtain and, in general, Since and T is a convergent matrix. Note that "ρ"(T) = , where "ρ"(T) represents the spectral radius of T, since is the only eigenvalue of T. Let T be an "n" × "n" matrix. The following properties are equivalent to T being a convergent matrix: A general iterative method involves a process that converts the system of linear

neg: Blocking oscillator the time T when the switch is open. The following abbreviations are used in the analysis: A more-detailed analysis would require the following: When the switch (transistor, tube) closes it places the source voltage V across the transformer primary. The magnetizing current I of the transformer is I = V×t/L; here t (time) is a variable that starts at 0. This magnetizing current I will "ride upon" any reflected secondary current I that flows into a secondary load (e.g. into the control terminal of the switch; reflected secondary current in primary = I/N). The "changing" primary current causes a "changing"

neg: Bionic (Christina Aguilera song) recorded at The Red Lips Room in Beverly Hills, California. The track was written by Aguilera, Kalenna Harper, John Hill and Switch. Hill and Switch also produced and provided musical instruments to "Bionic". "Bionic" is an electronic song and lasts for a duration of (three minutes and twenty-one seconds). It features "twitchy space-ace" rhythms, rapping verses and talks about an "echo-laden" invitation to "jet off to the new millennium". In the middle of the song, Aguilera spells out her name, "X-x-x-t-t-t-i-i-i-n-n-n-n-n-a". During the chorus, she sings, "Bionic, so damn Bionic, gonna get you with my electronic supersonic rocket, ay". Becky

neg: What's Goin' On Ai her first song to be used as a drama theme song. The single debuted at number two, her highest position to date. A month before the album's release date, Ai released a second single before from the album, the R&B dance song "I Wanna Know." It was used in a TV commercial for Pepsi Nex. "What's Goin On Ai" features a much wider variety of producers than Ai's previous albums. Previous album collaborators include T. Kura ("Music," "Love Is..."), who has worked with Ai since 2004, as well as DJ Yutaka ("Believe," "No Way") and Icedown ("Mirai"), who both worked

neg: Reductive group "T" is exactly the Lie algebra formula_11 of "T". Therefore, the Lie algebra of "G" decomposes into formula_11 together with 1-dimensional subspaces indexed by the set Φ of roots: For example, when "G" is the group "GL"("n"), its Lie algebra formula_14 is the vector space of all "n" × "n" matrices over "k". Let "T" be the subgroup of diagonal matrices in "G". Then the root-space decomposition expresses formula_14 as the direct sum of the diagonal matrices and the 1-dimensional subspaces indexed by the off-diagonal positions ("i", "j"). Writing "L"...,"L" for the standard basis for the weight lattice "X"("T") ≅

neg: Lindström–Gessel–Viennot lemma Theorem 1). The Lindström–Gessel–Viennot lemma can be used to prove the equivalence of the following two different definitions of Schur polynomials. Given a partition formula_90 of "n", the Schur polynomial formula_91 can be defined as: where the sum is over all semistandard Young tableaux "T" of shape "λ", and the weight of a tableau "T" is defined as the monomial obtained by taking the product of the "x" indexed by the entries "i" of "T". For instance, the weight of the tableau is formula_93. where "h" are the complete homogeneous symmetric polynomials (with "h" understood to be 0 if "i"

neg: Simplex of the regular simplex on a circle, and all vertex pairs connected by edges. The standard "n"-simplex (or unit "n"-simplex) is the subset of R given by The simplex Δ lies in the affine hyperplane obtained by removing the restriction "t" ≥ 0 in the above definition. The "n" + 1 vertices of the standard "n"-simplex are the points "e" ∈ R, where There is a canonical map from the standard "n"-simplex to an arbitrary "n"-simplex with vertices ("v", …, "v") given by The coefficients "t" are called the barycentric coordinates of a point in the "n"-simplex. Such a general

neg: Cotangent space the two alternate definitions of the cotangent space given above. Given a function "f" ∈ "I" (a smooth function vanishing at "x") we can form the linear functional d"f" as above. Since the map d restricts to 0 on "I" (the reader should verify this), d descends to a map from "I" / "I" to the dual of the tangent space, ("T""M"). One can show that this map is an isomorphism, establishing the equivalence of the two definitions. Just as every differentiable map "f" : "M" → "N" between manifolds induces a linear map (called the "pushforward" or "derivative") between

neg: Envelope (mathematics) by arc length. Consider the one-parameter family of normal lines to γ("I"). A line is normal to γ at γ("t") if it passes through γ("t") and is perpendicular to the tangent vector to γ at γ("t"). Let T denote the unit tangent vector to γ and let N denote the unit normal vector. Using a dot to denote the dot product, the generating family for the one-parameter family of normal lines is given by where Clearly (x − γ)·T = 0 if and only if x − γ is perpendicular to T, or equivalently, if and only if x −

neg: Diffusion "P" is the pressure, formula_86 is the mean free path, and "v" is the mean thermal speed: We can see that the diffusion coefficient in the mean free path approximation grows with "T" as "T" and decreases with "P" as 1/"P". If we use for "P" the ideal gas law "P" = "RnT" with the total concentration "n", then we can see that for given concentration "n" the diffusion coefficient grows with "T" as "T" and for given temperature it decreases with the total concentration as 1/"n". For two different gases, A and B, with molecular masses "m", "m" and

neg: Multi-attribute utility If attribute 2 is utility-independent of attribute 1: If the attributes are "mutually utility independent", then the utility function "u" has the following "multi-linear form": Where formula_58 is a constant which can be positive, negative or 0. These results can be generalized to any number of attributes. Given attributes 1...,"n", if any subset of the attributes is utility-independent of its complement, then the "n"-attribute utility function is multi-linear and has one of the following forms: where: It is useful to compare three different concepts related to independence of attributes: Additive-independence (AI), Utility-independence (UI) and Preference-independence (PI). AI and UI both

neg: Ordered pair denoted by the variant notation , but this notation also has other uses. The left and right projection of a pair "p" is usually denoted by "π"("p") and "π"("p"), or by "π"("p") and "π"("p"), respectively. In contexts where arbitrary "n"-tuples are considered, "π"("t") is a common notation for the "i"-th component of an "n"-tuple "t". In some introductory mathematics textbooks an informal (or intuitive) definition of ordered pair is given, such as For any two objects and , the ordered pair is a notation specifying the two objects and , in that order. This is usually followed by a comparison

neg: Spherical design Hong (1982). Shortly thereafter, Seymour and Zaslavsky (1984) proved that such designs exist of all sufficiently large sizes; that is, given positive integers "n" and "t", there is a number "N"("d","t") such that for every "N" ≥ "N"("d","t") there exists a spherical "t"-design of "N" points in dimension "d". However, their proof gave no idea of how big "N"("d","t") is. Good estimates for that were found later on. Besides these "large" sizes, there are many sporadic small spherical designs; many of them are related to finite group actions on the sphere and are of great interest in themselves. Recently, Bondarenko,

neg: T,O,U,C,H,I,N,G effects to elicit emotional and psychological responses in viewers. T,O,U,C,H,I,N,G T,O,U,C,H,I,N,G is a 12-minute short film directed by Paul Sharits in 1968. It uses many of the strategies characteristic of the structural film movement, including a static frame, flicker effects, flash frames and continual audio and visual repetition. The audio track consists exclusively of the filmmaker uttering the word "destroy" over and over until the word begins to lose its meaning and creates the impression of different combinations of words being spoken. Unlike many clearly algorithmically-driven films of the structural film movement, "T,O,U,C,H,I,N,G" does not simply follow a sequence of

neg: T,O,U,C,H,I,N,G T,O,U,C,H,I,N,G T,O,U,C,H,I,N,G is a 12-minute short film directed by Paul Sharits in 1968. It uses many of the strategies characteristic of the structural film movement, including a static frame, flicker effects, flash frames and continual audio and visual repetition. The audio track consists exclusively of the filmmaker uttering the word "destroy" over and over until the word begins to lose its meaning and creates the impression of different combinations of words being spoken. Unlike many clearly algorithmically-driven films of the structural film movement, "T,O,U,C,H,I,N,G" does not simply follow a sequence of mathematical transformation, but deploys combinations of audio and visual

neg: I-spline data transformation when monotonicity is desired (constraining the regression coefficients to be non-negative for a non-decreasing fit, and non-positive for a non-increasing fit). I-spline In the mathematical subfield of numerical analysis, an I-spline is a monotone spline function. A family of "I-spline" functions of degree "k" with "n" free parameters is defined in terms of the M-splines "M"("x"|"k", "t") where "L" is the lower limit of the domain of the splines. Since M-splines are non-negative, "I-splines" are monotonically non-decreasing. Let "j" be the index such that "t" ≤ "x" < "t". Then "I"("x"|"k", "t") is zero if "i" > "j",

neg: Plane partition partition is defined as a finite subset formula_9 of positive integer lattice points ("i", "j", "k") in formula_10, such that if ("r", "s", "t") lies in formula_9 and if ("i", "j", "k") satisfies formula_12, formula_13 and formula_14, then ("i", "j", "k") also lies in formula_9. By a result of Percy A. MacMahon, the generating function for PL("n") is given by This is sometimes referred to as the "MacMahon function". This formula may be viewed as the 2-dimensional analogue of Euler's product formula for the number of integer partitions of "n". There is no analogous formula known for partitions in higher

neg: Stable range condition stable range condition "SR"...") Less commonly, one has the notion of the stable range of an ideal "I" in a ring "R". The stable range of the pair ("R","I") is the smallest integer "n" such that for any elements "v", ... , "v" in "R" that generate the unit ideal "and" satisfy "v" 1 mod "I" and "v" 0 mod "I" for 0 ≤ "i" ≤ "n"-1, there exist "t", ... , "t" in "R" such that "v" - "v""t" for 1 ≤ "i" ≤ "n" also generate the unit ideal. As above, in this case we say that ("R","I")

neg: Symmetric cone Let "H" be the group of [[biholomorphism]]s of the tube "T". The Cayley transform shows that is isomorphic to the group "H" of biholomorphisms of the bounded domain "D". Since "AN" acts simply transitively on the tube "T" while "K" fixes "ic", they have trivial intersection. Given "g" in "H", take "s" in "AN" such that "g"("i")="s"("i"). then "gs" fixes "i" and therefore lies in "K". Hence "H" = "K" ⋅"A"⋅"N". So the product is a group. By a result of [[Henri Cartan]], "H" is a Lie group. Cartan's original proof is presented in . It can also be deduced

neg: Generation time in the next generation (the mother cell and the daughter cell). If the population dynamic is exponential with a growth rate "r" (i.e. "n"("t") ~ α.e, where "n"("t") is the size of the population at time "t"), then this measure of the generation time is given by: Indeed, formula_2 is such that "n"("t" + "T") = "R" "n"("t"), i.e. e = "R". This definition is a measure of the distance between generations rather than a renewal time of the population. Since many demographic models are female-based (that is, they only take females into account), this definition is often expressed as

neg: Merge sort "T"("n"), then the recurrence "T"("n") = 2"T"("n"/2) + "n" follows from the definition of the algorithm (apply the algorithm to two lists of half the size of the original list, and add the "n" steps taken to merge the resulting two lists). The closed form follows from the master theorem for divide-and-conquer recurrences. In the worst case, the number of comparisons merge sort makes is given by the sorting numbers. These numbers are equal to or slightly smaller than ("n" ⌈lg "n"⌉ - 2 + 1), which is between ("n" lg "n" - "n" + 1) and ("n" lg "n"