What is "rank"

Rank \Rank\ (r[a^][ng]k), a. [Compar. Ranker (r[a^][ng]k"[~e]r); superl. Rankest.] [AS. ranc strong, proud; cf. D. rank slender, Dan. rank upright, erect, Prov. G. rank slender, Icel. rakkr slender, bold. The meaning seems to have been influenced by L. rancidus, E. rancid.]

1. Luxuriant in growth; of vigorous growth; exuberant; grown to immoderate height; as, rank grass; rank weeds.

   And, behold, seven ears of corn came up upon one stalk, rank and good.
   --Gen. xli. 5.

2. Raised to a high degree; violent; extreme; gross; utter; as, rank heresy. ``Rank nonsense.''
   --Hare. ``I do forgive thy rankest fault.''
   --Shak.

3. Causing vigorous growth; producing luxuriantly; very rich and fertile; as, rank land.
   --Mortimer.

4. Strong-scented; rancid; musty; as, oil of a rank smell; rank-smelling rue.
   --Spenser.

5. Strong to the taste. ``Divers sea fowls taste rank of the fish on which they feed.''
   --Boyle.

6. Inflamed with venereal appetite. [Obs.]
   --Shak.

   Rank modus (Law), an excessive and unreasonable modus. See Modus, 3.

   To set (the iron of a plane, etc.) rank, to set so as to take off a thick shaving.
   --Moxon.

1570s, "arrange in lines;" 1590s, "put in order, classify; assign a rank to," from rank (n.). Related: Ranked; ranking.

early 14c., "row, line series;" c.1400, a row of an army, from Old French renc, ranc "row, line" (Modern French rang), from Frankish *hring or some other Germanic source (compare Old High German hring "circle, ring"), from Proto-Germanic *hringaz "circle, ring, something curved" (see ring (n.1)).\n

\nMeaning "a social division, class of persons" is from early 15c. Meaning "high station in society" is from early 15c. Meaning "a relative position" is from c.1600.

Old English ranc "proud, overbearing, showy," from Proto-Germanic *rankaz (cognates: Danish rank "right, upright," German rank "slender," Old Norse rakkr "straight, erect"), perhaps from PIE *reg- "to stretch, straighten" (see right (adj.)). In reference to plant growth, "vigorous, luxuriant, abundant, copious" it is recorded from c.1300. Related: Rankly; rankness.\n

\nSense evolved in Middle English to "large and coarse" (c.1300), then, via notion of "excessive and unpleasant," to "corrupt, loathsome, foul" (mid-14c.), perhaps from influence of Middle French rance "rancid." In 17c. also "lewd, lustful."\n

\nMuch used 16c. as a pejorative intensive (as in rank folly). This is possibly the source of the verb meaning "to reveal another's guilt" (1929, underworld slang), and that of "to harass, abuse," 1934, U.S. black dialect, though this also may be from the role of the activity in establishing social hierarchy (from rank (n.)).

Etymology 1

1. 1 Strong of its kind or in character; unmitigated; virulent; thorough; utter. 2 Strong in growth; growing with vigour or rapidity, hence, coarse or gross. adv. (context obsolete English) quickly, eagerly, impetuously. Etymology 2

   n. A row of people or things organized in a grid pattern, often soldiers [the corresponding term for the perpendicular columns in such a pattern is "file"]. v

2. 1 To place abreast, or in a line. 2 To have a ranking. 3 To assign a suitable place in a class or order; to classify. 4 (context US English) To take rank of; to outrank.

1. adj. very fertile; producing profuse growth; "rank earth"

2. very offensive in smell or taste; "a rank cigar"

3. conspicuously and outrageously bad or reprehensible; "a crying shame"; "an egregious lie"; "flagrant violation of human rights"; "a glaring error"; "gross ineptitude"; "gross injustice"; "rank treachery" [syn: crying(a), egregious, flagrant, glaring, gross]

4. complete and without restriction or qualification; sometimes used informally as intensifiers; "absolute freedom"; "an absolute dimwit"; "a downright lie"; "out-and-out mayhem"; "an out-and-out lie"; "a rank outsider"; "many right-down vices"; "got the job through sheer persistence"; "sheer stupidity" [syn: absolute, downright, out-and-out(a), rank(a), right-down, sheer(a)]

5. growing profusely; "rank jungle vegetation"

1. v. take or have a position relative to others; "This painting ranks among the best in the Western World"

2. assign a rank or rating to; "how would you rank these students?"; "The restaurant is rated highly in the food guide" [syn: rate, range, order, grade, place]

3. take precedence or surpass others in rank [syn: outrank]

1. n. a row or line of people (especially soldiers or police) standing abreast of one another; "the entrance was guarded by ranks of policemen"

2. relative status; "his salary was determined by his rank and seniority"

3. the ordinary members of an organization (such as the enlisted soldiers of an army); "the strike was supported by the union rank and file"; "he rose from the ranks to become a colonel" [syn: rank and file]

4. position in a social hierarchy; "the British are more aware of social status than Americans are" [syn: social station, social status, social rank]

5. the body of members of an organization or group; "they polled their membership"; "they found dissension in their own ranks"; "he joined the ranks of the unemployed" [syn: membership]

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This is the same as the dimension of the space spanned by its rows. It is a measure of the " nondegenerateness" of the system of linear equations and linear transformation encoded by A. There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics.

The rank is commonly denoted rank(A) or rk(A); sometimes the parentheses are not written, as in rank A.

Rank is a live album by the English rock band The Smiths. It was released in September 1988 by their British record company, Rough Trade, and reached No. 2 in the British charts. In the United States, the album was released on Sire Records and made No. 77.

Rank in the J programming language has several different meanings. In general, the concept of rank is used to treat an orthogonal array in terms of its sub-arrays. For instance, a two-dimensional array may be dealt with at rank 2 as the entire matrix, or at rank 1 to work with its implicit one-dimensional columns or rows, or at rank 0 to work at the level of its individual atoms.

Receptor Activator of Nuclear Factor κ B (RANK), also known as TRANCE Receptor or TNFRSF11A, is member of the tumor necrosis factor receptor (TNFR) molecular sub-family. RANK is the receptor for RANK-Ligand (RANKL) and part of the RANK/RANKL/OPG signaling pathway that regulates osteoclast differentiation and activation. It is associated with bone remodeling and repair, immune cell function, lymph node development, thermal regulation, and mammary gland development. Osteoprotegerin (OPG) is a decoy receptor for RANK, and regulates the stimulation of the RANK signaling pathway by competing for RANKL. The cytoplasmic domain of RANK binds TRAFs 1, 2, 3, 5, and 6 which transmit signals to downstream targets such as NF-κB and JNK.

RANK is constitutively expressed in skeletal muscle, thymus, liver, colon, small intestine, adrenal gland, osteoclast, mammary gland epithelial cells, prostate, vascular cell, and pancreas. Most commonly, activation of NF-κB is mediated by RANKL, but over-expression of RANK alone is sufficient to activate the NF-κB pathway.

RANKL (Receptor Activator for Nuclear factor κ B Ligand) is found on the surface of stromal cells, osteoblasts, and T cells.

In computer programming, rank with no further specifications is usually a synonym for (or refers to) "number of dimensions"; thus, a bi-dimensional array has rank two, a three-dimensional array has rank three and so on. Strictly, no formal definition can be provided which applies to every programming language, since each of them has its own concepts, semantics and terminology; the term may not even be applicable or, to the contrary, applied with a very specific meaning in the context of a given language.

In the case of APL the notion applies to every operand; and dyads ("binary functions") have a left rank and a right rank.

The box below instead shows how rank of a type and rank of an array expression could be defined (in a semi-formal style) for C++ and illustrates a simple way to calculate them at compile time.

Given the code above the rank of a type T can be calculated at compile time by

and the rank of an array-expression expr by

A Rank is a line of military personnel, drawn up in line abreast (i.e. standing side by side).

In mathematics, the rank of a differentiable map f : M → N between differentiable manifolds at a point p ∈ M is the rank of the derivative of f at p. Recall that the derivative of f at p is a linear map

df : TM → TN 
from the tangent space at p to the tangent space at f(p). As a linear map between vector spaces it has a well-defined rank, which is just the dimension of the image in TN:

rank(f) = dim(im(df)).

Rank is a 2002 fourteen-minute short film directed by David Yates. It was nominated for the British Academy Film Award for Best Short Film at the BAFTAs.

Rank is the surname of:

• J. Arthur Rank, 1st Baron Rank (1888–1972), British industrialist and film producer
• Joseph Rank (1854-1943), founder of Rank Hovis McDougall, one of the UK's largest food production and flour-milling businesses
• Kyle Rank (ice hockey, born 1982), Canadian ice hockey forward
• Kyle Rank (ice hockey, born 1987), American ice hockey goaltender
• Otto Rank (1884–1939), Austrian psychoanalyst, writer, teacher, and therapist

In graph theory, a branch of mathematics, the rank of an undirected graph is defined as the number , where is the number of vertices and is the number of connected components of the graph. Equivalently, the rank of a graph is the rank of the oriented incidence matrix associated with the graph.

Analogously, the nullity of an undirected graph is the nullity of its incidence matrix, given by the formula , where n and c are as above and m is the number of edges in the graph. The nullity is equal to the first Betti number of the graph. The sum of the rank and the nullity is the number of edges.