If we are to believe the list of titles printed in Malraux's latest book, La Metamorphose Des Dieux, Vol. 1 ( ( 1957 ), he is still engaged in writing a large novel under his original title.

If desired, sprinkle with 1 teaspoon drained crushed pineapple.

If the Af bond is linear then there are three reasonable positions for the hydrogen atoms: ( 1 ) The hydrogen atoms are centered and hence all lie on a sheet midway between the oxygen sheets ; ;

If, in a certain part of the range, it starts life 1 foot longer than do any of the other ( relatively large ) giants, and reaches maturity at, let us guess, 18 inches longer than the others, a quadrupling of the maturity length would result in a maximum of ( nearly ) 40 feet.

If, at any time during the assignment pass, the compiler finds that there are no more index words available for assignment, the warning message `` No More Index Words Available '' will be placed in the object program listing, the table will be altered to show that index words 1 through 96 are available, and the assignment will continue as before.

If the compiler finds that there are no more electronic switches available for assignment, the warning message `` No More Electronic Switches Available '' will be placed in the object program listing, the table will be altered to show that electronic switches 1 through 30 are available, and assignment will continue as before.

If the resulting four kilobyte table size is too large for a given target platform, the table lookup operation can be performed with a single 256-entry 32-bit ( i. e. 1 kilobyte ) table by the use of circular rotates.

Theorem: If K < sub > 1 </ sub > and K < sub > 2 </ sub > are the complexity functions relative to description languages L < sub > 1 </ sub > and L < sub > 2 </ sub >, then there is a constant c – which depends only on the languages L < sub > 1 </ sub > and L < sub > 2 </ sub > chosen – such that

If more than one player selects a tile in that row, then the player whose tile is in the leftmost column ( closest to 1 ) goes first.

If the color were fully green, its RGBA would be ( 0, 1, 0, 0. 5 ).

* If the balance factor of R is + 1, two different rotations are needed.

* If the balance factor of L is + 1, a single right rotation ( with P as the root ) is needed ( Left-Left case ).

If there is refraction at a collective spherical surface, or through a thin positive lens, O ' 2 will lie in front of O ' 1 so long as the angle u2 is greater than u1 ( under correction ); and conversely with a dispersive surface or lenses ( over correction ).

If the angle u1 is very small, O ' 1 is the Gaussian image ; and O ' 1 O ' 2 is termed the longitudinal aberration, and O ' 1R the lateral aberration of the pencils with aperture u2.

If the pencil with the angle u2 is that of the maximum aberration of all the pencils transmitted, then in a plane perpendicular to the axis at O ' 1 there is a circular disk of confusion of radius O ' 1R, and in a parallel plane at O ' 2 another one of radius O ' 2R2 ; between these two is situated the disk of least confusion.

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 the function R is well-defined, its value must lie in the range, with 1 indicating perfect correlation and − 1 indicating perfect anti-correlation.

If there is no number to its left, simply look at the column headed " 1 " in the previous row.

If a detector was placed at a distance of 1 m, the ion flight times would be X and Y ns.

If the boat floats, the mass of the boat ( plus contents ) as a whole divided by the volume below the waterline is equal to the density of water ( 1 kg / l ).

* The Lusternik – Schnirelmann theorem: If the sphere S < sup > n </ sup > is covered by n + 1 open sets, then one of these sets contains a pair ( x, − x ) of antipodal points.

The array on the game board is arranged with lettered rows ( A through I ) and numbered columns ( 1 through 12 ).

Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20, respectively, then replacing B by B + c < sub > 1 </ sub >-− 3 c < sub > 1 </ sub > will cause them to be renumbered from 0 through 9 and 4 through 23, respectively.

Chess is played on a square board of eight rows ( called ranks and denoted with numbers 1 to 8 ) and eight columns ( called files and denoted with letters a to h ) of squares.

It is common to display the Gregorian calendar in separate monthly grids of seven columns ( from Monday to Sunday, or Sunday to Saturday depending on which day is considered to start the week-this varies according to country ) and five to six rows ( or rarely, four rows when the month of February contains 28 days beginning on the first day of the week ), with the day of the month numbered in each cell, beginning with 1.

Rows 0 and 20 represent " off the board " beyond rows 1 and 19 respectively.

Ohs tries to move the football to rows 19 or 20 and Eks to rows 1 or 0.

Usually rows, representing the dependant variables, are referenced in decimal notation starting from 1, while columns representing the independent variables use 26-adic bijective numeration using the letters A-Z as numerals.

In such games the aim is to fill up the board and get more rows of three in total than the other player or to play with 4 people and get 1 row of 3.

Let P < sup >− 1 </ sup > DP be an eigendecomposition of M, where P is a unitary complex matrix whose rows comprise an orthonormal basis of eigenvectors of M, and D is a real diagonal matrix whose main diagonal contains the corresponding eigenvalues.

In modern commentary, the columns ( called files ) are labeled by the letters a to h from left to right from the white player's point of view, and the rows ( called ranks ) by the numbers 1 to 8, with 1 being closest to the white player, thus providing a standard notation called algebraic chess notation.

The vertical column of squares ( called files ) from White's left ( the queenside ) to his right ( the kingside ) are labeled a through h. The horizontal rows of squares ( called ranks ) are numbered 1 to 8 starting from White's side of the board.

If the error ranges from-1 to + 1, with the analog-to-digital converter used having a resolution of 0. 25, then the input variable's fuzzy set ( which, in this case, also applies to the output variable ) can be described very simply as a table, with the error / delta / output values in the top row and the truth values for each membership function arranged in rows beneath:

The rows correspond to the dimensions, and t, and the columns to the dimensional variables D, T, V. For instance, the 3rd column, ( 1, − 1 ), states that the V ( velocity ) variable has units of.

( The rows correspond to the dimensions t, m, and l, and the columns to the dimensional variables T, M, L and g. For instance, the 4th column, (− 2, 0, 1 ), states that the g variable has units of.

Here a < sub > 1 </ sub >, ..., a < sub > m </ sub > denote the rows of the matrix A.

The original track width of 1, 270 millimeters was equivalent to two potato rows.

In 1726, the Herrenhäuser Allee ( Herrenhausen alley ) was planted just through the gardens, connecting Hanover with the royal palace and gardens of Herrenhausen in the boroughs of the city ; it is almost exactly one geographical mile ( 1. 85 km ) long, and consists of four rows of lime trees.

With permutation matrices the determinant matches the signature, being + 1 or − 1 as the parity of the permutation is even or odd, for the determinant is an alternating function of the rows.

A Banach algebra is called " unital " if it has an identity element for the multiplication whose norm is 1, and " commutative " if its multiplication is commutative.

This applies to the I-indexed diagrams in the category of R-modules, with R a commutative ring ; it is not necessarily true in an arbitrary abelian category ( see Roos ' " Derived functors of inverse limits revisited " for examples of abelian categories in which lim ^ n, on diagrams indexed by a countable set, is nonzero for n > 1 ).

The theorem follows because * is ( commutative and ) associative, and 1 * μ = i, where i is the identity function for the Dirichlet convolution, taking values i ( 1 )= 1, i ( n )= 0 for all n > 1.

The morphisms in E between R → S < sub > 1 </ sub > and R → S < sub > 2 </ sub > are commutative triangles of the form ( R → S < sub > 1 </ sub >, R → S < sub > 2 </ sub >, S < sub > 1 </ sub > → S < sub > 2 </ sub >) where S < sub > 1 </ sub > → S < sub > 2 </ sub > is a ring map ( which preserves the identity ).

With these operations, R < sup > N </ sup > becomes a commutative ring with zero element ( 0, 0, 0, ...) and multiplicative identity ( 1, 0, 0 ,...).

If S is a commutative associative algebra over R, if I is an ideal of S such that the I-adic topology on S is complete, and if x < sub > 1 </ sub >, ..., x < sub > r </ sub > are elements of I, then there is a unique Φ: R < nowiki ></ nowiki > X < sub > 1 </ sub >, ..., X < sub > n </ sub >< nowiki ></ nowiki > → S with the following properties:

A field is a commutative ring where every non-zero element a is invertible ; i. e., has a multiplicative inverse b such that a ⋅ b = 1.

* The Laurent polynomial ring RX < sup >− 1 </ sup > is isomorphic to the group ring of the group Z of integers over R. More generally, the Laurent polynomial ring in n variables is isomorphic to the group ring of the free abelian group of rank n. It follows that the Laurent polynomial ring can be endowed with a structure of a commutative, cocommutative Hopf algebra.

Commutativity makes sense for a polygon of any finite number of sides ( including just 1 or 2 ), and a diagram is commutative if every polygonal subdiagram is commutative.

ijk = − 1 and the usual algebraic rules except the commutative law of multiplication ( a familiar example of such a noncommutative multiplication is matrix multiplication ).

A field is a commutative ring ( F ,+,*) in which 0 ≠ 1 and every nonzero element has a multiplicative inverse.

In other words, assume that p = p ( x < sub > 1 </ sub >,..., x < sub > n </ sub >) is a non-zero polynomial in n variables, and that there is a given monomial order on the set of all (" monic ") monomials in these variables, i. e., a total order of the free commutative monoid generated by x < sub > 1 </ sub >,..., x < sub > n </ sub >, with the unit as lowest element, and respecting multiplication.

An element of this ring is invertible if a ( 1 ) is invertible in R. If R is commutative, so is Ω ; if R is an integral domain, so is Ω.

Let be a commutative ring with 1, e. g. ( Instead we can take to be a field and can replace by the field ).