Denote the true weights by

Denote the sample of data which are independent realisations of random variables, having F as their distribution function, by x < sub > i </ sub > ( i = 1 ,..., n ).

Denote by the polynomial such that is compact.

Denote by the projection to the subspace.

Denote by the th ( partial ) computable function.

Denote by the phase difference

Denote by Ü the set of rational numbers in.

Denote, respectively, by and by the actual configuration of subsystem ( I ) and of the rest of the universe.

Denote the columns of V by ( these are the rows of the transposed matrix that appears in the decomposition )

Denote the set of rational numbers by Q.

Denote by the number of binary trees on n nodes.

Let x < sub > t </ sub > be a curve in a Riemannian manifold M. Denote by τ < sub > x < sub > t </ sub ></ sub >: T < sub > x < sub > 0 </ sub ></ sub > M → T < sub > x < sub > t </ sub ></ sub > M the parallel transport map along x < sub > t </ sub >.

Denote by τ < sub > tX </ sub > and τ < sub > tY </ sub >, respectively, the parallel transports along the flows of X and Y for time t. Parallel transport of a vector Z ∈ T < sub > x < sub > 0 </ sub ></ sub > M around the quadrilateral with sides tY, sX, − tY, − sX is given by

Denote this limit by y.

Denote by the orthogonal projection onto.

Denote the row vector of these components by

Denote the column vector of components of v by v:

Denote the row vector of components of α by α:

Denote by dY the differential of such a map.

Denote the DFT of the Even-indexed inputs by and the DFT of the Odd-indexed inputs by and we obtain:

Denote this Lie algebra by A < sub > L </ sub >.

b of the interval b we obtain a finite collection of points f ( t < sub > 0 </ sub >), f ( t < sub > 1 </ sub >), ..., f ( t < sub > n − 1 </ sub >), f ( t < sub > n </ sub >) on the curve C. Denote the distance from f ( t < sub > i </ sub >) to f ( t < sub > i + 1 </ sub >) by d ( f ( t < sub > i </ sub >), f ( t < sub > i + 1 </ sub >)), which is the length of the line segment connecting the two points.

Denote the vertices of a triangle as A, B, and C and the orthocenter as H, and let D, E, and F denote the feet of the altitudes from A, B, and C respectively.

Denote the three vertices of one triangle by a, b, and c, and those of the other by A, B, and C. Axial perspectivity means that lines ab and AB meet in a point, lines ac and AC meet in a second point, and lines bc and BC meet in a third point, and that these three points all lie on a common line called the axis of perspectivity.

Denote the area that casually affects point as.

Denote the orthocenter of triangle ABC as H, denote the sidelengths as a, b, and c, and denote the circumradius of the triangle as R. Then

Denote this probability.

Denote as Z the sum of the squared differences of the data points from the centroid ( also denoted in complex coordinates ), which is the point whose horizontal and vertical locations are the averages of those of the data points.

Now suppose ƒ is a bijective function from Z ( the positive integers ) to X. Denote the points of the image of Z under ƒ as

Let E → M be a smooth vector bundle over a differentiable manifold M. Denote the space of smooth sections of E by Γ ( E ).

Denote by P ( A ) the power set of A, i. e., the set of all subsets of A.

Denote the equivalence class of ( p, f ) by.

Denote by R the radius of a spherical grating.

Clearly, any line, l, of any bundle having one of these points of tangency, T, as vertex will be transformed into the entire pencil having the image of the second intersection of L and Q as vertex and lying in the plane determined by the image point and the generator of Af which is tangent to **zg at T.

On C there is a Af correspondence in which the Af points cut from C by a general line, l, of the pencil correspond to the point of intersection of the image of L and the plane of the pencil.

Since the load L, under actual cutting conditions is caused by Af, it can be seen that Af

In Korea, the Hangul alphabet was created by Sejong the Great Hangul is a unique alphabet: it is a featural alphabet, where many of the letters are designed from a sound's place of articulation ( P to look like the widened mouth, L to look like the tongue pulled in, etc.

To do this, Moseley measured the wavelengths of the innermost photon transitions ( K and L lines ) produced by the elements from aluminum ( Z = 13 ) to gold ( Z = 79 ) used as a series of movable anodic targets inside an x-ray tube.

* Animal ( 1977 film ), French film ( L ' Animal ) by Claude Zidi with Jean-Paul Belmondo and Raquel Welch

The Norse discovery was documented in the 13th century Icelandic Sagas and was corroborated by recent L ' Anse aux Meadows archeological evidence.

Besides HALT, Minsky's machine includes three assignment ( replacement, substitution ) operations: ZERO ( e. g. the contents of location replaced by 0: L ← 0 ), SUCCESSOR ( e. g. L ← L + 1 ), and DECREMENT ( e. g. L ← L − 1 ).

In this, the emperor was assisted by five chief lawyers: L. Fulvius Aburnius Valens, an author of legal treatises ; L. Volusius Maecianus, chosen to conduct the legal studies of Marcus Aurelius, and author of a large work on Fidei Commissa ( Testamentary Trusts ); L. Ulpius Marcellus, a prolific writer ; and two others.

Designed by famous yacht designer L. Francis Herreshoff, this is essentially the same pattern as an admiralty anchor, albeit with small diamond shaped flukes or palms.

* 1975 – Bus massacre in Lebanon: An attack by the Phalangist resistance kills 26 militia members of the P. F. L.

Naples, which was held by Alfonso's brother, Pedro de Aragon, was besieged in 1424 by the Genoese ships and Joan's troops, now led by Francesco Sforza, son of Muzio ( who had died at L ' Aquila ).

The term was popularized by G. L. Trager and Bernard Bloch in a 1941 paper on English phonology and went on to become part of standard usage within the American structuralist tradition.

This period is marked by his intense involvement with Remy de Gourmont in the publication of L ' Ymagier, a luxuriously produced " art " magazine devoted to the symbolic analysis of medieval and popular prints.

A fragment of his treatise On burning-glasses was published as (" Concerning wondrous machines ") by L. Dupuy in 1777, and also appeared in 1786 in the forty-second volume of the Histoire de l ' Academie des Instrumentistes.

Locke also noted that the conscience is influenced by " education, company, and customs of the country ", a criticism mounted by J. L. Mackie, who argued that the conscience should be seen as an " introjection " of other people into an agent's mind.