Sentence examples for contain all points from inspiring English sources

Further, the maximal ideal space XI of the resulting C⁎-algebra for the quotient module is shown to be contained in Z(I)∩∂Bn, where Z(I) is the zero variety for I, and to contain all points in ∂Bn that are limit points of Z(I ∩Bn.

For every knot, we identify the pentagons or hexagons around it that contain all points that are closer to this than any other knot.

In this approach, the unit cell is divided into two distinct regions: (i) first region contain all points inside the muffin-tin spheres around the atom (ii) second region is the interstitial region outside the muffin-tin spheres.

The main idea of the algorithm is to find a hyperplane H that can contain all points of the training set.

(A4) Through each point X not on a line l, at least two lines pass not meeting (parallel to) l. (A5) If a subset S of the points contains all points on the lines through pairs of distinct points of S, then the subset S contains all points of the geometric structure (see [11 14]).

Each K-dimensional bin contains all points pairs ( q i, q j ) ∈ P whose measurements {m k (q i, q j )} fall within the bin ranges.

An obvious candidate for such a curve is the convex hull, i.e. the smallest convex polygon that contains all points of the shape.

The convex polygon technique is based on the determination of the convex hull; the smallest convex region that contains all points belonging to a given region shape [37].

FIND-PARETO-SET V) is a recursive algorithm that FIND-PARETO-SET Vpoints in the rectangle V deFIND-PARETO-SET Vts is the initial ParecursiveIΓ (see Lemmalgorithms recthatle contains all points findsV. The allorithm starts from finding a ParetoΓ that does not dominate any other points in V (line 4).

The convex hull (mathbf {Co}(mathcal {S})) of a finite set of points (mathcal S={x_1), (ldots, x_m} subset mathbb {R}) is the minimal convex set containing all points (zin mathcal {S}), that is, (mathbf {Co} (mathcal {S}) =lbrace z= sum _{i=1}^{m} alpha _i x_i | alpha _i geqslant 0, sum _{i=1}^{m} alpha _i =1rbrace ).

Given sequences ({lambda ^{ k)}}) and ({mu ^{ k)}}), the iterative procedure produces the sequence ({x^{ k)}}) according to begin{aligned} {varvec{x}}^{ k+1)} = arg underset{{varvec{x}}in X}{min } L({varvec{x}},{varvec{lambda}} ^{ k)},{varvec{mu}} ^{ k)}) end{aligned} (8)We denote by (X^o) the open set containing all points of X excluding its boundary.