How to use dualize in a sentence? Find typical usage patterns (collocations)/phrases/context for "dualize" and check conjugation/comparative form for "dualize". Mastering all the usages of "dualize" from sentence examples published by news publications.
The points dualize to lines and the convex hull of the points dualizes to the upper and lower envelope of the set of lines. The vertices of the upper convex hull dualize to segments on the upper envelope. The vertices of the lower convex hull dualize to segments on the lower envelope. The range of slopes of the supporting lines of a point on the hull dualize to the x-interval of segment that point dualizes to.
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The points dualize to lines and the convex hull of the points dualizes to the upper and lower envelope of the set of lines. The vertices of the upper convex hull dualize to segments on the upper envelope. The vertices of the lower convex hull dualize to segments on the lower envelope. The range of slopes of the supporting lines of a point on the hull dualize to the x-interval of segment that point dualizes to.
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To dualize the Union, assuming its boundaries to be fixed, was one thing.
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To dualize the Union in the face of a movement for extension of boundaries was another.
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There are currently plans to upgrade US 50 in Queen Anne's County to a full limited access freeway, the freeway portion ending at an interchange with Maryland Route 404 atop the Queen Anne's/Talbot County border. This comes along with plans to fully dualize the latter highway in the state of Maryland.
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From Shahdara, the track mainly consisted of a single track until the city Peshawar. Construction works to dualize the entire track between Karachi to Shahdara were completed and inaugurated in January 2016. As part of the first phase of the CPEC railway project, the remaining stretch of track between Shahdara and Peshawar is to be upgraded to a dual track railway. The 676 kilometer portion between Lalamusa, north of Lahore, and Peshawar will require complete reconstruction with the addition of tunnels, culverts, and bridges, while over 900 kilometers south of Lalamusa towards Karachi will be upgraded to handle cars with a 25-ton axle load capacity.
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For any morphism of the form f: X \to F(A') in D, there exists a unique morphism h: A \to A' such that the following diagram commutes: The typical diagram of the definition of a universal morphism. We can dualize this categorical concept. A universal morphism from F to X is a unique pair (A, u: F(A) \to X) that satisfies the following universal property. For any morphism of the form f: F(A') \to X in D, there exists a unique morphism h: A' \to A such that the following diagram commutes: The most important arrow here is u: F(A) \to X which establishes the universal property.
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By the Principle of Duality in a projective plane, the dual of each point is a line, and the dual of a locus of points (a set of points satisfying some condition) is called an envelope of lines. Using Steiner's definition of a conic (this locus of points will now be referred to as a point conic) as the meet of corresponding rays of two related pencils, it is easy to dualize and obtain the corresponding envelope consisting of the joins of corresponding points of two related ranges (points on a line) on different bases (the lines the points are on). Such an envelope is called a line conic (or dual conic). In the real projective plane, a point conic has the property that every line meets it in two points (which may coincide, or may be complex) and any set of points with this property is a point conic.
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