A Bernstein theorem for special Lagrangian graphs by Jost J., Xin Y. L.

By Jost J., Xin Y. L.

We receive a Bernstein theorem for specified Lagrangian graphs in for arbitrary basically assuming bounded slope yet no quantitative limit.

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The standard equation of a circle is (x − h)2 + (y − k)2 = r2 where (h, k) are the coordinates of the center point, and r is the radius of the circle. In Descarta2D a circle is represented as Circle2D[{h, k}, r]. 6 Arcs 15 As demonstrated by the example, the function Point2D[circle] constructs the center point of the circle. The function Radius2D[circle] returns the radius of a circle. In[22]: Radius2D@c1D Out[22] 2 Descarta2D provides many functions for constructing circles. For example, we can construct a circle that passes through three given points.

Dividing an angle in radians by Degree converts the angle from radians to degrees. 4 Line Segments 13 We may want to construct lines with certain relationships to another line. For example, the following commands construct lines parallel and perpendicular to a given line through a given point. 4 -4 -2 0 2 4 Line Segments Perhaps it is more familiar to us that a line has a definite start point and end point. Such a line is called a line segment and is represented in Descarta2D as Segment2D[{x0, y0 }, {x1 , y1 }] where (x0 , y0 ) and (x1 , y1 ) are the coordinates of the start and end points, respectively, of the line segment.

Common transformations include translating, rotating, scaling and reflecting. A Descarta2D object can be transformed to produce a new object. 12 -2 0 2 4 Area and Arc Length Curves possess certain properties of interest such as area and length. These properties are independent of the position and orientation of the curve. In[37]: c1 = Circle2D@80, 0<, 2D; 8Area2D@c1D, Circumference2D@c1D< Out[37] 84 π, 4 π< Additionally, it may be of interest to compute the arc length of a portion of a curve or areas bounded by more than one curve.

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