Which is Monge Ampere equation?

The elliptic Monge–Ampère equation is a fully nonlinear partial differential equation, which originated in geometric surface theory and has been widely applied in dynamic meteorology, elasticity, geometric optics, image processing and others.

Which of the following is Monges equation?

Any Monge equation has a Monge cone. and expresses a relation between the differentials dxk. The Monge cone at a given point (x0., xn) is the zero locus of the equation in the tangent space at the point. The Monge equation is unrelated to the (second-order) Monge–Ampère equation.

What are the solutions to the equation?

A solution to an equation is a value of a variable that makes a true statement when substituted into the equation. The process of finding the solution to an equation is called solving the equation. To find the solution to an equation means to find the value of the variable that makes the equation true.

How do you find the complementary function?

Note: A complementary function is the general solution of a homogeneous, linear differential equation. To find the complementary function we must make use of the following property. ycf(x) = Ay1(x) + By2(x) where A, B are constants.

How many kinds of solutions of a differential equation are there and what are they?

We can place all differential equation into two types: ordinary differential equation and partial differential equations. A partial differential equation is a differential equation that involves partial derivatives.

What does a differential equation represent?

In mathematics, a differential equation is an equation that relates one or more functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.

What does solutions mean in math?

Scientific definitions for solution Mathematics A value or values which, when substituted for a variable in an equation, make the equation true. For example, the solutions to the equation x2 = 4 are 2 and -2.

How many solutions are there to the equation?

If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.

What are the complementary functions?

A complementary function is one part of the solution to a linear, autonomous differential equation. An ordinary differential equation (ODE) relates the sum of a function and its derivatives.

Why differential equations are used?

In biology and economics, differential equations are used to model the behavior of complex systems. The mathematical theory of differential equations first developed together with the sciences where the equations had originated and where the results found application.

What does the explain () method do in MongoDB?

For backwards compatibility with earlier versions of cursor.explain (), MongoDB interprets true as “allPlansExecution” and false as “queryPlanner”. For more information on the modes, see Verbosity Modes. The explain () method returns a document with the query plan and, optionally, the execution statistics.

What is a mongosh method?

This is a mongosh method. This is not the documentation for Node.js or other programming language specific driver methods. In most cases, mongosh methods work the same way as the legacy mongo shell methods. However, some legacy methods are unavailable in mongosh.

What is Monge’s theory of optimal transportation?

Given probability measures μ on X and ν on Y, Monge’s formulation of the optimal transportation problem is to find a transport map T : X → Y that realizes the infimum where T∗ ( μ) denotes the push forward of μ by T.

How do I get the execution statistics of a MongoDB plan?

In “allPlansExecution” mode, MongoDB returns statistics describing the execution of the winning plan as well as statistics for the other candidate plans captured during plan selection. cursor.explain () returns the queryPlanner and executionStats information for the evaluated method.