We construct a nonstandard Lagrangian, called the multiplicative form, for a homogeneous scalar field and a fermion field via the inverse calculus of variations with the equations of motion that still ...

The inverse problem in the calculus of variations for a given set of second order ordinary differential equations consists of deciding whether their solutions are those of Euler-Lagrange equations and ...

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\begin{align} \underset{\mathbf{W}}{\operatorname{arg,min}},, & |\mathbf{W}\mathbf{W}^\top \mathbf{X}-\mathbf{X}|_\mathrm{F}^2 & & \ \text{s.t.},,,,, & \mathbf{W ...

Calculus, the mathematical study of continuous change, stands as a cornerstone of advanced mathematics and its applications. As you delve into this powerful branch of mathematics, you’ll discover a ...