We present in this paper a novel approach to the long-standing problem of motion planning for non-holonomic systems. Our method is built upon a parabolic partial differential equation that arises in ...

This article was originally published with the title “A Graphical Solution of the Quadratic Equation” in SA Supplements Vol. 71 No. 1849supp (June 1911), p. 359 doi:10.1038 ...

Researchers have found a new way to solve high-degree polynomial equations, previously thought impossible for 200 years. This math breakthrough reopens algebra.

In this paper, three examples of non-Hermitian Hamiltonians were presented on which an approach was applied based on the Heisenberg equation of motion, namely a first-order equation in the coordinate ...

Minimization principles are at the core of physics. The most well-known is the principle of least action, which can be used to derive Newton’s laws of motion and Maxwell’s equations for electricity ...

In this paper, a class of slightly perturbed equations of the form F (x)= ξ -x+αΦ (x) will be treated graphically and symbolically, where Φ (x) is an analytic function of x. For graphical developments ...

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By employing traveling wave transformation, the FKP equation was transformed into an ordinary differential equation (ODE) to acquire exact wave solutions. A range of exact analytical solutions for the ...