Logarithmic convexity type continuous dependence results for discrete harmonic functions defined as solutions of the standard $C^0$ piecewise-linear approximation to Laplace's equation are proved.

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Scientists at the Institute for Photonic Quantum Systems (PhoQS) and the Paderborn Center for Parallel Computing (PC2) at ...

It can take years for humans to solve complex scientific problems. With AI, it can take a fraction of the time.

Charles Gilpin, Jr., Approximation of the Greatest Root of a Cubic Equation with Three Real Roots, The American Mathematical Monthly, Vol. 13, No. 6/7 (Jun. - Jul., 1906), pp. 140-141 ...

Blasting is considered an indispensable process in mining excavation operations. Generally, only a small percentage of the total energy of blasting is consumed in the fragmentation and displacement of ...

A new two-step second derivative block method (TSDBM) using Bernstein polynomial of convergence order six for solving Riccati Differential Equations (RDEs) is presented. The TSDBM is constructed on ...

The Rayleigh-Ritz approximation is employed to describe the deformation of the beam, incorporating various boundary conditions and defining the generalized coordinates. Finally, the Hamiltonian ...