The new proof broadly consists of three steps: derive the macroscopic theory from the mesoscopic one; derive the mesoscopic theory from the microscopic one; and then stitch them together in a single ...

The SUNDIALS suite consists of the following packages for ordinary differential equation (ODE) systems, differential-algebraic equation (DAE) systems, and nonlinear algebraic systems: Warning to users ...

But later, the White House published what might look like a complicated mathematical formula. But if you unpick the formula above it boils down to simple maths: take the trade deficit for the US ...

Masaki Kashiwara has won the 2025 Abel prize, sometimes called the Nobel prize of mathematics, for his work on algebraic analysis. Kashiwara, a professor at Kyoto University, Japan, received the ...

We study the classical linear partial differential equations: Poisson's equation and the heat equation. We learn about representation formulas for solutions, maximum principles, and energy estimates.

Mathematical modelling and real-time microfluidics-based measurements of nuclear shuttling dynamics of the transcription factor EB (TFEB) demonstrate its biphasic nature in response to nutrient ...

Université de Paris, Laboratoire Jacques-Louis, Lions (LJLL), Paris F-75005, France Sorbonne Université, CNRS, LJLL, Paris F-75005, France ...

In this paper, we present a precise and robust intensity-only Fourier-Equation-Solving method for measuring the azimuthal and radial mode purity of large-mode-number FMFs, and demonstrate this method ...

Euler inversion: Locating sources of potential-field data through inversion of Euler’s homogeneity equation. Geophysical Journal International ... While learning about the Euler deconvolution method, ...