Check the latest SOF IMO 2025 syllabus and exam pattern for Classes 1 to 12. Know section-wise topics, marking scheme, and ...

Abstract: The aim of this article is to publicize and prove the ";infinite-limit"; version of the final value theorem. The version we provide is a slight refinement of the classical literature in that ...

Abstract: We prove a robust converse barrier function theorem via the converse Lyapunov theory. While the use of a Lyapunov function as a barrier function is straightforward, the existence of a ...

Given a particle in Euclidean space, a central force is a force that points toward or away from the origin and depends only on the particle’s distance from the origin. If the particle’s position at ...

Click to see a step-by-step slideshow. STEP 1: Use the ruler to draw a vertical line, then draw a horizontal line directly from the end of the vertical line. ...rearrange the cubes so you have six ...

This paper describes the eccentricity, amplitude, phase shift, angular momentum, polarization, radial path, and orbital ...

The course gives an introduction to smooth manifolds. It covers tangent bundles, vector fields and integral curves (ordinary differential equations), Lie groups, differential forms, and integration.