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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Porro prism designs have the added benefit of folding the optical path so that the physical length of the binoculars is less than the focal length of the objective. Porro prism binoculars were made in such a way to erect an image in a relatively small space, thus binoculars using prisms started in this way.
Isoperimetric inequality. In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume. In -dimensional space the inequality lower bounds the surface area or perimeter of a set by its volume , where is a unit sphere. The equality holds only when is a sphere in .
t. e. The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US$ 1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved ...
In optics, chromatic aberration ( CA ), also called chromatic distortion and spherochromatism, is a failure of a lens to focus all colors to the same point. [1] It is caused by dispersion: the refractive index of the lens elements varies with the wavelength of light. The refractive index of most transparent materials decreases with increasing ...
Hilbert’s sixth problem was a proposal to expand the axiomatic method outside the existing mathematical disciplines, to physics and beyond. This expansion requires development of semantics of physics with formal analysis of the notion of physical reality that should be done. [9] Two fundamental theories capture the majority of the fundamental ...
Physics-informed neural networks for solving Navier–Stokes equations. Physics-informed neural networks (PINNs), also referred to as Theory-Trained Neural Networks (TTNs), are a type of universal function approximators that can embed the knowledge of any physical laws that govern a given data-set in the learning process, and can be described by partial differential equations (PDEs).They ...
Fixation disparity. Fixation disparity is a tendency of the eyes to drift in the direction of the heterophoria. While the heterophoria refers to a fusion-free vergence state, the fixation disparity refers to a small misalignment of the visual axes when both eyes are open in an observer with normal fusion and binocular vision. [1]