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In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this context, the partitioning is called simply a dissection (of one polytope into another).
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.
MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities.
SOCPs can be solved by interior point methods [2] and in general, can be solved more efficiently than semidefinite programming (SDP) problems. [3] Some engineering applications of SOCP include filter design, antenna array weight design, truss design, and grasping force optimization in robotics. [ 4 ]
Solving mathematical problems by computer simulation as opposed to traditional engineering methods. Numerical methods used in scientific computation, for example numerical linear algebra and numerical solution of partial differential equations
The language of mathematics has a wide vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject.
If both of these problems can be solved, then the minimal model program can be carried out. The existence of flips for 3-folds was proved by Mori (1988) . The existence of log flips, a more general kind of flip, in dimension three and four were proved by Shokurov ( 1993 , 2003 ) whose work was fundamental to the solution of the existence of log ...
The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...