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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.
Ornithoprion is a genus of extinct cartilaginous fish in the family Caseodontidae. The only species, O. hertwigi, lived during the Moscovian stage of the Pennsylvanian, between 315.2 and 307 million years ago, and is known from black shale deposits in what is now the Midwestern United States.
A cushion filled with stuffing. In geometry, the paper bag problem or teabag problem is to calculate the maximum possible inflated volume of an initially flat sealed rectangular bag which has the same shape as a cushion or pillow, made out of two pieces of material which can bend but not stretch.
The minimum pattern count problem: to find a minimum-pattern-count solution amongst the minimum-waste solutions. This is a very hard problem, even when the waste is known. [ 10 ] [ 11 ] [ 12 ] There is a conjecture that any equality-constrained one-dimensional instance with n sizes has at least one minimum waste solution with no more than n + 1 ...
Hilbert's problems ranged greatly in topic and precision. Some of them, like the 3rd problem, which was the first to be solved, or the 8th problem (the Riemann hypothesis), which still remains unresolved, were presented precisely enough to enable a clear affirmative or negative answer.
The problem remains open, but over a sequence of papers researchers have tightened the gap between the known lower and upper bounds. In particular, Norwood & Poole (2003) constructed a (nonconvex) universal cover and showed that the minimum shape has area at most 0.260437; Gerriets & Poole (1974) and Norwood, Poole & Laidacker (1992) gave ...
The content ranges from extremely difficult algebra and pre-calculus problems to problems in branches of mathematics not conventionally covered in secondary or high school and often not at university level either, such as projective and complex geometry, functional equations, combinatorics, and well-grounded number theory, of which extensive knowledge of theorems is required.
The satisfiability problem, also called the feasibility problem, is just the problem of finding any feasible solution at all without regard to objective value. This can be regarded as the special case of mathematical optimization where the objective value is the same for every solution, and thus any solution is optimal.