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The real part of every nontrivial zero of the Riemann zeta function is 1/2. The Riemann hypothesis is that all nontrivial zeros of the analytical continuation of the Riemann zeta function have a real part of 1 / 2 . A proof or disproof of this would have far-reaching implications in number theory, especially for the distribution of prime ...
Calabi transformed the Calabi conjecture into a non-linear partial differential equation of complex Monge–Ampère type, and showed that this equation has at most one solution, thus establishing the uniqueness of the required Kähler metric. Yau proved the Calabi conjecture by constructing a solution of this equation using the continuity ...
Of the cleanly formulated Hilbert problems, numbers 3, 7, 10, 14, 17, 18, 19, and 20 have resolutions that are accepted by consensus of the mathematical community. Problems 1, 2, 5, 6, [g] 9, 11, 12, 15, 21, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems.
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.
Frobenius coin problem with 2-pence and 5-pence coins visualised as graphs: Sloping lines denote graphs of 2x+5y=n where n is the total in pence, and x and y are the non-negative number of 2p and 5p coins, respectively.
1. Thoroughly mix the beef, 1/2 cup tomato soup, onion soup mix, bread crumbs and egg in a large bowl. Place the mixture into a 13 x 9 x 2-inch baking pan and firmly shape into an 8 x 4-inch loaf.
Reserve 2 to 3 tablespoons for the gravy and pour the rest over the meatloaf. Stick the meatloaf back in the over and bake until the thickest portion reaches 160°F, which will take about 15 minutes.
Then the Binet equation for () can be solved numerically for nearly any central force (/). However, only a handful of forces result in formulae for u {\displaystyle u} in terms of known functions. The solution for φ {\displaystyle \varphi } can be expressed as an integral over u {\displaystyle u}