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Though there are many approximate solutions (such as Welch's t-test), the problem continues to attract attention [4] as one of the classic problems in statistics. Multiple comparisons: There are various ways to adjust p-values to compensate for the simultaneous or sequential testing of hypotheses. Of particular interest is how to simultaneously ...
The second HK theorem defines an energy functional for the system and proves that the ground-state electron density minimizes this energy functional. In work that later won them the Nobel prize in chemistry , the HK theorem was further developed by Walter Kohn and Lu Jeu Sham to produce Kohn–Sham DFT (KS DFT).
Pages in category "Theorems in statistics" The following 55 pages are in this category, out of 55 total. ... Le Cam's theorem; Lehmann–Scheffé theorem;
The STEP support programme provides modules for individual additional study, along with hints and solutions. Furthermore, the book "Advanced Problems in Mathematics: Preparing for University" by Stephen Siklos, a former paper-setter for STEP, has been specifically written for students preparing for it.
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.In his 1972 paper, "Reducibility Among Combinatorial Problems", [1] Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete [2] (also called the Cook-Levin theorem) to show that there is a polynomial time many-one reduction ...
The formal foundation of TDDFT is the Runge–Gross (RG) theorem (1984) [1] – the time-dependent analogue of the Hohenberg–Kohn (HK) theorem (1964). [2] The RG theorem shows that, for a given initial wavefunction, there is a unique mapping between the time-dependent external potential of a system and its time-dependent density.
In mathematics, the Khintchine inequality, named after Aleksandr Khinchin and spelled in multiple ways in the Latin alphabet, is a theorem from probability, and is also frequently used in analysis. Consider N {\displaystyle N} complex numbers x 1 , … , x N ∈ C {\displaystyle x_{1},\dots ,x_{N}\in \mathbb {C} } , which can be pictured as ...
1905 Emanuel Lasker's original proof of the Lasker–Noether theorem took 98 pages, but has since been simplified: modern proofs are less than a page long. 1963 Odd order theorem by Feit and Thompson was 255 pages long, which at the time was over 10 times as long as what had previously been considered a long paper in group theory.