In theory exploration, it is hard to find syntactically complex properties. Especially, there have been not so much investigation on exploration of conditional properties. In this paper, we study how the top-down approach based on generalization can be used in theory exploration to find complex conditional properties through an example....
For definition 2 shows that all functions of p(x|h) can be calculated from T(x) and h, when T is sufficient for h. This point may look superficially as though it assumes the likelihood principle, but it does not. That all inferences about h depend on p(xobs|h) is, more or less...
Functions can be defined recursively on one or more of their arguments. These are called their recursive arguments. The recursive arguments of + and < > are their first arguments. Lemmas can also be presented as rewrite rules. The decision to represent them in this way constitutes a commitment...
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Generally, such a comparison is hampered by the more complex and rigid cage shape of the [DNTX]+ derivatives, since the division of such cage vibrations into certain stretching and ring deformations is more arbitrary and the vibrational coupling between different cage vibrations is more serious ...
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In this paper, we show that the conjecture on the Selberg integral of Schur polynomials is formally equivalent to their result, after applying a more complicated complex contour, thus leading to the proof of the An case at β = 1. To perform a double check, we also directly start from ...
So, D-mod1/2(BunG) represents the automorphic side: a category of specially crafted D-modules living on the stack of G-bundles. These objects encode the "functions" or "representations" tied to the group G’s action on the geometry, and the goal is to send them via the functor LG to...
This equation captures the essence of complex exponentiation and its relation to sinusoidal functions.Euler's Rule Without the work of Leonhard Euler, modern mathematics would not be where it is today. This can be said of many other past mathematicians such as Carl Friedrich Gauss, Pierre-Simon ...
We introduce a natural cell decomposition of a closed oriented surface associated with a pants decomposition, and an explicit groupoid cocycle on the cell decomposition which represents each point of the Teichm眉ller spaceTg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym...