In recent years, expansion-based techniques have been shown to be very powerful in theory and practice for solving quantified Boolean formulas (QBF), the extension of propositional formulas with existential and universal quantifiers over Boolean variables. Such approaches partially expand one type of va...
Arbitrary coefficient (Math.), a literal coefficient placed arbitrarily in an algebraic expression, the value of the coefficient being afterwards determined by the conditions of the problem. Meaning of Arbitrary coefficient from wikipedia - and approaches a value of 0 for individuals with arbitrarily ...
Given the above definitions, a number of algebraic considerations (reflecting different physical situations) are in row, based on the sheer fact that any of these coefficients affects (not only by its value, i.e. quantitatively, but also via its sign, qualitatively) the physical meaning of the...
at all times, where your body is in space and how to control its movement so that you land safely. We all have the ability, called proprioception or kinaesthesia, to know where our body is in relation to the world around us. If we didn’t, we wouldn’t be able ...
Let $T$ be a tile in $\\mathbb {Z}^n$, meaning a finite subset of $\\mathbb {Z}^n$. It may or may not tile $\\mathbb {Z}^n$, in the sense of $\\mathbb {Z}^n$ having a partition into copies of $T$. However, we prove that $T$ does tile $\\mathbb {Z}^d$ ...
(G,H) of finite groups such that. As a corollary of its proof we get that for every positive integernthere are infinitely many triples (H,N,G) of finite solvable groupssuch thatG/Nis cyclic of order,N/His cyclic of arbitrarily large prime order and. We investigate the seriesin the ...
Other mathy projects & numeric types I've written a number of other polynomial implementations and numeric types catering to various specific scenarios. Depending on what you're trying to do, another implementation of this same library might be more appropriate. All of my polynomial projects should...
That's cool, but we can almost certainly have done all that in code. What about a complex use case that involves some math?expression, err := govaluate.NewEvaluableExpression("(requests_made * requests_succeeded / 100) >= 90"); parameters := make(map[string]interface{}, 8) parameters[...
The corresponding errors for CP decomposition and binomial series are shown in f and g, respectively Full size image As shown in Fig. 1a, first the 3D kernel function \(\mathcal {K}_{g_z}^{tc}(L,H,h)\) is sampled on a rectilinear grid covering the region of interest:...
This way, the first and second derivatives of f˜ at x=x1/2 are simply given by(17a)f˜x(0)=A2,(17b)f˜xx(0)=2A3, so the curvature of the curve at point P0=(x1/2,f(x1/2)) is given by [9](18)κ=2A3(A22+1)3/2+O(hN−1), meaning that κ=2A3/(A22+1)3/...