I'm not sure I understand the meaning of chain, I have that chain is a finite sequence of symbols of some alphabet, alphabet being a non empty, finite set of symbols. So, for example, to me, the empty sequence of symbols shouldn't be a chain, because it is an empty sequence, mean...
After discussing it in the comments section, here is an example where only AC leads to a set that contains precisely one element of every element of a set. Assume a set x that contains infinitely many disjunctive and non-empty sets insofar as no pattern exists about the elements in the se...
math -fno-finite-math-only -fopenmp -D C10_USING_CUSTOM_GENERATED_MACROS -o/tmp/torchinductor_kulinseth/rf/crfks4ygnmnznafczrgu2spfbjzqasuvauzpfyqipjvsqvwpk2u5.so Output: clang: error: the clang compiler does not support '-march=native' clang: error: unsupported option '-fopenmp' clang:...
Identify the math term described. Set of numerical data. Explain how to solve equations that involve the quotient of two functions as the ones given below: 1) f(x)/g(x) = 5 2) f(x)/g(x) = -5. Explain what \pi represents in math....
Let G be SN, the finitary permutation (i.e., permutations with finite support) group on the set of positive integers N. We prove that G has the invariant von Neumann subalgebras rigidity (ISR, for short) property as introduced in Amrutam–Jiang’s work. More precisely, every G-invariant...
A vertex of a graph is the fundamental unit of which graphs are formed. They are also called nodes and appear as points when drawn. Each vertex is labeled independently and the vertex set is finite: {eq}V = \lbrace a, b, c, ... \rbrace {/eq} is a vertex set. An edge is an...
Unlike other data sets, // functions don't set the axis ranges automatically // since functions don't necessarily have a // finite range of x and y values. p.X.Min = 0 p.X.Max = 10 p.Y.Min = 0 p.Y.Max = 100 // Save the plot to a PNG file. if err := p.Save(4*vg...
in which the unique factorization property breaks down in a much more obvious manner." (The traditional example: in the ring (-5) one has 6=2·3=(1+-5)(1--5).) "In addition, we will be able to use these domains to show in a simple manner that a finite set of elements in a...
[] itemFeatures = Y.get(itemID); if (itemFeatures != null) { float value = (float) SimpleVectorMath.dot(itemFeatures, userFeatures); Preconditions.checkState(LangUtils.isFinite(value), "Bad estimate"); result[i] = value; } // else leave value at 0.0f } return result; } finally {...
This work gives sufficient conditions for uniqueness in distribution of semimartingale, obliquely reflecting Brownian motion in a nonpolyhedral, piecewise \(\mathcal {C}^2\) cone, with radially constant, Lipschitz continuous direction of reflection on each face. The conditions are shown to be verifie...