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To prove that this condition is sufficient to guarantee existence of a compatible second-order tensor field, we start with the assumption that a field exists such that =. We will integrate this field to find the vector field v {\displaystyle \mathbf {v} } along a line between points A {\displaystyle A} and B {\displaystyle B} (see Figure 2), i.e.,
In mathematics, specifically in the field of group theory, the McKay equality, formerly known as the McKay conjecture, is a theorem of equality between the number of irreducible complex characters of degree not divisible by a prime number to that of the normalizer of a Sylow -subgroup.
In mathematics, the support of a real-valued function is the subset of the function domain of elements that are not mapped to zero. If the domain of f {\displaystyle f} is a topological space , then the support of f {\displaystyle f} is instead defined as the smallest closed set containing all points not mapped to zero.
Hasse diagram of the natural numbers, partially ordered by "x≤y if x divides y".The numbers 4 and 6 are incomparable, since neither divides the other. In mathematics, two elements x and y of a set P are said to be comparable with respect to a binary relation ≤ if at least one of x ≤ y or y ≤ x is true.
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements. [1]
The smallest friendly number is 6, forming for example, the friendly pair 6 and 28 with abundancy σ(6) / 6 = (1+2+3+6) / 6 = 2, the same as σ(28) / 28 = (1+2+4+7+14+28) / 28 = 2. The shared value 2 is an integer in this case but not in many other cases. Numbers with abundancy 2 are also known as perfect numbers. There are several unsolved ...
definition remarks rational equivalence Z ~ rat Z' if there is a cycle V on X × P 1 flat over P 1, such that [V ∩ X × {0}] − [V ∩ X × {∞}] = [Z] − [Z' ]. the finest adequate equivalence relation (Lemma 3.2.2.1 in Yves André's book [2]) "∩" denotes intersection in the cycle-theoretic sense (i.e. with multiplicities) and [.] denotes the cycle associated to a subscheme. see also ...
Consider -dimensional Euclidean space with its usual Borel topology and σ-algebra. Consider a collection of Gaussian measures Γ = { γ i ∣ i ∈ I } , {\displaystyle \Gamma =\{\gamma _{i}\mid i\in I\},} where the measure γ i {\displaystyle \gamma _{i}} has expected value ( mean ) m i ∈ R n {\displaystyle m_{i}\in \mathbb {R} ^{n}} and ...