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This last non-simple continued fraction (sequence A110185 in the OEIS), equivalent to = [;,,,,,...], has a quicker convergence rate compared to Euler's continued fraction formula [clarification needed] and is a special case of a general formula for the exponential function:
In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
This means a DVR is an integral domain R that satisfies any and all of the following equivalent conditions: R is a local ring, a principal ideal domain, and not a field. R is a valuation ring with a value group isomorphic to the integers under addition. R is a local ring, a Dedekind domain, and not a field.
Similarly, the Tate conjecture is equivalent to: the so-called Tate realization, i.e. ℓ-adic cohomology, is a full functor : ( ()) (pure motives up to homological equivalence, continuous representations of the absolute Galois group of the base field k), which takes values in semi-simple representations. (The latter part is automatic in ...
A fractional ideal sheaf is a sub--module of . A fractional ideal sheaf J is invertible if, for each x in X , there exists an open neighborhood U of x on which the restriction of J to U is equal to O U ⋅ f , {\displaystyle {\mathcal {O}}_{U}\cdot f,} where f ∈ M X × ( U ) {\displaystyle f\in {\mathcal {M}}_{X}^{\times }(U)} and the product ...
In thermodynamics, the enthalpy of mixing (also heat of mixing and excess enthalpy) is the enthalpy liberated or absorbed from a substance upon mixing. [1] When a substance or compound is combined with any other substance or compound, the enthalpy of mixing is the consequence of the new interactions between the two substances or compounds. [1]
The Timex Sinclair 1000 (or T/S 1000) was the first computer produced by Timex Sinclair, a joint venture between Timex Corporation and Sinclair Research.It was launched in July 1982, with a US sales price of US$99.95, making it the cheapest home computer at the time; it was advertised as "the first computer under $100". [1]