In this paper we present a study of definability properties of fixed points of effective operators on the real numbers without the equality test. In particular we prove that Gandy theorem holds for the reals without the equality test. This provides a useful tool for dealing with recursive ...
Converting between decimal and two's complement is straightforward for positive numbers, a simple decimal to binary conversion. For negative numbers, the following algorithm is often used: (1) take the absolute value of the decimal number, (2) convert it to binary, (3) complement all of the...
2 Decreasing zero sequence is a basis in the set of real positive numbers The following result plays the crucial role in the proof of the main result. Lemma 1 Let be an arbitrary sequence of strictly decreasing real numbers, such that [Math Processing Error] (1) Then, (I) for every ...
ðF20 Þ inf F ¼ À1, or, also by ðF200 Þ, there exists a sequence fang1n¼1 of positive real numbers, such that lim n!1 FðanÞ ¼ À1. Most recently, Piri et al. [9] used the following condition ðF30 Þ instead of (F3). ðF30 Þ F is ...
Let G be the group of all nonzero real numbers under multiplication and N the subgroup of all positive real numbers. What are the cosets of N in G? Prove that a ring with a cyclic additive group must be commutative. If G is a finite group and...
In the sequel, ℝ, and ℕ denote the set of real numbers, the set of nonnegative real numbers and the set of positive integers, respectively. Definition 1 Let X be a nonempty set. A function is called a G-metric if the following conditions are satisfied: (G1) if , then ; (G...
On the Exceptional Set of the Sum of a Prime Number and a Fixed Degree of a Prime Number 来自 掌桥科研 喜欢 0 阅读量: 12 作者: ISAS Allakov 摘要: Let X be a sufficiently great real number and M denote the set of natural numbers not exceeding X which cannot be written as a ...
Two's complement is a way to interpret a binary number. In two's complement, positive numbers always start with a 0 and negative numbers always start with a 1. If the leading bit of a two's complement number is 0, the value is obtained by calculating the standard binary value of the...
Suppose that there exist positive numbers t0, r, R > 0 and a vector u0ɛ C – {0} such that (1) u≠tΛ(u) for t ɛ [0, 1] and u ɛ C with || u || = u, (2) u≠Λ(u) + tu0 for t≥ 0 and u ɛ C with || u || = R. (3) u≠Λ(u) + tu0 for...
Interest in Reidemeister numbers goes back to the 1930s, and checking whether a group hasR_\inftysheds some light on its automorphism group and on related fixed-point theorems. This is illustrated by results, e.g., for algebraic and Lie groups [46, Theorem 10.1], in algebraic topology [31...