A recursive definition of $p$-ary addition without carry

François Laubie

Displaying similar documents to “A recursive definition of $p$ -ary addition without carry”

Infinite games and chain conditions

Santi Spadaro (2016)

Fundamenta Mathematicae

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We apply the theory of infinite two-person games to two well-known problems in topology: Suslin’s Problem and Arhangel’skii’s problem on the weak Lindelöf number of the $G_{δ}$ topology on a compact space. More specifically, we prove results of which the following two are special cases: 1) every linearly ordered topological space satisfying the game-theoretic version of the countable chain condition is separable, and 2) in every compact space satisfying the game-theoretic version of the weak...

Improved upper bounds for nearly antipodal chromatic number of paths

Yu-Fa Shen, Guo-Ping Zheng, Wen-Jie HeK (2007)

Discussiones Mathematicae Graph Theory

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For paths Pₙ, G. Chartrand, L. Nebeský and P. Zhang showed that $a c^{'} (P ₙ) \leq (\binom{n - 2}{2}) + 2$ for every positive integer n, where ac’(Pₙ) denotes the nearly antipodal chromatic number of Pₙ. In this paper we show that $a c^{'} (P ₙ) \leq (\binom{n - 2}{2}) - n / 2 - ⎣ 10 / n ⎦ + 7$ if n is even positive integer and n ≥ 10, and $a c^{'} (P ₙ) \leq (\binom{n - 2}{2}) - (n - 1) / 2 - ⎣ 13 / n ⎦ + 8$ if n is odd positive integer and n ≥ 13. For all even positive integers n ≥ 10 and all odd positive integers n ≥ 13, these results improve the upper bounds for nearly antipodal chromatic number of Pₙ.

Submultiplicative functions and operator inequalities

Hermann König, Vitali Milman (2014)

Studia Mathematica

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Let T: C¹(ℝ) → C(ℝ) be an operator satisfying the “chain rule inequality” T(f∘g) ≤ (Tf)∘g⋅Tg, f,g ∈ C¹(ℝ). Imposing a weak continuity and a non-degeneracy condition on T, we determine the form of all maps T satisfying this inequality together with T(-Id)(0) < 0. They have the form Tf = ⎧ $(H \circ f / H) f^{' p}$ , f’ ≥ 0, ⎨ ⎩ $- A (H \circ f / H) | f^{'} |^{p}$ , f’ < 0, with p > 0, H ∈ C(ℝ), A ≥ 1. For A = 1, these are just the solutions of the chain rule operator equation. To prove this, we characterize the submultiplicative, measurable...

Common terms in binary recurrences

Erzsébet Orosz (2006)

Acta Mathematica Universitatis Ostraviensis

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The purpose of this paper is to prove that the common terms of linear recurrences $M (2 a, - 1, 0, b)$ and $N (2 c, - 1, 0, d)$ have at most $2$ common terms if $p = 2$ , and have at most three common terms if $p > 2$ where $D$ and $p$ are fixed positive integers and $p$ is a prime, such that neither $D$ nor $D + p$ is perfect square, further $a, b, c, d$ are nonzero integers satisfying the equations $a^{2} - D b^{2} = 1$ and $c^{2} - (D + p) d^{2} = 1$ .

Direct summands of systems of continuous linear transformations

Uri Fixman, Frank A. Zorzitto

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CONTENTSIntroduction............................................................................................................ 51. The category of $C^{N}$ -systems........................................................................... 82. The problem of split monomorphisms................................................................ 103. Internal hom and tensor product........................................................................... 134. Characterizations of split monomorphisms..........................................................

Acknowledgment to the paper: “Another proof that a chain of non-empty $H$ -closed subspaces has a non-empty intersection’

J. Mioduszewski (1971)

Colloquium Mathematicae

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A general upper bound in extremal theory of sequences

Martin Klazar (1992)

Commentationes Mathematicae Universitatis Carolinae

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We investigate the extremal function $f (u, n)$ which, for a given finite sequence $u$ over $k$ symbols, is defined as the maximum length $m$ of a sequence $v = a_{1} a_{2} . . . a_{m}$ of integers such that 1) $1 \leq a_{i} \leq n$ , 2) $a_{i} = a_{j}, i \neq j$ implies $| i - j | \geq k$ and 3) $v$ contains no subsequence of the type $u$ . We prove that $f (u, n)$ is very near to be linear in $n$ for any fixed $u$ of length greater than 4, namely that $f (u, n) = O (n 2^{O (α {(n)}^{| u | - 4})}) .$ Here $| u |$ is the length of $u$ and $α (n)$ is the inverse to the Ackermann function and goes to infinity very slowly. This result extends the estimates in [S] and...

Shifted values of the largest prime factor function and its average value in short intervals

Jean-Marie De Koninck, Imre Kátai (2016)

Colloquium Mathematicae

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We obtain estimates for the average value of the largest prime factor P(n) in short intervals [x,x+y] and of h(P(n)+1), where h is a complex-valued additive function or multiplicative function satisfying certain conditions. Letting $s_{q} (n)$ stand for the sum of the digits of n in base q ≥ 2, we show that if α is an irrational number, then the sequence ${(α s_{q} (P (n)))}_{n \in ℕ}$ is uniformly distributed modulo 1.

Boundedness results of solutions to the equation $x^{\prime\prime\prime}+ax^{\prime\prime}+g(x)x^{\prime}+h(x)=p(t)$ without the hypothesis $h(x)\,\operatorname{sgn}x\geq 0$ for $|x|>R$ .

Ján Andres (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi $h(x)\,\text{sgn}x\geq 0$ $for|x|>R$ , si dimostra l'esistenza di almeno una soluzione limitata sopprimendo l'ipotesi suddetta.

A dual space characterization of $P_{1}$ - and $P_{2}$ -lattices of order ω+

W. Zarębski (1982)

Colloquium Mathematicae

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Primefree shifted Lucas sequences

Lenny Jones (2015)

Acta Arithmetica

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We say a sequence $= {(s ₙ)}_{n \geq 0}$ is primefree if |sₙ| is not prime for all n ≥ 0, and to rule out trivial situations, we require that no single prime divides all terms of . In this article, we focus on the particular Lucas sequences of the first kind, $_{a} = {(u ₙ)}_{n \geq 0}$ , defined by u₀ = 0, u₁ = 1, and uₙ = aun-1 + un-2 for n≥2, where a is a fixed integer. More precisely, we show that for any integer a, there exist infinitely many integers k such that both of the shifted sequences $_{a} \pm k$ are simultaneously primefree. This...

Displaying similar documents to “A recursive definition of p -ary addition without carry”

Displaying similar documents to “A recursive definition of $p$ -ary addition without carry”