Negative Integer

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Paulo Roberto Prezotti Filho - One of the best experts on this subject based on the ideXlab platform.

Faradiba Sarquis Serpa - One of the best experts on this subject based on the ideXlab platform.

Valderio Anselmo Reisen - One of the best experts on this subject based on the ideXlab platform.

Apoloniusz Tyszka - One of the best experts on this subject based on the ideXlab platform.

  • a function f n 0 n 0 that cannot be bounded by a computable function and an infinite loop in mupad such that it takes as input a positive Integer n returns non Negative Integers g n m m 1 2 3 and f n g n m for any m f n
    2013
    Co-Authors: Apoloniusz Tyszka
    Abstract:

    For a positive Integer n, let f(n) denote the smallest non-Negative Integer b such that for each system S \subseteq {x_k=1,x_i+x_j=x_k,x_i*x_j=x_k: i,j,k \in {1,...,n}} with a solution in non-Negative Integers x_1,...,x_n, there exists a solution of S in {0,...,b}^n. We prove that the function f is strictly increasing and dominates all computable functions. We present an infinite loop in MuPAD which takes as input a positive Integer n and returns a non-Negative Integer on each iteration. Let g(n,m) denote the number returned on the m-th iteration, if n is taken as input. Then, g(n,m) \leq m-1, 0=g(n,1) N that cannot be bounded by any computable function. This code takes as input a non-Negative Integer n, immediately returns 0, and computes a system S of polynomial equations. If the loop terminates for S, then the next instruction is executed and returns \xi(n).

  • mupad codes which implement limit computable functions that cannot be bounded by any computable function
    arXiv: Computational Complexity, 2013
    Co-Authors: Apoloniusz Tyszka
    Abstract:

    For a positive Integer n, let f(n) denote the smallest non-Negative Integer b such that for each system S \subseteq {x_k=1,x_i+x_j=x_k,x_i*x_j=x_k: i,j,k \in {1,...,n}} with a solution in non-Negative Integers x_1,...,x_n, there exists a solution of S in {0,...,b}^n. We prove that the function f is strictly increasing and dominates all computable functions. We present an infinite loop in MuPAD which takes as input a positive Integer n and returns a non-Negative Integer on each iteration. Let g(n,m) denote the number returned on the m-th iteration, if n is taken as input. Then, g(n,m) \leq m-1, 0=g(n,1)<1=g(n,2) \leq g(n,3) \leq g(n,4) \leq ... and g(n,f(n))N that cannot be bounded by any computable function. This code takes as input a non-Negative Integer n, immediately returns 0, and computes a system S of polynomial equations. If the loop terminates for S, then the next instruction is executed and returns \xi(n).

Klaus L P Vasconcellos - One of the best experts on this subject based on the ideXlab platform.

  • first order non Negative Integer valued autoregressive processes with power series innovations
    Brazilian Journal of Probability and Statistics, 2015
    Co-Authors: Marcelo Bourguignon, Klaus L P Vasconcellos
    Abstract:

    In this paper, we introduce a first order non-Negative Integer valued autoregressive process with power series innovations based on the binomial thinning. This new model contains, as particular cases, several models such as the Poisson INAR(1) model (Al-Osh and Alzaid (J. Time Series Anal. 8 (1987) 261–275)), the geometric INAR(1) model (Jazi, Jones and Lai (J. Iran. Stat. Soc. (JIRSS) 11 (2012) 173–190)) and many others. The main properties of the model are derived, such as mean, variance and the autocorrelation function. Yule–Walker, conditional least squares and conditional maximum likelihood estimators of the model parameters are derived. An extensive Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. Special sub-models are studied in some detail. Applications to two real data sets are given to show the flexibility and potentiality of the new model.