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A note on Browkin’s and Cao’s cancellation algorithm

Tomski A., Zakarczemny M.

Technical Transactions

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2018

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Vol. 115, iss. 7

153--165

EN

In this paper, we follow our generalisation of the cancellation algorithm described in our previous paper [A. Tomski, M. Zakarczemny, On some cancellation algorithms, NNTDM. 23, 2017, p. 101–114]. For f being a natural-valued function defined on ℕs , s ≥1 we remove the divisors of all possible values of ƒ in the points in which the sum of coordinates is less than or equal to n. The least non-cancelled number is called the discriminator Dƒ(n). We find formulas, or at least an estimation for this discriminator, in the case of a broad class of sequences.

PL

Kontynuujemy badania nad generalizacją algorytmu sitowego Browkina i Cao, [A. Tomski, M. Zakarczemny, On some cancellation algorithms, NNTDM. 23, 2017, p. 101–114]. Niech f będzie funkcją o wartościach w zbiorze liczb naturalnych, określoną na ℕs , s ≥1. Usuwamy dzielniki wszystkich możliwych wartości funkcji ƒ, w punktach, w których suma współrzędnych nie przekracza n. Najmniejszą niewykreśloną liczbę naturalną nazywamy dyskryminatorem Dƒ(n). W artykule uogólniamy pojęcie dyskryminatora. Znajdujemy jawne wzory lub oszacowania na dyskryminator dla szerokiej klasy ciągów.

2

On a study of double gai sequence space

Subramanian N., Misra U. K.

Journal of Mathematics and Applications

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2013

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Vol. 36

95--111

EN

Let χ2 denote the space of all prime sense double gai sequences and Λ2 the space of all prime sense double analytic sequences. This paper is devoted to the general properties of χ2.

3

On some new quasi almost ∆m-lacunary strongly P-convergent double sequences defined by Orlicz functions

Khan V. A., Tabassum S.

Journal of Mathematics and Applications

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2011

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Vol. 34

45--52

EN

The idea of quasi almost P-convergent sequences defined as [...] was introduced by V.A.Khan and Q.M.D.Lohani [Mathematicki Vesnik, (60), 95-100 (2008)]. In this paper we introduce a new concept for quasi almost ∆m-lacunary strongly P-convergent double sequences defined by Orlicz function and give inclusion relations.

4

Time-parametric control : uniform convergence of the optimal value functions of discretized problems

Gugat M.

Control and Cybernetics

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1999

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Vol. 28, no 1

7-33

EN

The problem of time-optimal control of linear hyperbolic systems is equivalent to the computation of the root of the optimal value function of a time-parametric program, whose feasible set is described by a countable system of moment equations. To compute this root, discretized problems with a finite number of equality constraints can be used. In this paper, we show that on a certain time-interval, the optimal value functions of the discretized problems converge uniformly to the optimal value function of the original problem. We also give sufficient conditions fot Lipschitz and Hoelder continuity of the optimal value function of the original problem.