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Variables, functions and mappings
Published in Alan Jeffrey, Mathematics, 2004
The floor function, denoted by ⌊x⌋, is defined as the largest integer smaller than or equal to x, and the ceiling function, denoted by ⌈x⌉, is defined as the smallest integer larger than or equal to x. These two functions, which are used in computing and occur in most computer algebra languages, are illustrated in Fig. 2.9(h), with the floor function shown as the dotted ‘staircase function’ and the ceiling function as the solid “staircase function’. For purposes of comparison, the line y = x shown as the solid straight line passing between the floor and ceiling functions, has been added for comparison. It should be mentioned that in some computer languages the floor function is called the integer part function and denoted by int(x), when the symbol [x] is then used to denote the nearest integer function because it lies between ⌊x⌋ and ⌈x⌉.
Probability models
Published in Andrew Metcalfe, David Green, Tony Greenfield, Mahayaudin Mansor, Andrew Smith, Jonathan Tuke, Statistics in Engineering, 2019
Andrew Metcalfe, David Green, Tony Greenfield, Mahayaudin Mansor, Andrew Smith, Jonathan Tuke
where int[•] is the integer value of [•], also referred to as the floor function. A k-out-of-n system has the structure function φ(x)=int[∑i=1nxik].
Analysis of Population Control Techniques for Time-Dependent and Eigenvalue Monte Carlo Neutron Transport Calculations
Published in Nuclear Science and Engineering, 2022
Ilham Variansyah, Ryan G. McClarren
Sweezy et al.4 proposes the weight-based SR. In SR, we assign each initial particle with splitting number . For uniform, weight-based, and importance-based SR, the values for are, respectively, , , and . We split each particle into copies, and then Russian-roulette the last copy with surviving probability . The function denotes the floor function, which produces the greatest integer not greater than the variable argument. Finally, to ensure unbiased MC simulation, the surviving particle copies are assigned controlled weight , which happens to be identical to that of the CO techniques.
Distributed model-free adaptive predictive control for heterogeneous nonlinear multi-agent systems
Published in International Journal of Systems Science, 2022
Zhenzhen Pan, Zhongsheng Hou, Ronghu Chi
According to Lemma 4.2, grouping every Q matrices product together in (31), it can be seen where denotes the floor function. Denote Combined with the properties of the floor function Therefore, we can conclude that Consequently, Combining (35) and (36),
Sum of alternating-like series as definite integrals
Published in International Journal of Mathematical Education in Science and Technology, 2022
The function is welldefined and it can be written as Furthermore, for integers 0<q<p, it assumes the value where denotes the floor function.