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Mathematical Operations
Published in Theodore Louis, Behan Kelly, Introduction to Optimization for Environmental and Chemical Engineers, 2018
Zeroes are significant when they occur between significant digits. In the following examples, all zeroes are significant: 10001, 402, 1.1001, 500.09 has five, three, five, and four significant figures, respectively. Zeroes are not significant when they are used as placeholders. When used as a placeholder, a zero simply identifies where a decimal is located. For example, each of the following numbers has only one significant digit: 1000, 500, 60, 0.09, 0.0002. In the number 1200, 540, and 0.0032 there are two significant digits, and the zeroes are not significant. When zeroes follow a decimal and are preceded by a significant digit, the zeroes are significant. In the following examples, all zeroes are significant: 1.00, 15.0, 4.100, 1.90, 10.002, 10.0400. For 10.002, the zeroes are significant because they fall between two significant digits. For 10.0400, the first two zeroes are also significant because they fall between two significant digits; the last two zeroes are significant because they follow a decimal and are preceded by a significant digit. Thus, when approximate numbers are multiplied or divided in a problem, the result is expressed as a number having the same number of significant digits as the expression in the problem having the least number of significant digits.
Turn performance and flight maneuvers
Published in Mohammad H. Sadraey, Aircraft Performance, 2017
The denominator cannot be zero. Thus, the numerator is set equal to zero: V12[ρVSTKW2−ρ2V3S2CDoKW2]ρV2ST2KW2−ρ2V4S2CDo4KW2−1−ρV2ST2KW2−ρ2V4S2CDo4KW2−1=0
Quantum Quagmire: Dead End for Energy Miracles
Published in H. B. Glushakow, Energy Miracles, 2022
But in the case of a quantum mechanics “single-point charge” where the distance between the charge and itself is evidently zero, there is a big problem. The formula fails for a single particle because you would have to divide the result by zero. As we know, you cannot divide something by zero. To “divide” something means to separate it out into parts. You can divide a pie into eight slices or five and a half slices or 1000 slices. But you cannot “divide” it into “zero” slices because that is not dividing.
Four conceptions of infinity
Published in International Journal of Mathematical Education in Science and Technology, 2022
Magdalena Krátká, Petr Eisenmann, Jiří Cihlář
Finally, let us focus on two phenomena that are often discussed in the research, namely the indeterminateness of infinity and improper objects. Sierpinska (1994) describes students who think that a value g is the limit of a sequence A if the difference between A and g is infinitely small. Tsamir and Sheffer (2000, pp. 98–100) in their research concerning the understanding of the division by zero state that: 12% of grade 11 students in the higher course answered ∞ to all [tasks of the type a ÷ 0] … They regarded ∞ as a specific, numerical answer. Several higher achievers (13 %, 10 %, and 16 % in grade 9, 10, and 11, respectively) argued that division by zero is undefined because it is infinity, and infinity is undefined … This number (∞) is undefined either because its exact location on the number line is unknown or because its value can change.
A hybridized approach for design and optimization of combined economic emission dispatch
Published in Energy Sources, Part B: Economics, Planning, and Policy, 2021
Srinivasa Acharya, Ganesan Sivarajan, D. Vijaya Kumar, Subramanian Srikrishna
Based on the movement of waves from the low fitness position to the high fitness position, the amplitude of the wave gets increased, and the wavelength gets decreased. Hence, the fitness of the young waveis estimated after the transmission process. While,, is substituted by in the population and the amplitude of the wave is altered to. Moreover, remains to be a particular value even though its amplitude is decremented. Thus, there arises excess of impressionist’s energy depending on the inertial conflict, eddy detaching, and base resistance. Subsequent to each production, the wavelength of the wave is updated as demonstrated in Eq. (12) where, is described as a less positive integer for circumventing division-by-zero. This guarantees that elevated fitness waves will encompass minor wavelengths and are propagated in less significant limits.
Development of a Modified Seventh-Order WENO Scheme with New Nonlinear Weights
Published in International Journal of Computational Fluid Dynamics, 2021
Kaveh Fardipour, Kamyar Mansour
where are constant coefficients and, where are independent of the . One can find and for in Jiang and Shu (1996) and Balsara and Shu (2000). Using Equations (5)–(7) the linear weights and substencil of the seventh-order scheme are: The WENO approximation is a nonlinear combination of as where are the normalised nonlinear weights of each substencil and one can compute them as where are the non-normalised nonlinear weight of each substencil. Using Equation (12) one can conclude . The are designed in a way that in the smooth regions of the solution. Jiang and Shu (1996) used a formulation for the as where is an integer, is a tiny real number to avoid division by zero, and, are the smoothness indicators of substencils .