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Natural Numbers
Published in Nita H. Shah, Vishnuprasad D. Thakkar, Journey from Natural Numbers to Complex Numbers, 2020
Nita H. Shah, Vishnuprasad D. Thakkar
We have worked on natural numbers in the abstract form. The numbers should be written in the physical form. There are different systems in use. Systems like Roman numerals (I, II, III, IV, V, …, X, …, L, …, C, …, D, …, M, …) are less popular but are in use. The most popular system is position value–based system with ten symbols. Here ten is the number of fingers (including thumbs) of both the hands for a normal human being. There is a reason for writing 10 in words as with any base system; the number of symbols is written as 10 in the respective representation. This system has a set of symbols used to write the number. The value of the symbol depends on its position. The system we normally use has symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. In this system for number 265, 5 has value 5 itself whereas 6 has value 60 and 2 has value 200. In number 526, 6 has value 6 itself whereas 2 has value 20 and 5 has value 500. We can see here that the value associated to a digit depends on its position. In number 555, the value of the rightmost 5 is 5 itself whereas middle 5 has value 50 and the leftmost 5 has value 500. Even in this explanation, what is the interpretation of 50 and 500? Let us do a process to understand position-based value system.
Nuclear Incident Severity Determination and Public and Industry Perception of Incidents and the Impact This Has on Nuclear Power's Future
Published in Jonathan K. Corrado, Technology, Human Performance, and Nuclear Facilities, 2023
The INES provides simple and readily understandable information about nuclear incidents. The scale is logarithmic and similar in concept to the scale that measures the magnitude of earthquakes; each new level on the scale is ten times as severe as the previous one. For earthquakes, intensity can be evaluated in a quantitative fashion. However, judgments of the severity of a nuclear incident are more subjective and require extensive investigation. For this reason, an INES level is generally not assigned to an incident until a significant period of time following the event. Unfortunately, this means that the scale is sometimes not useful for rapid deployment of disaster aid.
Computer Number Systems
Published in Julio Sanchez, Maria P. Canton, Software Solutions for Engineers and Scientists, 2018
Julio Sanchez, Maria P. Canton
Note that in different numerical bases the same symbols represent different amounts. For this reason it is meaningless to say ten binary, or ten octal, or ten hexadecimal. Ten is the name given to the digit combination 10 in the decimal system. Since digit combinations in systems with other bases are unnamed, we are forced to use one-zero binary, one-zero octal, or one-zero hexadecimal. The same applies to the decimal designations of hundred, thousand, and their combinations. By the same token, it is incorrect to say one thousand hexadecimal, since the word thousand implies the decimal number system.
Proper Orthogonal Decomposition Mode Coefficient Interpolation: A Non-Intrusive Reduced-Order Model for Parametric Reactor Kinetics
Published in Nuclear Science and Engineering, 2023
Zachary K. Hardy, Jim E. Morel
The average and peak power density and fuel temperature as a function of time are shown in Fig. 15. For times s, the absorption cross section in region R is decreasing, adding reactivity to the system. This causes the power to increase at an increasingly fast rate. Through this period, the positive reactivity from the decreasing absorption is greater than the negative reactivity from temperature feedback. At s, the power peaks, and the temperatures have risen enough to cause the power to peak and begin to decline. The multigroup scalar flux profile at peak power time is shown in Fig. 16. For s, positive reactivity is still being added to the system from the cross-section ramp. This causes the power to trough and begin to rise until the ramp terminates at s. For the remainder of the simulation, temperature feedback drives the power asymptotically toward a new steady state. The complex dynamics and ten order-of-magnitude change in the solution make this benchmark problem an excellent test for the POD-MCI ROM.
Markov modeling of run length and velocity for molecular motors
Published in Applicable Analysis, 2022
James L. Buchanan, Robert P. Gilbert
Another series of numerical experiments was to attempt to determine numerically some of the parameters of the kinesin-1 model of Figure 4. MATLAB's constrained minimizer fmincon was used to find the values of various subsets of the parameters of the model, with the remaining parameters as given in Table 1. The objective function minimized the norm of the vector of relative errors between the calculated run length and velocity and the experimental measurements shown in Figure 5. Ten trials were run with initial guesses chosen by a random number generator based only on the expected order of magnitude of the parameter, which was assumed known. The values of the parameters were constrained to be positive. Table 2 shows that the minimization process obtained definite and reasonable values for subsets of at most four parameters. This is consistent with the derived two parameter Michaelis–Menten forms for run length and velocity. The minimizations were not always successful for subsets of four. This will be explored further.
Reliability analysis of chatter stability for milling process system with uncertainties based on neural network and fourth moment method
Published in International Journal of Production Research, 2020
Congying Deng, Jianguo Miao, Ying Ma, Bo Wei, Yi Feng
The back-propagation (BP) neural network utilises the error gradient descent algorithm to minimise the mean square error between the actual and predicted output values (Yu and Xu 2014; Ren et al. 2014; Yang et al. 2014). The topology structure of the BP neural network is shown in Figure 3, which is composed by the input layer, hidden layers and output layer. The number of neurons in the input and the output layers are determined by the number of the independent variables and the dependent variables respectively. And an empirical formula shown in Equation (9) is usually used to determine the number of neurons in the hidden layers. where q is the number of neurons in the hidden layer, n is the number of neurons in the input layer, and α is an integer between zero and ten.