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Computer Arithmetic Design Using Verilog HDL
Published in Joseph Cavanagh, Verilog HDL Design Examples, 2017
The combined behavioral and dataflow design module is shown in Figure 4.44 and uses the if and else conditional statements together with the continuous assignment statement assign. The inputs are an 8-bit dividend, a[7:0]; a 4-bit divisor, b[3:0]; and a scalar signal, start, which initiates the divide operation. The output is an 8-bit register rslt[7:0] containing the quotient and remainder. Shifting is accomplished by the left-shift operator (<<) as follows: rslt = rslt << 1. The test bench module is shown in Figure 4.45 illustrating a variety of dividends and divisors. The outputs are shown in Figure 4.46.
Low order nonstandard continualization of a beam lattice with next-nearest interactions: Enhanced prediction of the dynamic behavior
Published in Mechanics of Advanced Materials and Structures, 2022
Francisco Gómez-Silva, Ramón Zaera
In this section, different nonstandard continualization techniques are used. These techniques expand the particle displacements by means of the shift operator [22, 26] where refers to the dimensionless spatial derivative, being the dimensionless horizontal position variable. This pseudo-differential operator is here used in four different ways. First, this operator is applied to the discrete governing Eq. (8), which is then expanded by means of Padé approximants. Second, the Regularization method proposed by Bacigalupo and Gambarotta [27], who applied it to systems different than the one here considered, is employed. This technique has also been applied by Gómez-Silva and Zaera [22] to a beam lattice with nearest interactions. Finally, two different kinetic energy densities are employed, leading to two EKE models. For this purpose, the first spatial derivative is approximated by means of differences schemes and of the shift operator. First, a progressive difference scheme is used, as proposed by Rosenau [28] for axial systems, but including the second velocity gradient as considered by Gómez-Silva and Zaera [22] for a beam lattice system with nearest interactions. Second, a novel EKE, approximating the first spatial derivative through a central difference scheme, is proposed in this work. These models will be referred to in the rest of this article as Padé, Regularization, EKE I and EKE II models, respectively.
Rescheduling of unrelated parallel machines with job-dependent setup times under forecasted machine breakdown
Published in International Journal of Production Research, 2021
Shift operator. Figure 7 shows an example of a neighbour designed by a shift operator. A machine is selected based on one of the policies, and the shift operator selects a job randomly on the machine, and relocates it to another position, which is randomly determined by the regular policy. The intensification policy selects the best position based on the objective value among all of the possible positions.
Integration of time series forecasting in a dynamic decision support system for multiple reservoir management to conserve water sources
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2018
Hamed Zamani Sabzi, Shalamu Abudu, Reza Alizadeh, Leili Soltanisehat, Naci Dilekli, James Phillip King
where is defined as white noise process; is defined as a dependent variable; and is defined as backward shift operator (lag operator), which is calculated through Equation 5 as follows: