Monte Carlo Simulation of the Effect of Heterogeneous Too-Cheap Prices on the Average Price Preference for Remanufactured Products

A prevailing assumption in research on remanufactured products is “the cheaper, the better”. Customers prefer prices that are as low as possible. Customer price preference is modeled as a linear function with the minimal price at customers’ willingness to pay (WTP), which is assumed to be homogeneous and constant in the market. However, this linearity assumption is being challenged, as recent empirical studies have testified to customer heterogeneity in price perception and demonstrated the existence of too-cheap prices (TC). This study is the first attempt to investigate the validity of the linearity assumption for remanufactured products. A Monte Carlo simulation was conducted to estimate how the average market preference changes with the price of the remanufactured product when TC and WTP are heterogeneous across individual customers. Survey data from a previous study were used to fit and model the distributions of TC and WTP. Results show that a linear or monotonically decreasing relationship between price and customer preference may not hold for remanufactured products. With heterogeneous TC and WTP, the average price preference revealed an inverted U shape with a peak between the TC and WTP, independent of product type and individual customers’ preference function form. This implies that a bell-shaped or triangular function may serve as a better alternative than a linear function can when modeling market-price preference in remanufacturing research.

Study of Temperature Field Distribution in Topographic Bias Tunnel Based on Monitoring Data

In recent decades, numerous tunnels have been built in the cold region of China. However, the temperature field of topographically biased tunnels in the monsoon freeze zone has not been sufficiently studied. In this study, we monitored the temperature of the surrounding rock in two topographic bias sections of the Huitougou Tunnel and analyzed the results by fitting them to the monitoring results. The results showed that the temperature of the surrounding rock on both sides after tunnel excavation varied periodically in an approximate triangular function. As the distance from the cave wall increased, the annual average temperature of the surrounding rock did not change significantly, the amplitude decreased, and the delay time increased, while the annual maximum temperature decreased, and the annual minimum temperature increased. The heat generated by blasting, the heat of hydration of the primary and secondary lining, and the decorated concrete all caused a significant increase in the temperature of the surrounding rock within 4 m for a short period of time. Both construction and topographic factors led to asymmetry in the distribution of the surrounding rock temperature in different ways. The results of this paper are intended as a reference for other studies on temperature in deviated tunnels.

Methodology for Olive Pruning Windrow Assessment Using 3D Time-of-Flight Camera

The management of olive pruning residue has shifted from burning to shredding, laying residues on soil, or harvesting residues for use as a derivative. The objective of this research is to develop, test, and validate a methodology to measure the dimensions, outline, and bulk volume of pruning residue windrows in olive orchards using both a manual and a 3D Time-of-Flight (ToF) camera. Trees were pruned using trunk shaker targeted pruning, from which two different branch sizes were selected to build two separate windrow treatments with the same pruning residue dose. Four windrows were built for each treatment, and four sampling points were selected along each windrow to take measurements using both manual and 3D ToF measurements. Windrow section outline could be defined using a polynomial or a triangular function, although manual measurement required processing with a polynomial function, especially for high windrow volumes. Different branch sizes provided to be significant differences for polynomial function coefficients, while no significant differences were found for windrow width. Bigger branches provided less bulk volume, which implied that these branches formed less porous windrows that smaller ones. Finally, manual and 3D ToF camera measurements were validated, giving an adequate performance for olive pruning residue windrow in-field assessment.

Exact single travelling wave solutions to the fractional perturbed Gerdjikov–Ivanov equation in nonlinear optics

In this paper, exact single travelling wave solutions to the nonlinear fractional perturbed Gerdjikov–Ivanov equation are captured by the complete discrimination system for polynomial method and the trial equation method. In the classification, we can find out the original equation has rational function solutions, solitary wave solutions, triangular function periodic solutions, and elliptic function periodic solutions, which are normally very difficult to be obtained by other methods. In particular, the concrete parameters are set to show that the solutions in the classification can be realized in almost all cases.

Predictable Scenarios of Fuzzy Logic Analysis for Sprinkler Irrigation Control

MATLAB will be utilized to validate the various irrigation systems and report it; the air temperature, wind, and humidity will be member functions to improve the efficiency of irrigation performance before the irrigation process, and the fuzzy information system consists of fuzzy rules, which are derived from information of experts or from input-output learning of the system. Rules mimic human reasoning. Mamdani method is mostly applied in the fuzzy inference technique, and the generalized bell function is used for both of temperature and wind where the triangular function used for humidity. The principles were based on the last experiments and personal experiences, and the output will change into a crisp value from this procedure of defuzzification. There are many different methods to do defuzzification, but the most common technique is centroid method. The resultant surface graphic is enough to monitor, validate, and report the irrigation system efficiency to execute and schedule the irrigation practice management.

Non-Extra Pixel Interpolation

A non-extra pixel interpolation NPI is introduced for efficient image upscaling purposes. The NPI algorithm uses extended-triangular and linear scaling functions to match the pixel coordinates. The triangular function uses a modulo-operator with only two variables representing image pixels and scaling ratio. Every two variables of the linear scaling function represent the source/destination image pixels and scaling ratio. The traditional ceil function is used to round off non-integer pixel coordinates. The circshift and padarray functions are used to circularly shift the elements in array output by [Formula: see text]-amount in each dimension and pad elements of the [Formula: see text]th columns/rows by g-padsize in the shifted array, respectively. The [Formula: see text], [Formula: see text] and [Formula: see text] values are determined with respect to integer scaling ratios by a vector of [Formula: see text]-elements. The Exactness, Peak Signal-to-Noise Ratio, Signal-to-Noise Ratio and Discrete Fourier Transform techniques were used for objective evaluation purposes. Experiments demonstrated comparable results as well as the need for further researches.

Electrostatic Capacity of a Metallic Cylinder: Effect of the Moment Method Discretization Process on the Performances of the Krylov Subspace Techniques

When a straight cylindrical conductor of finite length is electrostatically charged, its electrostatic potential ϕ depends on the electrostatic charge qe, as expressed by the equation L(qe)=ϕ, where L is an integral operator. Method of moments (MoM) is an excellent candidate for solving L(qe)=ϕ numerically. In fact, considering qe as a piece-wise constant over the length of the conductor, it can be expressed as a finite series of weighted basis functions, qe=∑n=1Nαnfn (with weights αn and N, number of the subsections of the conductor) defined in the L domain so that ϕ becomes a finite sum of integrals from which, considering testing functions suitably combined with the basis functions, one obtains an algebraic system Lmnαn=gm with dense matrix, equivalent to L(qe)=ϕ. Once solved, the linear algebraic system gets αn and therefore qe is obtainable so that the electrostatic capacitance C=qe/V, where V is the external electrical tension applied, can give the corresponding electrostatic capacitance. In this paper, a comparison was made among some Krylov subspace method-based procedures to solve Lmnαn=gm. These methods have, as a basic idea, the projection of a problem related to a matrix A∈Rn×n, having a number of non-null elements of the order of n, in a subspace of lower order. This reduces the computational complexity of the algorithms for solving linear algebraic systems in which the matrix is dense. Five cases were identified to determine Lmn according to the type of basis-testing functions pair used. In particular: (1) pulse function as the basis function and delta function as the testing function; (2) pulse function as the basis function as well as testing function; (3) triangular function as the basis function and delta function as the testing function; (4) triangular function as the basis function and pulse function as the testing function; (5) triangular function as the basis function with the Galerkin Procedure. Therefore, five Lmn and five pair qe and C were computed. For each case, for the resolution of Lmnαn=gm obtained, GMRES, CGS, and BicGStab algorithms (based on Krylov subspaces approach) were implemented in the MatLab® Toolbox to evaluate qe and C as N increases, highlighting asymptotical behaviors of the procedures. Then, a particular value for N is obtained, exploiting both the conditioning number of Lmn and considerations on C, to avoid instability phenomena. The performances of the exploited procedures have been evaluated in terms of convergence speed and CPU-times as the length/diameter and N increase. The results show the superiority of BcGStab, compared to the other procedures used, since even if the number of iterations increases significantly, the CPU-time decreases (more than 50%) when the asymptotic behavior of all the procedures is in place. This superiority is much more evident when the CPU-time of BicGStab is compared with that achieved by exploiting Gauss elimination and Gauss–Seidel approaches.

Soliton solutions in different classes for the Kaup–Newell model equation

In this paper, we use the new defined direct algebraic method based on some particular Riccati equations to find exact solutions to a Kaup–Newell model equation. Several new solutions which represent long waves parallel to the magnetic fields have been obtained. Many solutions in generalized hyperbolic and triangular function forms, exponential or logarithmic, are expressed explicitly. Most of the solutions determined in the study are new in the related literature.

Solitons for the modified $(2 + 1)$-dimensional Konopelchenko–Dubrovsky equations

In the paper, we consider the modified $(2 + 1)$ ( 2 + 1 ) -dimensional Konopelchenko–Dubrovsky equations which possess high order nonlinear terms. Under the aid of Maple, we derive the exact traveling wave solutions of the mKDs by the auxiliary equation approach. Under some special conditions, Jacobi elliptic function solutions, degenerated triangular function solutions, and solitons for the mKD equations are constructed.