The aims of the paper are to present a modified symmetric fuzzy approach to find the best workable compromise solution for quadratic fractional programming problems (QFPP) with fuzzy crisp in both the objective functions and the constraints. We introduced a modified symmetric fuzzy by proposing a procedure, that starts first by converting the quadratic fractional programming problems that exist in the objective functions to crisp numbers and then converts the linear function that exists in the constraints to crisp numbers. After that, we applied the fuzzy approach to determine the optimal solution for our quadratic fractional programming problem which is supported theoretically and practically. The computer application for the algorithm was tested, and finally compared modified symmetric fuzzy approach with the modified simplex approach which is shown in the table 1. Finally, the procedures of numeric results in the paper indicate that modified symmetric fuzzy approach is reliable and saves valuable time.
Durability of hot mix asphalt (HMA) against moisture damage is mostly related to asphalt-aggregate adhesion. The objective of this work is to find the effect of nanoclay with montmorillonite (MMT) on Marshall properties and moisture susceptibility of asphalt mixture. Two types of asphalt cement, AC(40-50) and AC(60-70) were modified with 2%, 4% and 6% of Iraqi nanoclay with montmorillonite. The Marshall properties, Tensile strength ratio(TSR) and Index of retained strength(ISR) were determined in this work. The total number of specimens was 216 and the optimum asphalt content was 4.91% and 5% for asphalt cement (40-50) and (60-70) respectively. The results showed that the modification of asphalt cement with MMT led to increase Marsh
... Show MoreThis research studies the effect of adding five different percentages of polymer (2, 4, 6, 8, and 10% of cement weight) on cement mortar's fresh and hardened properties, which was cured at laboratory temperature for 7, 14, and 28 days. Workability increases with increasing polymer. The workability value was lowest (25.6 and 29.4) % in mixtures containing 2% and 4% of (SBR). Increasing polymer ratios significantly decreased mechanical properties (compressive and flexural strength). Therefore, the best results were at 2% SBR and 4% SBR at 28 days of age. An inverse relationship was recorded between the increase in SBR ratios and polymer-modified cement mortar's compressive and flexural strength values. In general, the high
... Show MoreMCA has gained a reputation for being a very useful statistical method for determining the association between two or more categorical variables and their graphical description. For performance this method, we must calculate the singular vectors through (SVD). Which is an important primary tool that allows user to construct a low-dimensional space to describe the association between the variables categories. As an alternative procedure to use (SVD), we can use the (BMD) method, which involves using orthogonal polynomials to reflect the structure of ordered categorical responses. When the features of BMD are combined with SVD, the (HD) is formed. The aim of study is to use alternative method of (MCA) that is appropriate with order
... Show MoreIn this work ,the modified williamos-Hall method was used to analysis the x-ray diffraction lines for powder of magnesium oxide nanoparticles (Mgo) .and for diffraction lines (111),(200),(220),(311) and (222).where by used special programs such as origin pro Lab and Get Data Graph ,to calculate the Full width at half maximum (FWHM) and integral breadth (B) to calculate the area under the curve for each of the lines of diffraction .After that , by using modified Williamson –Hall equations to determin the values of crystallite size (D),lattice strain (ε),stress( σ ) and energy (U) , where was the results are , D=17.639 nm ,ε =0.002205 , σ=0.517 and U=0.000678 respectively. And then using the scherrer method can by calculated the crystal
... Show MoreThe research endeavors to harness the benefits stemming from the integration of constraint theory into construction project management, with the primary goal of mitigating project completion delays. Additionally, it employs fuzzy analysis to determine the relative significance of fundamental constraints within projects by assigning them appropriate weights. The research problem primarily revolves around two key issues. Firstly, the persistent utilization of outdated methodologies and a heavy reliance on workforce experience without embracing modern computerized technologies. Secondly, the recurring problem of project delivery delays. Construction projects typically encompass five fundamental constraint types: cost restrictions, tim
... Show MoreLong memory analysis is one of the most active areas in econometrics and time series where various methods have been introduced to identify and estimate the long memory parameter in partially integrated time series. One of the most common models used to represent time series that have a long memory is the ARFIMA (Auto Regressive Fractional Integration Moving Average Model) which diffs are a fractional number called the fractional parameter. To analyze and determine the ARFIMA model, the fractal parameter must be estimated. There are many methods for fractional parameter estimation. In this research, the estimation methods were divided into indirect methods, where the Hurst parameter is estimated fir
... Show MoreOptimal control methods are used to get an optimal policy for harvesting renewable resources. In particular, we investigate a discretization fractional-order biological model, as well as its behavior through its fixed points, is analyzed. We also employ the maximal Pontryagin principle to obtain the optimal solutions. Finally, numerical results confirm our theoretical outcomes.
In this paper a Г-ring M is presented. We will study the concept of orthogonal generalized symmetric higher bi-derivations on Г-ring. We prove that if M is a 2-torsion free semiprime Г-ring , and are orthogonal generalized symmetric higher bi-derivations associated with symmetric higher bi-derivations respectively for all n ϵN.
The fractional free volume (Fh) in polystyrene (PS) as a function of neutron -irradiation dose has been measured, using positron annihilation lifetime (PAL) method. The results show that Fh values decreased with increasing n-irradiation dose up to a total dose of 501.03× 10-2 Gy.
A percentage reduction of 2.14 in Fh values is noticed after the initial n-dose corresponding to a percentage reduction in the free volume equal to 42.14/Gy.
The total n-dose induces a percentage reduction of 7.26, corresponding to a percentage reduction of 1.45/Gy. These results indicate that cross -linking is the predominant process induced by n-irradiation.
The results suggest that n-irradiation induces structure changes in PS, causing cross-linking