The fuzzy assignment models (FAMs) have been explored by various literature to access classical values, which are more precise in our real-life accomplishment. The novelty of this paper contributed positively to a unique application of pentagonal fuzzy numbers for the evaluation of FAMs. The new method namely Pascal’s triangle graded mean (PT-GM) has presented a new algorithm in accessing the critical path to solve the assignment problems (AP) based on the fuzzy objective function of minimising total cost. The results obtained have been compared to the existing methods such as, the centroid formula (CF) and centroid formula integration (CFI). It has been demonstrated that operational efficiency of this conducted method is exquisitely deve

In this paper, two of the local search algorithms are used (genetic algorithm and particle swarm optimization), in scheduling number of products (n jobs) on a single machine to minimize a multi-objective function which is denoted as  (total completion time, total tardiness, total earliness and the total late work). A branch and bound (BAB) method is used for comparing the results for (n) jobs starting from (5-18). The results show that the two algorithms have found the optimal and near optimal solutions in an appropriate times.

The current research aims to identify the extent to which cognitive economics skills are included in the content of the chemistry textbook for the third intermediate grade, and the research sample was represented in the chemistry textbook for the third intermediate grade. A list of knowledge economy skills was prepared (6) main skills (basic skills, communication skills, thinking skills, work skills Group, information-gathering skill, behavioral skills (and (20) sub-skills) (reading, writing, operations, computer skills and employability, oral expression and written communication, dialogue, persuasion, influence and arousal, analysis, problem-solving, decision-making, suggestions and hypotheses and employing them. Controlling, directing

The current research seeks to Analyze third intermediate chemistry book following sustainable development standards for academic year (2016-2017). To do this, a list of sustainable development standards that should be included in chemistry book was designed based on the previous studies. The first version of the list consisted of (50) sub-case divided into three standards (social, economic, and environmental) which was exposed to group of experts in teaching chemistry and teaching methods. The list has modified to (43) sub-case. The researcher followed the implicit and explicit meaning in his analysis: one for recording and repetition and the other for frequency. The result showed that third intermediate chemistry book has achieved (20)

Based on the needs of the scientific community, researchers tended to find new iterative schemes or develop previous iterative schemes that would help researchers reach the fixed point with fewer steps and with stability, will be define in this paper the multi_implicit four-step iterative (MIFSI) which is development to four-step implicit fixed point iterative, to develop the aforementioned iterative scheme, we will use a finite set of projective functions ,nonexpansive function and finite set from a new functions called generalized quasi like contractive which is an amalgamation of quasi contractive function and contractive like function , by the last function and a set of sequential organized steps, we will be able to prove the existen

One of the serious problems in any wireless communication system using multi carrier modulation technique like Orthogonal Frequency Division Multiplexing (OFDM) is its Peak to Average Power Ratio (PAPR).It limits the transmission power due to the limitation of dynamic range of Analog to Digital Converter and Digital to Analog Converter (ADC/DAC) and power amplifiers at the transmitter, which in turn sets the limit over maximum achievable rate.

        This issue is especially important for mobile terminals to sustain longer battery life time. Therefore reducing PAPR can be regarded as an important issue to realize efficient and affordable mobile communication services.

Iraqi oil crudes have some of the physical and chemical characteristics that distinguish it from other types of oil crudes in the world. Some of these features such us molecular composition, rheological, viscosity and emulsions are studied carefully by researchers. In this work, a comparative study of the linear and the non-linear optical properties for typical heavy and light crude oils of Iraqi origin was studied utilizing Z-scan technique. The He -Ne laser of wavelength 632.8 nm had been used for this purpose. These samples were collected from Basra and Kut oil fields. The values of the non-linear refractive index (n₂), non-linear absorption coefficient (β), and third-order electrical susceptibility (χ³) were e