We expand a new generalization of the two-dimensional differential trans-form method. The new generalization is based on the two-dimensional differ-ential transform method, fractional power series expansions, and conFORMABLE fractional derivative. We use the new method for solving a nonlinear con-FORMABLE fractional partial differential equation and a system of conFORMABLE fractional partial differential equation. Finally, numerical examples are pre-sented to illustrate the preciseness and effectiveness of the new technique.

In this paper we investigate further properties of the de-FORMABLE derivative and use the results to study the existence of solu-tions to the integro-di, erential equation D, R y(t) = h(y(t))+f(t,y(t))+ t 0 K(t,s,y(s))ds,t 2 [0,T], with initial condition y(0) = y0,where D, y(t) is the deFORMABLE derivative of y, 0 < ,< 1. We useWeissinger's , xed point theorem and Krasnoselskii's , xed point theorem to achieve our main results. An example is provided for illustration.

In the present work, the effect of aluminum on mechanical activation of hematite graphite- aluminum mixture has been investigated. Various amounts of aluminum powder (0 to 10 wt%) was added to hematite-graphite mixture (C/O=1 or 18.40 wt% graphite). Then, the mixture was mechanically treated by means of ball milling within different time periods, from 0 to 10 hours. XRD and SEM tests were carried out to study the effect of aluminum and milling time on activation mechanism of the mixture. It was found that existence of aluminum particles, as FORMABLE material, in the brittle hematite-graphite mixture could influence on the microscopic condition and subsequently on the behavior and intensity of mechanical activation of the mixture.

The proposed study is focused to introduce a novel integral transform op-erator, called Generalized Bivariate (GB) transform. The proposed trans-form includes the features of the recently introduced Shehu transform, ARA transform, and FORMABLE transform. It expands the repertoire of existing Laplace-type bivariate transforms. The primary focus of the present work is to elaborate fashionable properties and convolution theorems for the proposed transform operator. The existence, inversion, and duality of the proposed transform have been established with other existing transforms. Implementation of the proposed transform has been demonstrated by ap-plying it to different types of differential and integral equations. It validates the potential and trustworthiness of the GB transform as a mathematical tool. Furthermore, weighted norm inequalities for integral convolutions have been constructed for the proposed transform operator.

Nowadays, two-layer metallic sheets have become as a useful solution to produce multi-functional products. Generally, two-layer metallic sheets can have advantageous characteristics such as increasing formability of the low FORMABLE component, improving the corrosion and wear resistance and reducing weight and cost of manufactured products. Therefore, understanding the forming limit behavior of a two-layer metallic sheet has an essential role in the design of sheet metal forming processes. Forming limit diagram (FLD) is a suitable method to predict the formability of metallic sheets in sheet metal forming operations. The aim of this research was to determine the forming limit diagram in Aluminum-Copper two-layer metallic sheets experimentally. The forming limit diagram can be used as a criterion in order to predict necking initiation which may cause tearing in sheet metal forming processes. In this paper, the forming limit diagrams of Aluminum-Copper two-layer metallic sheets have been obtained through an experimental procedure for the first time.

The electrical properties of nanostructured piezoelectric materials have attracted the attention of many researchers in the last decade. These features are used in piezoelectric micro-sensors. Mechanical propulsion is usually the result of contact between a piezoelectric surface and a foreign object. In this paper, the effect of mechanical propulsion using an air wave (sound) or vacuum on a silicon diaphragm is investigated. The local stresses created on the diaphragm due to the impact of an air wave have a significant effect on the peak-to-peak voltage of the piezoelectric sensor, which can be measured by measuring changes in this parameter. To investigate this, a micromachined diaphragm of silicon was examined and it was found that fabricating a piezoelectric sensor on a thin and patterned diaphragm could increase the peak-to-peak voltage by about 1. 3 times. Detection of these stresses using piezoelectric material layered on the thin and FORMABLE diaphragm can act as a piezoelectric microphone or a barometer that the presence of microstructures on the diaphragm will increase their sensitivity.

Myths are communal dreams of human beings and mythological symbols are the artistic and secret language of the myths. They increase the deepness of the meanings when they are used in poems. Symbols with their FORMABLE and flexible nature are able to reflect the deep and rooted concepts and subjects in a comprehensive way due to the time and place conditions. They are able to produce different meanings and uses out of a single from and to continue their novelty and continuity with a consistent growth. Of course symbolic poets and artists due to their cultural background and their individual and social real needs, may pay special attention to the use of symbols; but the author of this article, while considering the theoretical bases of the usage of symbols and the related subjects, tries to survey the most important factors that lead poets to use plants symbols and myths. The author also tries to have a look at the uses of these kinds of symbols in the myths of different tribes and nations so that he can compare them in real and better way.

In this study, the energy absorption capacity of kevlar/elastomer composites under highspeed impact loading has been investigated experimentally and numerically. The compliance of the mechanical behavior of elastomeric composites with the theory of hyperelasticity complicates the analytical study. Therefore, numerical simulation due to the different and complex mechanisms of failure has gained large share in the design of composite structures. In the present study, the most advanced method of finite element modeling of composites i. e., Abaqus / Explicit has been used to determine their behavior during impact. For this purpose, planer shell elements were used to model the composite layers, and FORMABLE material model and the vumat were used to determine the behavior of the elastomeric composite failure model based on a damage criterion such as von mises failure criterion. Due to the lack aforementioned criteria in the commercial versions of the software and the importance of considering damages in numerical simulation for these composites, the criterion was written in Fortran software environment, and the analysis of the penetration phenomenon was added to the software capability in composite structure. In order to validate this model, an experimental test was performed on the kevlar/elastomer composite by a Gas gun device. Also, the study of deformation, output projectile velocity, and absorpted energy have been reported. The simulation results show a very good agreement with the experimental results.

In this research, grain size variation and grain distribution and the effect of different factors such as friction, tool rotational speed, linear velocity of the tool, cooling rate, tool geometry and tool penetration depth on the temperature change and grain size during the friction stir welding process of the aluminum alloy Al-2024 sheet with a thickness of 7. 8 mm has been investigated. In order to simulate the model of finite element friction stir welding, the Deform 3D software has been used. The tool is a rigid body and a sheet is considered as a FORMABLE plastic material. In order to validate, a comparison between simulation data and experimental results was performed. The effect of effective factors on the temperature of the welding and the amount of grain size variation in the cross section of the weld line have been discussed. Among the variables studied, increasing the cooling rate and the linear velocity of the tool reduce the temperature and grain size, and increase the temperature and grain size with increasing other variables. The results show that with the method presented in this paper, precise prediction of the effect of variation of the variables affecting temperature and grain size can be obtained. In the following, these results can be used to determine the optimum conditions for the friction stir welding process.