Let R be a 2-torision free prime ring and ?, ?? Aut(R). Furthermore, G: R×R?R is a symmetric generalized (?, ?)-Biderivation associated with a nonzero (?, ?)-Biderivation D. In this paper some certain identities are presented satisfying by the traces of G and D on an ideal of R which forces R to be commutative

Piezoelectric structures are nowadays used in many different applications. A better understanding of the influence of material properties and geometrical design on the performance of these structures helps to develop piezoelectric structures specifically designed for their application. Different equivalent circuits have been introduced in the literature to investigate the behaviour of piezoelectric transducers. The model parameters are usually determined from measurements covering the characteristic frequencies of the piezoelectric transducer. This article introduces an analytical technique for calculating the mechanical and electrical equivalent system parameters and characteristic frequencies based on material properties and geom

The current research deals with spatial relations as a tool to link urban landmarks in a homogeneous composition with monumental sculptures, by identifying these landmarks and the extent of their impact on them, which constitutes an urgent need to evaluate the appropriate place and its effects on them, so that this analytical study is a critical approach adopted in artistic studies of monumental models in Arabcapitals .The current research came in four chapters, the first chapter of which dealt with the research problem, its importance and the need for it, then its objectives that were determined in revealing the spatial relations and their impact on

So I present in the hands of the honorable reader what God Almighty has made easy for me in terms of what I dealt with in the rule (the principle of permissive things) and what branches from it and what is related to it.
This research was divided into an introduction, a preface, three demands, and a conclusion.
The preamble is to explain the meaning of the rule in language and terminology and the definition of the legal rule and what is related to it. The first requirement is to explain the rule that we have in our hands and the words related to its text - and is it a fundamentalist or jurisprudential rule? .
As for the second requirement - in the difference of scholars and their opinions in whether the origin of things is permi

In this study, the preparation and characterization of hyacinth plant /chitosan composite, as a heavy metal removal, were done. Water hyacinth plant (Eichhorniacrasspes) was collected from Tigris river in Baghdad. The root and shoot parts of plant were ground to powder. Composite materials were prepared at different ratios of plant part (from 2.9% to 30.3%, wt /wt) which corresponds to (30-500mg) of hyacinth plant (root and shoot) and chitosan. The results showed that all examined ratios of plant parts have an excellent absorption to copper (Cu (II)). Moreover, it was observed that 2.9% corresponds (30mg) of plant root revealed highest removal (82.7%) of Pb (II), while 20.23% of shoot removed 61% of Cd (II) within 24 hr

The population has been trying to use clean energy instead of combustion. The choice was to use liquefied petroleum gas (LPG) for domestic use, especially for cooking due to its advantages as a light gas, a lower cost, and clean energy. Residential complexes are supplied with liquefied petroleum gas for each housing unit, transported by pipes from LPG tanks to the equipment. This research aims to simulate the design and performance design of the LPG system in the building that is applied to a residential complex in Baghdad taken as a study case with eight buildings. The building has 11 floors, and each floor has four apartments. The design in this study has been done in two parts, part one is the design of an LPG system for one building, an