Introduction: Although soap industry is known from hundreds of years, the development accompanied with this industry was little. The development implied the mechanical equipment and the additive materials necessary to produce soap with the best specifications of shape, physical and chemical properties. Objectives: This research studies the use of vacuum reactive distillation VRD technique for soap production. Methods: Olein and Palmitin in the ratio of 3 to 1 were mixed in a flask with NaOH solution in stoichiometric amount under different vacuum pressures from -0.35 to -0.5 bar. Total conversion was reached by using the VRD technique. The soap produced by the VRD method was compared with soap prepared by the reaction - only method which

This paper is concerned with introducing and studying the o-space by using out degree system (resp. i-space by using in degree system) which are the core concept in this paper. In addition, the m-lower approximations, the m-upper approximations and ospace and i-space. Furthermore, we introduce near supraopen (near supraclosed) d. g.'s. Finally, the supra-lower approximation, supraupper approximation, supra-accuracy are defined and some of its properties are investigated.

Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

The theory of Topological Space Fiber is a new and essential branch of mathematics, less than three decades old, which is created in forced topologies. It was a very useful tool and played a central role in the theory of symmetry. Furthermore, interdependence is one of the main things considered in topology fiber theory. In this regard, we present the concept of topological spaces α associated with them and study the most important results.

The downhole flow profiles of the wells with single production tubes and mixed flow from more than one layer can be complicated, making it challenging to obtain the average pressure of each layer independently.  Production log data can be used to monitor the impacts of pressure depletion over time and to determine average pressure with the use of Selective Inflow Performance (SIP). The SIP technique provides a method of determining the steady state of inflow relationship for each individual layer. The well flows at different stabilized surface rates, and for each rate, a production log is run throughout the producing interval to record both downhole flow rates and flowing pressure. PVT data can be used to convert measured in-situ r

Background: The access cavity is a critical stage in root canal therapy and it may influence the subsequent steps of the treatment. The new minimally invasive endodontic access cavity preparation concept aims to preserve sound tooth structure by conserving as much intact dentine as possible including the pulp chamber's roof, to keep the teeth from fracturing during and after endodontic treatment. While there is great interest in such access opening designs in numerous publications, still there is a lack of scientific evidence to support the application of such modern access cavity designs in clinical practice. This review aims to critically examine the literature on minimal access cavity preparations, explain the effect of minimally inva

An optoelectronic flow-through detector for active ingredients determination in pharmaceutical formulations is explained. Two consecutive compact photodetector’s devices operating according to light-emitting diodes-solar cells concept where the LEDs acting as a light source and solar cells for measuring the attenuated light of the incident light at 180˚ have been developed. The turbidimetric detector, fabricated of ten light-emitting diodes and five solar cells only, integrated with a glass flow cell has been easily adapted in flow injection analysis manifold system. For active ingredients determination, the developed detector was successfully utilized for the development and validation of an analytical method for warfarin determination

The downhole flow profiles of the wells with single production tubes and mixed flow from more than one layer can be complicated, making it challenging to obtain the average pressure of each layer independently.  Production log data can be used to monitor the impacts of pressure depletion over time and to determine average pressure with the use of Selective Inflow Performance (SIP). The SIP technique provides a method of determining the steady state of inflow relationship for each individual layer. The well flows at different stabilized surface rates, and for each rate, a production log is run throughout the producing interval to record both downhole flow rates and flowing pressure. PVT data can be used to convert measured in-situ rates