The objective of this paper is, firstly, we study a new concept noted by algebra and discuss the properties of this concept. Secondly, we introduce a new concept related to the algebra such as smallest algebra. Thirdly, we introduce the notion of the restriction of algebra on a nonempty subset  of and investigate some of its basic properties. Furthermore, we present the relationships between field, monotone class, field and algebra. Finally, we introduce the concept of measure relative to the algebra and prove that every measure relative to the   is complete.

Research Summary

In The Name of Allah Most Gracious Most Merciful

The word injustice and its derivatives were repeated in the Holy Qur’an in several places, approximately (154) times. This is due to the severity of its danger, and that the most dangerous thing that our Islamic nation suffers from in our time is; It is injustice in all its forms and types, so we should all have an honest review of the sincere change in the right direction, and uncover cases of injustice and explain their causes and causes, and work to treat them and rid the wrongdoers of their injustice, and help them to correct their condition. To reveal their grievances and explain their causes and causes, and work to remedy them, and support them and mi

A new ligand complexes have been synthesis from reaction of metal ions of MnII , CoII , NiII , CuII , ZnII , CdII and PdII with schiff base [(E)-1-((2-amino-5-(3, 4, 5-trimethoxybenzyl) pyrimidin-4-ylimino) methyl) naphthalen-2-ol [HL)]. The prepared [HL] was characterized by FT-IR, UV-Vis spectroscopy, 1H13CNMR spectra Mass spectra and melting point. The compounds were characterized by techniques UV-Vis and FT-IR spectral studies, micro analysis (C.H.N), determination of atomic absorption, chloride content, molar conductivity measurements, magnetic susceptibility and melting point. The ligand acts as a monobasic tridentate, coordinating through deprotonated phenolic O and azomethine N atoms. The compounds are neutral electrolytic in dimeth

The electric quadrupole moments for some scandium isotopes (41, 43, 44, 45, 46, 47Sc) have been calculated using the shell model in the proton-neutron formalism. Excitations out of major shell model space were taken into account through a microscopic theory which is called core polarization effectives. The set of effective charges adopted in the theoretical calculations emerging about the core polarization effect. NushellX@MSU code was used to calculate one body density matrix (OBDM). The simple harmonic oscillator potential has been used to generate the single particle matrix elements. Our theoretical calculations for the quadrupole moments used the two types of effective interactions to obtain the best interaction compared with the exp

The deterioration of buried sewers during their lifetime can be affected by several factors leading to bad performance and can damage the infrastructure similar to other engineering structures. The Hydraulic deterioration of the buried sewers caused by sewer blockages while the structural deterioration caused by sewer collapses due to sewer specifications and the surrounding soil characteristics and the groundwater level. The main objective of this research is to develop deterioration models, which are used to predict changes in sewer condition that can provide assessment tools for determining the serviceability of sewer networks in Baghdad city. Two deterioration models were developed and tested using statistical software SPSS, the

This study describes the preparation of new series of tetra-dentate N₂O₂ dinuclear complexes (Cr³⁺, Co²⁺, Cu²⁺) of the Schiff base derived from condensation of 1-Hydroxy-naphthalene-2-carbaldehyde with 2-amino-5-(2-hydroxy-phenyl)-1,3,4-thiadiazole. The structures of the ligands were identified using IR, UV-Vis , mass,  elemental analysis and ¹H-NMR techniques. All prepared complexes have been characterized by conductance measurement, magnetic susceptibility, electronic spectra, infrared spectrum, theromgravimatric analysis (TGA) and metal analysis by atomic absorption. From stoichiometry of metal to ligand and all measurements show a octahedral geometry proposed for all

This study describes the preparation of new series of tetra-dentate N2O2 dinuclear complexes (Cr3+, Co2+, Cu2+) of the Schiff base derived from condensation of 1-Hydroxy-naphthalene-2-carbaldehyde with 2-amino-5-(2-hydroxy-phenyl)-1,3,4-thiadiazole. The structures of the ligands were identified using IR, UV-Vis , mass,  elemental analysis and 1H-NMR techniques. All prepared complexes have been characterized by conductance measurement, magnetic susceptibility, electronic spectra, infrared spectrum, theromgravimatric analysis (TGA) and metal analysis by atomic absorption. From stoichiometry of metal to ligand and all measurements show a octahedral geometry proposed for all complexes of the (Cr3+, Co2+, Cu2+). conductivity measurement shows t

The quote of a Canadian communication scientist (Marshall McLuhan) (“The world has become an electronic village”) has become an archaic information compared to the great and rapid development of communication in the last two decades of the 20th century and what will happen later in the 21st century, to the extent that the world is called, thanks to the internet, a “Small screen” and this fact is a sign of the great progress that has been made in this field. As for the other statement of the Canadian communication scientist mentioned before “the medium itself, is the message”, it has been renewed and developed in its meaning and it’s purpose. Each new technical development in the means of communication necessarily means a me

Quick and accurate quaternary mixture resolution of furosemide (FURO), carbamazepine (CARB), diazepam (DIAZ) and carvedilol (CARV) by using derivative spectrophotometric method was performed. FURO and CARV were determined by means of first (D1), second (D2), third (D3) and fourth (D4) derivative spectrophotometric methods, CARB was determined by using D1, D2, D3 derivatives, while D1 and D2 were used for the determination of DIAZ. The recommended methods were verified using laboratory prepared mixtures and then successfully applied for the pharmaceutical formulations analysis of the cited drugs. The results obtained revealed the efficiency of the proposed methods as quantitative tool of analysis of the quaternary mixture with no requirement