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.

In this work; Silicon dioxide (SiO2) plasma plume was prepared by laser induced plasma (LIP). The electron number density, plasma frequency and Debye length were calculated by reading the data of I-V curve of Langmuir probe which was used as a diagnostic method of measuring plasma properties. Pulsed Nd:YAG laser was used for measuring the electron number density of SiO2 plasma plume under vacuum environment with varying both vacuum pressure and axial distance from the target surface. Some physical properties of the plasma generated such as electron density, plasma frequency and Debye length have been measured experimentally and the effects of vacuum pressure and Langmuir probe distance from the target were studied on those variables. An

  In this study, Schiff's bases [S3,S4] were synthezied by condensation of N,N-dimethyl amino benzaldehyde with primary aromatic amine[N-(hydrazinyl methyl)benzamide]. These Sciff's bases were found to react with maleic anhydride and phthalic anhydride to give 1,3Oxazepine[S5,S6,S7,S8] in good yields.            The structures confired by m.p ,T.L.C.,FT.IR and 1H-NMR (of some of them).

This work contain many steps starting from esterification of isophthalic acid to yield diester compound [I] which was converted to their acid hydrazide [II], then the later compound reacted with ethylacetoacetate to yield pyrazol-5-one compound [III]. Afterword added acetyl chloride to give the compound [IV], the reaction of this compound with theiosemicarbazide led to produce a new carbothioamide compound [V], which was reacted with ethyl chloro acetate to yield the thioxoimidazolidin compound [VI]. The condensation reactions of this compound with different substituted aldehyde give new alkene derivatives [VII] ad. The synthesized compounds were characterized by melting points, FT-IR, 1H-NMR and Mass spectroscopy.

In this paper, the definition of fuzzy anti-inner product in a linear space is introduced. Some results of fuzzy anti-inner product spaces are given, such as the relation between fuzzy inner product space and fuzzy anti-inner product. The notion of minimizing vector is introduced in fuzzy anti-inner product settings.

In this paper the new starting material 2-(5-chloro-1H-benzo[d]imidazole-2-yl) aniline (1) was synthesized by the condensation reaction of 4-chloro-o-phenylenediamine and anthranilic acid .The new Mannich base derivatives were synthesized using formaldehyde and different secondary amines to synthesize a new set of benzimidazole derivatives(2-5). Also, the new Schiff-base derivatives (6-10) were synthesized from the reaction of compound (1) with various aromatic aldehydes and the closure-ring was done successfully using mercapto acetic acid to get the new thiazolidine derivatives(11-12).These new compounds were characterized using some physical techniques like:FT-IR Spectra and 1HNMR Spectra.

The nuclear structure of some cobalt (Co) isotopes with mass number A=56-60 has been studied depending on the effect of some physical properties such as the electromagnetic properties effects, such as, elastic longitudinal form factors, electric quadrupole moments, and magnetic dipole moments. The fp model space is used to present calculations using GXFP1 interaction by adopting the single particle wave functions of the harmonic oscillator. For all isotopes under consideration, the ⁴⁰Ca nucleus is regarded as an inert core in fp model-space, while valence nucleons are moving through 1f_7/2, 2p_3/2, 1f_5/2, and 2p_1/2 orbits. The effects of core-polarization are obtained by the first orde

Some esters were prepared from reaction of different molecular weight of PVA with some acid chloride (prepared by reaction of acid with thionyl chloride or phosphorous pentachloride)in the presence of pyridine. The thermal and reological properties were studied. The increasing Of bulky groups decreasing stability of the thermal and reological properties.

  A series of N- benzoyl  - 2 – alkyl -1- ( 2- thio – 1,3,4- thiadiazole -5- yl ) , have been synthesized from DL- α– amino acids , The methyl and sulfon thio ethers of these compounds were also prepared , representative samples of the prepared compounds were characterized from their IR- spectrum and elemental analysis .
 

In this paper, we introduce a new type of Drazin invertible operator on Hilbert spaces, which is called D-operator. Then, some properties of the class of D-operators are studied. We prove that the D-operator preserves the scalar product, the unitary equivalent property, the product and sum of two D-operators are not D-operator in general but the direct product and tenser product is also D-operator.