Since 1980s, the study of the extending module in the module theory has been a major area of research interest in the ring theory and it has been studied recently by several authors, among them N.V. Dung, D.V. Huyn, P.F. Smith and R. Wisbauer. Because the act theory signifies a generalization of the module theory, the author studied in 2017 the class of extending acts which are referred to as a generalization of quasi-injective acts. The importance of the extending acts motivated us to study a dual of this concept, named the coextending act. An S-act MS is referred to as coextending act if every coclosed subact of Ms is a retract of MS where a subact AS of MS is said to be coclosed in MS if whenever the Rees factor ⁄ is small in th

     A novel, safe and efficient method was developed to encapsulate a blend of essential oils (EOs) into biodegradable nanoparticles (NPs). The biodegradable and biocompatible nanoparticles were made from chitosan (CH) and lecithin (LE) . The quality of the essential oils was verified using gas chromatography/mass spectrometry (GC/MS). The synthesis of nanoparticles included emulsification, followed by sonication, homogenization, and extrusion. Transmission electron microscopy (TEM) indicated that the nanoparticles were spherical in shape with sizes ranging from 25 to 70 nm, while dynamic light scattering (DLS) showed high negative zeta potentials. The stability of the final formula was evaluated in gastric and intes

The aim of this book is to present a method for solving high order ordinary differential equations with two point boundary condition of the different kind, we propose semi-analytic technique using two-point osculatory interpolation to construct polynomial solution. The original problem is concerned using two-points osculatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, we discussion the existence and uniqueness of solutions and many examples are presented to demonstrate the applicability, accuracy and efficiency of the methods by compared with conventional method .i.e. VIDM , Septic B-Spline , , NIM , HPM, Haar wavelets on one hand and to confirm the order convergence on the other

In this work, we prove by employing mapping Cone that the sequence and the subsequence of the characteristic-zero are exact and subcomplex respectively in the case of partition (6,6,4) .

       In this paper normal self-injective hyperrings are introduced and studied. Some new relations between this concept and essential hyperideal, dense hyperideal, and divisible hyperring are studied. 

Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.

In this paper, some relations between the flows and the Enveloping Semi-group were studied. It allows to associate some properties on the topological compactification to any pointed flows. These relations enable us to study a number of the properties of the principles of flows corresponding with using algebric properties. Also in this paper proofs to some theorems of these relations are given.

    Eight electronic properties; HUMO, LUMO, HOMO-LUMO energy gap, dipole moment point-charge, dipole moment hybrid, molecular weight, heat of formation and zero-point energy of 60 normal and branched alkanes were examined using topology molecular indices. All the electronic properties were calculated using semi-empirical self-consistent molecular orbital theory. The relationship of electronic calculation properties with seven models of topology indices based on degree and/or distance were obtained in terms of their correlation, regression and principal component analysis. Most of the properties were well-modelled (r² > 0.82) by topology molecular indices except the dipole moment point-charge and hybrid. The PCA resulted

In this paper, the terms of Lascoux and boundary maps for the skew-partition (11,7,5) / (1,1,1) are found by using the Jacobi-Trudi matrix of partition. Further, Lascoux resolution is studied by using a mapping Cone without depending on the characteristic-free resolution of the Weyl module for the same skew-partition.

In this paper, the complex of Lascoux in the case of partition (3,3,2) has been studied by using diagrams ,divided power of the place polarization ) (k ij ,Capelli identites and the idea of mapping Cone .