In this research the effect of grain size and effect of La2O3 doping on densification rate for the initial and intermediate stages of sintering were studied .The experimental results for α – cristobilite powder are modeled using ( L2-Regression ) technique in studying the effect of grain size and La2O3 doping using three particles size (6.12, 8.92, 13.6 ) µm, with undoped initial powder and with La2O3 doping . The mathematical simulation showes that the densification rates increase as the initial particles sizes decrease and vice versa. This shows that the densification depends directly on the initial compact density which reflects the contacts area between the particles . However the densification rates in the intermediate stages were enhanced compared with that of the initial stage .This is due to completion of neck growth that facilitates the mass transport between the grains ,and also, the presence of the massive grains due to the grain growth . Al so it is show that the doping enhances the densification rates in the intermediate stage due to that , the dopants act against the grain boundaries movement causing discourage closing of porosity and encourage escaping of voids enhances the densification rates .
Let be a commutative ring with identity and let be an R-module. We call an R-submodule of as P-essential if for each nonzero prime submodule of and 0 . Also, we call an R-module as P-uniform if every non-zero submodule of is P-essential. We give some properties of P-essential and introduce many properties to P-uniform R-module. Also, we give conditions under which a submodule of a multiplication R-module becomes P-essential. Moreover, various properties of P-essential submodules are considered.
The soft sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these concepts to define new types of soft limit points, that we called soft turning points.Finally, we used these points to define new types of soft separation axioms and we study their properties.
Let R be associative; ring; with an identity and let D be unitary left R- module; . In this work we present semiannihilator; supplement submodule as a generalization of R-a- supplement submodule, Let U and V be submodules of an R-module D if D=U+V and whenever Y≤ V and D=U+Y, then annY≪R;. We also introduce the the concept of semiannihilator -supplemented ;modules and semiannihilator weak; supplemented modules, and we give some basic properties of this conseptes.
In this note we consider a generalization of the notion of a purely extending
modules, defined using y– closed submodules.
We show that a ring R is purely y – extending if and only if every cyclic nonsingular
R – module is flat. In particular every nonsingular purely y extending ring is
principal flat.
Weibull Distribution is one of most important distribution and it is mainly used in reliability and in distribution of life time. The study handled two parameter and three-parameter Weibull Distribution in addition to five –parameter Bi-Weibull distribution. The latter being very new and was not mentioned before in many of the previous references. This distribution depends on both the two parameter and the three –parameter Weibull distributions by using the scale parameter (α) and the shape parameter (b) in the first and adding the location parameter (g)to the second and then joining them together to produce a distribution with five parameters.
... Show MoreEvery finite dimensional normed algebra is isomorphic to the finite direct product of or , it is also proved these algebras are ultrasemiprime algebras. In this paper, the ultrasemiprime proof of the finite direct product of and is generalized to the finite direct product of any ultrasemiprime algebras.
Let R be a commutative ring with identity and let M be a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of semi-essential submodules which introduced by Ali S. Mijbass and Nada K. Abdullah, and we make simple changes to the definition relate with the zero submodule, so we say that a submodule N of an R-module M is called semi-essential, if whenever N ∩ P = (0), then P = (0) for each prime submodule P of M. Various properties of semi-essential submodules are considered.
Let be a non-zero right module over a ring with identity. The weakly second submodules is studied in this paper. A non-zero submodule of is weakly second Submodule when , where , and is a submodule of implies either or . Some connections between these modules and other related modules are investigated and number of conclusions and characterizations are gained.