the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$,  we mean an ideal $i$ of $r$ such that $ineq r$.  we say that a proper ideal $i$ of a ring $r$ is a  maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...

An absorbing substrate of complex refractive index n(2) - jk(2) at wavelength lambda can be coated by an absorbing thin film of complex refractive index n(1) - jk(1) and thickness d to achieve zero reflection at normal incidence. For given n(2),k(2) multiple solutions (n(1),k(1),d/lambda) are found that correspond to infinitely many distinct antireflection layers. This is demonstrated for a Si ...

The physical basis of Brownian motion in translationally invariant media are well understood, and models based on this type of transport have been applied to the interpretation of an enormous variety of physical phenomena. There is likewise a large literature on Brownian motion in the presence of absorbing boundaries. Perfectly absorbing boundaries are known to change the properties of Brownian...

Let G be an abelian group with identity e. R a graded multiplicative hyperring and ? : Igr(R) expansion function of Igr(R), where is the set all hyperideals R. In this paper, we introduce study concepts ?-primary 2-absorbing which are extended classes prime 2- absorbing R, respectively. Moreover, give basic properties these new types investigate relations among structures.

The energy absorbing capability is one of the most important aspects of crushing behavior of a structure subjected to axial impact. In this paper, a simple practical method is introduced to enhance the crushing behavior of this kind of structure. The axial impact of metallic energy absorbing thin-walled tubes with special shaped cross-section is simulated using LS-DYNA software. The effect of c...

The link between the African Monsoon systems and aerosol loading in Africa is studied using multi-year satellite observations of UV-absorbing aerosols and rain gauge measurements. The main aerosol types occurring over Africa are desert dust and biomass burning aerosols, which are UV-absorbing. The abundance of these aerosols over Africa is characterised in this paper using residues and Absorbin...