in this paper, we investigate various kinds of extensions of twin-good rings. moreover, we prove that every element of an abelian neat ring r is twin-good if and only if r has no factor ring isomorphic to z2  or z3. the main result of [24] states some conditions that any right self-injective ring r is twin-good. we extend this result to any regular baer ring r by proving that every element of a...

A newly developed friction-interlocking armor unit called the ‘Double cube’ (DC) was designed to improve performance of a concrete used in river/marine structures against currents/waves actions. The DC is an octagonal-shaped block made up two parts: upper cube set on lower base that either square or octagonal shape. innovative design aims provide good terms stability, allow for high tolerance p...

Artificial electromagnetic metamaterial produces exotic resonance, unusual characteristics not found in nature, but engineers can inherit the by controlling and manipulating their architecture. The design realization of dual-band, polarization, incident angle insensitive absorber (MA) is proposed. By shape structure, periodic pattern, dielectric layer thickness a significant way to realize high...

We present an analysis of structural features of all known galaxies with optical polar rings. We find a clear dichotomy for objects of this peculiar class. Bulge-dominated S0 galaxies possess only short narrow rings, while disk-dominated objects always have wide extended polar rings. We try by gas dynamical simulations to explain such a segregation by dependence of the ring-forming process on d...

A random tiling of rectangles and triangles displaying a decagonal phase is solved by Bethe Ansatz. Analogously to the solutions of the dodecagonal square triangle and the octagonal rectangle triangle tiling an exact expression for the maximum of the entropy is found.

the concept of fuzzy soft γ-ring is introduced; and some properties of fuzzy soft γ-rings are given. then the definitions of fuzzy soft γ-ideals are proposed and some of their theories are considered.

the concept of right (left) quotient (or residual) of an ideal η by anideal ν of an l-subring μ of a ring r is introduced. the right (left) quotients areshown to be ideals of μ . it is proved that the right quotient [η :r ν ] of an idealη by an ideal ν of an l-subring μ is the largest ideal of μ such that[η :r ν ]ν ⊆ η . most of the results pertaining to the notion of quotients(or residual) of ...