In [4] B. M. Schein considered systems of the form ( ; o; n),where is a set of functions closed under the composition "o" of functions (and hence ( ; o) is a function semigroup) and the set theoretic subtraction "n" (and hence is a subtraction algebra in the sense of [1]). He proved that every subtraction semigroup is isomorphic to a di erence semigroup of invertible functions. B. Zelinka [5] d...

Let $G$ be an abelian group with identity $e$. $R$ a $G$-graded commutative ring and $M$ graded $R$-module. In this paper we will obtain some results concerning the generalized 2-absorbing submodules their homogeneous components. Special attention has been paid, when rings are gr-Noetherian, to find extra properties of these submodules.

The trans-admittance-mode (TAM) might act as a transforming bridge for voltage-mode to current-mode conversion. In this study a new low voltage operated electronically tunable TAM biquad filter structure realizing all the seven standard filtering functions namely; low-pass (LP), band-pass (BP), high-pass (HP), regular-notch (RN), low-pass-notch (LPN), high-pass-notch (HPN) and all-pass (AP) fro...

Let R be a commutative semiring with $ 1 \neq0$ . In this paper, we study the concept of weakly 1-absorbing primary ideal which is generalization overccommutative semirings A proper I called if whenever nonunit elements $a,b,c \in R$ and $0 \neq abc I$, then $ab $or $c \sqrt{I}$. number results concerning ideals examples are given. And need special type k-ideal or subtractive helps to prove rel...

and the matrix here is in SL2(R). (This action of SL2(R) on the upper half-plane is essentially one of the models for the isometries of the hyperbolic plane.) The action (1.1) makes sense with C replaced by any field K, and gives a transitive group action of GL2(K) on the set K ∪{∞}. Just as over the complex numbers, the formula (1.2) shows the action of SL2(K) on K ∪ {∞} is transitive. Now tak...

Previously, a rat model of chronic compressive myelopathy that uses a water-absorbing polymer inserted under a spinal lamina was reported. However, the best size and coefficient of expansion of the polymer sheet have not yet been established. The aim of the present study was to optimize these properties in an ideal rat model of cervical compressive myelopathy. Thirty rats were used in this stud...