Let $(A,\mathfrak{m})$ be a Gorenstein local ring and let $M$, $N$ two Cohen-Macaulay $A$-modules with $M$ linked to via ideal $\mathfrak{q}$. $L$ another finitely generated $A$-module. We show that $\mathrm{Ext}^i_A(L,M) = 0 $ for all $i \gg 0$ if only $\mathrm{Tor}^A_i(L,N) 0$. If $D$ is module then we $\mathrm{Ext}^i_A(M, D) $\mathrm{Ext}^i_A(D^\dagger , N) 0$, where $D^\dagger \mathrm{Ext}^...

let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...

Six double mutants and a quadruple mutant were derived from four UV radiation-hypersensitive single mutants (rad-1, rad-2, rad-3 and rad-7). Sensitivities of the 11 strains to UV, gamma-radiation and methyl methanesulfonate (MMS) were compared. Of the six double mutants, only the rad-1;rad-2 and rad-3;rad-7 doubles were no more hypersensitive than the most sensitive single mutant to UV-radiatio...

In this paper, optimum trajectories in Earth Transfer Orbit (ETO) for a lunar transportation system are proposed. This paper aims at improving the payload ratio of the reusable orbital transfer vehicle (OTV), which transports the payload from Low Earth Orbit (LEO) to Lunar Low Orbit (LLO) and returns to LEO. In ETO, we discuss ballistic flight using chemical propulsion, multi-impulse flight usi...

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