We propose an analytic solution for the stochastic dynamics of a binary biological switch, defined as a DNA unit with two mutually exclusive configurations, each one triggering the expression of a different gene. Such a device could be used as a memory unit for biological computing systems designed to operate in noisy environments. We discuss a recent implementation of an exclusive switch in li...

In this paper, applying the concept of generalized A-valued norm on a right $H^*$-module and also the notion of ϕ-homomorphism of Finsler modules over $C^*$-algebras we first improve the definition of the Finsler module over $H^*$-algebra and then define ϕ-morphism of Finsler modules over $H^*$-algebras. Finally we present some results concerning these new ones.

In this work, some properties of amply weak essential supplemented modules are investigated. Let M be a projective and weakly module. Then every finitely M-generated module is supplemented. R any ring. if only generated R-module an e-supplement submodule in

The yield of chromosome aberrations was studied in Go human peripheral blood lymphocytes following in vitro exposure to 100, 250 and 500 rad of caesium-137 gamma radiation. The doses were given at various rates up to 400 rad per h with the longest exposures lasting for approx. 50 h. At 500 and 250 rad the dicentric yields fell by 66 and 64% when the dose rate was reduced from 400 to 10 rad per ...

Let $M_R$ be a module with $S=End(M_R)$. We call a submodule $K$ of $M_R$ annihilator-small if $K+T=M$, $T$ a submodule of $M_R$, implies that $ell_S(T)=0$, where $ell_S$ indicates the left annihilator of $T$ over $S$. The sum $A_R(M)$ of all such submodules of $M_R$ contains the Jacobson radical $Rad(M)$ and the left singular submodule $Z_S(M)$. If $M_R$ is cyclic, then $A_R(M)$ is the unique ...

let $m_r$ be a module with $s=end(m_r)$. we call a submodule $k$ of $m_r$ annihilator-small if $k+t=m$, $t$ a submodule of $m_r$, implies that $ell_s(t)=0$, where $ell_s$ indicates the left annihilator of $t$ over $s$. the sum $a_r(m)$ of all such submodules of $m_r$ contains the jacobson radical $rad(m)$ and the left singular submodule $z_s(m)$. if $m_r$ is cyclic, then $a_r(m)$ is the unique ...

Test ing the sat is f iabi l i ty of a Boolean fo rmu la over l inear constraints is not a s imple ma t ter. Ex is t ing AI systems handle tha t k ind o f problems w i t h a general proof method for their Boolean parts and a separate module for comb in ing l inear constraints. On the contrary, t rad i t i ona l operat ions research methods need the prob lem to be t ransformed, and solved w i t ...

‎A module $M$ is lifting if and only if $M$ is amply supplemented and‎ ‎every coclosed submodule of $M$ is a direct summand‎. ‎In this paper‎, ‎we are‎ ‎interested in a generalization of lifting modules by removing the condition‎"‎amply supplemented‎" ‎and just focus on modules such that every non-cosingular‎ ‎submodule of them is a summand‎. ‎We call these modules NS‎. ‎We investigate some gen...