We show, through a refinement of the work theorem, that the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states, is exactly given by =W-DeltaF=kTD(rho||rho[over ])=kT, where rho and rho[over ] are the phase-space density of the system measured at the same intermediate ...

‎‎a natural generalization of two dimensional cyclic code ($t{tdc}$) is two dimensional skew cyclic code‎. ‎it is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $r_n:=f[x,y;rho,theta]/_l$‎. ‎in this paper we characterize the left ideals of the ring $r_n$ with two methods and find the generator matrix for two dimensional s...

‎‎A natural generalization of two dimensional cyclic code ($T{TDC}$) is two dimensional skew cyclic code‎. ‎It is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=F[x,y;rho,theta]/_l$‎. ‎In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional s...

Let $D$ be the open disk $|x|< R$ of a complete ultrametric algebraically closed field $\mathbb K$. We define growth order $\rho(f)$, type $\sigma(f)$ cotype $\psi(f)$ and another expression $\theta(f)$ an analytic function in we show relations between number zeros $f$ ``maximum modulus'' involving $\rho,\sigma,\psi$. Then $\rho(f)$ lies $[\theta(f)-1, \theta(f)]$. Moreover, if $0< \rho(f)< +\i...

The Rho GDP dissociation inhibitor (GDI) forms a complex with the GDP-bound form of the Rho family small G proteins and inhibits their activation. The GDP-bound form complexed with Rho GDI is not activated by the GDP/GTP exchange factor for the Rho family members, suggesting the presence of another factor necessary for this activation. We have reported that the Rho subfamily members regulate th...

For a split reductive group $G$ over number field $k$, let $\rho$ be an $n$-dimensional complex representation of its dual $G^\vee(\mathbb{C})$. any irreducible cuspidal automorphic $\sigma$ $G(\mathbb{A})$, where $\mathbb{A}$ is the ring adeles in \cite{JL21}, authors introduce $(\sigma,\rho)$-Schwartz space $\mathcal{S}_{\sigma,\rho}(\mathbb{A}^\times)$ and $(\sigma,\rho)$-Fourier operator $\...

Actomyosin contraction generates mechanical forces that influence cell and tissue structure. During convergent extension in Drosophila melanogaster, the spatially regulated activity of the myosin activator Rho-kinase promotes actomyosin contraction at specific planar cell boundaries to produce polarized cell rearrangement. The mechanisms that direct localized Rho-kinase activity are not well un...

Dvl is a key protein that transmits the Wnt signal to the canonical beta-catenin pathway and the noncanonical planar cell polarity (PCP) pathway. We studied the roles of Rho-associated kinase (Rho-kinase), which is activated by Dvl in the PCP pathway of mammalian cells. The expression of Dvl-1, Wnt-1, or Wnt-3a activated Rho-kinase in COS cells, and this activation was inhibited by the Rho-bind...