We consider the lateral diffusion of receptors, or other membrane proteins, in the outer membranes of certain cells, and their capture by coated pits. It is shown, for the case in which the coated pits are in fixed random positions, that the long-time decay of the total number of uncaptured proteins is of the fractional exponential form, N(t) = N0 exp [-square root of (t/tau)], and not of the p...

The conformational dynamics of individual, flexible polymers in steady shear flow were directly observed by the use of video fluorescence microscopy. The probability distribution for the molecular extension was determined as a function of shear rate, gamma;, for two different polymer relaxation times, tau. In contrast to the behavior in pure elongational flow, the average polymer extension in s...

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 ...

Cononsolvency-induced micellization kinetics of a pyrene end-labeled diblock copolymer of N-isopropylacrylamide and oligo(ethylene glycol) methyl ether methacrylate, Py-PNIPAM-b-POEGMA, was investigated in detail via a combination of stopped-flow light-scattering and fluorescence techniques. Upon a stopped-flow jump from pure methanol to proper methanol/water mixtures, scattered light intensity...

Let $R$ be a commutative ring and $M$ be an $R$-module. In this paper, we investigate some properties of 2-absorbing submodules of $M$. It is shown that $N$ is a 2-absorbing submodule of $M$ if and only if whenever $IJLsubseteq N$ for some ideals $I,J$ of R and a submodule $L$ of $M$, then $ILsubseteq N$ or $JLsubseteq N$ or $IJsubseteq N:_RM$. Also, if $N$ is a 2-absorbing submodule of ...

Clinical syndromes associated with progressive supranuclear palsy-tau pathology now include progressive supranuclear palsy-parkinsonism (PSP-P), in addition to classic Richardson's syndrome (RS) and pure akinesia with gait freezing (PAGF). Although pathological heterogeneity of progressive supranuclear palsy (PSP) has also been established, attempts to correlate this with clinical findings have...

Variants in the gene encoding the triggering receptor expressed on myeloid cells 2 (TREM2) were recently found to increase the risk for developing Alzheimer's disease (AD). In the brain, TREM2 is predominately expressed on microglia, and its association with AD adds to increasing evidence implicating a role for the innate immune system in AD initiation and progression. Thus far, studies have fo...

Activity-dependent neuroprotective protein (ADNP) is deregulated in Alzheimer's disease (AD) and in schizophrenia and mutated in autism. In mice, ADNP is essential for brain formation and ADNP haploinsufficiency is associated with cognitive and social deficits and tauopathy. Tauopathy, a major pathology in AD, is also found in ~45% of frontotemporal dementias (FTDs). Tau transcript, a product o...

This paper builds a convergence analysis of explicit tau-leaping schemes for simulating chemical reactions from the viewpoint of stochastic differential equations. Mathematically, the chemical reaction process is a pure jump process on a lattice with state-dependent intensity. The stochastic differential equation form of the chemical master equation can be given via Poisson random measures. Bas...

Let R be a commutative ring with identity , and M is unitary left R-module”, “A proper submodule E of an R-module called weakly quasi-prime if whenever r, s ∈ R, m M, 0 ≠ rsm implies that rm or sm E”. “We introduce the concept quasi 2-absorbing as generalization submodule”, where r,s,t ∈M 0≠ rstm rtm stm E. we study basic properties 2-absorbing. Furthermore, relationships other classes module a...