In this thesis, we effectively construct a predecessor function for the type definitions in the raw hierarchy for any weakly-scattered theory. Using this predecessor function, we improve a recent bounding result by Sacks for weakly-scattered theories by removing the assumption of a predecessor function from the k-splitting hypothesis. We begin by giving an introduction to the infinitary logic C...

The aim of this paper is to introduce and study the notions of fuzzy upper $e$-limit set, fuzzy lower $e$-limit set and fuzzy $e$-continuously convergent functions. Properties and basic relationships among fuzzy upper $e$-limit set, fuzzy lower $e$- limit set and fuzzy $e$-continuity are investigated via fuzzy $e$-open sets.

stefan problem with kinetics is reduced to a system of nonlinear volterra integral equations of second kind and newton's method is applied to linearize it. product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. an example is provided to illustrated the applicability of the method.

Activation of large conductance Ca(2+)-activated K(+) channels is controlled by both cytoplasmic Ca(2+) and membrane potential. To study the mechanism of voltage-dependent gating, we examined mSlo Ca(2+)-activated K(+) currents in excised macropatches from Xenopus oocytes in the virtual absence of Ca(2+) (<1 nM). In response to a voltage step, I(K) activates with an exponential time course, fol...

and Applied Analysis 3 where R is the set of all real numbers; in particular, J(−x) = −J(x) for all x ∈ E ([28]). We say that a Banach space E has a weakly sequentially continuous duality mapping if there exists a gauge function φ such that the duality mapping Jφ is single valued and continuous from the weak topology to the weak topology; that is, for any {xn} ∈ E with xn ⇀ x, Jφ(xn) ∗ ⇀ Jφ(x)....

We analyze the dynamics of the helical edge modes of a quantum spin Hall state in the presence of a spatially nonuniform Rashba spin-orbit (SO) interaction. A randomly fluctuating Rashba SO coupling is found to open a scattering channel which causes localization of the edge modes for a weakly screened electron-electron (e-e) interaction. A periodic modulation of the SO coupling, with a wave num...

Cytoplasmic male sterility (CMS) has often been associated with abnormal mitochondrial open frames (ORF), orfH79 is a mitochondrial chimeric gene responsible for the CMS trait in Honglian (HL) rice. In this study, the weakly produced ORFH79 protein significantly inhibited the growth of E. coli in an oxygen culture, however, the growth of the transformants producing ORFH79 was indistinguishable ...

In this paper, we consider a sequence of open quantum graphs, with uniformly bounded data, and are interested in the asymptotic distribution their scattering resonances. Supposing that number leads our graphs is small compared to total edges, show most resonances close real axis. More precisely, same as square-root eigenvalues closed obtained by removing all leads.

We study open systems modeled as finite state machines with an interface for asynchronous communication with other open systems. An open system P is a partner of an open system S, if the two systems can be composed to a closed system S ⊕ P that is weakly terminating (does not have deadlocks nor livelocks). Known controller synthesis techniques allow us to construct a most permissive partner MP(...

This paper concerns the closed points, closed subspaces, open subspaces, weakly closed and weakly open subspaces, and effective divisors, on a non-commutative space.