On the functional central limit theorem and the law of the iterated logarithm for Markov processes

Summary Let X _tt0 be an ergodic stationary Markov process on a state space S. If  is its infinitesimal generator on L ²(S, dm), where m is the invariant probability measure, then it is shown that for all f in the range of } } 0)$$ " align="middle" border="0"> converges in distribution to the Wiener measure with zero drift and variance parameter ² =–2f, g=–2Âg, g where g is some element in the domain of  such that Âg=f (Theorem 2.1). Positivity of ² is proved for nonconstant f under fairly general conditions, and the range of  is shown to be dense in 1. A functional law of the iterated logarithm is proved when the (2+)th moment of f in the range of  is finite for some >0 (Theorem 2.7(a)). Under the additional condition of convergence in norm of the transition probability p(t, x, d y) to m(dy) as t , for each x, the above results hold when the process starts away from equilibrium (Theorems 2.6, 2.7 (b)). Applications to diffusions are discussed in some detail.This research was partially supported by NSF Grants MCS 79-03004, CME 8004499     

Picture Fuzzy Threshold Graphs with Application in Medicine Replenishment

In this study, a novel concept of picture fuzzy threshold graph (PFTG) is introduced. It has been shown that PFTGs are free from alternating 4-cycle and it can be constructed by repeatedly adding a dominating or an isolated node. Several properties about PFTGs are discussed and obtained the results that every picture fuzzy graph (PFG) is equivalent to a PFTG under certain conditions. Also, the underlying crisp graph (UCG) of PFTG is a split graph (SG), and conversely, a given SG can be applied to constitute a PFTG. A PFTG can be decomposed in a unique way and it generates three distinct fuzzy threshold graphs (FTGs). Furthermore, two important parameters i.e., picture fuzzy (PF) threshold dimension (TD) and PF partition number (PN) of PFGs are defined. Several properties on TD and PN have also been discussed. Lastly, an application of these developed results are presented in controlling medicine resources.     

Efficacious and sustained release of an anticancer drug mitoxantrone from new covalent organic frameworks using protein corona

Solid porous and crystalline covalent organic frameworks (COFs) are characterized by their higher specific BET surface areas and functional pore walls, which allow the adsorption of various bioactive molecules inside the porous lattices. We have introduced a perylene-based COF, PER@PDA-COF-1, which acts as an effective porous volumetric reservoir for an anticancer drug, mitoxantrone (MXT). The drug-loaded COF (MXT–PER@PDA-COF-1) exhibited zero cellular release of MXT towards cancer cells, which can be attributed to the strong intercalation between the anthracene-dione motif of the drug and the perylene-based COF backbone. Here, we have introduced a strategy involving the serum-albumin-triggered intracellular release of mitoxantrone from MXT–PER@PDA-COF-1. The serum albumin acts as an exfoliating agent and as a colloidal stabilizer in PBS medium (pH = 7.4), rapidly forming a protein corona around the exfoliated COF crystallites and inducing the sustained release of MXT from the COF into tumorigenic cells.

Solid porous and crystalline covalent organic frameworks (COFs) are characterized by their higher specific BET surface areas and functional pore walls, which allow the adsorption of various bioactive molecules inside the porous lattices.     

Existence of Surface Waves and Band Gaps in Periodic Heterogeneous Half-spaces

We find a sufficient condition for the existence of surface (Rayleigh) waves based on the Rayleigh-Ritz variational method. When specialized to a homogeneous half-space, the sufficient condition recovers the known criterion for the existence of subsonic surface waves. A simple existence criterion in terms of material properties is obtained for periodic half-spaces of general anisotropic materials. Further, we numerically compute the dispersion relation of the surface waves for a half-space of periodic laminates of two materials and demonstrate the existence of surface wave band gaps.     

Instabilities in free-surface electroosmotic flows

Instability of a thin electrolyte film undergoing a direct current electroosmotic flow has been investigated. The film with a compliant electrolyte–air interface is flowing over a rigid charged substrate. Unlike previous studies, inclusion of the Maxwell stresses in the formulation shows the presence of a new finite wavenumber shear-flow mode of instability, alongside the more frequently observed long-wave interfacial mode. The shear mode is found to be the dominant mode of instability when the electrolyte–solid and electrolyte–air interfaces are of opposite charge or of same charge but have very large zeta-potential at the electrolyte–air interface. The conditions for mode-switch (interfacial to shear) and the direction of the travelling waves are discussed through stability diagrams. Interestingly, the analysis shows that when the interfaces are of nearly same zeta potential, the ‘free’ electrolyte–air interface behaves more like a ‘stationary’ wall because of the ion transport in the reverse direction of the flow.     

Comment on the CP-violating electric charge of the magnetic monopole

It is shown, using an effective theory, that the electric charge that develops on a magnetic monopole, due to the presence of the CP-violating term \([\theta e^2 /(32\pi ^2 )]F_{\mu v}^a \tilde F^{\mu va} \) , does not vanish for massless fermions.