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     

Stereoselective reduction of arteannuin B and its chemical transformations

Absolute stereochemistry of dihydroarteannuin B 5 obtained by the reduction of arteannuin B 3 with Ni₂B, NaBH₄ or CdCl₂-Mg-MeOH-H₂O has been established by 2D NMR and single crystal X-ray diffraction studies. Some experiments aimed at the synthesis of dihydrodeoxyarteannuin B [C-4, 5 double bond isomer of 11] are also discussed.     

Energies of Charge Transfer for the Supramolecular Complexes of [60]- and [70]Fullerenes with a Series of meso-Tetraphenylporphyrins in the Solution State

Supramolecular complexes of [60]- and [70]fullerenes with various meso-tetraphenylporphyrins in toluene solutions have been studied by electronic absorption spectroscopy. Charge transfer (CT) absorption bands are observed in the visible region. Vertical ionization potentials (I _D ^V) of the meso-tetraphenylporphyrins are reported from a study of EDA interaction of these porphyrins with a number of electron acceptors like o-chloranil, p-chloranil, 2,3-dichloro-5,6-dicyanobenzoquinone (DDQ) and vitamin K. The dependence of the CT transition energy on the donor ionization potential has been utilized to estimate the vertical electron affinities (E _A ^V) of [60]- and [70]fullerenes in solution. The value of E _A ^V for [60]fullerene is found to be 0.10 eV lower in magnitude than that of [70]fullerene. We have extracted degrees of CT, and oscillator and transition dipole strengths of the fullerenes/meso-tetraphenylporphyrins complexes. The experimental results show that the CT complexes studied here have a neutral character in their ground states. Electronic coupling elements have been determined for fullerene/meso-tetraphenylporphyrin complexes. Values of the solvent reorganization energy indicate that the electron transfer process takes place at a faster rate in the case of [70]fullerene/meso-tetraphenylporphyrin complexes.     

In Vitro Anticancer Activity of Methanolic Extract of Justicia adhatoda Leaves with Special Emphasis on Human Breast Cancer Cell Line

Natural products are being targeted as alternative anticancer agents due to their non-toxic and safe nature. The present study was conducted to explore the in vitro anticancer potential of Justicia adhatoda (J. adhatoda) leaf extract. The methanolic leaf extract was prepared, and the phytochemicals and antioxidant potential were determined by LCMS analysis and DPPH radical scavenging assay, respectively. A docking study performed with five major alkaloidal phytoconstituents showed that they had a good binding affinity towards the active site of NF-κB. Cell viability assay was carried out in five different cell lines, and the extract exhibited the highest cytotoxicity in MCF-7, a breast cancer cell line. Extract-treated cells showed a significant increase in nitric oxide and reactive oxygen species production. Cell cycle analysis showed an arrest in cell growth at the Sub-G0 phase. The extract successfully inhibited cell migration and colony formation and altered mitochondrial membrane potential. The activities of superoxide dismutase and glutathione were also found to decrease in a dose-dependent manner. The percentage of apoptotic cells was found to increase in a dose-dependent manner in MCF-7 cells. The expressions of caspase-3, Bax, and cleaved-PARP were increased in extract-treated cells. An increase in the expression of NF-κB was found in the cytoplasm in extract-treated cells. J. adhatoda leaf extract showed a potential anticancer effect in MCF-7 cells.     

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.     

On Some Properties of (Θ+) Excited States

The mass splitting and the decay width of pentaquark (Θ⁺) at the higher angular momentum states have been investigated in the framework of flux tube model considering the diquark-diquark-antiquark configuration for Θ⁺ along with statistical model. A quasi particle model for diquark has been considered. The Regge trajectory of Θ⁺ has also been investigated with interesting some observations.     

On the two dimensional effective electron mass in quantum wells,inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures.