Stop times in fock space stochastic calculus

Summary A stop time S in the boson Fock space over L ₂()₊ is a spectral measure in [0,] such that {S([0,t])} is an adapted process. Following the ideas of Hudson [6], to each stop time S a canonical shift operator U ^Sis constructed in . When S({}) has the vacuum as a null vector U ^Sbecomes an isometry. When S({})=0 it is shown that admits a factorisation _S]{S where _{S is the range of U ^Sand _S] is a suitable subspace of called the Fock space upto time S. This, in particular, implies the strong Markov property of quantum Brownian motion in the boson as well as fermion sense and the Dynkin-Hunt property that the classical Brownian motion begins afresh at each stop time. The stopped Weyl and fermion processes are defined and their properties studied. A composition operation is introduced in the space of stop time to make it a semigroup. Stop time integrals are introduced and their properties constitute the basic tools for the subject.     

The new ether derivative of phenylpropanoid and bioactivity was investigated from the leaves of Piper betle L.

Abstract

A new ether derivative of phenylpropanoid compound, γ-(γ′-isohydroxychavicol)-chavicol octanyl ether (K1) along with one known phenylpropanoid named allyl-pyrocatechol or hydroxychavicol (2) were isolated from Piper betle var. kali collected from Tumluk district, West Bengal India. We first report the presence of compound K1 in the genus Piper. Their structures were established on the basis of various spectroscopic analyses. Compounds K1 and 2 showed excellent antioxidant DPPH free radical scavenging activity with IC₅₀ values of 4.61 and 4.12?µg/mL compared to ascorbic acid as a standard antioxidant drug with IC₅₀ value of 3.42?µg/mL, respectively. Evaluation of in vitro cytotoxic activities of compounds K1 and 2 showed significant effects against human oral cancer cell lines (AW13516 and AW8507), human hepatoma cell lines (HEPG2 and PLC-PRF-5) and a human pancreatic cell line (MIA-PA-CA-2), compared to Doxorubicin^® as a standard cytotoxic drug with GI₅₀ values of <10 and 18.18?µg/mL.     

Study of the development of thermoresistance in human pancreatic carcinoma cell lines using proteome analysis

In order to find candidate proteins that are potentially associated with the thermoresistant phenotype in combination with drug resistance, we analyzed the differential protein expression in vitro in the human pancreatic cancer cell line EPP85-181-P and classical and atypical multidrug-resistant variants and their thermoresistant counterparts using proteomics. This study identifies sets of proteins that may lead to the development of thermoresistance. These results provide a fundamental basis to elucidate the molecular mechanism of thermoresistance and chemoresistance phenomena that may assist the therapy of inoperable cancers.     

Synthesis and characterization of cobalt(II), nickel(II), copper(II), palladium(II) and dioxouranium(VI) complexes of the antipyrine Schiff base of 3-formylsalicylic acid

A new Schiff base has been synthesized from 4-aminoantipyrine and 3-formylsalicylic acid. The ligand has a dianionic tetradentate compartmental OONO donor system. The cobalt(II), nickel(II), copper(II) and dioxouranium(VI) complexes exist in phenolato-bridged dinuclear species, while palladium(II) gives a mononuclear complex with free –COOH groups. The complexes have been characterized by elemental analyses, i.r., u.v.-vis, thermal and magnetic measurements.     

Facile purification of rare cucurbiturils by affinity chromatography

A practical method for the separation and purification of cucurbituril (CB) hexamers was developed on the basis of affinity chromatography using aminopentylaminomethylated polystyrene beads. This recyclable resin, which can be used repeatedly, facilitates the general preparation of cucurbituril derivatives and compensates for the usually moderate yields and mixed products that characterize the acid-catalyzed synthesis of CB derivatives. This technique allows convenient, rapid isolation of rare substituted cucurbiturils, including hexacyclohexanocucurbit[6]uril and dodecamethylcucurbit[6]uril. [reaction: see text]     

Two-step photoionization of Na2: dependence on alignment

Laser light is used for two-step photoionization of Na₂. the first step depends on the moleculer orientation, the second step doesnot. This yields a method for the analysis of molecular alignment.     

Semiclassical statistical mechanics of two-dimensional hard-body fluids

The problem of calculating the thermodynamic properties of two-dimensional semiclassical hard-body fluids is studied. Explicit expressions are given for the first-order quantum corrections to the free energy, equation of state, and virial coefficients. The numerical results are calculated for the planar hard dumbbell fluid. Significant features are the increase in quantum corrections with increasing eta and increasing L*=L/sigma(0).