Gradient estimates for positive harmonic functions by stochastic analysis

We prove Cheng–Yau type inequalities for positive harmonic functions on Riemannian manifolds by using methods of Stochastic Analysis. Rather than evaluating an exact Bismut formula for the differential of a harmonic function, our method relies on a Bismut type inequality which is derived by an elementary integration by parts argument from an underlying submartingale. It is the monotonicity inherited in this submartingale which allows us to establish the pointwise estimates.     

Normals in a Minkowski Plane

In this paper we will establish bounds on the average number of normals through a point in a convex body in a Minkowski plane for certain classes of convex bodies. Also, a related Euler relation is discussed.     

A rare case of three rearrangements during the cycloaddition-elimination reaction of 4-methyl-5-phenylimino-Δ2-1,2,3,4-thiatriazoline with 2-pyridyl isothiocyanate

2-Pyridyl isothiocyanate ( 7 ), with its electrophilic and basic properties, gives a series of ring-transformation reactions with 4-methyl-5-phenylimino-1,2,3,4-thiatriazoline ( 1 ) at 60°. Two dithiazolidines, 8 and 10 , are formed as major products at an early stage of the reaction, whereas two thiadiazolidines, 9 and 11 , predominate at the end. The mechanism (Schemes II and III) has been elucidated by following the reaction course under a variety of conditions and by analyzing the products by ¹³C nmr spectroscopy.     

Convergence of simultaneous Hermite-Padé approximants to then-tuple ofq-hypergeometric series\{ {}_1\Phi _1 (_{(c,\gamma _j )}^{(1,1)} ;z)\} _{j = 1}^n

We investigate the convergence of simultaneous Hermite-Padé approximants to then-tuple of power series $$f_i (z) = \sum\limits_{k = 0}^\infty {C_k^{(i)} z^k ,} i = 1,2,...,n,$$ where $$C_0^{(i)} = 1;C_k^{(i)} = \prod\limits_{p = 0}^{k - 1} {\frac{1}{{(C - q^{\gamma i + p} )}},} k \ge 1.$$ HereC, q∈?, γ _i ∈?,i=1, 2,...,n. For |C|≠1, ifq=e^iθ, θ∈(0, 2π) and θ/2π is irrational, eachf _i (z),i=1,...,n, has a natural boundary on its circle of convergence. We show that “close-to-diagonal” and other sequences of Hermite-Padé approximants converge in capacity to (f ₁(z),..., f_n (z)) inside the common circle of convergence of eachf _i (z),i=1,...,n.     

Use of modifiers in on-line and off-line supercritical fluid extraction

For many applications using supercritical fluid extraction (SFE), modifiers may be required.This paper will present some findings regarding the use of various modifiers including methanol, hexane, acetone, chloroform, dichloromethane, toluene, and tributylphosphate, in on-line and off-line SFE with cryogenic adsorbent trapping. The specific applications involved the extractions of petroleum hydrocarbons and pesticides from naturally incurred soils.     

Laser-induced breakdown detection combined with asymmetrical flow field-flow fractionation: application to iron oxi/hydroxide colloid characterization

The combination of asymmetrical flow field-flow fractionation (AsFlFFF) with the laser-induced breakdown detection (LIBD) is presented as a powerful tool for the determination of colloid size distribution at trace particle concentrations. Detection limits (D1) of 1, 4, and 20 microg/L have been determined for a mixture of polystyrene reference particles with 20, 50, and 100 nm in size, respectively. This corresponds to injected masses of 1, 4, and 20 pg, which is lower than found in a previous study with the symmetrical FlFFF (SyFlFFF). The improvement is mainly due to the lower colloid background discharged from the AsFlFFF channel. The combined method of AsFlFFF-LIBD is then applied to the analysis of iron oxi/hydroxide colloids being considered as potential carriers for the radionuclide migration from a nuclear waste repository. Our LIBD arrangement is less sensitive for iron colloid detection as compared to reference polystyrene particles which results in a detection limit of approximately 240 microg/L FeOOH for the AsFlFFF-LIBD analysis. This is superior to the detection via UV-Vis absorbance and comparable to ICP-MS detection. Size information (mean size 11-18 nm) for different iron oxi/hydroxide colloids supplied by the present method is comparable to that obtained by sequential ultrafiltration and dynamic light scattering. A combined on-line ICP-MS detection is used to gain insight into the colloid-borne main and trace elements.     

DEVELOPMENT OF A PLAQUE REDUCTION ASSAY AND APPLICATION TO THE STUDY OF PSORALEN-DAMAGED DNA

Abstract— We have developed a procedure called a plaque reduction assay to assess the biological activity of duplex circular DNA modified by covalent adduct formation with psoralen derivatives. The replicating form (RF) of bacteriophage DNA modified by photochemical addition of a psoralen derivative was introduced into bacterial cells using the CaCI₂ transfection method. The transfected cells. plated upon a confluent lawn of cells permissive for the bacteriophage in the inoculum, provided a measure of the reduction in infectivity of the RF DNA which resulted from its covalent modification. Use of this assay is illustrated in studies which screened and compared the activities of several recently synthesized psoralen derivatives. We describe two new compounds. β-(8-psoralenoxy)-ethanol and β-(8-psoralenoxy)ethylamine that are significantly more active than either 8-methoxypsoralen or trioxsalen in the biological assay