Gap exponents for percolation processes with triangle condition

A study is made of the gap exponents for percolation processes with the triangle condition in the subcritical region. It is show that the gaps are given by _t =2 fort=2, 3,. Scaling theory predicts thatP _p (¦C ₀¦S(p))–(p _c –p) andE _p (1/¦C ₀¦; ¦C ₀¦S(p))–(p _c –p)³, whereS(p) is the typical cluster size. It is found that (p _c –p)P _p (|C ₀S(p) ^1–)(p _c –p)^1–2 and (p _c –p)³E _p (1/|C ₀|;|C ₀|S(p) ^1–))(p _c –p)^3–4.     

PHOTOBIOLOGICAL ACTIVITY OF 3,4''-DIMETHYL-8-METHOXYPSORALEN, A LINEAR FUROCOUMARIN WITH UNUSUAL DNA-BINDING PROPERTIES

The furocoumarin derivative 3,4'-dimethyl-8-methoxypsoralen (DMe-8-MOP) exhibits remarkable antiproliferative activity, but is devoid of skin phototoxicity. To gain insight into this peculiar behaviour we investigated non-covalent and covalent binding of DMe-8-MOP to calf thymus DNA, along with DNA-synthesis inhibition and mutagenic activity. The non-covalent interaction of DMe-8-MOP with the nucleic acid is quite poor as shown by equilibrium dialysis, spectroscopic, chiroptical and hydrodynamic techniques. However, it exhibits relevant photobinding ability to DNA using both isolated nucleic acid samples and cellular systems. Unlike the large majority of congeners, DMe-8-MOP undergoes predominantly photochemical monoaddition to the double helical polynucleotide. Upon examination of the products obtained by enzymatic hydrolysis of DMe-8-MOP photomodified DNA, the formation of an unusual furan side adduct is proposed, which could account for the peculiar photochemical and photobiological properties of the 3,4'-dimethyl furocoumarin derivative.     

SYNTHESIS AND PHOTOBIOLOGICAL PROPERTIES OF 4-HYDROXYMETHYL-4'-METHYLPSORALEN DERIVATIVES

The synthesis and the photobiological activity of two new hydroxymethyl derivatives of psoralen namely 4-hydroxymethyl-4'-methyl- and 4-hydroxymethyl-4'-methyl-8-rnethoxypsoralen are described. Both compounds exhibited efficient photobinding to DNA and RNA. The DNA-photobinding process was investigated using different nucleic acid structures such as double-helical DNA, ribosomal RNA, bacterial DNA and DNA organized in the nucleosomal arrangement. The test derivatives were able to induce cross-links to a similar extent as 8-methoxypsoralen (8-MOP), used as a reference photochemotherapeutic drug. In contrast to 8-MOP, they produced relatively high levels of ^lO₂. Most photobiological effects (DNA synthesis inhibition, T₂ phage sensitization, inhibition of tumor transmitting capacity) showed a good correlation with the extent of covalent photoaddition. On the other hand, the new 4-hydroxymethylpsoralens were unable to induce skin erythema, in striking contrast with 8-MOP. Thus, neither cross-linking of the nucleic acid nor ¹O₂ production were coupled with skin phototoxicity in this class of compounds. The new derivatives appear to represent an important beginning to development of new active photochemotherapeutic agents devoid of undesired phototoxic side effects.     

An overlapping additive Schwarz preconditioner for interpolation on the unit sphere with spherical radial basis functions

The problem of interpolation of scattered data on the unit sphere has many applications in geodesy and Earth science in which the sphere is taken as a model for the Earth. Spherical radial basis functions provide a convenient tool for constructing the interpolant. However, the underlying linear systems tend to be ill-conditioned. In this paper, we present an additive Schwarz preconditioner for accelerating the solution process. An estimate for the condition number of the preconditioned system will be discussed. Numerical experiments using MAGSAT satellite data will be presented.     

ZIF-Induced d-Band Modification in a Bimetallic Nanocatalyst: Achieving Over 44 % Efficiency in the Ambient Nitrogen Reduction Reaction

The electrochemical nitrogen reduction reaction (NRR) offers a sustainable solution towards ammonia production but suffers poor reaction performance owing to preferential catalyst–H formation and the consequential hydrogen evolution reaction (HER). Now, the Pt/Au electrocatalyst d-band structure is electronically modified using zeolitic imidazole framework (ZIF) to achieve a Faradaic efficiency (FE) of >44 % with high ammonia yield rate of >161 μg mg_cat⁻¹ h⁻¹ under ambient conditions. The strategy lowers electrocatalyst d-band position to weaken H adsorption and concurrently creates electron-deficient sites to kinetically drive NRR by promoting catalyst–N₂ interaction. The ZIF coating on the electrocatalyst doubles as a hydrophobic layer to suppress HER, further improving FE by >44-fold compared to without ZIF (ca. 1 %). The Pt/Au-N_ZIF interaction is key to enable strong N₂ adsorption over H atom.     

Solution to the Neumann problem exterior to a prolate spheroid by radial basis functions

We consider the exterior Neumann problem of the Laplacian with boundary condition on a prolate spheroid. We propose to use spherical radial basis functions in the solution of the boundary integral equation arising from the Dirichlet–to–Neumann map. Our approach is particularly suitable for handling of scattered data, e.g. satellite data. We also propose a preconditioning technique based on domain decomposition method to deal with ill-conditioned matrices arising from the approximation problem.     

A novel cyclodimerization of 3-methyl-3-butenenitrile. An efficient synthesis of 4-cyanoisophorone

Dimerization of 3-methyl-3-butenenitrile (1) by lithium dialkylamide gave selectively 3,5,5-trimethyl-1-amino-4-cyanocyclohexa-1,3-diene (2), which was easily hydrolyzed by aqueous acid to afford 4-cyanoisophorone (3,5,5-trimethyl-4-cyano-cyclohex-2-enone) (3) quantitatively.     

Non‐Thermal Corrections to Hawking Radiation Versus the Information Paradox**

We provide a model‐independent argument indicating that for a black hole of entropy N the non‐thermal deviations from Hawking radiation, per each emission time, are of order , as opposed to . This fact abolishes the standard a priory basis for the information paradox.     

BENZOFUROCOUMARINS: NEW MONOFUNCTIONAL DNA-PHOTOBINDING AGENTS

Abstract— The tetracyclic furocoumarin 2H-benzofuro[3,2-g]-1-benzo-pyran-2-one and its 4 and/or II methyl analogues have been investigated in their DN A-photobinding properties. Spectrophotometric and radioactivity measurements show that these compounds exhibit prominent ability to bind to the polynucleotide double helix by covalent photoaddition of the furocoumarin 3,4 double bond.
Denaturation-renaturation experiments demonstrate that no cross-link of DNA chains occurs. Benzopsoralens can thus be considered as a new class of monofunctional DNA-photobinding agents.     

Polynomial operators and local approximation of solutions of pseudo-differential equations on the sphere

We study the solutions of an equation of the form Lu=f, where L is a pseudo-differential operator defined for functions on the unit sphere embedded in a Euclidean space, f is a given function, and u is the desired solution. We give conditions under which the solution exists, and deduce local smoothness properties of u given corresponding local smoothness properties of f, measured by local Besov spaces. We study the global and local approximation properties of the spectral solutions, describe a method to obtain approximate solutions using values of f at points on the sphere and polynomial operators, and describe the global and local rates of approximation provided by our polynomial operators. The research of this author was supported, in part, by grant DMS-0204704 from the National Science Foundation and grant W911NF-04-1-0339 from the U.S. Army Research Office