Wiener's test for space-time random walks and its applications

This paper establishes a criterion for whether a -dimensional random walk on the integer lattice visits a space-time subset infinitely often or not. It is a precise analogue of Wiener's test for regularity of a boundary point with respect to the classical Dirichlet problem. The test obtained is applied to strengthen the harder half of Kolmogorov's test for the random walk.

     

Local partial regularity theorems for suitable weak solutions of a class of degenerate systems

A partial regularity theorem is established for a particular class of weak solutions to the systemu/t– div(K(u)u)=(u)¦¦², div((u))=0 on a bounded domain inR ^N . Under our assumptions, (u) may exhibit exponential decay, and thus the system may be degenerate. Our proof is based upon a blow-up argument.This work was supported in part by NSF Grant DMS9424448.     

Transition metal 1,2-bidentate thiolates as building blocks and their construction into cluster complexes

Simple fragments of transition metal 1,2-bidentate thiolates, the so-called building blocks of the general compositions ML₃, ML₂, ML, M(O)L₂, ML₂L, MLL, etc. have been proposed to constitute the di-, tri- and tetranuclear complexes concerned in this review. Structureal regularities and characteristics have been discussed and summarized according to the thiolato ligands edt and pdt, bdt and tdt, mp, and mpo, and mpp, respectively.Abbreviations H₂mpo o-mercaptophenol - Hmpo 2-mercaptopyridine-N-oxide - R₂dtc N,N-dialkyldithiocarbamate - Haet 2-aminoethanethiol - H₂bdt o-benzenedithiol - H₂pdt 1,2-propanedithiol - H₂tdt toluene-3,4-dithiol - Hmpp-mppH bis-(3-hydroxy-2-pyridyl)disulfide - Hmp-mpH bis-(2-oxyphenyl)disulfide - H₂edt 1,2-ethanedithiol - dppe 1,2-bis(diphenylphosphino)ethane - H₂tedt 3,4,5,6-tetrachlorobenzene-1,2-dithiol - H₂tpdt 3-thiapentane-1,5-dithiol - H₂mnt maleonitriledithiol - Him imidazole - Bz benzyl - py pyridine     

Some results on regularity in vector optimization

In this paper we suggest an approach to regularity in, vector optimization which extends the one given in [9]; some necessary or sufficient regularity conditions are given for a wide class of nondifferentiable vector optimization problems which embraces the convex ones.     

Bounds for the fundamental solutions of elliptic and parabolic equations

It is shown that any elloptic or parabolic operator in nondivergence form with measurable coefficients has a global fundamental solution verifying certain pointwise bounds.     

SBV REGULARITY OF GENUINELY NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS IN ONE SPACE DIMENSION

The problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered.An overview of the techniques involved in the proof is given,and a c...     

Powers of edge ideals with linear resolutions

We show that if G is a gap-free and diamond-free graph, then I(G)^s has a linear minimal free resolution for every s≥2.