Criteria for Geometric and Algebraic Transience for Discrete-Time Markov Chains

Journal of Theoretical Probability - We present new criteria for geometric and algebraic transience for discrete-time transient Markov chains on general state spaces, based on the moment of the...     

Multiplicity of Solutions of the Weighted p-Laplacian with Isolated Singularity and Diffusion Suppressed by Convection

In this paper, the authors study the multiplicity of solutions to the weighted p-Laplacian with isolated singularity and di?usion suppressed by convection ?div(|x|^α|?u|^p?2?u) + λ 1/|x|^β |?u|^p?2?u · x = |x|^γg(|x|) in B \ {0} subject to nonlinear Robin boundary value condition |x|^α|?u|^p?2?u · ?n = A ? ρu on ?B,where λ > 0, B ? R^N(N ≥ 2) is the unit ball centered at the origin, α > 0, p > 1, β ∈ R, γ > ?N, g ∈ C([0,1]) with g(0) > 0, A ∈ R, ρ > 0 and ?n is the unit outward normal. The same problem with di?usion promoted by convection, namely λ ≤ 0, has already been discussed by the last two authors (Song-Yin (2012)), where the existence, nonexistence and classi?cation of singularities for solutions are presented. Completely di?erent from [Song, H. J. and Yin, J. X., Removable isolated singularities of solutions to the weighted p-Laplacian with singular convection, Math. Meth. Appl. Sci., 35, 2012, 1089–1100], in the present case λ > 0, namely the di?usion is suppressed by the convection, non-singular solutions are not only existent but also may be in?nite which vary according only to the values of solutions at the isolated singular point. At the same time, the singular solutions may exist only if the di?usion dominates the convection.     

On the relative Wall-Witt groups

LetR* be a simplicial involutive ring. According to certain involutions onK(R*) and _ε L R _∗, there are 1/2-local splittings and . It is known [2] that _ε L _\ga ^α R _∗, the Wall-Witt group. SupposeI→R S is a split extension of discrete involutive rings withI ²=0, andI is a freeS-bimodule. Then we have and . The trace map Tr: Prim _n ∧*M(I ⊗ ℚ)→ ₀ ρ _n ;I ⊗ ℚ) is an isomorphism. We prove in Lemma 1 that the trace map Tr is ℤ/2-equivariant. In Theorem 2 we show that under a certain assumption the rational relative Wall-Witt group vanishes. Theorem 2 can be extended to a more general case (Theorem 3) by employing Goodwillie’s reduction technique [3]. This work was partially supported by KOSEF under Grant 923-0100-010-1.     

Symmetric Skorohod topology onn-variable functions and hierarchical Markov properties ofn-parameter processes

Summary We introduce a new Skorohod topology for functions of several variables. Since ann-variable function may be viewed as a one-variable function with values in the set of (n–1)-variable functions, this topology is defined by induction from the classical Skorohod topology for one-variable functions. This allows us to define the notion of completen-parameter symmetric Markov processes: Such processes are, for any 1pn, rawp-parameter Markov processes (in the sense of our previous paper [17]) with values in the space of (n–p)-variable functions. We prove, for these processes and their Bochner subordinates, a maximal inequality which implies the continuity of additive functionals associated with finite energy measures. We finally present several important examples.     

Comparison of the elastic and inelastic scatterings between152Sm+12C and148 Nd+16O

Angular distributions of elastic and inelastic scattering have been measured for¹⁵²Sm+¹²C at 63.2 MeV and¹⁴⁸Nd+¹⁶O at 90.9 MeV. An evident interference pattern in the inelastic scattering has been observed for the first time in a strong Coulomb coupling system.We are indebted to Dr. S. Pieper for supplying the Ptolemy Program. One of us (Chenglie Jiang) would like to acknowledge the Argonne National Laboratory for the opportunity given, to perform theoretical calculations with the code Ptolemy during his visit there. Thanks are also due to Mr. H. Folger (GSI, Germany) for supplying the targets. This work was supported in part by China National Nature Science Fundation.