The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in L is established for a class of stationary boundary-value problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angula...

Professional identity plays an important role in career development. Although many studies have examined professional identity, differences in cognitive-processing biases between Chinese student teachers with strong and weak professional identity are poorly understood. The current study adopted Tversky's social-cognitive experimental paradigm to explore cognitive-processing biases in Chinese st...

We study the long-standing open problem of giving ∀Σ1 separations for fragments of bounded arithmetic in the relativized setting. Rather than considering the usual fragments defined by the amount of induction they allow, we study Jeřábek’s theories for approximate counting and their subtheories. We show that the ∀Σ1 Herbrandized ordering principle is unprovable in a fragment of bounded arithmet...

In this article we introduce the notion of weak identities in a group and study their properties. We show that weak identities have some similar properties to ordinary ones. We use this notion to prove that any finitely generated solvable discriminating group is abelian, which answers a question raised in [3].

The computable Lipschitz reducibility was introduced by Downey, Hirschfeldt and LaForte under the name of strong weak truthtable reducibility [6]. This reducibility measures both the relative randomness and the relative computational power of real numbers. This paper proves that the computable Lipschitz degrees of computably enumerable sets are not dense. An immediate corollary is that the Solo...

We consider Markov chains {Γn} with transitions of the form Γn = f(Xn, Yn) Γn−1 + g(Xn, Yn), where {Xn} and {Yn} are two independent i.i.d. sequences. For two copies {Γn} and {Γn} of such a chain, it is well known that L(Γn)−L(Γn)⇒ 0 provided E[log(f(Xn, Yn))] < 0, where ⇒ is weak convergence. In this paper, we consider chains for which also ‖Γn − Γn‖ → 0, where ‖ · ‖ is total variation distanc...

This paper is devoted to the study of the trace properties and of the pointwise behaviour of vector fields C in R of the form wB, where w is a scalar function, the distributional divergence D · C of C is a Radon measure and B is a weakly differentiable vector field. We will consider in particular the case when B has locally bounded deformation (and we write B ∈ BDloc), i.e. the symmetric distri...

Hybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called H(↓,@). We show in detail that H(↓,@) is modally natural. We begin by studying its expressivity, and provide model ...