Classifying smooth lattice polytopes via toric fibrations

We show that any smooth Q-normal lattice polytope P of dimension n and degree d is a strict Cayley polytope if n?2d+1. This gives a sharp answer, for this class of polytopes, to a question raised by V.V. Batyrev and B. Nill.     

Evolution of Nonlinear Sloshing in a Tank Near Half the Fundamental Resonance

This article describes the evolution of shallow water waves in a tank that is closed at one end and is periodically forced at half the fundamental frequency at the other end. The nonlinear response occurs at the same order as the linear response and is governed by a forced Korteweg–de Vries ( K dV ) equation. Unlike the corresponding problem for a gas (or the hydraulic limit), there may be nonperiodic (beating) solutions and multiple steady solutions for the same frequency. The addition of a component at the fundamental frequency to the piston input can be used to cancel the nonlinear effects and leave only the linear response in the steady state.     

Parseval Frames Built Up from Generalized Shift-Invariant Systems

Wavelet systems, and many of its generalizations such as wavelet packets, shearlets, and composite dilation wavelets are generalized shift-invariant systems (GSI) in the sense of the work by Ron and Shen. It is well known that a wavelet system is never Z-shift invariant (SI). Nevertheless, one can modify it and construct a Z-SI system, called a quasi-affine system, which shares most of the frame properties of the wavelet system. The analogue of a quasi-affine system for a GSI system is called an oblique oversampling: it is shift invariant with respect to a fixed lattice. Assumptions on a GSI system X were given by Ron and Shen to ensure that any oblique oversampling is a Parseval frame for ${L^2(\mathbb{R}^n)}$ whenever X is. We show that these assumptions are not satisfied for some of the wavelet generalizations mentioned above and that elements implicit in their work provide other sufficient conditions on the system under which any oblique oversampling is a Parseval frame for ${L^2(\mathbb{R}^n)}$ (shift invariant with respect to a fixed lattice). Moreover, in the orthonormal setting it is shown that completeness yields a shift-invariant Parseval frame for suitable proper subspaces of ${L^2(\mathbb{R}^n)}$ , too.     

An optimization problem with volume constraint for a degenerate quasilinear operator

We consider the optimization problem of minimizing with a constraint on the volume of {u>0}. We consider a penalization problem, and we prove that for small values of the penalization parameter, the constrained volume is attained. In this way we prove that every solution u is locally Lipschitz continuous and that the free boundary, ∂{u>0}∩Ω, is smooth.     

On a notion of partially conditionally identically distributed sequences

A notion of conditionally identically distributed (c.i.d.) sequences has been studied as a form of stochastic dependence weaker than exchangeability, but equivalent to it in the presence of stationarity. We extend such notion to families of sequences. Paralleling the extension from exchangeability to partial exchangeability in the sense of de Finetti, we propose a notion of partially c.i.d. dependence, which is shown to be equivalent to partial exchangeability for stationary processes. Partially c.i.d. families of sequences preserve attractive limit properties of partial exchangeability, and are asymptotically partially exchangeable. Moreover, we provide strong laws of large numbers and two central limit theorems. Our focus is on the asymptotic agreement of predictions and empirical means, which lies at the foundations of Bayesian statistics. Natural examples of partially c.i.d. constructions are interacting randomly reinforced processes satisfying certain conditions on the reinforcement.     

Extinction properties of multi-type continuous-state branching processes

Recently in Barczy et al. (2015), the notion of a multi-type continuous-state branching process (with immigration) having $d$-types was introduced as a solution to an $d$-dimensional vector-valued SDE. Preceding that, work on affine processes, originally motivated by mathematical finance, in Duffie et al. (2003) also showed the existence of such processes. See also more recent contributions in this direction due to Gabrielli and Teichmann (2014) and Caballero and Pérez Garmendia (2017). Older work on multi-type continuous-state branching processes is more sparse but includes Watanabe (1969) and Ma (2013), where only two types are considered. In this paper we take a completely different approach and consider multi-type continuous-state branching process, now allowing for up to a countable infinity of types, defined instead as a super Markov chain with both local and non-local branching mechanisms. In the spirit of Engländer and Kypriano (2004) we explore their extinction properties and pose a number of open problems.     

One-step fabrication of glucose sensors based on entrapment of glucose oxidase within poly(ester-sulfonic acid) coatings

A simple, rapid, reproducible and effective one-step procedure for biosensor construction, based on casting mixed poly(ester-sulfonic acid)-glucose oxidase solutions onto solid electrodes is described. The cation exchanger simultaneously performs the entrapment, charge permselectivity and antifouling functions. The discrimination against potential interferences is accompanied with a fast and sensitive response to glucose. With flow injection operation, 180 samples can be processed per hour, with a detection limit of 3 × 10^?6 M. The effects of numerous experimental variables are explored. These properties of poly(ester-sulfonic acid) ionomers, coupled with their availability as aqueous dispersions, make them attractive and versatile for biosensor work.