A nilpotent IP polynomial multiple recurrence theorem

We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibman's result that polynomial mappings into a nilpotent group form a group and a multiparameter version of the nilpotent Hales-Jewett theorem due to Bergelson and Leibman.Comment: v4: switch to TeXlive 2016 and biblate

Estabilização uniforme e controlabilidade exata para um sistema hiperbolico

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnologico2012-10-17T01:35:48

Sharp Gradient Bounds for the Diffusion Semigroup

Precise regularity estimates on diffusion semigroups are more than a mere theoretical curiosity. They play a fundamental role in deducing sharp error bounds for higher-order particle methods. In this thesis error bounds which are of consequence in iterated applications of Wiener space cubature (Lyons and Victoir [29]) and a related higher-order method by Kusuoka [21] are considered. Regularity properties for a wide range of diffusion semigroups are deduced. In particular, semigroups corresponding to solutions of stochastic differential equations (SDEs) with non-smooth and degenerate coefficients. Precise derivative bounds for these semigroups are derived as functions of time, and are obtained under a condition, known as the UFG condition, which is much weaker than Hormander's criterion for hypoellipticity. Moreover, very relaxed differentiability assumptions on the coefficients are imposed. Proofs of exact error bounds for the associated higher-order particle methods are deduced, where no such source already exists. In later chapters, a local version of the UFG condition - `the LFG condition' - is introduced and is used to obtain local gradient bounds and local smoothness properties of the semigroup. The condition's generality is demonstrated. In later chapters, it is shown that the V0 condition, proposed by Crisan and Ghazali [8], may be completely relaxed. Sobolev-type gradient bounds are established for the semigroup under very general differentiability assumptions of the vector fields. The problem of considering regularity properties for a semigroup which has been perturbed by a potential, and a Langrangian term are also considered. These prove important in the final chapter, in which we discuss existence and uniqueness of solutions to the Cauchy problem

Integer Vector Addition Systems with States

This paper studies reachability, coverability and inclusion problems for Integer Vector Addition Systems with States (ZVASS) and extensions and restrictions thereof. A ZVASS comprises a finite-state controller with a finite number of counters ranging over the integers. Although it is folklore that reachability in ZVASS is NP-complete, it turns out that despite their naturalness, from a complexity point of view this class has received little attention in the literature. We fill this gap by providing an in-depth analysis of the computational complexity of the aforementioned decision problems. Most interestingly, it turns out that while the addition of reset operations to ordinary VASS leads to undecidability and Ackermann-hardness of reachability and coverability, respectively, they can be added to ZVASS while retaining NP-completness of both coverability and reachability.Comment: 17 pages, 2 figure

Constant & time-varying hedge ratio for FBMKLCI stock index futures

This paper examines hedging strategy in stock index futures for Kuala Lumpur Composite Index futures of Malaysia. We employed two different econometric methods such as-vector error correction model (VECM) and bivariate generalized autoregressive conditional heteroskedasticity (BGARCH) models to estimate optimal hedge ratio by using daily data of KLCI index and KLCI futures for the period from January 2012 to June 2016 amounting to a total of 1107 observations. We found that VECM model provides better results with respect to estimating hedge ratio for spot month futures and one-month futures, while BGACH shows better for distance futures. While VECM estimates time invariant hedge ratio, the BGARCH shows that hedge ratio changes over time. As such, hedger should rebalance his/her position in futures contract time to time in order to reduce risk exposure

Recent advances in algorithmic problems for semigroups

In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite group $G$, often represented as a matrix group. Such problems might not be decidable in general. In fact, they gave rise to some of the earliest undecidability results in algorithmic theory. However, the situation changes when the group $G$ satisfies additional constraints. In this survey, we give an overview of the decidability and the complexity of several algorithmic problems in the cases where $G$ is a low-dimensional matrix group, or a group with additional structures such as commutativity, nilpotency and solvability.Comment: survey article for SIGLOG New