On the permutation behaviour of Dickson polynomials of the second kind

The known permutation behaviour of the Dickson polynomials of the second kind in characteristic 3 is expanded and simplified. (C) 2002 Elsevier Science (USA).

The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

Population balance modelling of granulation with a physically based coalescence kernel

It was previously published by the authors that granules can either coalesce through Type I (when granules coalesce by viscous dissipation in the surface liquid layer before their surfaces touch) or Type II (when granules are slowed to a halt during rebound, after their surfaces have made contact) (AIChE J. 46 (3) (2000) 529). Based on this coalescence mechanism, a new coalescence kernel for population balance modelling of granule growth is presented. The kernel is constant such that only collisions satisfying the conditions for one of the two coalescence types are successful. One constant rate is assigned to each type of coalescence and zero is for the case of rebound. As the conditions for Types I and II coalescence are dependent on granule and binder properties, the coalescence kernel is thus physically based. Simulation results of a variety of binder and granule materials show good agreement with experimental data. (C) 2002 Elsevier Science Ltd. All rights reserved.

The effect of water, brine and ethanol flotation on the quality and shelf life of macadamia kernels 2. Kernel pieces

Raw macadamia kernel pieces were immersed in water (specific gravity 1.00 g/cm(3)), brine (SG 1.02 g/cm(3)) or ethanol solution (SG 0.97 g/cm(3)) for 30 or 60 s, then re-dried to below 1.5% moisture (wet basis) and stored under vacuum for 0, 4 and 12 months. Flotation in water had no effect on the quality or shelf life of the kernel pieces over 12 months storage, as measured by sensory evaluation of the kernels and chemical analysis of the kernel oil. Immersion in a salt solution caused unacceptable changes in quality during storage, increasing as storage time increased. Flotation in dilute ethanol also caused unacceptable quality changes during storage. Therefore, only flotation of macadamia kernel pieces in water can be recommended for commercial operations. Microbiological concerns with such a process still need to be addressed.

Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.

Exploração da implementação actual de IPv6 no Kernel do Linux

A presente dissertação visa retratar a exploração do suporte do protocolo Internet versão seis (IPv6) no kernel do Linux, conjuntamente com a análise detalhada do estado da implementação dos diferentes aspectos em que se baseia o protocolo. O estudo incide na experimentação do funcionamento em geral do stack, a identificação de inconsistências deste em relação aos RFC’s respectivos, bem como a simulação laboratorial de cenários que reproduzam casos de utilização de cada uma das facilidades analisadas. O objectivo desta dissertação não é explicar o funcionamento do novo protocolo IPv6, mas antes, centrar-se essencialmente na exploração do IPv6 no kernel do Linux. Não é um documento para leigos em IPv6, no entanto, optou-se por desenvolver uma parte inicial onde é abordado o essencial do protocolo: a sua evolução até à aprovação e a sua especificação. Com base no estudo realizado, explora-se o suporte do IPv6 no Kernel do Linux, fazendo uma análise detalhada do estado de implementação dos diferentes aspectos em que se baseia o protocolo. Bem como a realização de testes de conformidade IPv6 em relação aos RFC’s.

The usefulness of ultrasound in the classification of chronic liver disease

Chronic Liver Disease is a progressive, most of the time asymptomatic, and potentially fatal disease. In this paper, a semi-automatic procedure to stage this disease is proposed based on ultrasound liver images, clinical and laboratorial data. In the core of the algorithm two classifiers are used: a k nearest neighbor and a Support Vector Machine, with different kernels. The classifiers were trained with the proposed multi-modal feature set and the results obtained were compared with the laboratorial and clinical feature set. The results showed that using ultrasound based features, in association with laboratorial and clinical features, improve the classification accuracy. The support vector machine, polynomial kernel, outperformed the others classifiers in every class studied. For the Normal class we achieved 100% accuracy, for the chronic hepatitis with cirrhosis 73.08%, for compensated cirrhosis 59.26% and for decompensated cirrhosis 91.67%.

Real-time scheduling of parallel tasks in the Linux Kernel

This paper proposes a global multiprocessor scheduling algorithm for the Linux kernel that combines the global EDF scheduler with a priority-aware work-stealing load balancing scheme, enabling parallel real-time tasks to be executed on more than one processor at a given time instant. We state that some priority inversion may actually be acceptable, provided it helps reduce contention, communication, synchronisation and coordination between parallel threads, while still guaranteeing the expected system’s predictability. Experimental results demonstrate the low scheduling overhead of the proposed approach comparatively to an existing real-time deadline-oriented scheduling class for the Linux kernel.

Enhancing the real-time capabilities of the Linux Kernel

The mainline Linux Kernel is not designed forhard real-time systems; it only fits the requirements of soft realtimesystems. In recent years, a kernel developer communityhas been working on the PREEMPT-RT patch. This patch(that aims to get a fully preemptible kernel) adds some realtimecapabilities to the Linux kernel. However, in terms ofscheduling policies, the real-time scheduling class of Linux islimited to the First-In-First-Out (SCHED_FIFO) and Round-Robin (SCHED_RR) scheduling policies. These scheduling policiesare however quite limited in terms of realtime performance.Therefore, in this paper, we report one importantcontribution for adding more advanced real-time capabilitiesto the Linux Kernel. Specifically, we describe modificationsto the (PREEMPT-RT patched) Linux kernel to supportreal-time slot-based task-splitting scheduling algorithms. Ourpreliminary evaluation shows that our implementation exhibitsa real-time performance that is superior to the schedulingpolicies provided by the current version of PREMPT-RT. Thisis a significant add-on to a widely adopted operating system.

Run-time monitoring approach for the shark kernel

Typically common embedded systems are designed with high resource constraints. Static designs are often chosen to address very specific use cases. On contrast, a dynamic design must be used if the system must supply a real-time service where the input may contain factors of indeterminism. Thus, adding new functionality on these systems is often accomplished by higher development time, tests and costs, since new functionality push the system complexity and dynamics to a higher level. Usually, these systems have to adapt themselves to evolving requirements and changing service requests. In this perspective, run-time monitoring of the system behaviour becomes an important requirement, allowing to dynamically capturing the actual scheduling progress and resource utilization. For this to succeed, operating systems need to expose their internal behaviour and state, making it available to the external applications, usually using a run-time monitoring mechanism. However, such mechanism can impose a burden in the system itself if not wisely used. In this paper we explore this problem and propose a framework, which is intended to provide this run-time mechanism whilst achieving code separation, run-time efficiency and flexibility for the final developer.

On the requirements of interpolating polynomials for path motion constraints

In the framework of multibody dynamics, the path motion constraint enforces that a body follows a predefined curve being its rotations with respect to the curve moving frame also prescribed. The kinematic constraint formulation requires the evaluation of the fourth derivative of the curve with respect to its arc length. Regardless of the fact that higher order polynomials lead to unwanted curve oscillations, at least a fifth order polynomials is required to formulate this constraint. From the point of view of geometric control lower order polynomials are preferred. This work shows that for multibody dynamic formulations with dependent coordinates the use of cubic polynomials is possible, being the dynamic response similar to that obtained with higher order polynomials. The stabilization of the equations of motion, always required to control the constraint violations during long analysis periods due to the inherent numerical errors of the integration process, is enough to correct the error introduced by using a lower order polynomial interpolation and thus forfeiting the analytical requirement for higher order polynomials.

Recurrence relations for Clifford algebra-valued orthogonal polynomials

The theory of orthogonal polynomials of one real or complex variable is well established as well as its generalization for the multidimensional case. Hypercomplex function theory (or Clifford analysis) provides an alternative approach to deal with higher dimensions. In this context, we study systems of orthogonal polynomials of a hypercomplex variable with values in a Clifford algebra and prove some of their properties.

Ehrhart polynomials, successive minima, and an Ehrhart theory for rational dilates of a rational polytope

Magdeburg, Univ., Fak. für Mathematik, Diss., 2011

Low autocorrelation sequences and flat polynomials

Magdeburg, Univ., Fak. für Mathematik, Habil.-Schr., 2014

Asymptotics of orthogonal polynomials via the Koosis theorem

The main aim of this short paper is to advertize the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a new theorem about asymptotics of orthogonal polynomi- als for which the Koosis theorem seems to be the most natural tool. Namely, we consider the case when a SzegÄo measure on the unit circumference is perturbed by an arbitrary measure inside the unit disk and an arbitrary Blaschke sequence of point masses outside the unit disk.