Reply to: Comments on “Particle Swarm Optimization with Fractional-Order Velocity”

We agree with Ling-Yun et al. [5] and Zhang and Duan comments [2] about the typing error in equation (9) of the manuscript [8]. The correct formula was initially proposed in [6, 7]. The formula adopted in our algorithms discussed in our papers [1, 3, 4, 8] is, in fact, the following: ...

Fractional Order Generalized Information

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.

Fractional order modelling of dynamic backlash

This paper studies the dynamical properties of systems with backlash and impact phenomena. This type of non-linearity can be tackled in the perspective of the fractional calculus theory. Fractional and integer order models are compared and their influence upon the emerging dynamics is analysed. It is demonstrated that fractional models can memorize dynamical effects due to multiple micro-collisions.

Presentations for some monoids of injective partial transformations on a finite chain.

Communications in Algebra, 33 (2005), p. 587-604

Using interval graphs in an order processing optimization problem

In this paper we address an order processing optimization problem known as minimization of open stacks (MOSP). We present an integer pro gramming model, based on the existence of a perfect elimination scheme in interval graphs, which finds an optimal sequence for the costumers orders.

Abelian kernels of monoids of order-preserving maps and of some of its extensions

Semigroup Forum vol. 68 (2004), p. 335–356

The cardinal and the idempotent number of various monoids of transformations on a finite chain

Bulletin of the Malaysian Mathematical Sciences Society, 2, 34 (1),(2011), p. 79–85

The cardinal of various monoids of transformations that preserve a uniform partition

Bulletin of the Malaysian Mathematical Sciences Society

A mathematical model for supermarket order picking

Order picking consists in retrieving products from storage locations to satisfy independent orders from multiple customers. It is generally recognized as one of the most significant activities in a warehouse (Koster et al, 2007). In fact, order picking accounts up to 50% (Frazelle, 2001) or even 80% (Van den Berg, 1999) of the total warehouse operating costs. The critical issue in today’s business environment is to simultaneously reduce the cost and increase the speed of order picking. In this paper, we address the order picking process in one of the Portuguese largest companies in the grocery business. This problem was proposed at the 92nd European Study Group with Industry (ESGI92). In this setting, each operator steers a trolley on the shop floor in order to select items for multiple customers. The objective is to improve their grocery e-commerce and bring it up to the level of the best international practices. In particular, the company wants to improve the routing tasks in order to decrease distances. For this purpose, a mathematical model for a faster open shop picking was developed. In this paper, we describe the problem, our proposed solution as well as some preliminary results and conclusions.

On the monoids of transformations that preserve the order and a uniform partition

Communications in Algebra

Análise de um veículo todo o terreno do tipo KARTCROSS

O presente trabalho descreve a análise feita a um veículo de todo o terreno. O kartcross/buggy em estudo é usado em provas do tipo Baja, sendo estas provas longas e com traçados sinuosos. O veículo, já construído, foi testado através de softwares, a nível estrutural e ciclístico, pretendendo-se assim efetuar engenharia inversa sobre o mesmo. No decorrer da sua utilização normal o kartcross/buggy sofre vários tipos de solicitações, como sejam aceleração, travagem e força centrípta em curva. Portanto, o veículo deve ser capaz de suportar estes esforços e ter uma boa habilidade. Além dos testes em uso corrente foi analisada também a rigidez torsional do quadro do veículo e do veículo completo, podendo-se assim melhorar estes valores. A nível ciclístico foram analisados os parâmetros das suspensões como o camber, convergência/divergência, caster, entre outros. Da análise destes parâmetros e possível fazerem-se melhorias de forma a que o veículo tenha um melhor desempenho. Para validar os testes computacionais efetuados foi reproduzido experimentalmente o teste da rigidez torsional. No final, compararam-se os valores numéricos com os experimentais e aferir se o modelo se encontra bem representado.

Detection and identification of dengue virus isolates from Brazil by a simplified reverse transcription - polymerase chain reaction (RT-PCR) method

We show here a simplified RT-PCR for identification of dengue virus types 1 and 2. Five dengue virus strains, isolated from Brazilian patients, and yellow fever vaccine 17DD as a negative control, were used in this study. C6/36 cells were infected and supernatants were collected after 7 days. The RT-PCR, done in a single reaction vessel, was carried out following a 1/10 dilution of virus in distilled water or in a detergent mixture containing Nonidet P40. The 50 µl assay reaction mixture included 50 pmol of specific primers amplifying a 482 base pair sequence for dengue type 1 and 210 base pair sequence for dengue type 2. In other assays, we used dengue virus consensus primers having maximum sequence similarity to the four serotypes, amplifying a 511 base pair sequence. The reaction mixture also contained 0.1 mM of the four deoxynucleoside triphosphates, 7.5 U of reverse transcriptase, 1U of thermostable Taq DNA polymerase. The mixture was incubated for 5 minutes at 37ºC for reverse transcription followed by 30 cycles of two-step PCR amplification (92ºC for 60 seconds, 53ºC for 60 seconds) with slow temperature increment. The PCR products were subjected to 1.7% agarose gel electrophoresis and visualized by UV light after staining with ethidium bromide solution. Low virus titer around 10 3, 6 TCID50/ml was detected by RT-PCR for dengue type 1. Specific DNA amplification was observed with all the Brazilian dengue strains by using dengue virus consensus primers. As compared to other RT-PCRs, this assay is less laborious, done in a shorter time, and has reduced risk of contamination

The interrogation of witnesses abroad in execution of a european investigation order: an examination from eyes of the defence

European Master Human Rights and Democratisation

Detection of enteroviruses in cases of neurological disorders in the State of Pará, Brazil

Eighty-one cerebrospinal fluid (CSF) samples mainly from cases of aseptic meningitis and motor deficiency syndrome were sent to the Virology Section of Evandro Chagas Institute, Belém Pará, in the period of January 1995 to January 1996 in order to isolate viruses. All samples were inoculated onto HEp-2 cell culture and newborn mice, with negative results. The probability of isolating viruses by these methods is reduced because of the low concentration of viral particles in these specimens. In order to obtain more information about the etiology of these cases, a group of 23 samples were selected to be tested by a more sensitive technique than the virus isolation - the reverse transcription polymerase chain reaction (RT-PCR). Specific primers directed to conserved regions in the enterovirus genome were used, considering that this group of viruses is frequently associated with these neurological disorder. The age of the patients ranged from 1 to 55 years and nearly all of them lived in Belém, State of Pará, North of Brazil. Of 15 samples analyzed by RT PCR nine (60%) were positive; of these, 6 (66.6%) had motor deficiency and 3 (33.3%) developed aseptic meningitis. These results show that it is important to investigate enterovirus as cause of these syndromes.

Fractional Order Generalized Information

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.