Fractional order electromagnetics

The Maxwell equations constitute a formalism for the development of models describing electromagnetic phenomena. The four Maxwell laws have been adopted successfully in many applications and involve only the integer order differential calculus. Recently, a closer look for the cases of transmission lines, electrical motors and transformers, that reveal the so-called skin effect, motivated a new perspective towards the replacement of classical models by fractional-order mathematical descriptions. Bearing these facts in mind this paper addresses the concept of static fractional electric potential. The fractional potential was suggested some years ago. However, the idea was not fully explored and practical methods of implementation were not proposed. In this line of thought, this paper develops a new approximation algorithm for establishing the fractional order electrical potential and analyzes its characteristics.

Murine (endemic) typhus in Brazil: case report and review

Murine typhus has been increasingly recognized worldwide and is becoming a relevant differential diagnosis in febrile conditions. In Brazil, murine typhus has never received much attention. We present a recently diagnosed case and a literature review that suggests that the disease could be more prevalent in Southeastern Brazil than acknowledged until now.

Control and Dynamics of Fractional Order Systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades due to the progress in the area of nonlinear dynamics. This article discusses several applications of fractional calculus in science and engineering, namely: the control of heat systems, the tuning of PID controllers based on fractional calculus concepts and the dynamics in hexapod locomotion.

Fractional Dynamics and Control of Distributed Parameter Systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of some distributed parameter systems.

System Modeling and Control Through Fractional-Order Algorithms

The theory of fractional calculus goes back to the beginning of thr throry of differential calculus but its inherent complexity postponed the applications of the associated concepts. In the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area of automaticcontrol preliminary work has already been carried out but the proposed algorithms are restricted to the frequency domain. The paper discusses the design of fractional-order discrete-time controllers. The algorithms studied adopt the time domein, which makes them suited for z-transform analusis and discrete-time implementation. The performance of discrete-time fractional-order controllers with linear and non-linear systems is also investigated.

ASSESSMENT OF THE PRESENCE OF Toxocara EGGS IN SOILS OF AN ARID AREA IN CENTRAL-WESTERN ARGENTINA

With the aim of studying the contamination of soils with eggs of Toxocara spp. in an arid area in the central-western region of Argentina, 76 soil samples were collected from 18 towns belonging to six provinces of central-western Argentina. They were processed by the centrifugal flotation method. No eggs of Toxocara spp. were found. It can be concluded that the negative results are directly related to the characteristics of the environment and climate present in the studied area. The finding of eggs in soils depends on several factors: the presence of canine or feline feces, the hygienic behavior of pet owners, the presence of stray animals without veterinary supervision, the weather and environmental conditions, and laboratory techniques used; and all these circumstances must be considered when comparing the results found in different geographical regions. In order to accurately define the importance of public spaces in the transmission of infection to humans, it is important to consider the role of backyards or green spaces around housing in small towns, where the population is not used to walking pets in public spaces, and in such cases a significant fraction of the population may acquire the infection within households.

Hydatid cysts in muscles: clinical manifestations, diagnosis, and management of this atypical presentation

ABSTRACTINTRODUCTION: Hydatid cysts are rarely detected in muscle tissue (0.7-0.9%), even in endemic countries. The aim of this study was to present information regarding the clinical manifestations, diagnosis, and management of muscle echinococcosis.METHODS: Twenty-two patients with hydatid cysts in the muscle were followed from January 2006 through December 2014.RESULTS: Twenty-four sites of muscle involvement were observed in the 22 patients. Fifteen (68%) of our patients were women, while seven (32%) were men. The mean age was 28.1 ± 15.4 (6-61) years. The most frequent locations were the thigh (27.2%) and the paravertebral region (13.6%). Most patients reported a painless slow-growing mass with normal overlying skin. Most (90.2%) cases were treated by surgical excision and fine-needle aspiration.CONCLUSIONS: Primary muscle hydatid cyst should be considered in the differential diagnosis in cystic masses of the muscular system without pain and localized enlargement of soft tissue, especially in endemic areas. Hydatid cyst should be investigated using serological tests and imaging modalities. If possible, total surgical excision of hydatid cyst in the muscle should be performed.

Contractions in the 2-wasserstein lenght space and thermalization of granular media

An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) | if uniformly controlled | will quantify contractivity (limit expansivity) of the flow.

On the stability of periodic orbits in Rn

We consider an autonomous differential system in Rn with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the transversal intersection of n ¡ 1 codimension one hypersurfaces and is an alternative to the use of the first order variational equations. We apply it to study the stability of the periodic orbits in several examples, including a periodic solution found by Steklov studying the rigid body dynamics.

Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

Euclidean geometric invariant of framed knots in manifolds

We present an invariant of a three dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. An important feature of our work is that we are not using any nontrivial representation of the manifold fundamental group or knot group.

Horospheres in hyperbolic geometry

In this paper we investigate the role of horospheres in Integral Geometry and Differential Geometry. In particular we study envelopes of families of horocycles by means of “support maps”. We define invariant “linear combinations” of support maps or curves. Finally we obtain Gauss-Bonnet type formulas and Chern-Lashof type inequalities.

A 10-year experience in paediatric spontaneous cerebral hemorrhage: which children with headache need more than a clinical examination?

INTRODUCTION: When a child is seen in a clinic with a headache, stroke is certainly not the first on the list of differential diagnoses. In western countries, stroke is typically associated with adults and the elderly. Although rare, haemorrhagic strokes are not exceptional in the paediatric population, as their incidence is around 1/100 000/year. Prompt diagnosis is essential, since delayed treatment may lead to disastrous prognosis in these children. MATERIALS AND METHODS: This is a retrospective review of paediatric cases with spontaneous cerebral haemorrhage that presented in two university hospitals in the last ten years. The experience of these primary and tertiary referral centres comprises 22 consecutive cases that are analysed according to aetiology, presenting symptoms, treatment and outcome. RESULTS: 77% of the children diagnosed with haemorrhagic stroke presented with headaches. 41% of them had a sudden onset, while 9% developed headaches over a period of hours to weeks. While 9% presented only with headaches, the majority had either subtle (diplopia, balance problems) or obvious (focal deficits, unilateral weakness and decreased level of consciousness) concomitant neurological signs. 55% had an arteriovenous malformation (AVM), 18% had an aneurysm and 14% had a cavernous malformation. In 14% the aetiology could not be determined. The majority of haemorrhages (82%) were supratentorial, while 18% bled into the posterior fossa. All children underwent an emergency cerebral CT scan followed by specific investigations. The treatment was dependent on the aetiology as well as the mass effect of the haematoma. In 23% an emergent evacuation of the haematoma was performed. Two children (9%) died, and 75% had a favourable clinical outcome. CONCLUSION: Headaches in children are a common problem, and a small minority may reveal an intracranial haemorrhage with poor prognosis if not treated promptly. Although characterisation of headaches is more difficult in a paediatric population, sudden, unusual or intense headaches should lead to imaging work-up. Any neurological finding, even one as subtle as hemianopsia or dysmetria, should alarm the physician and should be followed by emergency imaging investigation. If the cerebral CT reveals a haemorrhage, the child should be referred immediately to a neurosurgical referral centre without further investigation. The outcome is grim for children presenting in coma with fixed, dilated pupils. The long-term result overall for children after spontaneous intracranial haemorrhage is not dismal and depends critically on specialised management.

Valproic acid related idiosyncratic drug induced hepatotoxicity in a glioblastoma patient treated with temozolomide.

Glioblastoma patients undergoing treatment with surgery followed by radiation and temozolomide chemotherapy often develop a state of immunosuppression and are at risk for opportunistic infections and reactivation of hepatitis and herpes viruses. We report the case of a 48-year-old glioblastoma patient who developed acute cholestatic hepatitis with hepatic failure during adjuvant treatment with temozolomide and the integrin inhibitor cilengitide. A viral hepatitis was excluded and valproic acid treatment was stopped. Upon normalisation of the liver tests, temozolomide treatment was resumed without perturbation of the liver tests. Valproic acid related idiosyncratic drug induced hepatotoxicity should be considered as a differential diagnosis in glioblastoma patients undergoing adjuvant therapy.