A method for plotting the complementary root locus using the root-locus (positive gain) rules

The root-locus method is a well-known and commonly used tool in control system analysis and design. It is an important topic in introductory undergraduate engineering control disciplines. Although complementary root locus (plant with negative gain) is not as common as root locus (plant with positive gain) and in many introductory textbooks for control systems is not presented, it has been shown a valuable tool in control system design. This paper shows that complementary root locus can be plotted using only the well-known construction rules to plot root locus. It can offer for the students a better comprehension on this subject. These results present a procedure to avoid problems that appear in root-locus plots for plants with the same number of poles and zeros.

On Complementary Root Locus of Biproper Transfer Functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Arcabouço geofísico, isostasia e causas do magmatismo cenozóico da província Borborema e de sua margem continental (Nordeste do Brasil)

The Borborema Province (BP) is a geologic domain located in Northeastern Brazil. The BP is limited at the south by the São Francisco craton, at the west by the Parnaíba basin, and both at the north and east by coastal sedimentary basins. Nonetheless the BP surface geology is well known, several key aspects of its evolution are still open, notably: i)its tectonic compartmentalization established after the Brasiliano orogenesis, ii) the architecture of its cretaceous continental margin, iii) the elastic properties of its lithosphere, and iv) the causes of magmatism and uplifting which occurred in the Cenozoic. In this thesis, a regional coverage of geophysical data (elevation, gravity, magnetic, geoid height, and surface wave global tomography) were integrated with surface geologic information aiming to attain a better understanding of the above questions. In the Riacho do Pontal belt and in the western sector of the Sergipano belt, the neoproterozoic suture of the collision of the Sul domain of the BP with the Sanfranciscana plate (SFP) is correlated with an expressive dipolar gravity anomaly. The positive lobule of this anomaly is due to the BP lower continental crust uplifting whilst the negative lobule is due to the supracrustal nappes overthrusting the SFP. In the eastern sector of the Sergipano belt, this dipolar gravity anomaly does not exist. However the suture still can be identified at the southern sector of the Marancó complex arc, alongside of the Porto da Folha shear zone, where the SFP N-S geophysical alignments are truncated. The boundary associated to the collision of the Ceará domain of the BP with the West African craton is also correlated with a dipolar gravity anomaly. The positive lobule of this anomaly coincides with the Sobral-Pedro II shear zone whilst the negative lobule is associated with the Santa Quitéria magmatic arc. Judging by their geophysical signatures, the major BP internal boundaries are: i)the western sector of the Pernambuco shear zone and the eastern continuation of this shear zone as the Congo shear zone, ii) the Patos shear zone, and iii) the Jaguaribe shear zone and its southwestern continuation as the Tatajuba shear zone. These boundaries divide the BP in five tectonic domains in the geophysical criteria: Sul, Transversal, Rio Grande do Norte, Ceará, and Médio Coreaú. The Sul domain is characterized by geophysical signatures associated with the BP and SFP collision. The fact that Congo shear zone is now proposed as part of the Transversal domain boundary implies an important change in the original definition of this domain. The Rio Grande do Norte domain presents a highly magnetized crust resulted from the superposition of precambrian and phanerozoic events. The Ceará domain is divided by the Senador Pompeu shear zone in two subdomains: the eastern one corresponds to the Orós-Jaguaribe belt and the western one to the Ceará-Central subdomain. The latter subdomain exhibits a positive ENE-W SW gravity anomaly which was associated to a crustal discontinuity. This discontinuity would have acted as a rampart against to the N-S Brasiliano orogenic nappes. The Médio Coreaú domain also presents a dipolar gravity anomaly. Its positive lobule is due to granulitic rocks whereas the negative one is caused by supracrustal rocks. The boundary between Médio Coreaú and Ceará domains can be traced below the Parnaíba basin sediments by its geophysical signature. The joint analysis of free air anomalies, free air admittances, and effective elastic thickness estimates (Te) revealed that the Brazilian East and Equatorial continental margins have quite different elastic properties. In the first one 10 km < Te < 20 km whereas in the second one Te ≤ 10 km. The weakness of the Equatorial margin lithosphere was caused by the cenozoic magmatism. The BP continental margin presents segmentations; some of them have inheritance from precambrian structures and domains. The segmentations conform markedly with some sedimentary basin features which are below described from south to north. The limit between Sergipe and Alagoas subbasins coincides with the suture between BP and SFP. Te estimates indicates concordantly that in Sergipe subbasin Te is around 20 km while Alagoas subbasin has Te around 10 km, thus revealing that the lithosphere in the Sergipe subbasin has a greater rigidity than the lithosphere in the Alagoas subbasin. Additionally inside the crust beneath Sergipe subbasin occurs a very dense body (underplating or crustal heritage?) which is not present in the crust beneath Alagoas subbasin. The continental margin of the Pernambuco basin (15 < Te < 25 km) presents a very distinct free air edge effect displaying two anomalies. This fact indicates the existence in the Pernambuco plateau of a relatively thick crust. In the Paraíba basin the free air edge effect is quite uniform, Te ≈ 15 km, and the lower crust is abnormally dense probably due to its alteration by a magmatic underplating in the Cenozoic. The Potiguar basin segmentation in three parts was corroborated by the Te estimates: in the Potiguar rift Te ≅ 5 km, in the Aracati platform Te ≅ 25 km, and in the Touros platform Te ≅ 10 km. The observed weakness of the lithosphere in the Potiguar rift segment is due to the high heat flux while the relatively high strength of the lithosphere in the Touros platform may be due to the existence of an archaean crust. The Ceará basin, in the region of Mundaú and Icaraí subbasins, presents a quite uniform free air edge effect and Te ranges from 10 to 15 km. The analysis of the Bouguer admittance revealed that isostasy in BP can be explained with an isostatic model where combined surface and buried loadings are present. The estimated ratio of the buried loading relative to the surface loading is equal to 15. In addition, the lower crust in BP is abnormally dense. These affirmations are particularly adequate to the northern portion of BP where adherence of the observed data to the isostatic model is quite good. Using the same above described isostatic model to calculate the coherence function, it was obtained that a single Te estimate for the entire BP must be lower than 60 km; in addition, the BP north portion has Te around 20 km. Using the conventional elastic flexural model to isostasy, an inversion of crust thickness was performed. It was identified two regions in BP where the crust is thickened: one below the Borborema plateau (associated to an uplifting in the Cenozoic) and the other one in the Ceará domain beneath the Santa Quitéria magmatic arc (a residue associated to the Brasiliano orogenesis). On the other hand, along the Cariri-Potiguar trend, the crust is thinned due to an aborted rifting in the Cretaceous. Based on the interpretation of free air anomalies, it was inferred the existence of a large magmatism in the oceanic crust surrounding the BP, in contrast with the incipient magmatism in the continent as shown by surface geology. In BP a quite important positive geoid anomaly exists. This anomaly is spatially correlated with the Borborema plateau and the Macaú-Queimadas volcanic lineament. The integrated interpretation of geoid height anomaly data, global shear velocity model, and geologic data allow to propose that and Edge Driven Convection (EDC) may have caused the Cenozoic magmatism. The EDC is an instability that presumably occurs at the boundary between thick stable lithosphere and oceanic thin lithosphere. In the BP lithosphere, the EDC mechanism would have dragged the cold lithospheric mantle into the hot asthenospheric mantle thus causing a positive density contrast that would have generated the main component of the geoid height anomaly. In addition, the compatibility of the gravity data with the isostatic model, where combined surface and buried loadings are present, together with the temporal correlation between the Cenozoic magmatism and the Borborema plateau uplifting allow to propose that this uplifting would have been caused by the buoyancy effect of a crustal root generated by a magmatic underplating in the Cenozoic

Multidisciplinary treatment approach for crown fracture and crown-root fracture - a case report

The increased incidence of traumatic injuries to anterior teeth is a consequence of leisure activities, where the most common injuries are crown fractures. Treatment of the dental trauma is complex and requires a comprehensive and accurate diagnostic and treatment plan. It is also important to consider the biological, functional, esthetic and economic aspects, as well as the patient's desire. The purpose of this article is to report a case that shows the multidisciplinary approach required to successfully manage the rehabilitation of a maxillary central incisor with a complex crown fracture and a maxillary lateral incisor, that at first presented an oblique crown-root fracture, and after the orthodontic extrusion, suffered a more apical new crown-root fracture.

Treatment of root perforation by intentional reimplantation: a case report

Intentional reimplantation is defined as a procedure in which an intentional tooth extraction is performed followed by reinsertion of the extracted tooth into its own alveolus. Int his paper, intentional reimplantation is described and discussed as a treatment approach to root canal instrument separation in conjunction with root perforation. An 8-year follow-up case report is presented. The reimplanted tooth is now a fixed bridge abutment. Although successful in this case, the intentional reimplantation procedure should be considered a treatment of last resort, that is, when another treatment option is not viable for the treatment of root perforation/instrument retrieval.

Multidisciplinary treatment of a fractured root: a case report

Aim: To describe the orthodontic, periodontal and prosthetic management of a case with a 3 mm root fracture below the crest of the alveolar bone.Methods: The root was extruded and periodontal surgery carried out to improve aesthetics and dental function.Conclusion: A multidisciplinary approach to the management of dental root fractures is necessary for successful treatment. (Aust Orthod J 2010; 26: 90-94)

Effect of calcium hydroxide-based materials on periapical tissue healing and orthodontic root resorption of endodontically treated teeth in dogs

This study evaluated periapical tissue healing and orthodontic root resorption of endodontically treated teeth sealed with calcium hydroxide in dogs. The sample consisted of three contralateral pairs of maxillary incisors and two contralateral pairs of mandibular incisors in each of two dogs using a split mouth design. After biomechanical preparation of the teeth in the first group (n = 10), a Ca(OH)(2) dressing was placed for 14 days before root canal filling with Ca(OH)(2)-based sealer (Sealapex) and gutta-percha points. In the second group (n = 10), root canals were obturated immediately after the mechanical preparation with gutta-percha points and zinc oxide and eugenol (ZOE)-based sealer (Endofill). After completion of endodontic treatment, the teeth were moved with an orthodontic appliance with a calibrated force of 200 g, reactivated every 21 days. After 105 days, the animals were killed and the teeth were removed upon completion of active treatment, without a period of recovery, and prepared for histomorphological analysis. All sections of each tooth were graded subjectively on a scale from one to four to obtain the average of the 16 histomorphological parameters analysed. Evaluation of the differences between the two treatment protocols was made with Mann-Whitney U-test. It was observed that the teeth treated with Ca(OH)(2)-based materials provided better outcomes (P = 5%), with complete repair of all root resorption areas, high rate of biological closure of the main canal and apical accessory canals by newly formed cementum, less intense and extensive chronic inflammatory infiltrate, and better organization of the periodontal ligament. Under the tested conditions, Ca(OH)(2)-based materials had a favourable action on periapical tissue healing and repair of orthodontic root resorption in endodontically treated dogs' teeth.

Periapical tissue reactions to calcium hydroxide and MTA after external root resorption as a sequela of delayed tooth replantation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Crown and crown-root fractures: an evaluation of the treatment plans for management proposed by 154 specialists in restorative dentistry

Traumatic tooth injuries involve function and aesthetics and cause damage that range from minimal enamel loss to complex fractures involving the pulp tissue and even loss of the tooth crown. Technical knowledge and clinical experience are essential to establish an accurate diagnosis and provide a rational treatment. The purpose of this study was to evaluate the knowledge of Restorative Dentistry specialists about the management of crown and crown-root fractures based on treatment plans proposed by these professionals for these cases. A descriptive questionnaire was mailed to 245 Restorative Dentistry specialists with questions referring to their professional profile and the treatment plans they would propose for the management of crown and crow-root fractures resulting from dental trauma. One hundred and fifty-four questionnaires were returned properly filled. The data were subjected to descriptive statistics and the chi-square test was used to determine the frequency and the level of the significance among the variables. The analysis of data showed that in spite of having a specialist title, all interviewees had great difficulty in planning the treatments. As much as 42.8% of the participants were unable to treat all types of dental trauma. Complicated and uncomplicated crown-root fractures posed the greatest difficulties for the dentists to establish adequate treatment plans because these fractures require multidisciplinary knowledge and approach for a correct case planning and prognosis.

Integrated treatment to resolve a horizontal root fracture

Root fractures are defined as those that involve cement, dentin and pulp, comprising from 0.5 to 7% of injuries in permanent dentition. Diagnosis is made through clinical and radiographic exams, the latter frequently being limited by the position of the fracture. Treatment varies according to the displacement and vitality of the fragments. The authors present a clinical case of recurrent trauma of tooth 21 causing a horizontal root fracture in the middle third. After several attempts at endodontic treatment, the option was to remove the apical fragment by surgery. The postoperative period of 4 years shows very satisfactory results with regard to wound repair and tooth mobility, or implantation of the coronal segment.

Treatment of root surface in delayed tooth replantation: a review of literature

The time elapsed between a trauma and tooth replantation usually ranges from 1 to 4 h. The chances of root surface damage are higher when tooth replantation is not performed immediately or if the avulsed tooth is not stored in an adequate medium. This invariably leads to necrosis of pulp tissue, periodontal ligament cells and cementum, thus increasing the possibility of root resorption, which is the main cause of loss of replanted teeth. This paper presents a comprehensive review of literature on root surface treatments performed in cases of delayed tooth replantation with necrotic cemental periodontal ligament. Journal articles retrieved from PubMed/MedLine, Bireme and Scielo databases were reviewed. It was observed that, when there are no periodontal ligament remnants and contamination is under control, replacement resorption and ankylosis are the best results and that, although these events will end up leading to tooth loss, this will happen slowly with no loss of the alveolar ridge height, which is important for future prosthesis planning.

Intracanal dressing and root canal filling materials in tooth replantation: a literature review

The prognosis of tooth replantation is usually related to the need of endodontic treatment, which has a direct relationship with the occurrence of root resorptions. Several studies have been undertaken in an attempt to prevent, delay, or treat these complications, which are the main causes of loss of replanted teeth. This literature review examines research evidence on intracanal dressings and root canal filling materials used in cases of tooth replantation. A comprehensive search was performed in the Medline/Pubmed, Bireme and Scielo full-text electronic journal databases to retrieve English-language articles referring to these topics that had been published between 1964 and 2010. Calcium hydroxide (CH) remains the usually recommended choice as an intracanal medicament in replanted teeth; however, there is evidence to support the initial use of a corticosteroid-antibiotic combination such as Ledermix paste to control potential early resorption, prior to the introduction of CH where the beneficial effect in the treatment of progressive root resorption has been well proven. Regarding root filling materials, CH-containing sealers are a good option because of their biological properties. Accurate diagnosis and adequate treatment plan may constitute very complex tasks, particularly in tooth avulsion because several variables are involved. In addition to the technical knowledge and clinical experience directed toward the quality of treatment, patient education may favorably influence the survival of replanted teeth.

Multidisciplinary approach for the treatment of a complicated crown-root fracture in a young patient: A case report

Crown-root fractures in permanent teeth cause esthetic and functional problems. This paper reports the case of a complicated crown-root fracture in the maxillary right central inc sor of a young patient who was treated with a multidisciplinary approach in two phases. A modified Widman flap, root canal therapy, glass fiber post cementation, and adhesive tooth fragment reattachment were performed shortly after an accident. Satisfactory esthetic and functional outcomes were obtained. However, the patient did not attend follow-up visits and returned after 7 years. During this second phase, the clinical and radiographic examination showed stability and adaptation of the fragment and good periodontal health conditions, but crown darkening and a radiolucent image associated with the root apex of the fractured tooth were also observed. The periapical lesion was surgically removed by apicoectomy, and the esthetics were recovered with a direct composite res n veneer on the traumatized tooth. (Quintessence Int 2011;42:729-735)

Analysis of the healing process in delayed tooth replantation after root canal filling with calcium hydroxide, Sealapex and Endofill: a microscopic study in rats

The major concern in the therapeutics of tooth replantation refers to the occurrence of root resorption and different approaches have been proposed to prevent or treat these complications. The purpose of this study was to evaluate tissue response to delayed replantation of anterior rat teeth treated endodontically using calcium hydroxide, Sealapex, and Endofill without the placement of gutta-percha cones. Thirty rats had their right upper incisor extracted and maintained in dry storage for 60 min. After removal of the dental papilla, enamel organ, pulp tissue, and periodontal ligament remnants, the teeth were immersed in 2% sodium fluoride phosphate acidulated, pH 5.5, for 10 min. The root canals were dried with absorbent paper points and the teeth were assigned to three groups (n = 10) according to the filling material. Group I - calcium hydroxide and propyleneglycol paste, Group II - Sealapex, and Group III - Endofill. The sockets were irrigated with saline and the teeth were replanted. Replacement resorption, inflammatory resorption and ankylosis were observed in all groups. Although the occurrence of inflammatory resorption was less frequent in Group I, there were no statistically significant differences among the groups. It may be concluded that compared to the paste, filling the root canals with Sealapex and Endofill sealers without the placement of gutta-percha cones did not provide better results.

Effect of root surface treatment with propolis and fluoride in delayed tooth replantation in rats

Replantation is an acceptable option for treatment of an avulsed permanent tooth. Nevertheless, an extended extraoral period damages the periodontal ligament and results in external root resorption. The purpose of this study was to assess by histologic and histometric analysis, the influence of propolis 15% (natural resinous substance collected by Apis mellifera bees from various plants) and the fluoride solution used as root surface treatment on the healing process after delayed tooth replantation. Thirty Wistar (Rattus norvegicus albinus) rats were submitted to extraction of their upper right incisor. The teeth were maintained in a dry environment for 60 min. After this, the pulp was extirpated and the papilla, enamel organ and periodontal ligament were removed with scalpel. The teeth were divided into three experimental groups: Group I - teeth immersed in 20 ml of physiologic saline; Group II - teeth immersed in 20 ml of 2% acidulated phosphate sodium fluoride; Group III - teeth immersed in 20 ml of 15% propolis. After 10 min of immersion in the solutions, the root canals were dried and filled with calcium hydroxide paste and the teeth were replanted. The animals were euthanized 60 days after replantation. The results showed that similar external root resorption was seen in the propolis and fluoride groups. Teeth treated with physiologic saline tended to have more inflammatory root resorption compared with those treated with fluoride or propolis. However, the comparative analysis did not reveal statistically significant differences (P > 0.05) between the treatment modalities when used for delayed tooth replantation.