Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

Effect of 2% Chlorhexidine Digluconate on the Bond Strength to Normal Versus Caries-affected Dentin

This study evaluated the effect of 2% chlorhexidine digluconate (CHX) used as a therapeutic primer on the long-term bond strengths of two etch-and-rinse adhesives to normal (ND) and caries-affected (CAD) dentin. Forty extracted human molars with coronal carious lesions, surrounded by normal dentin, were selected for this study. The flat surfaces of two types of dentin (ND and CAD) were prepared with a water-cooled high-speed diamond disc, then acidetched, rinsed and air-dried. In the control groups, the dentin was re-hydrated with distilled water, blot-dried and bonded with a three-step (Scotchbond Multi-Purpose-MP) or two-step (Single Bond 2-SB) etch-and-rinse adhesive. In the experimental groups, the dentin was rehydrated with 2% CHX (60 seconds), blot-dried and bonded with the same adhesives. Resin composite build-ups were made. The specimens were prepared for microtensile bond testing in accordance with the non-trimming technique, then tested either immediately or after six-months storage in artificial saliva. The data were analyzed by ANOVA/Bonferroni tests (alpha=0.05). CHX did not affect the immediate bond strength to ND or CAD (p>0.05). CHX treatment significantly lowered the loss of bond strength after six months as seen in the control bonds for ND (p<0.05), but it did not alter the bond strength of CAD (p>0.05). The application of NIP on CHX-treated ND or CAD produced bonds that did not change over six months of storage.

Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

Estimates of the real structured radius of stability of linear dynamic systems

A question is examined as to estimates of the norms of perturbations of a linear stable dynamic system, under which the perturbed system remains stable in a situation R:here a perturbation has a fixed structure.

Composite filling removal with erbium:yttrium-aluminum-garnet laser: morphological analyses

Considering the increase in esthetic restorative materials and need for improvement in unsatisfactory restoration substitution with minimal inadvertent removal of healthy tissues, this study assessed the efficacy of erbium:yttrium-aluminum-garnet (Er:YAG) laser for composite resin removal and the influence of pulse repetition rate on the morphological analyses of the cavity by scanning electron microscope. Composite resin fillings were placed in cavities (1.0 mm deep) prepared in bovine teeth, and the 75 specimens were randomly assigned to five groups according to the technique used for composite filling removal (high-speed diamond bur, group I, as a control, and Er:YAG laser, 250 mJ output energy and 80 J/cm(2) energy density, using different pulse repetition rates: group II, 2 Hz; group III, 4 Hz; group IV, 6 Hz; group V, 10 Hz). After the removal, the specimens were split in the middle, and we analyzed the surrounding and deep walls to check for the presence of restorative material. The estimation was qualitative. The surfaces were examined with a scanning electron microscope. The results revealed that the experimental groups presented bigger amounts of remaining restorative material. The scanning electron microscopy (SEM) analyses showed irregularities of the resultant cavities of the experimental groups that increased proportionally with increase in repetition rate.

Bond strength of Epiphany (TM) Sealer combined with different adhesive systems photo-activated with LED and QTH

The Epiphany (TM) Sealer is a new dual-curing resin-based sealer and has been introduced as an alternative to gutta-percha and traditional root canal sealers. The canal filling is claimed to create a seal with the dentinal tubules within the root canal system producing a `monoblock` effect between the sealer and dentinal tubules. Therefore, considering the possibility to incorporate the others adhesive systems, it is important to study the bond strength of the resulting cement. Forty-eight root mandibular canines were sectioned 8-mm below CEJ. The dentine discs were prepared using a tapered diamond bur and irrigated with 1% NaOCl and 17% EDTA. Previous the application Epiphany (TM) Sealer, the Epiphany (TM) Primer, AdheSE, and One Up Bond F were applied to the root canal walls. The LED and QTH (Quartz Tungsten Halogen) were used to photo-activation during 45 s with power density of 400 and 720 mW/cm(2), respectively. The specimens were performed on a universal testing machine at a cross-head speed of 1 mm/min until bond failure occurred. The force was recorded and the debonding values were used to calculate Push-out bond strength. The analysis of variance (ANOVA) and Tukey`s post-hoc tests showed significant statistical differences (P < 0.05) to Epiphany (TM) Sealer/Epiphany (TM) Primer/QTH and EpiphanyTM Sealer/AdheSE/QTH, which had the highest mean values of bond strength. The efficiency of resin-based filling materials are dependent the type of light curing unit used including the power density, the polymerization characteristics of these resin-based filling materials, depending on the primer/adhesive used.

Bond Strength of Epiphany Sealer Prepared with Resinous Solvent

This study evaluated in vitro the bond strength of Epiphany sealer prepared with resinous solvent of Epiphany system (Thinning resin) by using a push-out test. Forty maxillary canines were sectioned transversally below the cementoenamel junction to provide 4-mm-thick dentin disks that were centered in aluminum rings and embedded in acrylic resin. Root canals were prepared with tapered diamond bur. Intraradicular dentin was treated with 1% NaOCl for 30 minutes, 17% ethylenediaminetetraacetic acid for 5 minutes, and flushed with distilled water for 1 minute. The specimens were randomly distributed into 4 groups (n = 10) according to the filling material: GI, Epiphany without photoactivation; GII, Epiphany prepared with solvent without photoactivation; Gill, Epiphany followed by photoactivation; and GIV, Epiphany prepared with solvent followed by photoactivation. After the setting time, the specimens were submitted to the push-out test. The highest mean value (14.91 +/- 2.82 MPa) was obtained with Epiphany prepared with solvent followed by photoactivation (GIV), which was statistically different (P < .01) from the other groups. Groups I (8.15 +/- 2.47 MPa), II (9.46 +/- 2.38 MPa), and III (9.80 +/- 2.51 MPa) had inferior bond strength values and were statistically similar among themselves (P > .01). The resinous solvent of Epiphany system increased the bond strength of Epiphany sealer to dentin walls when followed by photoactivation. (J Endod 2009;35: 251-255)

Effects of Ethanol on the Surface and Bulk Properties of a Microwave-Processed PMMA Denture Base Resin

Purpose: This study evaluated the effect of different concentrations of ethanol on hardness, roughness, flexural strength, and color stability of a denture base material using a microwave-processed acrylic resin as a model system. Materials and Methods: Sixty circular (14 x 4 mm) and 60 rectangular microwave-polymerized acrylic resin specimens (65 x 10 x 3 mm(3)) were employed in this study. The sample was divided into six groups according to the ethanol concentrations used in the immersion solution, as follows: 0% (water), 4.5%, 10%, 19%, 42%, and 100%. The specimens remained immersed for 30 days at 37 degrees C. The hardness test was performed by a hardness tester equipped with a Vickers diamond penetrator, and a surface roughness tester was used to measure the surface roughness of the specimens. Flexural strength testing was carried out on a universal testing machine. Color alterations (Delta E) were measured by a portable spectrophotometer after 12 and 30 days. Variables were analyzed by ANOVA/Tukey`s test (alpha = 0.05). Results: For the range of ethanol-water solutions for immersion (water only, 4.5%, 10%, 19.5%, 42%, and 100%), the following results were obtained for hardness (13.9 +/- 2.0, 12.1 +/- 0.7, 12.9 +/- 0.9, 11.2 +/- 1.5, 5.7 +/- 0.3, 2.7 +/- 0.5 VHN), roughness (0.13 +/- 0.01, 0.15 +/- 0.07, 0.13 +/- 0.05, 0.13 +/- 0.02, 0.23 +/- 0.05, 0.41 +/- 0.19 mu m), flexural strength (90 +/- 12, 103 +/- 18, 107 +/- 16, 90 +/- 25, 86 +/- 22, 8 +/- 2 MPa), and color (0.8 +/- 0.6, 0.8 +/- 0.3, 0.7 +/- 0.4, 0.9 +/- 0.3, 1.3 +/- 0.3, 3.9 +/- 1.5 Delta E) after 30 days. Conclusions: The findings of this study showed that the ethanol concentrations of tested drinks affect the physical properties of the investigated acrylic resin. An obvious plasticizing effect was found, which could lead to a lower in vivo durability associated with alcohol consumption.

Physical Properties of an Acrylic Resin after Incorporation of an Antimicrobial Monomer

Purpose: This study evaluated the effect of the incorporation of the antimicrobial monomer methacryloyloxyundecylpyridinium bromide (MUPB) on the hardness, roughness, flexural strength, and color stability of a denture base material. Materials and Methods: Ninety-six disk-shaped (14-mm diameter x 4-mm thick) and 30 rectangular (65 x 10 x 3.3 mm(3)) heat-polymerized acrylic resin specimens were divided into three groups according to the concentration of MUPB (w/w): (A) 0%, (B) 0.3%, (C) 0.6%. Hardness was assessed by a hardness tester equipped with a Vickers diamond penetrator. Flexural strength and surface roughness were tested on a universal testing machine and a surface roughness tester, respectively. Color alterations (Delta E) were measured by a portable spectrophotometer after 12 and 36 days of immersion in water, coffee, or wine. Variables were analyzed by ANOVA/Tukey HSD test (alpha = 0.05). Results: The following mean results (+/-SD) were obtained for hardness (A: 15.6 +/- 0.6, B: 14.6 +/- 1.7, C: 14.8 +/- 0.8 VHN; ANOVA: p = 0.061), flexural strength (A: 111 +/- 17, B: 105 +/- 12, C: 88 +/- 12 MPa; ANOVA: p = 0.008), and roughness (A: 0.20 +/- 0.11, B: 0.20 +/- 0.11, C: 0.24 +/- 0.08 mu m; ANOVA: p = 0.829). Color changes of immersed specimens were significantly influenced by solutions and time (A: 9.1 +/- 3.1, B: 14.8 +/- 7.5, C: 13.3 +/- 6.1 Delta E; ANOVA: p < 0.05). Conclusions: The incorporation of MUPB affects the mechanical properties of a denture base acrylic resin; however, the only significant change was observed for flexural strength and may not be critical. Color changes were slightly higher when resin containing MUPB was immersed in wine for a prolonged time; however, the difference has debatable clinical relevance.

The oral medicine of tooth wear

This review illustrates, through a series of case histories, how oral medicine insights aid the diagnosis and management of patients with excessive tooth wear. The cases reviewed are drawn from the records of 500 southeast Queensland patients referred to the author over a 12 year period. Patients most at risk of dental erosion have work and sports dehydration, caffeine addiction, gastro-oesophageal reflux, asthma, diabetes mellitus, hypertension or other systemic diseases or syndromes that predispose to xerostomia. Saliva protects the teeth from the extrinsic and intrinsic acids which cause dental erosion. Erosion, exacerbated by attrition and abrasion, is the main cause of tooth wear. These cases illustrate that teeth, oral mucosa, salivary glands, skin and eyes should be examined for evidence of salivary hypofunction and attendant medical conditions. Based on comprehensive oral medicine, dietary analyses and advice, it would seem patients need self-management plans to deal with incipient chronic tooth wear. The alternative is the expensive treatment of pain, occlusal damage and pulp death required to repair the effects of acute severe tooth wear.

Emmetropization in chicks uses optical vergence and relative distance cues to decode defocus

When visual information is confined to one object plane, the emmetropization end-point is adjusted in accord with the corresponding incident optical vergence at the eye [Proceedings of the 7th International Conference on Myopia (2000) 113]. We now report the effect of adding extra visual information beyond the target plane. Visual conditions were controlled using a cone-lens system: black Maltese cross targets on white opaque backgrounds (OMX) were attached to the open faces of 2.5 cm translucent cones fitted with either 0, +25 or +40 D imaging lenses. An alternative target (TMX) was made by substituting the opaque target background for a transparent background, which allowed access to visual information beyond the target plane. The imaging devices were applied to 7-day-old chicks and worn for 4 days. Prior to this treatment, on day 2, some chicks underwent ciliary nerve section (CNS) to preclude accommodation. All treatments were monocular. Refractive errors and axial ocular dimensions were measured using retinoscopy and A-scan ultrasonography under halothane anesthesia. Treatment effects were specified as mean ( +/-S.D.) interocular differences. Eyes with the OMX/ + 40 D lens combination remained emmetropic ( +0.73 +/-3.57 D), consistent with the target plane being approximately conjugate with the retina. Switching to the TMX caused a hyperopic shift in refractive error ( + 3.78 +/- 3.41 D). This relative shift towards hyperopia in switching from the OMX to the TMX target also occurred for the other two lens powers. Thus, the OMX/ + 25 D lens induced myopia ( - 7.00 +/-5.88 D), corresponding to the imposed hyperopic defocus (target plane now imaged behind the retina), and switching to the TMX resulted in a reduction in myopia (-1.73 +/-5.36 D), The OMX/0 D lens combination produced the largest myopic shift, and here, switching to the TMX condition almost eliminated the myopic response (-15.50 +/-6.62 D cf. -0.56 +/-1.24 D). This relative hyperopic shift associated with switching from the OMX to the TMX target was eliminated by CNS surgery. Thus, the two CNS/TMX groups were both more myopic than the equivalent no CNS/TMX groups ( + 40 D lens: -2.66 +/-2.34 D; +25 D lens: -7.97 +/-6.87 D). When the visual information is restricted to one plane, incident optical vergence appears to direct emmetropization. Adding Visual information at other distances produces a shift in the end-point of ernmetropization in the direction of the added information. That these effects are dependent on the integrity of the accommodation system implies that accommodation plays a role in emmetropization and represents the first reported evidence of this kind. Published by Elsevier Science Ltd.

Corneal endothelial response to induced myopia in the chicken

Purpose: To investigate the role of corneal endothelial surface enlargement in the chicken myopia model in inducing corneal endothelial changes. Methods: Lid suture was performed on one eye of 1-day-old cockerels. Five chickens were killed at 1 week, and four chickens killed at each of 3 weeks, 6 weeks, and 10 weeks postnatal. The endothelial morphology was obtained by flat mounting the endothelial surface and the subsequent digitisation. Comparisons were undertaken between the control unsutured eye and the lid-sutured eye endothelium, and between the central endothelial areas compared to the peripheral endothelial areas in both the myopic and the normal corneas. Calculation of the contribution to the endothelial change by hypertrophy and mitosis were calculated using Bahn's formula. Results: Total endothelial surface area increased significantly over time in the myopic model compared to control eyes but the mean cell area of endothelial cells remained the same for both the enlarged myopic endothelial surface area and in the normal controls. Sampling from the central and the peripheral corneal endothelial surface also disclosed no difference. The mean cell area did increase steadily with age but was the same for both normal and myopic corneas. Conclusions: It would appear that there are equal contributions from hypertrophy and mitosis in the myopic group and the normal corneal group with a slightly increasing trend towards mitotic activity in the myopic corneal endothelial layer.