Perfect imaging of three object points with only two analytic lens surfaces in two dimensions

In this work, a new two-dimensional analytic optics design method is presented that enables the coupling of three ray sets with two lens profiles. This method is particularly promising for optical systems designed for wide field of view and with clearly separated optical surfaces. However, this coupling can only be achieved if different ray sets will use different portions of the second lens profile. Based on a very basic example of a single thick lens, the Simultaneous Multiple Surfaces design method in two dimensions (SMS2D) will help to provide a better understanding of the practical implications on the design process by an increased lens thickness and a wider field of view. Fermat?s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The transformation of these functional differential equations into an algebraic linear system of equations allows the successive calculation of the Taylor series coefficients up to an arbitrary order. The evaluation of the solution space reveals the wide range of possible lens configurations covered by this analytic design method. Ray tracing analysis for calculated 20th order Taylor polynomials demonstrate excellent performance and the versatility of this new analytical optics design concept.

Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

Numerical quadrature over a rectangular domain in two or more dimensions /

"This work was supported in part by the Office of Naval Research under Contract Nonr-1834(27)."

Statnote 14: the correlation of two variables (Pearson's 'r')

Pearson's correlation coefficient (‘r’) is one of the most widely used of all statistics. Nevertheless, care needs to be used in interpreting the results because with large numbers of observations, quite small values of ‘r’ become significant and the X variable may only account for a small proportion of the variance in Y. Hence, ‘r squared’ should always be calculated and included in a discussion of the significance of ‘r’. The use of ‘r’ also assumes that the data follow a bivariate normal distribution (see Statnote 17) and this assumption should be examined prior to the study. If the data do not conform to such a distribution, the use of a non-parametric correlation coefficient should be considered. A significant correlation should not be interpreted as indicating ‘causation’ especially in observational studies, in which the two variables may be correlated because of their mutual correlations with other confounding variables.

The Deformed Trigonometric Functions of two Variables

MSC 2010: 33B10, 33E20

Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32

Monogenic polynomials of four variables with binomial expansion

In the recent past one of the main concern of research in the field of Hypercomplex Function Theory in Clifford Algebras was the development of a variety of new tools for a deeper understanding about its true elementary roots in the Function Theory of one Complex Variable. Therefore the study of the space of monogenic (Clifford holomorphic) functions by its stratification via homogeneous monogenic polynomials is a useful tool. In this paper we consider the structure of those polynomials of four real variables with binomial expansion. This allows a complete characterization of sequences of 4D generalized monogenic Appell polynomials by three different types of polynomials. A particularly important case is that of monogenic polynomials which are simply isomorphic to the integer powers of one complex variable and therefore also called pseudo-complex powers.

Perception of HIV among pregnant women in the public health system in two municipalities of the state of São Paulo

Aim: To verify the knowledge of pregnant women on mother-to-child transmission (MTCT) of HIV, the availability of HIV tests in the public health system and counseling on the disease in two cities, Birigui and Piacatu, São Paulo State, Brazil. Methods: This is a descriptive and exploratory research using as samples, the files of 141 pregnant women attending the Basic Health Unit. Data were collected by survey, followed by a semi-structured questionnaire with open and closedend questions. Data were analyzed on Epi Info™ 7.1.4, by the Chi-square and Exact Fisher tests. Results: From all the 141 pregnant women, 119 were interviewed and 92.4% reported to have been informed about the need of taking the HIV test during prenatal exams. However, only 5.9% were counseled and 20.2% reported to be aware of how to prevent MTCT of HIV, usually mentioning lactation suppression and prescribed medication. The association between the knowledge about how to prevent MTCT of HIV and some social, demographic and economic variables like ethnics, educational level, home location, occupation, age and parenting was not verified. Conclusions: It is necessary to advise pregnant women on the importance of taking the HIV test regardless of the examination outcome, which was not observed in the cities where the research was conducted.

In two waters: contemporary evolution of lagoonal and marine white seabream (Diplodus sargus) populations

Brackish water ecosystems are often exposed to wide variations in environmental variables, including temperature and salinity, which may cause strong selective pressures on organisms modifying the genetic patterns of species. The aim of this work was to test whether there is a ‘divergence-with-gene flow’ in coastal lagoon populations of white seabream (Diplodus sargus) (Ria Formosa, S Portugal and Mar Menor, SE Spain) respect to four marine populations, by using partial sequences of cyt b mitochondrial gene and information from nine microsatellite loci. Genetic diversity was highest in both coastal lagoons (Mar Menor and Ria Formosa) considering mitochondrial and nuclear markers. Although some of FST population pairwise comparisons were not significant, analyses of molecular variance (AMOVAs) detected differences between groups (coastal lagoon and marine) close to significance. Also, only two haplotypes (Cytb-17 and Cytb-18) were detected in both coastal lagoon sampling sites and these localities (Mar Menor and Ria Formosa) showed the highest number of singletons, some of them with a high number of mutations, as has been already described for other Mar Menor populations (Pomatochistus marmoratus and Holothuria polii). Also, several tests detected significant positive and balancing selection considering mtDNA and microsatellite data. These data support the hypothesis of selection as one of the drivers of the genetic differences found between coastal lagoon and marine populations. The life strategy adopted by Diplodus sargus in coastal lagoons allows it to decrease its mortality rate and improve the heritability of its genes. Also, the increase time spent in coastal lagoons with different temperatures and salinities favours the fitness selection and the maintenance of exclusive haplotypes and genotypes in coastal lagoon inhabitants favouring the ‘divergence-with-gene-flow’.

Molecular analysis of exons 8, 9 and 10 of the fibroblast growth factor receptor 2 (FGFR2) gene in two families with index cases of Apert Syndrome

Introduction: Apert syndrome (AS) is a craniosynostosis condition caused by mutations in the Fibroblast Growth Factor Receptor 2 (FGFR2) gene. Clinical features include cutaneous and osseous symmetric syndactily in hands and feet, with variable presentations in bones, brain, skin and other internal organs. Methods: Members of two families with an index case of Apert Syndrome were assessed to describe relevant clinical features and molecular analysis (sequencing and amplification) of exons 8, 9 and 10 of FGFR2 gen. Results: Family 1 consists of the mother, the index case and half -brother who has a cleft lip and palate. In this family we found a single FGFR2 mutation, S252W, in the sequence of exon 8. Although mutations were not found in the study of the patient affected with cleft lip and palate, it is known that these diseases share signaling pathways, allowing suspected alterations in shared genes. In the patient of family 2, we found a sequence variant T78.501A located near the splicing site, which could interfere in this process, and consequently with the protein function.

Homozygous Inactivating Mutation In Nanos3 In Two Sisters With Primary Ovarian Insufficiency.

Despite the increasing understanding of female reproduction, the molecular diagnosis of primary ovarian insufficiency (POI) is seldom obtained. The RNA-binding protein NANOS3 poses as an interesting candidate gene for POI since members of the Nanos family have an evolutionarily conserved function in germ cell development and maintenance by repressing apoptosis. We performed mutational analysis of NANOS3 in a cohort of 85 Brazilian women with familial or isolated POI, presenting with primary or secondary amenorrhea, and in ethnically-matched control women. A homozygous p.Glu120Lys mutation in NANOS3 was identified in two sisters with primary amenorrhea. The substituted amino acid is located within the second C2HC motif in the conserved zinc finger domain of NANOS3 and in silico molecular modelling suggests destabilization of protein-RNA interaction. In vitro analyses of apoptosis through flow cytometry and confocal microscopy show that NANOS3 capacity to prevent apoptosis was impaired by this mutation. The identification of an inactivating missense mutation in NANOS3 suggests a mechanism for POI involving increased primordial germ cells (PGCs) apoptosis during embryonic cell migration and highlights the importance of NANOS proteins in human ovarian biology.

Photoelastic Analysis Of Fixed Partial Prosthesis Crown Height And Implant Length On Distribution Of Stress In Two Dental Implant Systems.

The aim of this study was to evaluate by photoelastic analysis stress distribution on short and long implants of two dental implant systems with 2-unit implant-supported fixed partial prostheses of 8 mm and 13 mm heights. Sixteen photoelastic models were divided into 4 groups: I: long implant (5 × 11 mm) (Neodent), II: long implant (5 × 11 mm) (Bicon), III: short implant (5 × 6 mm) (Neodent), and IV: short implants (5 × 6 mm) (Bicon). The models were positioned in a circular polariscope associated with a cell load and static axial (0.5 Kgf) and nonaxial load (15°, 0.5 Kgf) were applied to each group for both prosthetic crown heights. Three-way ANOVA was used to compare the factors implant length, crown height, and implant system (α = 0.05). The results showed that implant length was a statistically significant factor for both axial and nonaxial loading. The 13 mm prosthetic crown did not result in statistically significant differences in stress distribution between the implant systems and implant lengths studied, regardless of load type (P > 0.05). It can be concluded that short implants showed higher stress levels than long implants. Implant system and length was not relevant factors when prosthetic crown height were increased.

Preservation Of The External Jugular Vein In Bilateral Radical Neck Dissections: Technique In Two Cases And Review Of The Literature.

Context. The possibility of cephalic venous hypertension with the resultant facial edema and elevated cerebrospinal fluid pressure continues to challenge head and neck surgeons who perform bilateral radical neck dissections during simultaneous or staged procedures. Case Report. The staged procedure in patients who require bilateral neck dissections allows collateral venous drainage to develop, mainly through the internal and external vertebral plexuses, thereby minimizing the risks of deleterious consequences. Nevertheless, this procedure has disadvantages, such as a delay in definitive therapy, the need for a second hospitalization and anesthesia, and the risk of cutting lymphatic vessels and spreading viable cancer cells. In this paper, we discuss the rationale and feasibility of preserving the external jugular vein. Considering the limited number of similar reports in the literature, two cases in which this procedure was accomplished are described. The relevant anatomy and technique are reviewed and the patients' outcomes are discussed. Conclusion. Preservation of the EJV during bilateral neck dissections is technically feasible, fast, and safe, with clinically and radiologically demonstrated patency.

Physiological limitations in two sugarcane varieties under water suppression and after recovering

Increasing water scarcity and depleted water productivity in irrigated soils are inducing farmers to adopt improved varieties, such as those with high-capacity tolerance. The use of tolerant varieties of sugarcane might substantially avoid the decline of productivity under water deficit. This research aimed to evaluate the harmful effects of drought on the physiology of two sugarcane varieties (RB867515 and RB962962) during the initial development. Young plants were subjected to irrigation suspension until total stomata closure, and then rewatered. Significant reduction on stomatal conductance, transpiration, and net photosynthesis were observed. RB867515 showed a faster stomatal closure while RB962962 slowed the effects of drought on the gas exchanges parameters with a faster recovering after rewatering. Accumulation of carbohydrates, amino acids, proline, and protein in the leaves and roots of the stressed plants occurred in both varieties, substantially linked to reduction of the leaf water potential. Due to the severity of stress, this accumulation was not enough to maintain the cell turgor pressure, so relative water content was diminished. Water stress affected the contents of chlorophyll (a, b, and total) in both varieties, but not the levels of carotenoids. There was a significant reduction in dry matter under stress. In conclusion, RB962962 variety endured stressed conditions more than RB867515, since it slowed down the damaging effects of drought on the gas exchanges. In addition, RB962962 presented a faster recovery than RB867515, a feature that qualifies it as a variety capable of enduring short periods of drought without major losses in the initial stage of its development.

Vertical alveolar crest bone maintenance around implants in two-stage surgery: an in situ study in dogs

The aim of this study was to evaluate in situ changes in the alveolar crest bone height around immediate implant-supported crowns in comparison to tooth-supported crowns (control) with the cervical margins located at the bone crest level, without occlusal load. In Group I, after extraction of 12 mandibular premolars from 4 adult dogs, implants from Branemark System (MK III TiU RP 4.0 x 11.5 mm) were placed to retain complete acrylic crowns. In Group II, premolars were prepared to receive complete metal crowns. Sixteen weeks after placement of the crowns (38 weeks after tooth extraction), the height of the alveolar bone crest was measured with a digital caliper. Data were analyzed statistically by the Mann-Whitney test at 5% significance level. The in situ analysis showed no statistically significant difference (p=0.880) between the implant-supported and the tooth-supported groups (1.528 + 0.459 mm and 1.570 + 0.263 mm, respectively). Based on the findings of the present study, it may be concluded that initial peri-implant bone loss may result from the remodeling process necessary to establish the biological space, similar to which occurs with tooth-supported crowns.