On a Limit of Perturbed Conservation Laws with Diffusion and Non-Positive Dispersion

We consider a conservation law perturbed by a linear diffusion and a general form of non-positive dispersion. We prove the convergence of the corresponding solution to the entropy weak solution of the hyperbolic conservation law.

Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.

Um estudo exploratório sobre a imagem conceitual de estudantes universitários acerca do conceito de limite de função

Esta é uma pesquisa de caráter exploratório, cujo objetivo foi investigar os elementos que compõem a imagem conceitual de estudantes universitários sobre o conceito de limite de uma função de uma variável real. O estudo envolveu 25 estudantes do curso de licenciatura em matemática de duas universidades públicas no estado do Pará (Brasil) e constituiu-se de duas etapas. Primeiramente, aplicamos um questionário que continha tarefas relacionadas aos aspectos conceituais de limite de uma função de uma variável. A segunda etapa consistiu na realização de entrevistas com seis sujeitos que foram selecionados devido às imagens conceituais evocadas por eles na etapa anterior, e que por sua vez, encontravam-se em conformidade com os quatro Temas de Discussão (TD) que nortearam essas entrevistas. A análise dos resultados baseou-se, sobretudo, na teoria de Tall e Vinner (1981) e Vinner (1991), bem como nos estudos realizados por Cottril et al (1996), Jordaan (2005), Juter (2006), Nair (2009), dentre outros, que compuseram a fundamentação teórica do presente estudo. Dentre os resultados obtidos, ressaltamos que os estudantes relacionam o conceito de limite de uma função de uma variável real com interpretações estáticas e/ou dinâmicas que, em alguns momentos, constituíram-se como fatores de conflito potencial, conforme destacado por Vinner (1991). Além disso, evidenciamos que algumas das imagens conceituais evocadas pelos sujeitos investigados não se fizeram coerentes, fato que os influenciou a construir uma definição conceitual pessoal diferente da definição conceitual formal de limite de uma função de uma variável real.

La comprensión de la aproximación a un número en el acceso al significado de límite de una función en un punto

Esta investigación estudia la influencia de la comprensión de la aproximación a un número y de los modos de representación en la construcción de la concepción dinámica del límite en estudiantes de Bachillerato. El análisis de realizó usando el análisis implicativo (Gras, Suzuki, Guillet y Spagnolo, 2008). Los resultados indican que la construcción paulatina de la concepción dinámica del límite se realiza mediante procesos diferenciados de aproximación en el dominio y en el rango, y, dentro de estos últimos, aquellos en los que las aproximaciones laterales coinciden de las que no coinciden. Además, nuestros resultados indican que el modo numérico o el modo algebraico-numérico desempeñan un papel relevante en el desarrollo de la comprensión de la concepción dinámica de límite.

¿Cómo estudiantes para profesor de matemáticas comprenden el aprendizaje del límite de una función?

En este estudio presentamos una investigación que tiene como objetivo generar información sobre cómo estudiantes para profesor de educación secundaria (EPS) comprenden el proceso de aprendizaje de las matemáticas. El contexto que hemos utilizado es la actividad de anticipar respuestas de los estudiantes de Bachillerato que reflejen diferentes niveles de desarrollo conceptual de la comprensión del concepto de límite de una función, como una actividad relevante vinculada a la competencia docente. Los resultados muestran dos formas distintas de considerar la comprensión del concepto de límite por parte de los EPS que tienen implicación sobre cómo anticipan las respuestas de los estudiantes y sobre las características de los problemas que plantean para apoyar el aprendizaje de la concepción dinámica de límite de los estudiantes.

¿Qué caracteriza el conocimiento del profesor de matemáticas en la planificación del concepto de límite al infinito de una función para su enseñanza?

Se reportan avances de una investigación que se interesa por determinar las características del conocimiento matemático para la enseñanza del concepto de límite al infinito de una función que pone en acción el profesor en la planificación del tópico. El estudio se fundamenta en el modelo Conocimiento Matemático para la Enseñanza (MKT). En el estudio participan dos profesores de matemáticas de España y uno de México. Los datos se obtienen mediante una entrevista semiestructurada que involucró aspectos sobre los datos personales, el aula de clases, la planificación del profesor y del investigador sobre el tópico. El análisis de los daros se realiza en tres fases: generación de las unidades de análisis, agrupamiento en categorías de dichas unidades y determinación de las características del conocimiento del profesor. Los resultados evidencian que el profesor pone en acción los subdominios del MKT cuando planifica la enseñanza del concepto de límite al infinito de una función.

Effects of glycopyrrolate on cardiorespiratory function in horses anesthetized with halothane and xylazine

Objective-To evaluate cardiopulmonary effects of glycopyrrolate in horses anesthetized with halothane and xylazine.Animals-6 horses.Procedure-Horses were allocated to 2 treatment groups in a randomized complete block design. Anesthesia was maintained in mechanically ventilated horses by administration of halothane (1% end-tidal concentration) combined with a constant-rate infusion of xylazine hydrochloride (1 mg/kg/h, IV). Hemodynamic variables were monitored after induction of anesthesia and for 120 minutes after administration of glycopyrrolate or saline (0.9% NaCl) solution. Glycopyrrolate (2.5 mug/kg, IV) was administered at 10-minute intervals until heart rate (HR) increased at least 30% above baseline or a maximum cumulative dose of 75 mug/kg had been injected. Recovery characteristics and intestinal auscultation scores were evaluated for 24 hours after the end of anesthesia.Results-Cumulative dose of glycopyrrolate administered to 5 horses was 5 mug/kg, whereas 1 horse received 75 mug/kg. The positive chronotropic effects of glycopyrrolate were accompanied by an increase in cardiac output, arterial blood pressure, and tissue oxygen delivery. Whereas HR increased by 53% above baseline values at 20 minutes after the last glycopyrrolate injection, cardiac output and mean arterial pressure increased by 38% and 31%, respectively. Glycopyrrolate administration was associated with impaction of the large colon in I horse and low intestinal auscultation scores lasting 24 hours in 3 horses.Conclusions and Clinical Relevance-The positive chronotropic effects of glycopyrrolate resulted in improvement of hemodynamic function in horses anesthetized with halothane and xylazine. However, prolonged intestinal stasis and colic may limit its use during anesthesia.

Testicular biopsy with Tru-Cut needle in conjunction with fibrin adhesive or nylon suture: assessment of post-biopsy testicular function in rams

Testicular biopsy has been a complementary technique for clinical and research purposes to evaluate reproductive function in males. However, hemorrhage, inflammation, degeneration, and adhesion are factors that might limit the use of this procedure. In order to minimize these potential problems, fibrin glue derived from snake venom, a tissue adhesive with sealing, hemostatic, and healing properties, was used in conjunction with bilateral testicular biopsy with the Tru-Cut needle and was compared with a more conventional technique that uses nylon suture. Thirty mature rams were randomly assigned to three groups of 10 animals each, as follows: nonsurgical control group (no scrotal surgery, or biopsy); biopsy + glue group (fibrin glue on puncture sites and skin incisions) and biopsy + suture group (compression with swab on puncture sites and suturing of skin incision). The surgeries of the rams in the biopsy groups were performed on the same day, which was designated Day 0 for all three groups. Data of scrotal circumference, number of spermatozoa per ejaculum, percentage of morphologically abnormal spermatozoa, spermatozoa motility, and serum testosterone concentrations from Days -7, 20, 40, 60, 80 and 100 were evaluated. There were no significant differences between groups within days for any of the parameters evaluated. In conclusion, the testicular biopsy procedure using the Tru-Cut needle in conjunction with conventional nylon suture or the more novel fibrin glue in rams did not affect any of the parameters of testicular function evaluated in this study and was shown to be relatively simple, safe and efficient. (C) 2002 Published by Elsevier B.V. B.V.

Local order and magnetic field effects on the electronic properties of disordered binary alloys in the quantum site percolation limit

Electronic properties of disordered binary alloys are studied via the calculation of the average Density of States (DOS) in two and three dimensions. We propose a new approximate scheme that allows for the inclusion of local order effects in finite geometries and extrapolates the behavior of infinite systems following finite-size scaling ideas. We particularly investigate the limit of the Quantum Site Percolation regime described by a tight-binding Hamiltonian. This limit was chosen to probe the role of short range order (SRO) properties under extreme conditions. The method is numerically highly efficient and asymptotically exact in important limits, predicting the correct DOS structure as a function of the SRO parameters. Magnetic field effects can also be included in our model to study the interplay of local order and the shifted quantum interference driven by the field. The average DOS is highly sensitive to changes in the SRO properties and striking effects are observed when a magnetic field is applied near the segregated regime. The new effects observed are twofold: there is a reduction of the band width and the formation of a gap in the middle of the band, both as a consequence of destructive interference of electronic paths and the loss of coherence for particular values of the magnetic field. The above phenomena are periodic in the magnetic flux. For other limits that imply strong localization, the magnetic field produces minor changes in the structure of the average DOS. © World Scientific Publishing Company.

On q–Analogues of Caputo Derivative and Mittag–Leffler Function

Mathematics Subject Classification: 33D60, 33E12, 26A33

Incompressible limit and well-posedness of PDE models of tissue growth

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. A coupled system of equations describes the cell density and the nutrient concentration and the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state.

The Influence Of Body Weight On Sexual Function And Quality Of Life In Women With Polycystic Ovary Syndrome.

To assess sexual function (SF) and quality of life (QOL) in women with polycystic ovary syndrome (PCOS). A cross-sectional study was conducted to assess 56 women with PCOS and 102 control women with regular menstrual cycles. To assess SF and QOL in Brazilian women with PCOS with Female Sexual Function Index (FSFI) and the WHOQOL-bref questionnaires. Women with PCOS had a worse evaluation to arousal, lubrication, satisfaction, pain and total FSFI, and there was no difference in sexual desire and orgasm. Besides, they had a worse evaluation concerning health status than controls. The body mass index was inversely correlated to the QOL, especially to the physical, psychological, environment aspects and self-assessment of QOL, but it did not show correlation to the SF. Women with PCOS had a worse sexual function and self-assessment of health condition in comparison to controls. The body weight as isolated symptom was correlated to the worsening in quality of life, but not with the worsening of sexual function.

Role Of The Different Sexuality Domains On The Sexual Function Of Women With Premature Ovarian Failure.

Women with premature ovarian failure (POF) often manifest complaints involving different aspects of sexual function (SF), regardless of using hormone therapy. SF involves a complex interaction between physical, psychological, and sociocultural aspects. There are doubts about the impact of different complaints on the global context of SF of women with POF. To evaluate the percentage of influence of each of the sexuality domains on the SF in women with POF. Cross-sectional study with 80 women with POF, matched by age to 80 women with normal gonadal function. We evaluated SF through the Female Sexual Function Index (FSFI), a comparison between the POF and control groups using the Mann-Whitney test. Component exploratory factor analysis was used to assess the proportional influence of each domain on the composition of the overall SF for women in the POF group. SF was evaluated using FSFI. Exploratory Factor Analysis for components was used to evaluate the role of each domain on the SF of women with POF. The FSFI score was significantly worse for women with POF, with a decrease in arousal, lubrication, orgasm, satisfaction, and dyspareunia. Exploratory factor analysis of SF showed that the domain with greater influence in the SF was arousal, followed by desire, together accounting for 41% of the FSFI. The domains with less influence were dyspareunia and lubrication, which together accounted for 25% of the FSFI. Women with POF have impaired SF, determined mainly by changes in arousal and desire. Aspects related to lubrication and dyspareunia complaints have lower determination coefficient in SF. These results are important in adapting the approach of sexual disorders in this group of women. Benetti-Pinto CL, Soares PM, Giraldo HPD, and Yela DA. Role of the different sexuality domains on the sexual function of women with premature ovarian failure. J Sex Med 2015;12:685-689.

Dependence of the crossover exponent with the diffusion rate in the generalized contact process model

We study how the crossover exponent, phi, between the directed percolation (DP) and compact directed percolation (CDP) behaves as a function of the diffusion rate in a model that generalizes the contact process. Our conclusions are based in results pointed by perturbative series expansions and numerical simulations, and are consistent with a value phi = 2 for finite diffusion rates and phi = 1 in the limit of infinite diffusion rate.

Flow cytometry as a tool in the evaluation of blood leukocyte function in Chelonia mydas (Linnaeus, 1758) (Testudines, Cheloniidae)

Chelonia mydas is a sea turtle that feeds and nests on the Brazilian coast and a disease called fibropapillomatosis is a threat to this species. Because of this, it is extremely necessary to determine a methodology that would enable the analysis of blood leukocyte function in these sea turtles. In order to achieve this aim, blood samples were collected from C. mydas with or without fibropapillomas captured on the São Paulo north coast. Blood samples were placed in tubes containing sodium heparin and were transported under refrigeration to the laboratory in sterile RPMI 1640 cell culture medium. Leukocytes were separated by density gradient using Ficoll-PaqueTM Plus, Amershan Biociences®. The following stimuli were applied in the assessment of leukocyte function: Phorbol Miristate-Acetate (PMA) for oxidative burst activity evaluation and Zymosan A (Saccharomyces cerevisiae) Bio Particles®, Alexa Fluor® 594 conjugate for phagocytosis evaluation. Three cell populations were identified: heterophils, monocytes and lymphocytes. Monocytes were the cells responsible for phagocytosis and oxidative burst.