On Modified Method of Simplest Equation for Obtaining Exact Solutions of Nonlinear PDEs: Case of Elliptic Simplest Equation

2010 Mathematics Subject Classification: 74J30, 34L30.

Exact Solutions of Nonlocal Pluriparabolic Problems

MSC 2010: 44A35, 44A40

Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05

Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element

We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case of the geometrically exact planar Bernoulli beam element presented in this work, these transformation functions at the nodes are given as rotations. However, due to an intrinsic coupling between rotational and translational components of the deformation function, the formulation provides for a good approximation of the deflection of the beam, as well as of the resultant forces and moments. As both the translational and the rotational components of the deformation function are defined on the logarithmic space, we propose to refer to the novel approach as the “Logarithmic finite element method”, or “LogFE” method.

[the Teaching Of Social Sciences In Health: Between Practice And Theory].

The models of teaching social sciences and clinical practice are insufficient for the needs of practical-reflective teaching of social sciences applied to health. The scope of this article is to reflect on the challenges and perspectives of social science education for health professionals. In the 1950s the important movement bringing together social sciences and the field of health began, however weak credentials still prevail. This is due to the low professional status of social scientists in health and the ill-defined position of the social sciences professionals in the health field. It is also due to the scant importance attributed by students to the social sciences, the small number of professionals and the colonization of the social sciences by the biomedical culture in the health field. Thus, the professionals of social sciences applied to health are also faced with the need to build an identity, even after six decades of their presence in the field of health. This is because their ambivalent status has established them as a partial, incomplete and virtual presence, requiring a complex survival strategy in the nebulous area between social sciences and health.

Study of C- and O-glycosylflavones in sugarcane extracts using liquid chromatography: exact mass measurement mass spectrometry

The flavonoids present in sugarcane (Saccharum officinarum) extracts were analyzed by liquid chromatography - mass spectrometry (LC-MS), and a study of the fragmentation patterns of selected flavonoids was conducted using orthogonal acceleration time-of-flight electrospray ionization mass spectrometry (ESI-oa-ToF MS). Seven C- and O-glycosylflavones were identified in the extracts, namely, schaftoside, isoschaftoside, luteolin-8-C-(rhamnosylglucoside), vitexin, orientin, tricin-7-O-neohesperidoside and tricin-7-O-glucoside. Of these, five were identified in the absence of direct comparison with their respective standards. The described method also permitted the differentiation of the 6-C and 8-C isomeric flavones, schaftoside and isoschaftoside. The combination of fragmentation data and exact mass measurement showed to be complimentary to the HPLC-UV-MS techniques previously utilized for isomers discrimination in sugarcane studies.

Exact time-dependent solutions for a self-regulating gene

The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.

Age of Child, More than HPV Type, Is Associated with Clinical Course in Recurrent Respiratory Papillomatosis

Background: RRP is a devastating disease in which papillomas in the airway cause hoarseness and breathing difficulty. The disease is caused by human papillomavirus (HPV) 6 or 11 and is very variable. Patients undergo multiple surgeries to maintain a patent airway and in order to communicate vocally. Several small studies have been published in which most have noted that HPV 11 is associated with a more aggressive course. Methodology/Principal Findings: Papilloma biopsies were taken from patients undergoing surgical treatment of RRP and were subjected to HPV typing. 118 patients with juvenile-onset RRP with at least 1 year of clinical data and infected with a single HPV type were analyzed. HPV 11 was encountered in 40% of the patients. By our definition, most of the patients in the sample (81%) had run an aggressive course. The odds of a patient with HPV 11 running an aggressive course were 3.9 times higher than that of patients with HPV 6 (Fisher's exact p = 0.017). However, clinical course was more closely associated with age of the patient (at diagnosis and at the time of the current surgery) than with HPV type. Patients with HPV 11 were diagnosed at a younger age (2.4y) than were those with HPV 6 (3.4y) (p = 0.014). Both by multiple linear regression and by multiple logistic regression HPV type was only weakly associated with metrics of disease course when simultaneously accounting for age. Conclusions/Significance Abstract: The course of RRP is variable and a quarter of the variability can be accounted for by the age of the patient. HPV 11 is more closely associated with a younger age at diagnosis than it is associated with an aggressive clinical course. These data suggest that there are factors other than HPV type and age of the patient that determine disease course.

Cosmic distance duality relation and the shape of galaxy clusters

Context. Observations in the cosmological domain are heavily dependent on the validity of the cosmic distance-duality (DD) relation, eta = D(L)(z)(1+ z)(2)/D(A)(z) = 1, an exact result required by the Etherington reciprocity theorem where D(L)(z) and D(A)(z) are, respectively, the luminosity and angular diameter distances. In the limit of very small redshifts D(A)(z) = D(L)(z) and this ratio is trivially satisfied. Measurements of Sunyaev-Zeldovich effect (SZE) and X-rays combined with the DD relation have been used to determine D(A)(z) from galaxy clusters. This combination offers the possibility of testing the validity of the DD relation, as well as determining which physical processes occur in galaxy clusters via their shapes. Aims. We use WMAP (7 years) results by fixing the conventional Lambda CDM model to verify the consistence between the validity of DD relation and different assumptions about galaxy cluster geometries usually adopted in the literature. Methods. We assume that. is a function of the redshift parametrized by two different relations: eta(z) = 1+eta(0)z, and eta(z) = 1+eta(0)z/(1+z), where eta(0) is a constant parameter quantifying the possible departure from the strict validity of the DD relation. In order to determine the probability density function (PDF) of eta(0), we consider the angular diameter distances from galaxy clusters recently studied by two different groups by assuming elliptical (isothermal) and spherical (non-isothermal) beta models. The strict validity of the DD relation will occur only if the maximum value of eta(0) PDF is centered on eta(0) = 0. Results. It was found that the elliptical beta model is in good agreement with the data, showing no violation of the DD relation (PDF peaked close to eta(0) = 0 at 1 sigma), while the spherical (non-isothermal) one is only marginally compatible at 3 sigma. Conclusions. The present results derived by combining the SZE and X-ray surface brightness data from galaxy clusters with the latest WMAP results (7-years) favors the elliptical geometry for galaxy clusters. It is remarkable that a local property like the geometry of galaxy clusters might be constrained by a global argument provided by the cosmic DD relation.

Chemical evolution of the Galactic bulge as traced by microlensed dwarf and subgiant stars IV. Two bulge populations

Based on high-resolution (R approximate to 42 000 to 48 000) and high signal-to-noise (S/N approximate to 50 to 150) spectra obtained with UVES/VLT, we present detailed elemental abundances (O, Na, Mg, Al, Si, Ca, Ti, Cr, Fe, Ni, Zn, Y, and Ba) and stellar ages for 12 new microlensed dwarf and subgiant stars in the Galactic bulge. Including previous microlensing events, the sample of homogeneously analysed bulge dwarfs has now grown to 26. The analysis is based on equivalent width measurements and standard 1-D LTE MARCS model stellar atmospheres. We also present NLTE Li abundances based on line synthesis of the (7)Li line at 670.8 nm. The results from the 26 microlensed dwarf and subgiant stars show that the bulge metallicity distribution (MDF) is double-peaked; one peak at [Fe/H] approximate to -0.6 and one at [Fe/H] approximate to +0.3, and with a dearth of stars around solar metallicity. This is in contrast to the MDF derived from red giants in Baade's window, which peaks at this exact value. A simple significance test shows that it is extremely unlikely to have such a gap in the microlensed dwarf star MDF if the dwarf stars are drawn from the giant star MDF. To resolve this issue we discuss several possibilities, but we can not settle on a conclusive solution for the observed differences. We further find that the metal-poor bulge dwarf stars are predominantly old with ages greater than 10 Gyr, while the metal-rich bulge dwarf stars show a wide range of ages. The metal-poor bulge sample is very similar to the Galactic thick disk in terms of average metallicity, elemental abundance trends, and stellar ages. Speculatively, the metal-rich bulge population might be the manifestation of the inner thin disk. If so, the two bulge populations could support the recent findings, based on kinematics, that there are no signatures of a classical bulge and that the Milky Way is a pure-disk galaxy. Also, recent claims of a flat IMF in the bulge based on the MDF of giant stars may have to be revised based on the MDF and abundance trends probed by our microlensed dwarf stars.

EVOLUTION OF FLORAL MORPHOLOGY AND POLLINATION SYSTEM IN BIGNONIEAE (BIGNONIACEAE)

The radiation of angiosperms is associated with shifts among pollination modes that are thought to have driven the diversification of floral forms. However, the exact sequence of evolutionary events that led to such great diversity in floral traits is unknown for most plant groups. Here, we characterize the patterns of evolution of individual floral traits and overall floral morphologies in the tribe Bignonieae (Bignoniaceae). We identified 12 discrete traits that are associated with seven floral types previously described for the group and used a penalized likelihood tree of the tribe to reconstruct the ancestral states of those traits at all nodes of the phylogeny of Bignonieae. In addition, evolutionary correlations among traits were conducted using a maximum likelihood approach to test whether the evolution of individual floral traits followed the correlated patterns of evolution expected under the ""pollination syndrome"" concept. The ancestral Bignonieae flower presented an Anemopaegma-type morphology, which was followed by several parallel shifts in floral morphologies. Those shifts occurred through intermediate stages resulting in mixed floral morphologies as well as directly from the Anemopaegma-type morphology to other floral types. Positive and negative evolutionary correlations among traits fit patterns expected under the pollination syndrome perspective, suggesting that interactions between Bignonieae flowers and pollinators likely played important roles in the diversification of the group as a whole.

Evolutionary dynamics on rugged fitness landscapes: Exact dynamics and information theoretical aspects

The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the random energy model (REM) and by a ferromagnetic version of the REM. The solution method uses the mapping of the evolutionary dynamics into a quantum Ising chain in a transverse field and the Suzuki-Trotter formalism to calculate the transition probabilities between configurations at different times. We find that in the case of the REM landscape the dynamics can exhibit three distinct regimes: pure diffusion or stasis for short times, depending on the fitness of the initial configuration, and a spin-glass regime for large times. The dynamic transition between these dynamical regimes is marked by discontinuities in the mean-fitness as well as in the overlap with the initial reference sequence. The relaxation to equilibrium is described by an inverse time decay. In the ferromagnetic REM, we find in addition to these three regimes, a ferromagnetic regime where the overlap and the mean-fitness are frozen. In this case, the system relaxes to equilibrium in a finite time. The relevance of our results to information processing aspects of evolution is discussed.

Exact nonequilibrium work generating function for a small classical system

We obtain the exact nonequilibrium work generating function (NEWGF) for a small system consisting of a massive Brownian particle connected to internal and external springs. The external work is provided to the system for a finite-time interval. The Jarzynski equality, obtained in this case directly from the NEWGF, is shown to be valid for the present model, in an exact way regardless of the rate of external work.

A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures

This paper addresses the development of a hybrid-mixed finite element formulation for the quasi-static geometrically exact analysis of three-dimensional framed structures with linear elastic behavior. The formulation is based on a modified principle of stationary total complementary energy, involving, as independent variables, the generalized vectors of stress-resultants and displacements and, in addition, a set of Lagrange multipliers defined on the element boundaries. The finite element discretization scheme adopted within the framework of the proposed formulation leads to numerical solutions that strongly satisfy the equilibrium differential equations in the elements, as well as the equilibrium boundary conditions. This formulation consists, therefore, in a true equilibrium formulation for large displacements and rotations in space. Furthermore, this formulation is objective, as it ensures invariance of the strain measures under superposed rigid body rotations, and is not affected by the so-called shear-locking phenomenon. Also, the proposed formulation produces numerical solutions which are independent of the path of deformation. To validate and assess the accuracy of the proposed formulation, some benchmark problems are analyzed and their solutions compared with those obtained using the standard two-node displacement/ rotation-based formulation.

Shell curvature as an initial deformation: A geometrically exact finite element approach

An alternative approach for the analysis of arbitrarily curved shells is developed in this paper based on the idea of initial deformations. By `alternative` we mean that neither differential geometry nor the concept of degeneration is invoked here to describe the shell surface. We begin with a flat reference configuration for the shell mid-surface, after which the initial (curved) geometry is mapped as a stress-free deformation from the plane position. The actual motion of the shell takes place only after this initial mapping. In contrast to classical works in the literature, this strategy enables the use of only orthogonal frames within the theory and therefore objects such as Christoffel symbols, the second fundamental form or three-dimensional degenerated solids do not enter the formulation. Furthermore, the issue of physical components of tensors does not appear. Another important aspect (but not exclusive of our scheme) is the possibility to describe exactly the initial geometry. The model is kinematically exact, encompasses finite strains in a totally consistent manner and is here discretized under the light of the finite element method (although implementation via mesh-free techniques is also possible). Assessment is made by means of several numerical simulations. Copyright (C) 2009 John Wiley & Sons, Ltd.