On the Logarithmic Asymptotics of the Sixth Painleve' Equation (Summer 2007)

We study the solutions of the sixth Painlev\'e equation with a logarithmic asymptotic behavior at a critical point. We compute the monodromy group associated to the solutions by the method of monodromy preserving deformations and we characterize the asymptotic behavior in terms of the monodromy itself.Comment: LaTeX with 8 figure

Nonlinear Differential Equations Satisfied by Certain Classical Modular Forms

A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, which yields a single nonlinear third-order equation, called a generalized Chazy equation. As byproducts, a table of divisor function and theta identities is generated by means of q-expansions, and a transformation law under \Gamma_0(4) for the second complete elliptic integral is derived. More generally, it is shown how Picard-Fuchs equations of triangle subgroups of PSL(2,R) which are hypergeometric equations, yield systems of nonlinear equations for weight-1 forms, and generalized Chazy equations. Each triangle group commensurable with \Gamma(1) is treated.Comment: 40 pages, final version, accepted by Manuscripta Mathematic

Can i have a second child? dilemmas of mothers of children with pervasive developmental disorder: a qualitative study

<p>Abstract</p> <p>Background</p> <p>Pervasive developmental disorder (PDD) has an uncertain etiology, no method of treatment, and results in communication deficiencies and other behavioral problems. As the reported recurrence risk is 5%-10% and there are no methods of either prevention or prenatal testing, mothers of PDD children may face unique challenges when contemplating second pregnancies. The purpose of this study was to explore the mothers' lived experiences of second child-related decision-making after the birth of a child with PDD.</p> <p>Methods</p> <p>The participants for this study were restricted to mothers living within the greater Tokyo metropolitan area who had given birth to a first child with PDD within the past 18 years. The ten participants were encouraged to describe their experiences of second-child related decision-making after the birth of a child with PDD on the basis of semi-structured interviews. Data analysis was performed by using Interpretive Phenomenological Analysis (IPA), which is concerned with understanding what the participant thinks or believes about the topic under discussion.</p> <p>Results</p> <p>We identified two superordinate themes. The first was balancing hopes and fears, in which hope was the potential joy to be gained by the birth of a new child without PDD and fears were characterized as uncertainty of PDD and perception of recurrence risk, burden on later-born children, and negative effects on a child with PDD.</p> <p>The second superordinate theme was assessing the manageability of the situation, which was affected by factors as diverse as severity of PDD, relationship between mother and father, and social support and acceptance for PDD. Our 10 participants suffered from extreme psychological conflict, and lack of social support and acceptance for PDD created numerous practical difficulties in having second children.</p> <p>Conclusions</p> <p>Our participants faced various difficulties when considering second pregnancies after the birth of children with PDD in the Japanese society. As lack of social support and acceptance for PDD also played a large role in second child-related decision-making, creating a social environment that more fully accepts those disabled and providing flexible support systems for families of children with PDD are crucial.</p

THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS VIBRATIONAL RESPONSE ANALYSIS OF MISTUNED BLADED DISK SYSTEM OF GROUPED BLADES

ABSTRACT For the purpose of the efficient analysis of a mistuned Waded disk system, a new analysis method which applies the substructure synthesis method and the modal analysis method is proposed. Using the proposed method, the vibrational characteristics of the grouped blades structure are studied. From the results, it is found that the grouped blades structure is very sensitive to the mistuning. It is also found that the mixed grouped blades structure (a bladed disk system consisting of some different types of grouped blades relating to the number of blades contained) has an undesirable effect on the forced response. Moreover, by comparing the vibrational characteristics of the integral shroud blades (ISB) structure with those of the grouped blades structure, it is clarified that the reliability of the ISB structure is superior to other sauctures also from the viewpoint of the mistuning. INTRODUCTION Some Waded disks of steam turbines consist of grouped blades in which several blades are connected into one group by elements such as a shroud or stub. When carrying out a vibration response analysis for such a bladed disk of grouped blades, the effect of the disk is usually neglected under the assumption that the stiffness of the disk is sufficiently larger than that of the blade, in order to avoid the complicated calculation. And even if taking the disk into account, all blades on a disk are assumed to be identical (tuned system). In a real bladed disk, however, the vibration of grouped blades is coupled with each other through the disk and furthermore, the vibrational characteristics of blades on a disk vary slightly due to manufacturing and material tolerances (mistuned system). Therefore, in the forced response of a mistuned system by a harmonic excitation, Eq.(1), which is a conditional equation of resonance for a tuned system (e.g.. Wagner and Griffm 1996), is no longer effective because of the split of natural frequencies or the distortion of vibrational modes, and a difference in the amplitudes among individual blades appears, causing certain blades to respond remarkably. Moreover, blades become responsive over a wider excitation frequency range than the tuned system

Matching procedure for the sixth Painleve' equation

The matching procedure is a constructive way of using the isomonodromy deformation method, to obtain the critical behavior of Painleve' VI transcendents and solve the connection problem. This procedure yields two and one parameter families of solutions, including trigonometric and logarithmic behaviors, and three classes of solutions with Taylor expansion at a critical point

Velocity encoded cardiovascular magnetic resonance to assess left atrial appendage emptying

<p>Abstract</p> <p>Background</p> <p>The presence of impaired left atrial appendage (LAA) function identifies patients who are prone to thrombus formation in the LAA and therefore being at high risk for subsequent cardioembolic stroke. LAA function is typically assessed by measurements of LAA emptying velocities using transesophageal echocardiography (TEE) in clinical routine. This study aimed at evaluating the feasibility of assessing LAA emptying by velocity encoded (VENC) cardiovascular magnetic resonance (CMR).</p> <p>Methods</p> <p>This study included 30 patients with sinus rhythm (n = 18) or atrial fibrillation (n = 12). VENC-CMR velocity measurements were performed perpendicular to the orifice of the LAA. Peak velocities were measured of passive diastolic LAA emptying (e-wave) in all patients. Peak velocities of active, late-diastolic LAA emptying (a-wave) were assessed in patients with sinus rhythm. Correlation and agreement was analyzed between VENC-CMR and TEE measurements of e- and a-wave peak velocities.</p> <p>Results</p> <p>A significant correlation and good agreement was found between VENC-CMR and TEE measurements of maximal e-wave velocities (r = 0.61, P < 0.001; mean difference 0 ± 10 cm/s). The a-wave was detectable by VENC-CMR in all patients with sinus rhythm. Correlation was also significant for measurements of peak a-wave velocities between VENC-CMR and TEE (r = 0.71, P < 0.001). There was no significant correlation of LAA emptying velocities with clinical characteristics and only a modest negative correlation of passive LAA emptying with LA function.</p> <p>Conclusions</p> <p>The assessment of active and passive LAA emptying by VENC-CMR is feasible. Further evaluation is required of potential future clinical applications such as risk stratification for cardioembolic stroke.</p