Some Growth and Distortion Theorems for Close-to-Convex Harmonic Functions in the Unit Disc

MSC 2010: 30C45, 30C55

Some Distortion Theorems for Starlike Harmonic Functions

MSC 2010: 30C55, 30C45

Applications of Subordination Principle to Log-Harmonic Mappings

MSC 2010: 30C45, 30C55

Expression of Potato virus Y cytoplasmic inclusion protein in tobacco results in disorganization of parenchyma cells, distortion of epidermal cells, and induces mitochondrial and chloroplast abnormalities, formation of membrane whorls and atypical lipid accumulation

Infection of plant cells by potyviruses induces the formation of cytoplasmic inclusions ranging in size from 200 to 1000 nm. To determine if the ability to form these ordered, insoluble structures is intrinsic to the potyviral cytoplasmic inclusion protein, we have expressed the cytoplasmic inclusion protein from Potato virus Y in tobacco under the control of the chrysanthemum ribulose-1,5-bisphosphate carboxylase small subunit promoter, a highly active, green tissue promoter. No cytoplasmic inclusions were observed in the leaves of transgenic tobacco using transmission electron microscopy, despite being able to clearly visualize these inclusions in Potato virus Y infected tobacco leaves under the same conditions. However, we did observe a wide range of tissue and sub-cellular abnormalities associated with the expression of the Potato virus Y cytoplasmic inclusion protein. These changes included the disruption of normal cell morphology and organization in leaves, mitochondrial and chloroplast internal reorganization, and the formation of atypical lipid accumulations. Despite these significant structural changes, however, transgenic tobacco plants were viable and the results are discussed in the context of potyviral cytoplasmic inclusion protein function.

Empirical measurement of the Enright phenomenon, a distortion of perceived driving speed

Purpose: In 1970, Enright observed a distortion of perceived driving speed, induced by monocular application of a neutral density (ND) filter. If a driver looks out of the right side of a vehicle with a filter over the right eye, the driver perceives a reduction of the vehicle’s apparent velocity, while applying a ND filter over the left eye increases the vehicle’s apparent velocity. The purpose of the current study was to provide the first empirical measurements of the Enright phenomenon. Methods: Ten experienced drivers were tested and drove an automatic sedan on a closed road circuit. Filters (0.9 ND) were placed over the left, right or both eyes during a driving run, in addition to a control condition with no filters in place. Subjects were asked to look out of the right side of the car and adjust their driving speed to either 40 km/h or 60 km/h. Results: Without a filter or with both eyes filtered subjects showed good estimation of speed when asked to travel at 60 km/h but travelled a mean of 12 to 14 km/h faster than the requested 40 km/h. Subjects travelled faster than these baselines by a mean of 7 to 9 km/h (p < 0.001) with the filter over their right eye, and 3 to 5 km/h slower with the filter over their left eye (p < 0.05). Conclusions: The Enright phenomenon causes significant and measurable distortions of perceived driving speed under realworld driving conditions.

Practical improvements to simultaneous computation of multi-view geometry and radial lens distortion

This paper discusses practical issues related to the use of the division model for lens distortion in multi-view geometry computation. A data normalisation strategy is presented, which has been absent from previous discussions on the topic. The convergence properties of the Rectangular Quadric Eigenvalue Problem solution for computing division model distortion are examined. It is shown that the existing method can require more than 1000 iterations when dealing with severe distortion. A method is presented for accelerating convergence to less than 10 iterations for any amount of distortion. The new method is shown to produce equivalent or better results than the existing method with up to two orders of magnitude reduction in iterations. Through detailed simulation it is found that the number of data points used to compute geometry and lens distortion has a strong influence on convergence speed and solution accuracy. It is recommended that more than the minimal number of data points be used when computing geometry using a robust estimator such as RANSAC. Adding two to four extra samples improves the convergence rate and accuracy sufficiently to compensate for the increased number of samples required by the RANSAC process.

Application of a new discreet form of Gauss’ theorem for measuring volume

Volume measurements are useful in many branches of science and medicine. They are usually accomplished by acquiring a sequence of cross sectional images through the object using an appropriate scanning modality, for example x-ray computed tomography (CT), magnetic resonance (MR) or ultrasound (US). In the cases of CT and MR, a dividing cubes algorithm can be used to describe the surface as a triangle mesh. However, such algorithms are not suitable for US data, especially when the image sequence is multiplanar (as it usually is). This problem may be overcome by manually tracing regions of interest (ROIs) on the registered multiplanar images and connecting the points into a triangular mesh. In this paper we describe and evaluate a new discreet form of Gauss’ theorem which enables the calculation of the volume of any enclosed surface described by a triangular mesh. The volume is calculated by summing the vector product of the centroid, area and normal of each surface triangle. The algorithm was tested on computer-generated objects, US-scanned balloons, livers and kidneys and CT-scanned clay rocks. The results, expressed as the mean percentage difference ± one standard deviation were 1.2 ± 2.3, 5.5 ± 4.7, 3.0 ± 3.2 and −1.2 ± 3.2% for balloons, livers, kidneys and rocks respectively. The results compare favourably with other volume estimation methods such as planimetry and tetrahedral decomposition.

Parents’ experience of time distortion following diagnosis of a serious or lethal fetal anomaly

PURPOSE: To explore the experience of couples who continued pregnancy following a diagnosis of serious or lethal fetal anomaly. STUDY DESIGN: Thirty-one male and female participants were recruited from a high-risk maternal–fetal medicine clinic in Washington State. Data were collected using in-depth interviews during pregnancy and after the birth of their baby. Transcribed interviews were thematically analyzed through the phenomenological lens of Merleau-Ponty. FINDINGS: Participants described how time became reconfigured and reconstituted as they tried to compress a lifetime of love for their future child into a limited period. Participants’ concepts of time became distorted and were related to their perceptual lived experience rather than the schedule-filled,regimented, linear clock time that governed the health professionals. CONCLUSION: Living in distorted time may be a mechanism parents use to cope with overwhelming and disorienting feelings when their unborn baby is diagnosed with a fetal anomaly.

Exploring the fundamental theorem of arithmetic in excel 2007

This paper discusses how fundamentals of number theory, such as unique prime factorization and greatest common divisor can be made accessible to secondary school students through spreadsheets. In addition, the three basic multiplicative functions of number theory are defined and illustrated through a spreadsheet environment. Primes are defined simply as those natural numbers with just two divisors. One focus of the paper is to show the ease with which spreadsheets can be used to introduce students to some basics of elementary number theory. Complete instructions are given to build a spreadsheet to enable the user to input a positive integer, either with a slider or manually, and see the prime decomposition. The spreadsheet environment allows students to observe patterns, gain structural insight, form and test conjectures, and solve problems in elementary number theory.

The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

The validity of the Adler-Bardeen theorem in the supersymmetric U(1) gauge model

Using the dimensional reduction regularization scheme, we show that radiative corrections to the anomaly of the axial current, which is coupled to the gauge field, are absent in a supersymmetric U(1) gauge model for both 't Hooft-Veltman and Bardeen prescriptions for γ5. We also discuss the results with reference to conventional dimensional regularization. This result has significant implications with respect to the renormalizability of supersymmetric models.

Transient state work fluctuation theorem for a classical harmonic oscillator linearly coupled to a harmonic bath

Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.