Calculation of light delay for coupled microrings by FDTD technique and Pade approximation

The Pade approximation with Baker's algorithm is compared with the least-squares Prony method and the generalized pencil-of-functions (GPOF) method for calculating mode frequencies and mode Q factors for coupled optical microdisks by FDTD technique. Comparisons of intensity spectra and the corresponding mode frequencies and Q factors show that the Pade approximation can yield more stable results than the Prony and the GPOF methods, especially the intensity spectrum. The results of the Prony method and the GPOF method are greatly influenced by the selected number of resonant modes, which need to be optimized during the data processing, in addition to the length of the time response signal. Furthermore, the Pade approximation is applied to calculate light delay for embedded microring resonators from complex transmission spectra obtained by the Pade approximation from a FDTD output. The Prony and the GPOF methods cannot be applied to calculate the transmission spectra, because the transmission signal obtained by the FDTD simulation cannot be expressed as a sum of damped complex exponentials. (C) 2009 Optical Society of America

Bieberbach's Conjecture, the de Branges and Weinstein Functions and the Askey-Gasper Inequality

The Bieberbach conjecture about the coefficients of univalent functions of the unit disk was formulated by Ludwig Bieberbach in 1916 [Bieberbach1916]. The conjecture states that the coefficients of univalent functions are majorized by those of the Koebe function which maps the unit disk onto a radially slit plane. The Bieberbach conjecture was quite a difficult problem, and it was surprisingly proved by Louis de Branges in 1984 [deBranges1985] when some experts were rather trying to disprove it. It turned out that an inequality of Askey and Gasper [AskeyGasper1976] about certain hypergeometric functions played a crucial role in de Branges' proof. In this article I describe the historical development of the conjecture and the main ideas that led to the proof. The proof of Lenard Weinstein (1991) [Weinstein1991] follows, and it is shown how the two proofs are interrelated. Both proofs depend on polynomial systems that are directly related with the Koebe function. At this point algorithms of computer algebra come into the play, and computer demonstrations are given that show how important parts of the proofs can be automated.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

Thermodynamic functions of element 105 in neutral and ionized states

The basic thermodynamic functions, the entropy, free energy, and enthalpy, for element 105 (hahnium) in electronic configurations d^3 s^2, d^3 sp, and d^4s^1 and for its +5 ionized state (5f^14) have been calculated as a function of temperature. The data are based on the results of the calculations of the corresponding electronic states of element 105 using the multiconfiguration Dirac-Fock method.

Histone H1 overexpressed to high level in tobacco affects certain developmental programs but has limited effect on basal cellular functions.

Histone H1, a major structural component of chromatin fiber, is believed to act as a general repressor of transcription. To investigate in vivo the role of this protein in transcription regulation during development of a multicellular organism, we made transgenic tobacco plants that overexpress the gene for Arabidopsis histone H1. In all plants that overexpressed H1 the total H1-to-DNA ratio in chromatin increased 2.3-2.8 times compared with the physiological level. This was accompanied by 50-100% decrease of native tobacco H1. The phenotypic changes in H1-overexpressing plants ranged from mild to severe perturbations in morphological appearance and flowering. No correlation was observed between the extent of phenotypic change and the variation in the amount of overexpressed H1 or the presence or absence of the native tobacco H1. However, the severe phenotypic changes were correlated with early occurrence during plant growth of cells with abnormally heterochromatinized nuclei. Such cells occurred considerably later in plants with milder changes. Surprisingly, the ability of cells with highly heterochromatinized nuclei to fulfill basic physiological functions, including differentiation, was not markedly hampered. The results support the suggestion that chromatin structural changes dependent on H1 stoichiometry and on the profile of major H1 variants have limited regulatory effect on the activity of genes that control basal cellular functions. However, the H1-mediated chromatin changes can be of much greater importance for the regulation of genes involved in control of specific developmental programs.

Numerical Results for the Generalized Mittag-Leffler Function

Mathematics Subject Classification: 33E12, 33FXX PACS (Physics Abstracts Classification Scheme): 02.30.Gp, 02.60.Gf

On a Generalization of a Theorem due to Larcombe on the Sum of a 3F2 Series

MSC 2010: 33C20

On Some Generalizations of Classical Integral Transforms

MSC 2010: 44A15, 44A20, 33C60

New Coefficient Conditions for Functions Starlike with Respect to Symmetric Points

2000 Mathematics Subject Classification: Primary 30C45, secondary 30C80.

Measuring the managerial benefits of tax compliance : a fresh approach

Managerial benefits of tax compliance have been identified by many authors in the tax compliance costs literature; they have however often been ignored when measuring the net effect of tax compliance on business taxpayers because it was believed that the measurement of such benefits was impossible or difficult. This paper first discusses the theoretical issues surrounding the valuation of managerial benefits, including the related tax/ accounting costs overlap problem; it then proposes a fresh approach for measuring managerial benefits. The proposed measurement model incorporates a subjective evaluation of useful accounting information by owner‑managers and objective measurements of accounting costs. Two main components of managerial benefits are identified: the incremental value of managerial accounting information and the savings on reporting costs. A study of small businesses conducted in late 2006, compared accounting practices between tax complying entities (TCEs) and tax compliance free entities (TFEs) and investigated how accounting information was valued by owner-managers in TCEs. The research adopted a mixed methodological design including a major quantitative phase followed by a minor qualitative phase. The results show that while a vast majority of TFEs maintained basic accounting functions, record keeping requirements imposed by tax compliance led to the implementation of more sophisticated accounting systems in TCEs. It was also found that TCE owner-managers assigned a relatively significant value to the managerial accounting information that is generated as a result of record keeping imposed by tax compliance, suggesting that substantial managerial benefits might be derived.

Teaching pharmacy students how to manage effectively in a highly competitive environment

Aims To evaluate if a revamped business management course for 4th year undergraduate pharmacy students had achieved the course aims of not only improving pharmacy students’ perceived understanding of pharmacy business management topics but also increasing their confidence in their business management knowledge and skills. Background Student feedback from previous years had indicated that the cohort had struggled to translate theoretical business management concepts learned in the classroom into practice in the workplace. To address this problem the course has been changed to a ‘flipped classroom’ format with face-to-face time focusing on case-based scenarios and interactive classroom discussion with some role plays. Method Both course assessment throughout the semester and a student survey informed the evaluation process. Results After completing the course, students felt they had increased their knowledge of business management concepts but many indicated that they lacked the confidence to undertake basic management functions. Conclusions Further course restructuring is required with a greater focus on skills development.

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.

Biodiversity and ecological assessments of Indian sacred groves

Sacred groves are patches of forests preserved for their spiritual and religious significance. The practice gained relevance with the spread of agriculture that caused large-scale deforestation affecting biodiversity and watersheds. Sacred groves may lose their prominence nowadays, but are still relevant in Indian rural landscapes inhabited by traditional communities. The recent rise of interest in this tradition encouraged scientific study that despite its pan-Indian distribution, focused on India's northeast, Western Ghats and east coast either for their global/regional importance or unique ecosystems. Most studies focused on flora, mainly angiosperms, and the faunal studies concentrated on vertebrates while lower life forms were grossly neglected. Studies on ecosystem functioning are few although observations are available. Most studies attributed watershed protection values to sacred groves but hardly highlighted hydrological process or water yield in comparison with other land use types. The grove studies require diversification from a stereotyped path and must move towards creating credible scientific foundations for conservation. Documentation should continue in unexplored areas but more work is needed on basic ecological functions and ecosystem dynamics to strengthen planning for scientifically sound sacred grove management.

Interactions of Penny-Shaped Cracks in Three-Dimensional Solids

The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is developed in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.

Dynamic interaction of an elastic container with fluid

The vibration analysis of an elastic container with partially filled fluid was investigated in this paper. The container is made of a thin cylinder and two circular plates at the ends. The axis of the cylinder is in the horizontal direction. It is difficult to solve this problem because the complex system is not axially symmetric. The equations of motion for this system were derived. An incompressible and ideal fluid model is used in the present work. Solutions of the equations were obtained by the generalized variational method. The solution was expressed in a series of normalized generalized Fourier's functions. This series converged rapidly, and so its approximate solution was obtained with high precision. The agreement of the calculated values with the experimental result is good. It should be mentioned that with our method, the computer time is less than that with the finite-element method.