Search for designs of nonpolarizing interference systems

This research looks into methods for searching of designs of nonpolarizing interference systems, which provide a small discrepancy between spectral characteristics of the energy reflection/transmission coefficient for s- and p- polarizations. The layer thickness of these systems is a multiple of a quarter wavelength. Depending on the method used, the number of film-forming materials can vary from two to four. Analysis of spectral characteristics shows that in the spectral range of interest the discrepancy between the integral characteristics for s- and p-polarizations is less than 2%.

On the Intriguing Search for Good Permutations

The intriguing search for permutations that generate generalised van der Corput sequences with exceptionally small discrepancy forms an important part of the research work of Henri Faure. On the occasion of Henri’s 80th birthday we aim to survey (some of) his contributions over the last four decades which considerably improved our understanding of one-dimensional van der Corput sequences and inspired a lot of related work. We recall and compare the different approaches in the search for generalised van der Corput sequences with low discrepancy, i.e., using a single generating permutation versus using a sequence of permutations. Throughout, we collect, sharpen and extend open questions which all stem from the extensive work of Henri and his coworkers and which will hopefully inspire more work in the future.

Неполяризующие интерференционные системы, содержащие металлические слои

The structure of nonpolarizing interference systems containing metallic layers is considered. The technique of searching metal-dielectric interference systems, providing a small discrepancy between the spectral characteristics reflection (transmission) for s- and p- polarizations, is presented. The constructions developed on the basis of the presented method have a rather simple structure that ensures the ease of their implementation. Analysis of the spectral characteristics showed that in the spectral range (460–580) nm, the difference between the integral reflection coefficients for s- and p- polarizations does not exceed 1%.

Normal Numbers and the Normality Measure

In a paper published in this journal, Alon, Kohayakawa, Mauduit, Moreira and Rödl proved that the minimal possible value of the normality measure of an N-element binary sequence satisfies \begin{equation*} \biggl( \frac{1}{2} + o(1) \biggr) \log_2 N \leq \min_{E_N \in \{0,1\}^N} \mathcal{N}(E_N) \leq 3 N^{1/3} (\log N)^{2/3} \end{equation*} for sufficiently large N, and conjectured that the lower bound can be improved to some power of N. In this note it is observed that a construction of Levin of a normal number having small discrepancy gives a construction of a binary sequence EN with (EN) = O((log N)2), thus disproving the conjecture above.

Dynamic Stiffness Identification of Bolted Joints

The joint has a significant effect on the dynamic characteristic of the mechanism, and the identification of the stiffness of the joints has become a key problem. In this paper, a method is presented for identifying the dynamic characteristic of joints. An experiment is designed to test the dynamic parameter of the bolted joints specimen; the identification method, based on experiment, has a high accuracy result. By taking a specimen to experiment and identify the dynamic characteristic of joints, the relationship between the preload on the bolts and the joints stiffness is acquired. In order to validate the accuracy of the result, the FEM software is used to simulate. There are only a small discrepancy between the results of identification and simulation.

Arbitrage Profitability of Box Spreads in the KOSPI200 Options Market

This study explores the arbitrage profitability of box spread strategies to test the KOSPI200 options market efficiency. using minute-by-minute data for the December 2003 - June 2004 period. The sample consists of 39.445 and 38.318 observations for small discrepancy and large discrepancy in exercise prices. respectively. In the case of credit box spreads, there were 681 (2%) and 2.293 (6%) arbitrage observations for small and large discrepancies, while debit box spreads showed 831 (2%) and 3.098 (8%) observations for small and large discrepancies. In general, mean profit and median profit were different, and the arbitrage profit varied over time. The time to option expiration did not impact the arbitrage profit. Also, the arbitrage profit of box spreads was significantly higher on Fridays for large discrepancy, and it varied across weekdays except the case of small-discrepancy debit box spread. Both arbitrage opportunities and profits substantially decreased as execution time increased. Our overall results suggest that the KOSPI200 options market has been efficient.