Connections Between Single-Level and Bilevel Multiobjective Optimization

The relationship between bilevel optimization and multiobjective optimization has been studied by several authors, and there have been repeated attempts to establish a link between the two. We unify the results from the literature and generalize them for bilevel multiobjective optimization. We formulate sufficient conditions for an arbitrary binary relation to guarantee equality between the efficient set produced by the relation and the set of optimal solutions to a bilevel problem. In addition, we present specially structured bilevel multiobjective optimization problems motivated by real-life applications and an accompanying binary relation permitting their reduction to single-level multiobjective optimization problems.     

Reconstruction of Solar Spectral Surface UV Irradiances Using Radiative Transfer Simulations

UV radiation exerts several effects concerning life on Earth, and spectral information on the prevailing UV radiation conditions is needed in order to study each of these effects. In this paper, we present a method for reconstruction of solar spectral UV irradiances at the Earth's surface. The method, which is a further development of an earlier published method for reconstruction of erythemally weighted UV, relies on radiative transfer simulations, and takes as input (1) the effective cloud optical depth as inferred from pyranometer measurements of global radiation (300–3000 nm); (2) the total ozone column; (3) the surface albedo as estimated from measurements of snow depth; (4) the total water vapor column; and (5) the altitude of the location. Reconstructed daily cumulative spectral irradiances at Jokioinen and Sodankylä in Finland are, in general, in good agreement with measurements. The mean percentage difference, for instance, is mostly within ±8%, and the root mean square of the percentage difference is around 10% or below for wavelengths over 310 nm and daily minimum solar zenith angles (SZA) less than 70°. In this study, we used pseudospherical radiative transfer simulations, which were shown to improve the performance of our method under large SZA (low Sun).     

A Bombieri-Vinogradov type exponential sum result with applications

We prove a Bombieri-Vinogradov type result for linear exponential sums over primes. Then we apply it to show that, for any irrational α and some θ>0, there are infinitely many primes p such that p+2 has at most two prime factors and ‖αp+β‖<p−θ.     

Generalization of Matsui’s Algorithm 1 to linear hull for key-alternating block ciphers

We consider linear approximations of an iterated block cipher in the presence of several strong linear approximation trails. While the effect of such trails in Matsui’s Algorithm 2, also called the linear hull effect, has been previously studied by a number of authors, their effect on Matsui’s Algorithm 1 has not been investigated until now. The goal of this paper is to fill this gap and examine how to generalize Matsui’s Algorithm 1 to work also on linear hulls. We restrict to key-alternating ciphers and develop a mathematical framework for this kind of attacks. The complexity of the attack increases with the number of linear trails that have significant contribution to the correlation. We show how to reduce the number of trails and thus the complexity using related keys. Further, we illustrate our theory by experimental results on a reduced round version of the block cipher PRESENT.     

Langmuir-Blodgett films of hydrophobins HFBI and HFBII

Hydrophobins are small fungal proteins, which have remarkable surface-chemical properties. They self-assemble at hydrophobic/hydrophilic interfaces and work as adhesive agents and coatings. Sixteen layer Langmuir-Blodgett films of hydrophobins HFBI and HFBII from the fungus Trichoderma reesei were prepared and studied using grazing-incidence X-ray diffraction and reflectivity techniques. Both kind of films contain hexagonally ordered crystallites on the substrate with unit cell parameters of a = b = 54 Å (HFBI) and a = b = 55 Å (HFBII). The structure is similar to the structure of monolayer Langmuir-Blodgett films.     

Using a time-delay and integration camera at a non-zero viewing angle under vibration conditions

The use of a TDI camera is restricted to cases of viewing from the direction of the surface normal. Our previous work indicated that a TDI camera can be used with viewing angles up to 30° from the surface normal which extends the usability of TDI for visual inspection applications. The objective of this paper is to examine the use of a TDI camera at a non-zero viewing angle under vibration conditions. The effects caused by vibration of the surface to be viewed become critical when using a TDI camera at non-zero viewing angles. A method of approximating the TDI performance under vibration conditions was determined and evaluated experimentally. The resulting measurements support the approximating method developed here.     

On the exceptional set in Goldbach’s problem in short intervals

Let 1/5 < θ ≤ 1. We prove that there exists a positive constant δ such that the number of even integers in the interval [X, X + X ^θ] which are not a sum of two primes is 《 X ^θ−δ. The proof uses the circle method, a sieve method, exponential sum estimates and zero-density estimates for L-functions. Current address: Department of Mathematics, 20014 University of Turku, Finland. Author’s address: Department of Mathematics, University of London, Royal Holloway, Egham, Surrey TW20 0EX, UK