Probabilities of the deviation of the sample mean from its median

One investigates the asymptotic behavior of as n, where is the sample mean constructed from the independent, identically distributed random variables X₁...,X_n, >0. One considers the powerlike and the exponential rates of decrease of this probability.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 130–136, 1983.     

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.     

Finite-temperature phase diagram of a polarized fermi gas in an optical lattice

We present phase diagrams for a polarized Fermi gas in an optical lattice as a function of temperature, polarization, and lattice filling factor. We consider the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma or breached pair, and BCS phases, and the normal state and phase separation. We show that the FFLO phase appears in a considerable portion of the phase diagram. The diagrams have two critical points of different nature. We show how various phases leave clear signatures to momentum distributions of the atoms which can be observed after time of flight expansion.     

Creation of a monopole in a spinor condensate

We propose a method to create a monopole structure in a multicomponent condensate by applying the basic methods used to create vortices and solitons experimentally in single-component condensates. We also show that by using a two-component structure for a monopole, we can avoid many problems related to the previously suggested three-component monopole. We discuss the observation and dynamics of such a monopole structure, and note that the dynamics of the two-component monopole differs from the dynamics of the three-component monopole.     

Quasi-two-dimensional superfluid fermionic gases

We study a quasi-two-dimensional superfluid Fermi gas where the confinement in the third direction is due to a strong harmonic trapping. We investigate the behavior of such a system when the chemical potential is varied and find strong modifications of the superfluid properties due to the discrete harmonic oscillator states. We show that such quasi-two-dimensional behavior can be created and observed with current experimental capabilities.     

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.     

Boundedness of a class of bi-parameter square functions in the upper half-space

We consider a class of bi-parameter kernels and related square functions in the upper half-space, and give an efficient proof of a boundedness criterion for them. The proof uses modern probabilistic averaging methods and is based on controlling double Whitney averages over good cubes.     

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.     

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