On the construction of new bent functions from the max-weight and min-weight functions of old bent functions

Given a bent function f (x) of n variables, its max-weight and min-weight functions are introduced as the Boolean functions f + (x) and f − (x) whose supports are the sets {a ∈ Fn2 | w( f ⊕la) = 2n−1+2 n 2 −1} and {a ∈ Fn2 | w( f ⊕la) = 2n−1−2 n 2 −1} respectively, where w( f ⊕ la) denotes the Hamming weight of the Boolean function f (x) ⊕ la(x) and la(x) is the linear function defined by a ∈ Fn2 . f + (x) and f − (x) are proved to be bent functions. Furthermore, combining the 4 minterms of 2 variables with the max-weight or min-weight functions of a 4-tuple ( f0(x), f1(x), f2(x), f3(x)) of bent functions of n variables such that f0(x) ⊕ f1(x) ⊕ f2(x) ⊕ f3(x) = 1, a bent function of n + 2 variables is obtained. A family of 4-tuples of bent functions satisfying the above condition is introduced, and finally, the number of bent functions we can construct using the method introduced in this paper are obtained. Also, our construction is compared with other constructions of bent functions.

Ordinal Cost Sharing.

We ask how the three known mechanisms for solving cost sharing problems with homogeneous cost functions - the value, the proportional, and the serial mechanisms - should be extended to arbitrary problem. We propose the Ordinality axiom, which requires that cost shares be invariante under all transactions preserving the nature of a cost sharing problem.

equivalence of almost bent and almost perfect nonlinear functions and their generalizations

Vectorial Boolean function, almost bent, almost perfect nonlinear, affine equivalence, CCZ-equivalence

An approximate Hahn–Banach theorem for positively homogeneous functions

This note provides an approximate version of the Hahn–Banach theorem for non-necessarily convex extended-real valued positively homogeneous functions of degree one. Given p : X → R∪{+∞} such a function defined on the real vector space X, and a linear function defined on a subspace V of X and dominated by p (i.e. (x) ≤ p(x) for all x ∈ V), we say that can approximately be p-extended to X, if is the pointwise limit of a net of linear functions on V, every one of which can be extended to a linear function defined on X and dominated by p. The main result of this note proves that can approximately be p-extended to X if and only if is dominated by p∗∗, the pointwise supremum over the family of all the linear functions on X which are dominated by p.

On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions

AMS Subject Classification 2010: 41A25, 41A27, 41A35, 41A36, 41A40, 42Al6, 42A85.

Melting and freezing of spherical bismuth nanoparticles confined in a homogeneous sodium borate glass

The melting temperature and the crystallization temperature of Bi nanoclusters confined in a sodium borate glass were experimentally determined as functions of the cluster radius. The results indicate that, on cooling, liquid Bi nanodroplets exhibit a strong undercooling effect for a wide range of radii. The difference between the melting temperature and the freezing temperature decreases for decreasing radius and vanishes for Bi nanoparticles with a critical radius R = 1.9 nm. The magnitude of the variation in density across the melting and freezing transitions for Bi nanoparticles with R = 2 nm is 40% smaller than for bulk Bi. These experimental results support a basic core-shell model for the structure of Bi nanocrystals consisting of a central crystalline volume surrounded by a structurally disordered shell. The volume fraction of the crystalline core decreases for decreasing nanoparticle radius and vanishes for R = 1.9 nm. Thus, on cooling, the liquid nanodroplets with R < 1.9 nm preserve, across the liquid-to-solid transformation, their homogeneous and disordered structure without crystalline core.

Bias-corrected Pearson estimating functions for Taylor`s power law applied to benthic macrofauna data

Estimation of Taylor`s power law for species abundance data may be performed by linear regression of the log empirical variances on the log means, but this method suffers from a problem of bias for sparse data. We show that the bias may be reduced by using a bias-corrected Pearson estimating function. Furthermore, we investigate a more general regression model allowing for site-specific covariates. This method may be efficiently implemented using a Newton scoring algorithm, with standard errors calculated from the inverse Godambe information matrix. The method is applied to a set of biomass data for benthic macrofauna from two Danish estuaries. (C) 2011 Elsevier B.V. All rights reserved.

A method for the design of MRI radiofrequency coils based on triangular and pulse basis functions

This paper presents a numerical technique for the design of an RF coil for asymmetric magnetic resonance imaging (MRI) systems. The formulation is based on an inverse approach where the cylindrical surface currents are expressed in terms of a combination of sub-domain basis functions: triangular and pulse functions. With the homogeneous transverse magnetic field specified in a spherical region, a functional method is applied to obtain the unknown current coefficients. The current distribution is then transformed to a conductor pattern by use of a stream function technique. Preliminary MR images acquired using a prototype RF coil are presented and validate the design method. (C) 2002 Elsevier Science B.V. All rights reserved.

Stochastic generation of homogeneous isotropic turbulence with well-defined-spectra

A precise and simple computational model to generate well-behaved two-dimensional turbulent flows is presented. The whole approach rests on the use of stochastic differential equations and is general enough to reproduce a variety of energy spectra and spatiotemporal correlation functions. Analytical expressions for both the continuous and the discrete versions, together with simulation algorithms, are derived. Results for two relevant spectra, covering distinct ranges of wave numbers, are given.

Stochastic generation of homogeneous isotropic turbulence with well-defined-spectra

A precise and simple computational model to generate well-behaved two-dimensional turbulent flows is presented. The whole approach rests on the use of stochastic differential equations and is general enough to reproduce a variety of energy spectra and spatiotemporal correlation functions. Analytical expressions for both the continuous and the discrete versions, together with simulation algorithms, are derived. Results for two relevant spectra, covering distinct ranges of wave numbers, are given.

The Bonenblust-Hille inequality for homogeneous polynomials is hypercontractive

The Bohnenblust-Hille inequality says that the $\ell^{\frac{2m}{m+1}}$ -norm of the coefficients of an $m$-homogeneous polynomial $P$ on $\Bbb{C}^n$ is bounded by $\| P \|_\infty$ times a constant independent of $n$, where $\|\cdot \|_\infty$ denotes the supremum norm on the polydisc $\mathbb{D}^n$. The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be $C^m$ for some $C>1$. Combining this improved version of the Bohnenblust-Hille inequality with other results, we obtain the following: The Bohr radius for the polydisc $\mathbb{D}^n$ behaves asymptotically as $\sqrt{(\log n)/n}$ modulo a factor bounded away from 0 and infinity, and the Sidon constant for the set of frequencies $\bigl\{ \log n: n \text{a positive integer} \le N\bigr\}$ is $\sqrt{N}\exp\{(-1/\sqrt{2}+o(1))\sqrt{\log N\log\log N}\}$.

HouSI: Heuristic for delimitation of housing submarkets and price homogeneous areas

This paper seeks to address the problem of the empirical identification of housing market segmentation,once we assume that submarkets exist. The typical difficulty in identifying housing submarkets when dealing with many locations is the vast number of potential solutions and, in such cases, the use of the Chow test for hedonic functions is not a practical solution. Here, we solve this problem by undertaking an identification process with a heuristic for spatially constrained clustering, the"Housing Submarket Identifier" (HouSI). The solution is applied to the housing market in the city of Barcelona (Spain), where we estimate a hedonic model for fifty thousand dwellings aggregated into ten groups. In order to determine the utility of the procedure we seek to verify whether the final solution provided by the heuristic is comparable with the division of the city into ten administrative districts.

Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.

Using non-homogeneous Poisson models with multiple change-points to estimate the number of ozone exceedances in Mexico City

In this paper, we consider some non-homogeneous Poisson models to estimate the probability that an air quality standard is exceeded a given number of times in a time interval of interest. We assume that the number of exceedances occurs according to a non-homogeneous Poisson process (NHPP). This Poisson process has rate function lambda(t), t >= 0, which depends on some parameters that must be estimated. We take into account two cases of rate functions: the Weibull and the Goel-Okumoto. We consider models with and without change-points. When the presence of change-points is assumed, we may have the presence of either one, two or three change-points, depending of the data set. The parameters of the rate functions are estimated using a Gibbs sampling algorithm. Results are applied to ozone data provided by the Mexico City monitoring network. In a first instance, we assume that there are no change-points present. Depending on the adjustment of the model, we assume the presence of either one, two or three change-points. Copyright (C) 2009 John Wiley & Sons, Ltd.

Estimating the number of ozone peaks in Mexico City using a non-homogeneous Poisson model

In this paper, we consider the problem of estimating the number of times an air quality standard is exceeded in a given period of time. A non-homogeneous Poisson model is proposed to analyse this issue. The rate at which the Poisson events occur is given by a rate function lambda(t), t >= 0. This rate function also depends on some parameters that need to be estimated. Two forms of lambda(t), t >= 0 are considered. One of them is of the Weibull form and the other is of the exponentiated-Weibull form. The parameters estimation is made using a Bayesian formulation based on the Gibbs sampling algorithm. The assignation of the prior distributions for the parameters is made in two stages. In the first stage, non-informative prior distributions are considered. Using the information provided by the first stage, more informative prior distributions are used in the second one. The theoretical development is applied to data provided by the monitoring network of Mexico City. The rate function that best fit the data varies according to the region of the city and/or threshold that is considered. In some cases the best fit is the Weibull form and in other cases the best option is the exponentiated-Weibull. Copyright (C) 2007 John Wiley & Sons, Ltd.