a comparison of fictitious domain methods appropriate for spectral hp element discretisations abstract the fictitious domain finite cell and fat boundary method which are commonly adopted for fluid structure interaction fsi problems have been considered and implemented in a spectral hp element code for a 1d test problem the finite cell and fat boundary method are extended for the general case of a deformable solid in a fluid and analysed furthermore a new implicit variation of the fat boundary method is proposed the 1d framework allows for a clear and detailed analysis of the different approaches and to highlight the similarities and differences between the methods exponential p convergence which is typical for smooth solutions discretised with spectral hp elements is demonstrated for all methods except the classic fictitious domain formulation this overview can be considered as a starting point to study the capability advantages and disadvantages of these methods for fluid structure interaction problems in a more realistic setting and in higher dimensions

elastic scatterer interaction via generalized born series and far field approximations methods for solving elastic wave scattering problems in three dimensions 3d with multiple inhomogeneities are discussed a problem of homogeneous isotropic elastic defects in an otherwise homogeneous isotropic elastic full space is formulated as a boundary integral equation this equation is solved by discretizing the surface of each scatterer in a fashion known as the boundary element method the resulting matrix equation may be solved in a fully implicit manner but an implicit iterative method is more efficient with this hybrid method a portion of the nonsingular integral operator is expanded in a neumann series terms in this series correspond physically to nth order born approximations of the scatterers interaction the relative advantage of this hybrid scheme depends on the number of iterations required except for closely situated strong scatterers terms beyond the first few orders are not significant and thus the method can be quite advantageous when the separation is large another appro

a unified boundary element method for the analysis of sound and shell like structure interactions i formulation and verification a unified boundary element method bem is developed in this paper to model both the exterior acoustic field and the elastic shell like structure in a coupled analysis the conventional boundary integral equation bie for three dimensional 3d elastodynamics is applied to thin shell like structures which can have arbitrary shapes and small thicknesses the nearly singular integrals existing in the bie when applied to thin bodies are transformed to nonsingular line integrals and are evaluated accurately and efficiently for the exterior 3d acoustic domain the burton and miller composite bie formulation is employed to overcome the fictitious eigenfrequency difficulty fed and the thin shape breakdown tsb conforming c0 quadratic elements are employed in the discretization of the two sets of bies the developed bie formulations are valid for both radiation and scattering problems and for all wave numbers numerical examples using spherical and cylindrical shells including nonuniform thickness and nond

new constructions of resilient functions with strictly almost optimal nonlinearity via non overlap spectra functions abstract the design of n variable t resilient functions with strictly almost optimal sao nonlinearity 2 n 1 2 n 2 n even appears to be a rather difficult task the known construction methods commonly use a rather large number exactly i t 1 n 2 n 2 i of affine subfunctions in n 2 variables which can induce some algebraic weaknesses making these functions susceptible to certain types of guess and determine cryptanalysis and dynamic cube attacks in this paper the concept of non overlap spectra functions is introduced which essentially generalizes the idea of disjoint spectra functions on different variable spaces two general methods to obtain a large set of non overlap spectra functions are given and a new framework for designing infinite classes of resilient functions with sao nonlinearity is developed based on these unlike previous construction methods our approach employs only a few n 2 variable affine subfunctions in the design resulting in a more favourable algebraic structure it is shown that these new resilient sao functions properly include all the existing classes of resilient sao functions as a subclass moreover it is shown that the new class provides a better resistance against fast algebraic attacks than the known functions with sao nonlinearity and in addition these functions are more robust to guess and determine cryptanalysis and dynamic cube attacks

results on highly nonlinear boolean functions with provably good immunity to fast algebraic attacks abstract in the last decade algebraic and fast algebraic attacks are regarded as the most successful attacks on lfsr based stream ciphers since the notion of algebraic immunity was introduced the properties and constructions of boolean functions with maximum algebraic immunity have been researched in a large number of papers however there are few results with respect to boolean functions with provably good immunity against fast algebraic attacks in previous literatures only carlet feng function was proven to have good immunity to fast algebraic attacks in this paper we first study a large family of highly nonlinear boolean functions in terms of the immunity to fast algebraic attacks which includes the functions of tu deng the functions of tang et al and the functions of jin et al based on a sufficient and necessary condition for measuring the immunity of boolean functions against fast algebraic attacks using bivariate polynomial representation we propose an efficient method for estimating the immunity of the functions of such family then we prove that a family of 2 k variable boolean functions including the function recently constructed by tang et al are almost perfect algebraic immune for any integer k 3 more exactly they achieve optimal algebraic immunity and almost perfect immunity to fast algebraic attacks the functions of such family are balanced and have optimal algebraic degree besides we prove a lower bound on their nonlinearity based on the work of tang et al which is better than that of carlet feng function it is also checked for 3 k 9 that the exact nonlinearity of such functions is very good which is slightly smaller than that of carlet feng function and some functions of this family even have a slightly larger nonlinearity than tang s et al function to sum up among the known functions with provably good immunity against fast algebraic attacks the functions of this family make a trade off between the exact value and the lower bound of nonlinearity

acoustic scattering by a modified werner method a modified integral werner method is used to calculate pressure scattered by an axisymmetric body immersed in a perfect and compressible fluid subject to a harmonic acoustic field this integral representation is built as the sum of a potential of a simple layer and a potential of volume it is equivalent to the exterior helmholtz problem with neumann boundary condition for all real wave numbers of the incident acoustic field for elastic structure scattering problems the modified werner method is coupled with an elastodynamic integral formulation in order to account for the elastic contribution of the displacement field at the fluid structure interface the resulting system of integral equations is solved by the collocation method with a quadratic interpolation the introduction of a weighting factor in the modified werner method decreases the number of volume elements necessary for a good convergence of results this approach becomes very competitive when it is compared with other integral methods that are valid for all wave numbers a numerical comparison with an experiment on a tungsten carbide end capped cylinder allows a glimpse of the interesting possibilities for using the coupling of the modified werner method and the integral elastodynamic equation used in this research

on the construction of cryptographically significant boolean functions using objects in projective geometry spaces recently several construction methods of highly nonlinear boolean functions with relatively good algebraic properties were proposed these approaches manage in optimizing most of the relevant cryptographic criteria but not all of them at the same time usually either the nonlinearity bounds are rather loose though the actual nonlinearity is relatively high or the functions do not provide a good resistance to fast algebraic cryptanalysis in this paper we develop a theoretical framework for using objects in suitable projective geometry spaces for construction of highly nonlinear boolean functions this allows us to establish tight bounds on the nonlinearity using simple counting arguments thus avoiding rather complicated estimates of certain trace sums our method generates a class of almost fully optimized functions that is the functions apart from very high nonlinearity also have the maximum algebraic degree and optimal algebraic immunity compared to the classes of functions proposed by carlet and feng wang and zeng our functions achieve a slightly better nonlinearity which is traded off against a little worse resistance against fast algebraic attacks on the other hand compared to the functions by tang and tu and deng our nonlinearity is somewhat lower but the algebraic properties are slightly better

some efficient boundary integral strategies for time harmonic wave problems in an elastic halfspace abstract when boundary integral equation boundary element methods bie bems are used for halfspace problems such as occur frequently in elastodynamics the fullspace stokes fundamental solution or halfspace lamb fundamental solution can be used to formulate the bie both stokes and lamb approaches have advantages and disadvantages this paper presents systematic strategies based on the bem for 3d halfspace elastodynamic problems wherein the best features of formulations based on the stokes and the lamb solutions are exploited strategies are illustrated and numerical results are given for point sources and radiation from a spherical void in a halfspace

constructions of cryptographically significant boolean functions using primitive polynomials it is known that boolean functions used in stream and block ciphers should have good cryptographic properties to resist algebraic attacks up until now there have been several constructions of boolean functions achieving optimum algebraic immunity however most of their nonlinearities are very low carlet and feng studied a class of boolean functions with optimum algebraic immunity and deduced the lower bound of its nonlinearity which is good but not very high moreover the main practical problem with this construction is that it cannot be implemented efficiently in this paper we put forward a new method to construct cryptographically significant boolean functions by using primitive polynomials and construct three infinite classes of boolean functions with good cryptographic properties balancedness optimum algebraic degree optimum algebraic immunity and a high nonlinearity

comments on constructions of cryptographically significant boolean functions using primitive polynomials we show that the first of the two constructions by q wang j peng h kan and x xue ieee transactions on information theory vol 56 no 6 pp 3048 3053 2010 of boolean functions satisfying the main criteria for filter functions in stream ciphers is the same as the construction studied by k feng and the author at asiacrypt 2008 lncs 5350 pp 425 440 we observe that the bounds shown on the nonlinearities of the functions in this ieee paper are similar to those shown in the asiacrypt paper we point out that these kinds of functions can be implemented in a more efficient way than usually believed

on symmetric boolean functions with high algebraic immunity on even number of variables in this paper we put forward an efficient method to study the symmetric boolean functions with high algebraic immunity on even number of variables we obtain some powerful necessary conditions for symmetric boolean functions to achieve high algebraic immunity by studying the weight support of some specific types of boolean functions of low degrees with these results we prove that the algebraic immunity of a large class of symmetric correlation immune boolean functions namely the symmetric palindromic functions is not high besides we construct all symmetric boolean functions with maximum algebraic immunity and give a description for those with submaximum algebraic immunity we also determine the hamming weight degrees and nonlinearity of the symmetric boolean functions with maximum algebraic immunity

solving the hypersingular boundary integral equation for the burton and miller formulation this paper presents an easy numerical implementation of the burton and miller bm formulation where the hypersingular helmholtz integral is regularized by identities from the associated laplace equation and thus needing only the evaluation of weakly singular integrals the helmholtz equation and its normal derivative are combined directly with combinations at edge or corner collocation nodes not used when the surface is not smooth the hypersingular operators arising in this process are regularized and then evaluated by an indirect procedure based on discretized versions of the calderon identities linking the integral operators for associated laplace problems the method is valid for acoustic radiation and scattering problems involving arbitrarily shaped three dimensional bodies unlike other approaches using direct evaluation of hypersingular integrals collocation points still coincide with mesh nodes as is usual when using conforming elements using higher order shape functions with the boundary element method model size kept fixed reduces the overall numerical integration effort while increasing the solution accuracy to reduce the condition number of the resulting bm formulation at low frequencies a regularized version ik k2 of the classical bm coupling factor i k is proposed comparisons with the combined helmholtz integral equation formulation method of schenck are made for four example configurations two of them featuring non smooth surfaces

radiation impedance of tubes with different flanges numerical and experimental investigations end corrections for open ended cylindrical tubes are determined theoretically and experimentally for the zero and low frequencies the wave equation is solved numerically by using a finite difference method for higher frequencies the complex radiation impedance is measured and for circular flanges calculated with the boundary element method for low frequencies the bem links up with the fdm and for higher frequencies fits with experimental results various flanges found in particular in musical instruments are considered circular flanges of various sizes spherical and cylindrical flanges square flanges the normalised flange used for loudspeaker testing short flaring horns and a disk at a certain distance above the open end analytical fit formulas are proposed for each case

on time harmonic elastic wave analysis by the boundary element method for moderate to high frequencies abstract certain inherent difficulties in obtaining accurate boundary element solutions to problems of elastodynamics at moderate to high frequencies are examined some procedures for overcoming or compensating for these difficulties are described in addition results demonstrating the effectiveness of these procedures are presented finally the use of these procedures in solving transient problems via fourier transform inversion is illustrated

more balanced boolean functions with optimal algebraic immunity and good nonlinearity and resistance to fast algebraic attacks in this paper three constructions of balanced boolean functions with optimal algebraic immunity are proposed it is checked that at least for small numbers of input variables these functions have good behavior against fast algebraic attacks as well other cryptographic properties such as algebraic degree and nonlinearity of the constructed functions are also analyzed lower bounds on the nonlinearity are proved which are similar to the best bounds obtained for known boolean functions resisting algebraic attacks and fast algebraic attacks moreover it is checked that for the number n of variables with 5 n 19 the proposed n variable boolean functions have in fact very good nonlinearity

acoustic radiation from vibrating surfaces at characteristic frequencies the application of boundary integral methods to the problem of acoustic radiation suffers from nonexistence or nonuniqueness problems at the characteristic frequencies of the associated interior dirichlet problem to overcome this difficulty an iterative overdetermination scheme is developed first the surface integral helmholtz equation is discretized and at noncharacteristic frequencies the resulting system of linear algebraic equations can be solved directly yielding the values of the acoustic pressure at the boundary nodal points at characteristic frequencies the system matrix becomes ill conditioned and the direct solution is not possible an approximate surface impedance function is then assumed to serve as a basis for the computation of approximate farfield pressures these are then utilized to form an overdetermined system which is solved with the least squares procedure this solution can be used to compute the next order approximation and the process is continued the method is applied to the cylindrical transducer problem and proves to yield good results at characteristic frequencies it is also used to solve a structural radiation problem for which no characteristic frequencies are found nonexistence of such frequencies for problems of this type is conjectured although no general proof is given

hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions abstract a weakly singular form of the hypersingular boundary integral equation bie traction equation for 3 d elastic wave problems is developed in this paper all integrals involved are at most weakly singular and except for a stronger smoothness requirement on boundary elements regular quadrature and collocation procedures used for conventional bies are sufficient for the discretization of the original hypersingular bie this weakly singular form of the hypersingular bie is applied to the composite bie formulation which uses a linear combination of the conventional bie and the hypersingular bie to remove the fictitious eigenfrequencies existing in the conventional bie formulation for elastic wave problems numerical examples employing different types of boundary elements clearly demonstrate the effectiveness and efficiency of the developed formulation

a boundary integral equation method for radiation and scattering of elastic waves in three dimensions etude du rayonnement et de la diffusion d ondes elastiques par des obstacles de forme arbitraire

on the computation of the derivatives of potentials on a boundary by using boundary integral equations this work presents a new recursion scheme to compute the cartesian derivatives of potentials on the smooth surface of a connected solid the advocated strategy solely appeals to boundary integral equations and a very few informations regarding the surface geometry the whole algorithm is carefully tested against analytical solutions both for interior and exterior problems by implementing a collocation points method

an elastodynami c hybrid boundary element study for elastic guided wave interactions with a surface breaking defect elastic guided wave interactions with various defects are explored for investigating defect characterization possibilities by using a hybrid boundary element method bem in combination with an elastodynamic boundary integral equation and the lamb wave normal mode expansion technique the bem code accuracy is verified based on energy conservation and available bench marking data for guided wave scattering problems through two dimensional 2 d parametric studies for an arbitrarily shaped defect from a surface breaking crack model to a round surface defect a waveguide cross section including a defect is locally selected as a model for a given incident mode frequency and a specific set of material properties mode reflection and transmission factors are numerically calculated to evaluate mode sensitivities and to obtain the potentially good classification features it turns out that the guided wave scattering profiles show quite different behaviors as functions of incident mode frequency defect shape and size in providing us with enough rich feature extraction information for defect classification and sizing analysis the theoretical analysis can be used to establish efficient guidelines for both data acquisition and feature selection in a pattern recognition analysis program of study sample results are presented

a new upper bound on the block error probability after decoding over the erasure channel motivated by cryptographic applications we derive a new upper bound on the block error probability after decoding over the erasure channel the bound works for all linear codes and is in terms of the generalized hamming weights it turns out to be quite useful for reed muller codes for which all the generalized hamming weights are known whereas the full weight distribution is only partially known for these codes the error probability is related to the cryptographic notion of algebraic immunity we use our bound to show that the algebraic immunity of a random balanced m variable boolean function is of order m 2 1 o 1 with probability tending to 1 as m goes to infinity

highly nonlinear boolean functions with optimal algebraic immunity and good behavior against fast algebraic attacks inspired by the previous work of tu and deng we propose two infinite classes of boolean functions of 2k variables where k 2 the first class contains unbalanced functions having high algebraic degree and nonlinearity the functions in the second one are balanced and have maximal algebraic degree and high nonlinearity as shown by a lower bound that we prove as a byproduct we also prove a better lower bound on the nonlinearity of the carlet feng function thanks to a combinatorial fact first conjectured by the authors and later proved by cohen and flori we are able to show that they both possess optimal algebraic immunity it is also checked that at least for numbers of variables n 16 functions in both classes have a good behavior against fast algebraic attacks compared with the known boolean functions resisting algebraic attacks and fast algebraic attacks both of them possess the highest lower bounds on nonlinearity these bounds are however not enough for ensuring a sufficient nonlinearity for allowing resistance to fast correlation attack nevertheless as for previously found functions with the same features there is a gap between the bound that we can prove and the actual values computed for bounded numbers of variables n 38 moreover these values are very good the infinite class of functions we propose in construction 2 presents among all currently known constructions the best provable tradeoff between all the important cryptographic criteria

improving the upper bounds on the covering radii of binary reed muller codes by deriving bounds on character sums of boolean functions and by using the characterizations due to kasami of those elements of the reed muller codes whose hamming weights are smaller than twice and a half the minimum distance we derive an improved upper bound on the covering radius of the reed muller code of order 2 and we deduce improved upper bounds on the covering radii of the reed muller codes of higher orders

algebraic immunity for cryptographically significant boolean functions analysis and construction recently algebraic attacks have received a lot of attention in the cryptographic literature it has been observed that a boolean function f used as a cryptographic primitive and interpreted as a multivariate polynomial over f sub 2 should not have low degree multiples obtained by multiplication with low degree nonzero functions in this paper we show that a boolean function having low nonlinearity is also weak against algebraic attacks and we extend this result to higher order nonlinearities next we present enumeration results on linearly independent annihilators we also study certain classes of highly nonlinear resilient boolean functions for their algebraic immunity we identify that functions having low degree subfunctions are weak in terms of algebraic immunity and we analyze some existing constructions from this viewpoint further we present a construction method to generate boolean functions on n variables with highest possible algebraic immunity spl lceil n 2 spl rceil this construction first presented at the 2005 workshop on fast software encryption fse 2005 has been the first one producing such functions these functions are obtained through a doubly indexed recursive relation we calculate their hamming weights and deduce their nonlinearities we show that they have very high algebraic degrees we express them as the sums of two functions which can be obtained from simple symmetric functions by a transformation which can be implemented with an algorithm whose complexity is linear in the number of variables we deduce a very fast way of computing the output to these functions given their input