interaction of an edge dislocation with a coated elliptic inclusion this paper presents an analytical solution for plane elasticity problems of an elliptically cylindrical layered media subject to an arbitrary edge dislocation based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique the general expressions of the displacements and stresses where an edge dislocation is located in matrix coating layer and inclusion are obtained the numerical results of image forces exerted on a generalized edge dislocation are carried out by using the generalized peach koehler equation as a numerical illustration both the image forces and equilibrium positions are presented for different material combinations and relative thickness of a coating layer the result shows that the thickness and the shear modulus of the coating layer have a strong influence on the stability of dislocation

an extended boundary element method formulation for the direct calculation of the stress intensity factors in fully anisotropic materials copyright 2016 john wiley sons ltd we propose a formulation for linear elastic fracture mechanics in which the stress intensity factors are found directly from the solution vector of an extended boundary element method formulation the enrichment is embedded in the boundary element method formulation rather than adding new degrees of freedom for each enriched node therefore a very limited number of new degrees of freedom is added to the problem which contributes to preserving the conditioning of the linear system of equations the stroh formalism is used to provide boundary element method fundamental solutions for any degree of anisotropy and these are used for both conventional and enriched degrees of freedom several numerical examples are shown with benchmark solutions to validate the proposed method copyright 2016 john wiley sons ltd

on singularities in composite piezoelectric wedges and junctions abstract the plane problems of piezoelectric wedges and multi material wedges junctions involving piezoelectrics are studied in this paper the study is focused on the singular behaviour of electroelastic fields at the corner of wedges and junctions the polarization orientation of the piezoelectric medium may be arbitrary the problem is formulated by extending lekhnitskii s complex potential functions in the homogeneous piezoelectric cases of a half plane and a semi infinite crack it is shown that the singularity is invariant with respect to the direction of polarization and explicit solutions are derived for homogeneous boundary condition combinations in general cases involving multi material systems the order of singularity is determined by solving a transcendental characteristic equation derived on the basis of boundary conditions and geometry the accuracy of the numerical algorithm is verified by comparing with the existing results for pure elastic wedges numerical results of homogeneous piezoelectric wedges indicate that electric boundary conditions have a significant effect on the order of singularities a selected set of practically useful wedges and junctions involving piezoelectrics are studied to examine the influence of wedge angle polarization orientation material types and boundary and interface conditions on the order of singularity of electroelastic fields

on the elastic fields of an elliptical inhomogeneity under plane deformation a generalized and unified approach is presented for the two dimensional plane problem of an elliptical inhomogeneity in an isotropic elastic medium the analysis is based upon the use of conformal mapping and laurent series expansion of muskhelishvili s complex potentials the resulting elastic fields are derived explicitly in both transformed and physical planes for the inhomogeneity and the surrounding matrix the associated expressions are universal in the sense of being applicable to generalized geometries and applied loads the application of the general solution is illustrated by several examples and the resulting solutions are verified with those existing in the literature the results advanced here can be used as building blocks for dealing with more complex problems involving a wide variety of geometry and loading conditions

constructing symmetric boolean functions with maximum algebraic immunity symmetric boolean functions with even variables 2k and maximum algebraic immunity ai f k have been constructed in braeken s thesis 2006 in this paper we show more constructions of such boolean functions including the generalization of a result and prove a conjecture raised in braeken s thesis 2006

on interface crack in laminated anisotropic medium in this paper the interface crack problems of a multilayered anisotropic medium under a state of generalized plane deformation are considered within the framework of anisotropic theory a general solution procedure is introduced such that it can be uniformly applied to media with transversely isotropic orthotropic monoclinic etc layers the problem is reduced to the solution of a system of singular integral equations by means of fourier transform method and the stiffness matrix formulation a jacobi polynomial technique is then used to solve the integral equations numerically the stress intensity factors are provided the stress intensity factors have been calculated numerically and displayed graphically

interface crack in bi piezothermoelastic media and the interaction with a point heat source abstract using the extended version of eshelby stroh s formulation and the method of analytical continuation the problems of interface cracks are reduced to a hilbert problem of vector form a general explicit closed form solution for piezothermoelastic interface crack problem is then obtained the whole field solutions of temperature heat flux displacements electric field stress and electric induction are given the explicit expressions for the crack opening displacements and electric potential are also provided a solution is obtained for the interaction problem between the interface cracks and a point heat source

anisotropic elastic plates with holes cracks inclusions subjected to out of plane bending moments the problems of anisotropic plates containing holes cracks and or inclusions have been studied extensively for two dimensional deformations although the correspondence between the two dimensional problems and the plate bending problems has been observed long time ago without clarifying the involved mathematical details one still cannot get the solutions of the plate bending problems directly from the solutions of the corresponding two dimensional problems based upon the correspondence relation recently we developed a stroh like formalism for the bending theory of anisotropic plates by this newly developed formalism most of the relations for bending problems can be organized into the forms for two dimensional problems thus by using the stroh like formalism the analytical solutions for problems of anisotropic plates with holes cracks inclusions subjected to out of plane bending moments can be obtained directly from the solutions of the corresponding two dimensional problems the stresses or resultant bending moments around the hole crack inclusion boundaries are also given explicitly in this paper since the explicit closed form solutions for the present cases have not been found in the literature comparison is made with some special cases of which the analytical solutions exist which shows that our solutions are exact simple and general

on the unified approach to anisotropic and isotropic elasticity for singularity interface and crack in dissimilar media abstract proposed in this paper is the equivalence between anisotropic and isotropic elasticity for two dimensional deformation under certain conditions that is the isotropic elasticity can be reconstructed in the same framework of the anisotropic elasticity when the interface between dissimilar media lies along a straight line therefore many known solutions for an anisotropic bimaterial are valid for a bimaterial of which one or both of the constituent materials are isotropic the usefulness of the equivalence is that the solutions for singularities and cracks in an anisotropic isotropic bimaterial can easily be obtained without solving the boundary value problems directly the interaction solutions of singularities interfaces and cracks in infinite anisotropic bimaterial are summarized to be used for the cases of isotropic isotropic and anisotropic isotropic bimaterials conservation integrals also have the similar analogy between anisotropic and isotropic elasticity so that j integral and j based mutual integral m are expressed in the same complex forms for anisotropic and isotropic materials when both end points of the integration paths are on the straight interface the use of j and m integrals together with the present equivalence are exemplified to obtain energy release rate stress intensity factors and t stresses of interfacial cracks lying in the interface of anisotropic anisotropic isotropic isotropic or anisotropic isotropic solids

image decomposition method for the analysis of a mixed dislocation in a general multilayer the elastic solutions for a mixed dislocation in a general multilayer with n dissimilar anisotropic layers are obtained via a generalized image decomposition method the original problem is decomposed into n homogeneous subproblems with strategically placed continuously distributed image virtual dislocations which satisfy the consistency conditions for degen erate nm m n layer problems the image dislocations are used to satisfy the interface or free surface conditions and represent the unknowns of the problem the resulting singular cauchy integral equations are transformed into non singular fredholm integral equations of the second kind using certain h and i integral transforms the fredholm integral equations are then solved via the classical nystrom method the general decomposition and the elimination of all singular integrals yield an exact formulation of the problem the approximation arises only in the nystrom method the dislocation mixity and the number of layers dissimilar in thickness and elastic anisotropy can be handled without difficulty constrained only by the number of linear algebraic equations in the nystrom method for large n for the numerical study image forces on a dislocation in two and three layer systems are calculated the accuracy of the results is verified by checking the boundary conditions and by comparison with previous results the dependence of the image force on the dislocation position and mix ity and on the layer thicknesses and elastic anisotropies is also illustrated via numerical investigations 2006 elsevier ltd all rights reserved

alternative solution methods for crack problems in plane anisotropic elasticity with examples two dimensional crack problems of homogeneous anisotropic linear elasticity are solved using the riemann hilbert method to this end the riemann hilbert problem of line discontinuity is formulated for anisotropic plane problems and the necessary parameters and functions are identified for illustration the method is applied to obtain the complete stress field and the stress intensity factors for a crack in an infinite anisotropic plate which is loaded on a part of one of its faces then the well established method of continuously distributed edge dislocations is considered and illustrated via some example problems e g an infinite anisotropic plate under uniform farfield loads containing 1 a closed frictional crack and a pair of arbitrarily located single edge dislocations and 2 an infinite row of equally spaced parallel open cracks the illustrative examples reveal that the first method oaers an eaective solution technique for problems where unbalanced tractions are applied on crack surfaces whereas for problems with self equilibrating loads applied on the crack faces the second method is generally well suited in addition the method of resultant forces along the crack is discussed and its formulation in terms of the dislocation density functions and also the crack opening displacements which is new is presented the solutions to some of the example problems are provided in some detail and for others just the key formulae e g stress functions and stress intensity factors are calculated and analyzed in brief this paper presents the generalization of the riemann hilbert method from isotropic to anisotropic in plane elasticity problems and also provides a collection of certain basic two dimensional anisotropic crack problems some of the results here are also new 7 2000 elsevier science ltd all rights reserved

the anisotropic elastic solid with an elliptic hole or rigid inclusion abstract the two dimensional problem of an elliptic hole in a solid of general anisotropy subject to an arbitrarily prescribed traction on the hole surface is studied stroh s complex formalism is adopted here but real form solutions are obtained for the displacement and the hoop stress around the hole for an arbitrarily prescribed traction the solutions are in the form of an infinite series however through the use of a conjugate function they can be expressed in closed form directly in terms of the applied traction we also consider an elliptic rigid inclusion subject to a force and a torque again real form solutions are obtained for the interface stress the hoop stress around the rigid inclusion and the rotation of the rigid inclusion when there is no torque applied at the inclusion the traction vector at the surface of the rigid inclusion is in the direction of the applied force and is a constant when the ellipse is a circle this is an unexpected result since the material surrounding the rigid inclusion is of general anisotropy

on the global avalanche characteristics between two boolean functions and the higher order nonlinearity the criterion for the global avalanche characteristics gac of cryptographic functions is an important property to measure the correlation between two arbitrary boolean functions we propose two new criteria called the sum of squares indicator and the absolute indicator of the cross correlation between two boolean functions the two indicators generalize the gac criterion based on the properties of the cross correlation function we deduce the rough lower and the rough upper bounds on the two indicators by hamming weights of two boolean functions and generalize some properties between the walsh spectrum and the cross correlation function furthermore we give the tight upper and the tight lower bounds on the two indicators finally we show some relationships between the upper bounds on the two indicators and the higher order nonlinearity

stress distribution at sharp and rounded v notches in quasi orthotropic plane abstract the eigensolution of the quasi orthotropic wedge problem is presented the degenerate orthotropic material of the wedge is characterized by doubled roots of the characteristic equation using the method of singular integral equations the distribution of the stress field in the quasi orthotropic plane weakened by semi infinite rounded v notch was obtained the edge of the notch was free of load and the asymptotic stress field defined by a stress intensity factor was set at the infinity on this basis the relationship between stress intensity factor at the sharp notch vertex and the normal stress at the vertex of corresponding rounded v notch with the same opening angle was established as it was shown in the example this relationship is asymptotic for finite notched bodies and it can be used to calculate a notch stress intensity factor based on a stress concentration results obtained for a notch rounded with small radius of curvature

correlation immunity of nonlinear combining functions for cryptographic applications corresp pseudonoise generators for cryptographic applications consisting of several linear feedback shift registers with a nonlinear combining function have been proposed as running key generators in stream ciphers these running key generators eau sometimes be broken by ciphertext only correlation attacks on individual subsequences a new class of combining functions is presented which provides better security against such attacks the security is quantified by the smallest number m 1 of subsequences that must be simultaneously considered in a correlation attack a necessary condition for such m th order correlation immunity is proved a recursive construction is given that permits the construction of an m th order immune combining function for n subsequences for any m and n with 1 leq m finally the trade off between the length of the linear equivalent of the nonlinear generator and the order m of its immunity against correlation attacks is considered

boundary integral equations for 2d elasticity and its application in discrete dislocation simulation in finite body 2 numerical implementation in the previous paper by yu and diab 2013 several sets of boundary integral equations are derived for general anisotropic materials and corresponding equations for materials with different classes of symmetry are deduced the work presented herein implements two sets of boundary element schemes to numerically solve the stress field the integration on the element that has the singular point of the kernel is bounded and can be evaluated analytically four benchmark elastic problems are solved numerically to show the advantage of the two schemes over the conventional boundary element formulation in eliminating the boundary layer effect the one with the weaker singularity has better convergence and gives more accurate results the presented formulation also provides a direct approach to solve for stress field in a finite solid body in the presence of dislocations combined with discrete dislocations dynamics boundary value problems with dislocations in finite bodies can be solved two examples bending of a single crystal beam and pure shearing of a polycrystalline solid are simulated by discrete dislocation dynamics using the scheme that has the weaker singularity the comparisons with the published results using the well established superposition technique validate the proposed formulation and show its quick convergence

integral identities for a semi infinite interfacial crack in anisotropic elastic bimaterials the focus of the article is on the analysis of a semi infinite crack at the interface between two dissimilar anisotropic elastic materials loaded by a general asymmetrical system of forces acting on the crack faces recently derived symmetric and skew symmetric weight function matrices are introduced for both plane strain and antiplane shear cracks and used together with the fundamental reciprocal identity betti formula in order to formulate the elastic fracture problem in terms of singular integral equations relating the applied loading and the resulting crack opening the proposed compact formulation can be used to solve many problems in linear elastic fracture mechanics for example various classic crack problems in homogeneous and heterogeneous anisotropic media as piezoceramics or composite materials this formulation is also fundamental in many multifield theories where the elastic problem is coupled with other concurrent physical phenomena

an interfacially cracked orthotropic rectangular bi material subjected to antiplane shear loading abstract an interfacially cracked rectangular bi material composed of two dissimilar orthotropic elastic media is analyzed the crack is parallel to or perpendicular to the boundary surfaces under the action of antiplane shear loading the problem is reduced to a singular integral equation of the first kind by employing the fourier series method for four types of boundary conditions including the f f type c c type f c type and c f type numerical results of stress intensity factors are obtained by using the lobatto chebyshev method the results show that in addition to the geometric factor stress intensity factors are dependent on the material properties the influences of the material properties on stress intensity factors are examined and compared under different boundary conditions

full field analysis of a planar anisotropic layered half plane for concentrated forces and edge dislocations the problem of a planar anisotropic elastic layered halfplane subjected to concentrated forces and edge dislocations applied either in the layer or in the halfplane is analysed one of the objectiv

on the general treatment of an oblique crack near a bimaterial interface under antiplane loading this article provides a comprehensive theoretical treatment of the interaction between an arbitrarily located and oriented crack and a bimaterial interface under antiplane loading the analysis is based upon the use of an integral transform method and a self consistent iterative sci technique the resulting singular integral equations are solved using chebyshev polynomials to provide closed form expressions for the stress distribution along the interface and the stress intensity factor at the crack typical examples are provided to show the effect of the location and orientation of the crack and the material combination upon the interfacial stress distribution and the stress intensity factor of the crack the presented method can be extended to treat more complex interaction problems

the lower bounds on the second order nonlinearity of three classes of boolean functions with high nonlinearity the rth order nonlinearity of boolean functions is an important cryptographic criterion associated with some attacks on stream and block ciphers it is also very useful in coding theory since it is related to the covering radii of reed muller codes this paper tightens the lower bounds of the second order nonlinearity of three classes of boolean functions in the form f x tr x d in n variables where 1 d 2 m 1 3 and n 2m or 2 d 2 m 2 m 1 2 1 n 2m and m is odd or 3 d 2 2 r 2 r 1 1 and n 4r

on continuous triangular norms the problem of converging to any given continuous triangular norm by a sequence of continuous archimedean triangular norms is studied such a sequence is built up in a constructive way the class of well founded triangular norms is introduced it is proved that a sequence of triangular norms converges to a given continuous triangular norm if and only if this convergence is uniform finally we prove that every continuous triangular norm is a uniform limit of continuous archimedean triangular norms

boundary layers in wedges of laminated composite strips under generalized plane deformation part i asymptotic solutions abstract based upon lekhnitskii s formulation and the stroh formalism the structure of the asymptotic solutions has been examined for the boundary layer on the wedge type cross section of a laminated composite strip the composite strip is assumed under the so called generalized plane deformation which includes tension bending and or torsion by the terminal tractions as well as the generalized plane strain problem the solution structures are obtained with the aid of numerical calculation for various kinds of wedge geometry including the free edge and the delamination cracks with the crack faces opened or closed finally the nature of the asymptotic solutions is discussed including the mode mixity of singular stress field ahead of the wedge tip it is found that for a free edge problem the mode mixity of the singular asymptotic traction vector on the interfacial plane near the free edge remains invariant under varying types of remote loadings once a pair of adjacent materials or ply orientations is given and that accordingly one single scaling parameter governs the near field response

on the covering radii of binary reed muller codes in the set of resilient boolean functions let r sub t n be the set of t resilient boolean functions in n variables and let spl rho spl circ t r n be the maximum distance between t resilient functions and the rth order reed muller code rm r n we prove that spl rho spl circ t 2 6 16 for t 0 1 2 and spl rho spl circ 3 2 7 32 from which we derive the lower bound spl rho spl circ t 2 n spl ges 2 sup n 2 with t spl les n 4 using a result from coding theory on the covering radius of n 3 th and n 4 th order reed muller codes we establish exact values of the covering radius of rm n 3 n in the set of 1 resilient boolean functions in n variables when spl lfloor n 2 spl rfloor 1 mod 2 and lower bounds of rm n 4 n in the set of 2 resilient boolean functions in n variables this result leads again to different lower bounds for general dimensions n and r 0 or 3 mod 4

an internal crack in a half plane solid with clamped boundary abstract an internal crack in a half plane solid with clamped boundary is analyzed a system of singular integral equations is derived for the material whose response is general anisotropic numerical method is then used to investigate the solutions to the system of equations results are presented for the stress intensity factors for orthotropic material the effects of the orientation of the crack the material angle and the degree of anisotropy are also discussed in some detail in particular when the crack is perpendicular to the clamped boundary and when one of the material principal axes is along the crack faces our numerical analysis shows that the result for the stress intensity factor k i under uniform pressure loading is exactly the same as that for k ii under uniform shear loading furthermore these stress intensity factors are invariant under the 90 degrees of rotation of the material principal axes

general solutions for thermopiezoelectrics with various holes under thermal loading abstract the thermoelectroelastic problems for a hole of various shapes embedded in an infinite matrix are considered in this paper using stroh s formalism and the technique of conformal mapping a unified solution is obtained in closed form for an infinite thermopiezoelectric plate with various holes induced by thermal loads the loads may be uniform remote heat flow point heat source and temperature discontinuity further a detailed discussion on the critical points for the mapping function of a piezoelectric plate with polygonal holes is presented and the study shows that the transformation is nonsingle valued a simple approach is given to treat such a situation as an application of the proposed solutions a system of singular integral equations for the unknown temperature discontinuity and the dislocation of elastic displacement and electric potential defined on crack faces is developed and solved numerically numerical results are presented to illustrate the application of the proposed formulation

anti plane stress analysis of orthotropic rectangular planes weakened by multiple defects the solution of a volterra type screw dislocation problem in an orthotropic rectangular plane with finite length and width and various boundary conditions is obtained by means of a separation of variables technique a distributed dislocation method is employed to obtain integral equations of the plane with cracks and cavities under an anti plane traction the ensuing equations are of the cauchy singular type and have been solved numerically several examples are presented to demonstrate the applicability of the proposed solution

two classes of symmetric boolean functions with optimum algebraic immunity construction and analysis this paper discusses two classes of symmetric boolean functions for each class a necessary and sufficient condition for having optimum algebraic immunity is proposed the algebraic degree and nonlinearity of the boolean functions are also completely determined and then we prove several of braeken s conjectures about the algebraic degree and nonlinearity of the boolean functions with optimum algebraic immunity in the two classes

recursive lower bounds on the nonlinearity profile of boolean functions and their applications the nonlinearity profile of a boolean function i e the sequence of its minimum hamming distances nlr f to all functions of degrees at most r for r ges 1 is a cryptographic criterion whose role against attacks on stream and block ciphers has been illustrated by many papers it plays also a role in coding theory since it is related to the covering radii of reed muller codes we introduce a method for lower bounding its values and we deduce bounds on the second order nonlinearity for several classes of cryptographic boolean functions including the welch and the multiplicative inverse functions used in the s boxes of the advanced encryption standard aes in the case of this last infinite class of functions we are able to bound the whole profile and we do it in an efficient way when the number of variables is not too small this allows showing the good behavior of this function with respect to this criterion as well

the second order reed muller code of length 64 has covering radius 18 corresp the assertion of the title is proved by first showing that the covering radius of r 2 6 cannot exceed 18 and then constructing a weight 18 coset leader

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

best affine and quadratic approximations of particular classes of boolean functions in this paper we consider the problem of computing best low order approximations of boolean functions we focus on the best quadratic approximations of a subclass of cubic functions with arbitrary number of variables and we provide formulas for their efficient calculation our methodology is developed upon properties of the best affine approximations of quadratic functions for which formulas for their direct computation not by means of the walsh hadamard transform are given we determine the cubic functions in the above subclass that achieve the maximum second order nonlinearity thus yielding a lower bound for the covering radius of the second order reed muller code ssr rm 2 n in ssr rm 3 n simple extensions of these results to some special cases of higher degree functions are seen to hold furthermore a preliminary analysis of well known constructions for bent functions in terms of their second order nonlinearity is performed that indicates potential weaknesses if construction parameters are not properly chosen

on the peak to mean envelope power ratio of phase shifted binary codes the peak to mean envelope power ratio pmepr of a code employed in orthogonal frequency division multiplexing ofdm systems can be reduced by permuting its coordinates and by rotating each coordinate by a fixed phase shift motivated by some previous designs of phase shifts using suboptimal methods the following question is considered in this paper for a given binary code how much pmepr reduction can be achieved when the phase shifts are taken from a 2h ary phase shift keying 2h psk constellation a lower bound on the achievable pmepr is established which is related to the covering radius of the binary code generally speaking the achievable region of the pmepr shrinks as the covering radius of the binary code decreases the bound is then applied to some well understood codes including nonredundant bpsk signaling bch codes and their duals reed muller codes and convolutional codes it is demonstrated that most presumably not optimal phase shift designs from the literature attain or approach our bound

continuous fuzzy conjunctions and disjunctions several functions have been used to implement conjunction and disjunction in fuzzy logic and to implement intersection and union in fuzzy set theory usually t norms and t conorms are used but for some applications these may not be the best function classes in this paper i propose specific requirements which a function should satisfy if it is to be used to implement conjunction or intersection or disjunction or union and compare the functions proposed for conjunction to t norms in addition to stating basic properties of the resulting function classes i give theorems on polynomial approximation within each class and on the existence of functions in either class with specified values at particular points

integral identities based on symmetric and skew symmetric weight functions for a semi infinite interfacial crack in anisotropic magnetoelectroelastic bimaterials abstract in this paper we address a semi infinite interfacial crack problem in an anisotropic magnetoelectroelastic mee bimaterial system subjected to a magnetoelectromechanical asymmetric load on the crack surface first the symmetric and skew symmetric weight functions are derived for a two dimensional 2 d deformation problem using these weight functions and extending the betti formula to mee materials the integral identities are further obtained and the present crack problem is formulated in terms of singular integral equations which establish the relationship between the applied external load and the generalized displacement jump across the crack faces the illustrative examples in relation to mode iii and mode i and mode ii problems show that the method developed in this study avoids the use of green s function and is very convenient for the fracture analysis of mee solids in which a multi field coupled effect is observed

explicit solutions for collinear interface crack problems abstract by combining stroh s formalism the method of analytical continuation and the translating technique introduced in this paper the explicit full domain solutions for the problems of collinear interface cracks between dissimilar anisotropic media have been presented to define a proper bimaterial stress intensity factor the full domain solution is applied to the near tip of an interface crack the results show that the effect of material properties is totally reflected through the oscillation index e and the bimaterial constants d 11 d 22 and d 33 which have inverse relations with young s moduli e 1 e 2 and shear modulus g 23 g 31 respectively for the purpose of illustration three typical examples are solved explicitly such as a semi infinite interface crack a finite interface crack and two collinear interface cracks

the crack problem for nonhomogeneous materials under antiplane shear loading a displacement based formulation abstract this paper presents a displacement based integral equation formulation for the mode iii crack problem in a nonhomogeneous medium with a continuously differentiable shear modulus which is assumed to be an exponential function i e g x g0exp x this formulation leads naturally to a hypersingular integral equation the problem is solved for a finite crack and results are given for crack profiles and stress intensity factors the results are affected by the parameter describing the material nonhomogeneity this study is motivated by crack problems in strain gradient elasticity theories where higher order singular integral equations naturally arise even in the slope based formulation

on the construction of boolean functions with optimal algebraic immunity in this correspondence we introduce a method to construct boolean functions in any number of variables with optimal algebraic immunity remarkably all functions of this type with an odd number of variables can be obtained in this way we study some cryptographic properties such as balancedness algebraic degree of the constructed functions moreover a lower bound of the number of boolean functions with optimal algebraic immunity is given

mode iii crack in a laminated medium antiplane deformation of a laminated medium with a semi infinite crack parallel to the interfaces between the layers is considered the homogeneous elastic and isotropic layers of two different types are arranged periodically this allows the reduction of the initial boundary value problem to the wiener hopf equation by combined application of the laplace and the discrete fourier transforms for the specific case of an exponentially decaying load the solution is obtained in closed form by means of rapidly convergent triple integrals the simple expressions for the stress intensity factor and the energy release rate are derived for some limiting cases the solution is found to be consistent with previous results a parametric study gave an opportunity to examine the accuracy of the known approximate sandwich model of multilayered composites

idempotent integral as limit of g integrals we show that sup and inf decomposable measures can be obtained as limits of families of pseudo additive measures with respect to generated pseudo additions the corresponding integrals with respect to sup or inf decomposable measures can be obtained as limits of families of g integrals

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

on the lower bounds of the second order nonlinearities of some boolean functions the rth order nonlinearity of a boolean function is an important cryptographic criterion in analyzing the security of stream as well as block ciphers it is also important in coding theory as it is related to the covering radius of the reed muller code r r n in this paper we deduce the lower bounds of the second order nonlinearities of the following two types of boolean functions 1 f l x tr 1 n lx d with d 2 2 r 2 r 1 and l f 2 n where n 6r 2 f x y tr 1 t xy 2 i 1 where x y f 2 t n 2t n 6 and i is an integer such that 1

slightly curved or kinked cracks in anisotropic elastic solids abstract slightly curved or kinked cracks in anisotropic elastic solids are studied via a perturbation analysis valid for the second order accuracy in the deviation of the crack surfaces from a straight line the analysis is based on complex variable representations in the stroh formalism and known solutions for a perfectly straight reference crack first and second order perturbation solutions are given for the stress intensity factors at the tip of a finite curved crack under remote stresses in a solid with arbitrary anisotropy and are used to establish an approximate relationship between the apparent and local stress intensities at a crack tip in view of the possible shielding effects of the crack surface morphology near the tip the role of anisotropy is examined for a number of problems including circular arc cracks slightly jogged or kinked cracks cosine wavy cracks etc in several cases further insight into the anisotropic effect on crack curving or kinking is provided by specializing the general perturbation formulae to cracks in materials with orthotropic symmetry in the limiting case of a crack with an infinitesimal branch length comparison with numerical results reported in the literature indicates that our perturbation solutions are accurate over the full range of practically important branch angles up to nearly 150 for anisotropic elastic solids various fracture criteria such as those based on energy release rate g and stress intensity factors k 1 and k 11 cease to give consistent predictions on crack behaviour by investigating the effects of mode mixity material anisotropy and non singular t stress on the behaviour of a nearly symmetric crack path in an orthotropic solid we show that the k based fracture criteria lead to very peculiar perhaps even physically unreasonable predictions such as i branch angle at a mixed mode crack tip becomes infinite as the compliances perpendicular and parallel to the crack s vv s vv reach a four fold difference ii the sign of the branch angle is reversed when s vv s vv 4 with the consequence of reversing the role of the non singular t stress on the stability of a symmetric fracture path namely the path becomes stable for t 0 and unstable for t k t becomes a local minimum with respect to crack angle once s vv s vv 4 in contrast the g based criterion gives reasonable predictions such as i cracks under mixed mode loading always tend to branch toward symmetric orientations ii material and loading asymmetries play an equivalent role in affecting crack branching near a symmetric orientation iii a compressive t stress always tends to stabilize a symmetric fracture path while a tensile t stress destabilizes such a path for general crack path stability the role of anisotropy can be manifested through i the value of t stress at the crack tip and ii the variation of fracture resistance with respect to crack orientation

a first order perturbation analysis of a non ideal crack in a piezoelectric material abstract in this paper a first order perturbation analysis is carried out on a symmetrically perturbed non ideal crack for three kinds of electric boundary conditions namely permeable impermeable and conducting crack boundary condition by using the extended stroh formula the two domain problems are reduced to standard riemann hilbert problems and the singular integral equations of the internal electric field inside the permeable crack are solved the stress and electric intensity factors seifs are determined to the first order of accuracy the results indicate that for a symmetrically perturbed non ideal crack the electro mechanical loading at infinity does not affect the first order solution for the mode i intensity factor for general piezoelectric materials the energy release rate and the seifs are determined by remote mechanical loads only and the perturbation effect on the seifs and energy release rate is small the electric field distribution inside crack is constant for the zeroth order solution and quadratic for the first order solution which is different from the constant electric field distribution for an ideal permeable crack the internal electric concentration near the crack tip caused by the perturbation reveals that the dielectric inside the crack probably breaks down before the matrix does when the matrix is subjected to a not too high electro mechanical load at infinity the seifs and the energy release rate are also given for the non ideal crack under the impermeable and conducting electric boundary condition respectively for all three kinds of electric boundary conditions the lateral stresses 11 13 have no contribution to the seifs to the first order of accuracy

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

a finite element approach to three dimensional singular stress states in anisotropic multi material wedges and junctions abstract a finite element formulation is developed to determine the order and angular variation of singular stress states due to material and geometric discontinuities in anisotropic materials the formulation applies to any two dimensional geometry that is prismatic in the third direction and has three dimensional displacement fields in some special cases the three dimensional fields become uncoupled antiplane and inplane fields and this formulation yields the uncoupled results the formulation provides for the determination of the asymptotic stress and displacement fields present at interior singular points of three dimensional structures the displacement field of the sectorial finite element is quadratic in the angular coordinate direction and asymptotic in the radial direction measured from the singular point the formulation of yamada and okumura 1983 hybrid and mixed finite element methods pp 325 343 wiley chichester for inplane problems is adapted for this purpose the simplicity and accuracy of the formulation are demonstrated by comparison with several analytical solutions for both isotropic and anisotropic multi material wedges and junctions the nature and speed of convergence associated with the element suggests that it could be employed in developing two dimensional and three dimensional enriched elements for use along with standard elements to yield accurate and computationally efficient solutions to problems having complex global geometries leading to singular stress states

effects of change of reference coordinates on the stress analyses of anisotropic elastic materials abstract when the displacements are independent of the x 3 coordinate the eigenvalues and eigenvectors of the anisotropic elasticity constants depend on the orientation of the x 1 x 2 axes it is shown that the components of the eigenvectors which are complex values transform according to the law of transformation for tensors of order one the transformation of the eigenvalues is more complicated the effects of change of the reference coordinates on the form of general solution are discussed also discussed is the form of general solution when the eigenvalue p is a multiple root finally we show that as the angle of rotation of the coordinate axes varies from 0 to 2 each p traverses a circle in the complex plane which is orthogonal to the unit circle with center at the origin a graphical solution of the eigenvalue p for a given is presented some functions of p which are invariant to the rotation of the coordinate axes are obtained

an exact correspondence between plane piezoelectricity and generalized plane strain in elasticity we consider an anisotropic body bounded by a cylindrical surface which is infinitely long in the axial direction suppose the body is loaded in such a way that the field variables do not vary along the generators an exact correspondence is established between the plane piezoelectric equations and those of generalized plane strain in elasticity in particular we show that by setting a linkage between the two sets of material constants any problem of a plane deformation in piezoelectricity may be solved as a generalized plane strain in elasticity and vice versa the assertation is true for rectilinearly as well as for cylindrically anisotropic solids the equivalence is found for the most general anisotropic case which links the fields between a monoclinic piezoelectric body of class m and a fully anisotropic triclinic elastic solid a few degenerate systems are also identified in addition these correspondences can be extended to inhomogeneous media applied to composite materials or polycrystalline aggregates they imply that results for effective elastic tensors immediately give the formulae for the effective electroelastic tensors and vice versa we also demonstrate that the connection can be used to extend the scope of the invariant stress theorem proved by cherkaev lurie and milton in illustration we present solutions for the plane problem of an elliptical inhomogeneity in an unbounded piezoelectric medium subjected to a uniform loading at infinity lekhnitskii9s complex potential approach together with the conformal mapping technique are employed general solutions of the fields inside the inhomogeneity and the matrix are obtained the results are analytically proven to be identical with the existing solutions of the corresponding purely elastic boundary value problem

two perfectly bonded dissimilar orthotropic strips with an interfacial crack normal to the boundaries the problem of an interface crack between two bonded dissimilar semi infinitely long orthotropic strips of finite width is analyzed under arbitrary anti plane shear loading by using the finite fourier transform technique the mixed boundary value problem is reduced to triple series equations which are then transformed to a singular integral equation for the case of either stress free or clamped boundaries the solutions to the problem are obtained in closed form respectively in particular explicit expressions for stress field and further stress intensity factors at each crack tip are determined for uniform anti plane shear loading some the well known results can be taken as the special cases of the present results

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

reed muller codes achieve capacity on erasure channels we introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding rather than relying on the precise structure of the codes our method exploits code symmetry in particular the technique applies to any sequence of linear codes where the blocklengths are strictly increasing the code rates converge and the permutation group of each code is doubly transitive in other words we show that symmetry alone implies near optimal performance an important consequence of this result is that a sequence of reed muller codes with increasing blocklength and converging rate achieves capacity this possibility has been suggested previously in the literature but it has only been proven for cases where the limiting code rate is 0 or 1 moreover these results extend naturally to all affine invariant codes and thus to extended primitive narrow sense bch codes this also resolves in the affirmative the existence question for capacity achieving sequences of binary cyclic codes the primary tools used in the proof are the sharp threshold property for symmetric monotone boolean functions and the area theorem for extrinsic information transfer functions

construction of k lipschitz triangular norms and conorms from empirical data this paper examines the practical construction of k lipschitz triangular norms and conorms from empirical data we apply a characterization of such functions based on k convex additive generators and translate k convexity of piecewise linear strictly decreasing functions into a simple set of linear inequalities on their coefficients this is the basis of a simple linear spline fitting algorithm which guarantees k lipschitz property of the resulting triangular norms and conorms

an exact and explicit treatment of an elliptic hole problem in thermopiezoelectric media abstract this paper presents an exact solution for the problem of an elliptic hole or a crack in a thermopiezoelectric solid first based on the extended version of eshelby stroh s formulation the generalized 2d problems of an elliptical hole in a thermopiezoelectric medium subject to uniform heat flow and mechanical electrical loads at infinity are studied according to exact boundary conditions at the rim of the hole the complex potentials in the medium and the electric field inside the hole are obtained in closed form respectively then when the hole degenerates into a crack the explicit solutions for the field intensity factors near the crack tip and the electric field inside the crack are presented it is shown that the singularities of all the field are dependent on the material constants the applied heat load and mechanical loads at infinity but not on the applied electric loads it is also found that the electric field inside the crack is linearly variable which is different from the result based on the impermeable crack model

partition of unity enrichment for bimaterial interface cracks partition of unity enrichment techniques are developed for bimaterial interface cracks a discontinuous function and the two dimensional near tip asymptotic displacement functions are added to the finite element approximation using the framework of partition of unity this enables the domain to be modelled by finite elements without explicitly meshing the crack surfaces the crack tip enrichment functions are chosen as those that span the asymptotic displacement fields for an interfacial crack the concept of partition of unity facilitates the incorporation of the oscillatory nature of the singularity within a conforming finite element approximation the mixed mode complex stress intensity factors for bimaterial interfacial cracks are numerically evaluated using the domain form of the interaction integral good agreement between the numerical results and the reference solutions for benchmark interfacial crack problems is realized copyright 2004 john wiley sons ltd

mixed boundary value problems of two dimensional anisotropic thermoelasticity with elliptic boundaries abstract the two dimensional mixed boundary value problems for an anisotropic thermoelastic body containing an elliptic hole boundary are considered in this paper by using the formalism of stroh phil mag 7 625 646 the approach of analytic function continuation and the technique of conformal mapping a unified analytical solution for elliptic hole boundaries and for general anisotropic thermoelastic media is provided as an application two typical examples associated with mixed boundary value problems are solved completely one is an indentation problem over an elliptic hole boundary the other is a partially reinforced elliptic hole under a remote uniform heat flow both the contact stress under the rigid stamp and the bonded stress along the reinforced segment are studied in detail and shown in graphic form

a unified definition for stress intensity factors of interface corners and cracks abstract based upon linear fracture mechanics it is well known that the singular order of stresses near the crack tip in homogeneous materials is a constant value 1 2 which is nothing to do with the material properties for the interface cracks between two dissimilar materials the near tip stresses are oscillatory due to the order of singularity being 1 2 i e and 1 2 the oscillation index e is a constant related to the elastic properties of both materials while for the general interface corners their singular orders depend on the corner angle as well as the elastic properties of the materials owing to the difference of the singular orders of homogeneous cracks interface cracks and interface corners their associated stress intensity factors are usually defined separately and even not compatibly since homogenous cracks and interface cracks are just special cases of interface corners in order to build a direct connection among them a unified definition for their stress intensity factors is proposed in this paper based upon the analytical solutions obtained previously for the multibonded anisotropic wedges the near tip solutions for the general interface corners have been divided into five different categories depending on whether the singular order is distinct or repeated real or complex to provide a stable and efficient computing approach for the general mixed mode stress intensity factors the path independent h integral based on reciprocal theorem of betti and rayleigh is established in this paper the complementary solutions needed for calculation of h integral are also provided in this paper to illustrate our results several different kinds of examples are shown such as cracks in homogenous isotropic or anisotropic materials central or edge notches in isotropic materials interface cracks and interface corners between two dissimilar materials

boundary layers in wedges of laminated composite strips under generalized plane deformation part ii complete numerical solutions abstract a procedure for finding complete numerical solutions for the elastic boundary layer field in wedges of a laminated composite strip under the generic loadings of generalized plane deformation is discussed together with numerical examples for free edge problems and delamination crack problems the procedure yields the solution in terms of loading parameters and is applicable to an arbitrary wedge angle and ply orientation and any type of loadings within the range of generalized plane deformation for the free edge problem the so called free edge stress intensity and the mode vector are defined and the free edge stress intensity is found to be a single parameter governing the fracture or failure behaviour near the free edge for a given pair of adjacent materials plies the effect of relative ply thickness upon the stress intensity and the energy release rate is also discussed for various types of loadings

smoothly generated archimedean approximation of continuous triangular norms a constructive method is given for approximating a given continuous triangular norm by a sequence of smoothly generated archimedean triangular norms in the uniform metric

elastic study on singularities interacting with interfaces using alternating technique part i anisotropic trimaterial abstract schwarz neumann s alternating technique is applied to singularity problems in an anisotropic trimaterial which denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces linear elastic materials under general plane deformations are assumed in which the plane of deformation is perpendicular to the two parallel interface planes it is well known that if the solution is known for singularities in a homogeneous anisotropic medium the solution for the same singularities in an anisotropic bimaterial can be constructed by the method of analytic continuation it is shown here that the solution for singularities in a homogeneous medium may also be used as a base of the solution for the same singularities in a trimaterial the alternating technique is applied to derive the trimaterial solution in a series form whose convergence is guaranteed the solution procedure is universal in the sense that no specific information about the singularity is needed the energetic forces exerted on a dislocation due to interfaces are also evaluated from the trimaterial solution the trimaterial solution studied here can be applied to a variety of problems e g a bimaterial including a half plane problem a finite thin film on semi infinite substrate and a finite strip of thin film etc some examples are presented to verify the usefulness of the obtained solutions

analysis of perfectly bonded wedges and bonded wedges with an interfacial crack under antiplane shear loading antiplane shear deformation of perfectly bonded wedges as well as bonded wedges with an interface crack are studied in this paper the solution of governing differential equations is accomplished by means of the mellin transform for two edge bonded isotropic wedges with perfect bonding along the common edge closed form solutions are obtained for stress fields and analytical relations are given for the strength of singularity at the apex however for bonded wedges with an interfacial crack first it is necessary to express the traction free condition of the crack faces in the form of a singular integral equation which is done in this paper by describing an exact analytical method the resultant singular integral equations are then solved analytically and the obtained results including the stress intensity factors at the crack tips are plotted a comparison of the results in the special cases shows a complete agreement with those cited in the literature however when the crack tip coincides with the wedge apex a strength of singularity of unity has been observed

on archimedean triangular norms abstract the behaviour of the additive generator functions related to a sequence of convergent continuous archimedean triangular norm where the limit triangular norm is continuous archimedean is examined in this paper it is proved that the related generator functions converge to the generator function of the limit triangular norm in some sense under the assumption that the limit triangular norm is strict a bit weaker convergence is proved if the limit triangular norm has 0 divisor an example is given for the fact that the stronger type of convergence cannot be obtained in the 0 divisor limit case

singularities interfaces and cracks in dissimilar anisotropic media for a non pathological bimaterial in which an interface crack displays no oscillatory behaviour it is observed that apart possibly from the stress intensity factors the structure of the near tip field in each of the two blocks is independent of the elastic moduli of the other block collinear interface cracks are analysed under this non oscillatory condition and a simple rule is formulated that allows one to construct the complete solutions from mode iii solutions in an isotropic homogeneous medium the general interfacial crack tip field is found to consist of a two dimensional oscillatory singularity and a one dimensional square root singularity a complex and a real stress intensity factors are proposed to scale the two singularities respectively owing to anisotropy a peculiar fact is that the complex stress intensity factor scaling the oscillatory fields however defined does not recover the classical stress intensity factors as the bimaterial degenerates to be non pathological collinear crack problems are also formulated in this context and a strikingly simple mathematical structure is identified interactive solutions for singularity interface and singularity interface crack are obtained the general results are specialized to decoupled antiplane and in plane deformations for this important case it is found that if a material pair is non pathological for one set of relative orientations of the interface and the two solids it is non pathological for any set of orientations for bonded orthotropic materials an intuitive choice of the principal measures of elastic anisotropy and dissimilarity is rationalized a complex variable representation is presented for a class of degenerate orthotropic materials throughout the paper the equivalence of the lekhnitskii and stroh formalisms is emphasized the article concludes with a formal statement of interfacial fracture mechanics for anisotropic solids

the degeneration of image singularities from anisotropic materials to isotropic materials for an elastic half plane abstract the degeneration of image singularities from an anisotropic material to an isotropic material for a half plane is discussed in this study the green s functions for anisotropic and isotropic half planes with traction free boundary subjected to concentrated forces and dislocations have been obtained by many authors it was commonly accepted that the solution of isotropic problem cannot be derived from anisotropic solutions however we believe that this possibility exists as we will demonstrate in this paper anisotropic materials include only image singularities of order o 1 r i e forces and dislocations existing on image points there are many image points for anisotropic materials and the locations of these image points depend on the material constants however isotropic materials have only one image point with higher order image singularities o 1 r2 o 1 r3 from the analysis provided in this study it is found that the higher order image singularities for an isotropic half plane are generated by combining the concentrated forces and dislocations when an anisotropic material degenerates to an isotropic material the solutions of higher order image singularities for isotropic material are dependent therefore these image singularities can be combined to form only three or four simpler image singularities acting on an image point of the isotropic material

some results on the covering radii of reed muller codes let r r m be the rth order reed muller code of length 2 sup m and let rho r m be its covering radius r

mixed boundary value problems of two dimensional anisotropic elasticity with perturbed boundaries the mixed boundary value problems of two dimensional anisotropic elasticity are considered in this paper the boundary treated may be the one perturbed by a straight line or an ellipse a general solution up to the first order perturbation has been found by using stroh9s formalism analytical continuation method conformal mapping function and perturbation technique as to higher order perturbation solutions general procedure is depicted in this paper in order to illustrate the use of general solution two typical examples are solved completely one is a cosine wave shaped surface indented by a rigid flat ended punch the other is a triangular hole boundary indented by a rigid stamp

improving the lower bound on the higher order nonlinearity of boolean functions with prescribed algebraic immunity the recent algebraic attacks have received a lot of attention in cryptographic literature the algebraic immunity of a boolean function quantifies its resistance to the standard algebraic attacks of the pseudorandom generators using it as a nonlinear filtering or combining function very few results have been found concerning its relation with the other cryptographic parameters or with the rth order nonlinearity as recalled by carlet at crypto 06 many papers have illustrated the importance of the r th order nonlinearity profile which includes the first order nonlinearity the role of this parameter relatively to the currently known attacks has been also shown for block ciphers recently two lower bounds involving the algebraic immunity on the rth order nonlinearity have been shown by carlet none of them improves upon the other one in all situations in this paper we prove a new lower bound on the rth order nonlinearity profile of boolean functions given their algebraic immunity that improves significantly upon one of these lower bounds for all orders and upon the other one for low orders

boundary integral equations for 2d elasticity and its application in discrete dislocation dynamics simulation in finite body 1 general theory abstract a unified approach originating from cauchy integral theorem is presented to derive boundary integral equations for two dimensional elasticity problems several sets of boundary integral equations are derived and their relations are revealed explicit expressions for materials with different symmetry planes are listed special attention is given to the formulation that is based on the tractions and the tangential derivatives of displacements along solid boundary since its integral kernels have the weakest singularities the formulation is further extended to include singular points such as dislocations and line forces in a finite body so that the singular stress field can be directly obtained from solving the integral equations on the external boundary without involving the linear superposition technique that was often used in the literature its application in simulating discrete dislocation motion in a finite solid body is discussed

on the resistance of boolean functions against algebraic attacks using univariate polynomial representation in the past few years algebraic attacks against stream ciphers with linear feedback function have been significantly improved as a response to the new attacks the notion of algebraic immunity of a boolean function f was introduced defined as the minimum degree of the annihilators of f and f 1 an annihilator of f is a nonzero boolean function g such that f g 0 while several constructions of boolean functions with optimal algebraic immunity have been proposed there is no significant progress concerning the resistance against the so called fast algebraic attacks in this paper we provide a framework to assess the resistance of boolean functions against the new algebraic attacks including fast algebraic attacks the analysis is based on the univariate polynomial representation of boolean functions and necessary and sufficient conditions are presented for a boolean function to have optimal behavior against all the new algebraic attacks finally we introduce a new infinite family of balanced boolean functions described by their univariate polynomial representation by applying the new framework we prove that all the members of the family have optimal algebraic immunity and we efficiently evaluate their behavior against fast algebraic attacks

image singularities of green s functions for isotropic elastic bimaterials subjected to concentrated forces and dislocations abstract green s functions for isotropic materials in the two dimensional problem for elastic bimaterials with perfectly bonded interface are reexamined in the present study although the green s function for an isotropic elastic bimaterial subjected to a line force or a line dislocation has been discussed by many authors the physical meaning and the structure of the solution are not clear in this investigation the green s function for an elastic bimaterial is shown to consist of eight green s functions for a homogeneous infinite plane one of the novel features is that green s functions for bimaterials can be expressed directly by knowing green s functions for the infinite plane if the applied load is located in material 1 the solution for the half plane of material 1 is constructed with the help of five green s functions corresponding to the infinite plane however the solution for the half plane of material 2 only consists of three green s functions for the infinite plane one of the five green s functions of material 1 and all the three green s functions of material 2 have their singularities located in the half plane where the load is applied and the other four image singularities of material 1 are located outside the half plane at the same distance from the interface as that of the applied load the nature and magnitude of the image singularities for both materials are presented explicitly from the principle of superposition and classified according to different loads it is known that for the problem of anisotropic bimaterials subjected to concentrated forces and dislocations the image singularities are simply concentrated forces and dislocations with the stress singularity of order o 1 r however higher orders o 1 r2 and o 1 r3 of stress singularities are found to exist in this study for isotropic bimaterials the highest order of the stress singularity is o 1 r3 for the image singularities of material 1 and is o 1 r2 for material 2 using the present solution green s functions associated with the problems of elastic half plane with free and rigidly fixed boundaries for homogeneous isotropic elastic solid are obtained as special cases

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

singularities interacting with interfaces and cracks abstract solutions to singularities such as point force point moment edge dislocation and transformation strain spot embedded in bonded elastic blocks of dissimilar materials are found to relate to the solutions to the same singularities in an infinite homogeneous plane by a formula independent of the nature of the singularities this universal result is then used to analyze the interactions between singularities and interface cracks the complete solutions and stress intensity factors are presented for two important interface crack configurations

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

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

counting boolean functions with specified values in their walsh spectrum the problem of counting boolean functions with specified number s of walsh coefficients w in their walsh spectrum is discussed in this paper strategies to solve this problem shall help solving many more problems related to desired cryptographic features of boolean functions such as nonlinearity resiliency algebraic immunity etc in an attempt to study this problem we present a new framework of solutions we give results for w 2 n 1 and for all s in line with a previous work of wu 1998 12 we also provide various results such as existence and construction for some s when w 0 multiplicities for all w and naive bounds on s for w 2 n 2