construction of nonlinear resilient boolean functions using small affine functions in this correspondence we use affine functions on a small number of variables to construct resilient functions on a large number of variables we show that by properly combining these functions it is possible to achieve high nonlinearity and high algebraic degree an important contribution of the correspondence is to show that for each order of resiliency m it is possible to find infinitely many odd and even positive integers n such that it is possible to construct maximum degree n variable m resilient functions having nonlinearity strictly greater than 2 sup n 1 2 sup spl lfloor n 2 spl rfloor we also present construction of some important functions on a small number of variables

a linear approximation for the regular reflection of a weak shock at a wedge abstract the problem of shock reflection by a wedge in the flow dominated by the unsteady potential flow equation is an important problem in weak regular reflection the flow behind the reflected shock is immediately supersonic and becomes subsonic further downstream the reflected shock is transonic its position is a free boundary for the unsteady potential equation which is degenerate at the sonic line in self similar coordinates applying the special partial hodograph transformation used in zhouping xin huicheng yin transonic shock in a nozzle i 2 d case comm pure appl math lvii 2004 1 51 zhouping xin huicheng yin transonic shock in a nozzle ii 3 d case ims preprint 2003 we derive a nonlinear degenerate elliptic equation with nonlinear boundary conditions in a piecewise smooth domain when the angle between incident shock and wedge is small we can see the weak regular reflection as the disturbance of normal reflection as in chen shuxing linear approximation of shock reflection at a wedge with large angle comm partial differential equations 21 78 1996 1103 1118 by linearizing the resulted nonlinear equation and boundary conditions with the above viewpoint in chen shuxing linear approximation of shock reflection at a wedge with large angle comm partial differential equations 21 78 1996 1103 1118 we obtain a linear degenerate elliptic equation with mixed boundary conditions in a curved quadrilateral domain by means of elliptic regularization techniques a delicate a priori estimate and compact arguments we show that the solution of the linearized problem is smooth in the interior and lipschitz continuous up to the degenerate boundary

mixed boundary value problems for elliptic and parabolic differential equations of second order on considere les problemes aux valeurs limites mixtes suivants lu f 1 dans mu f 2 sur u f 3 sur avec l operateur elliptique et pu f 1 dans 0 t mu f 2 sur 0 t u f 3 sur 0 t 0 pour des operateurs p paraboliques pour des operateurs obliques generaux m et pour des domaines ou et se rencontrent a des angles arbitraires on montre l existence de solutions classiques quand les angles sont non nuls et f 3 est continue de holder

decrypting a class of stream ciphers using ciphertext only pseudonoise sequences generated by linear feedback shift registers 1 with some nonlinear combining function have been proposed 2 5 for cryptographic applications as running key generators in stream ciphers in this correspondence it will be shown that the number of trials to break these ciphers can be significantly reduced by using correlation methods by comparison of computer simulations and theoretical results based on a statistical model the validity of this analysis is demonstrated rubin 6 has shown that it is computationally feasible to solve a cipher proposed by pless 2 in a known plaintext attack using as few as 15 characters here the number of ciphertext symbols is determined to perform a ciphertext only attack on the pless cipher using the correlation attack our conclusion from the analysis is that the pseudonoise generator s output sequence and the sequences generated by the linear feedback shift registers should be uncorrelated this leads to constraints for the nonlinear combining function to be used

on the existence of 10 2 7 488 resilient functions using a heuristic search combined with some algebraic techniques several examples for 10 variable boolean functions with nonlinearity 488 algebraic degree 7 and resiliency degree 2 were constructed this construction affirmatively answers the open problem about the existence of such functions

existence and regularity of solution of mixed boundary value problem of a busemann equation with nonlinear absorb term abstract the busemann equation is a classical equation coming from fluid dynamics the well posed problem and regularity of solution of busemann equation with nonlinear term are interesting and important the busemann equation is elliptic in y 0 and is degenerate at the line y 0 in r 2 with a special nonlinear absorb term we study a nonlinear degenerate elliptic equation with mixed boundary conditions in a piecewise smooth domain by means of elliptic regularization technique a delicate prior estimate and compact argument we show that the solution of mixed boundary value problem of busemann equation is smooth in the interior and lipschitz continuous up to the degenerate boundary on some conditions the result is better than the result of classical boundary degenerate elliptic equation

existence and regularity of the solution of a mixed boundary value problem for the keldysh equation with a nonlinear absorption term abstract the keldysh equation is a more general form of the classic tricomi equation from fluid dynamics its well posedness and the regularity of its solution are interesting and important the keldysh equation is elliptic in y 0 and is degenerate at the line y 0 in r 2 adding a special nonlinear absorption term we study a nonlinear degenerate elliptic equation with mixed boundary conditions in a piecewise smooth domain similar to the potential fluid shock reflection problem by means of an elliptic regularization technique a delicate a priori estimate and compact argument we show that the solution of a mixed boundary value problem of the keldysh equation is smooth in the interior and lipschitz continuous up to the degenerate boundary under some conditions we believe that this kind of regularity result for the solution will be rather useful

on the existence of 9 3 5 240 resilient functions using a heuristic search technique several examples for 9 variable boolean functions with nonlinearity 240 algebraic degree 5 and resiliency degree 3 were constructed this construction affirmatively answers the open problem about the existence of such functions

optimal holder regularity for mixed boundary value problems abstract we continue our study of mixed boundary value problems lu 1 in mu 2 on u 3 on for second order elliptic operators l and first order oblique operators m a best possible estimate of the regularity of u is proved under weak hypotheses on the coefficients of l and m

a spectral characterization of correlation immune combining functions it is shown that a boolean combining function f x of n variables is mth order correlation immune if and only if its walsh transform f omega vanishes for all omega with hamming weight between 1 and m inclusive this result is used to extend slightly siegenthaler s ieee trans comput vol c 34 pp 81 85 jan 1985 characterization of the algebraic normal form of correlation immune combining functions

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

existence and uniqueness analysis of a detached shock problem for the potential flow abstract we study a problem for two dimensional steady potential and isentropic euler equations in a bounded domain where an artificial detached shock interacts with a wedge using the stream function we obtain a free boundary problem for the subsonic state and the detached artificial shock curve and we prove that such configuration admits a unique solution in certain weighted holder spaces the proof is based on various holder and schauder estimates for second order elliptic equations and fixed point theorems moreover we pose an energy principle and remark that the physical attached shock is the minimizer of the energy functional

pointwise estimates for oblique derivative problems in nonsmooth domains abstract there is a long history of studying boundary value problems for elliptic and parabolic differential equations when the equation is posed in a domain with sufficiently smooth boundary in this paper we prove some pointwise estimates and regularity results for solutions when a directional derivative is prescribed on the boundary which satisfies an interior cone condition we consider very weak hypotheses on the data of the problem in particular we consider an optimal relation between the interior cone and the direction of the prescribed directional derivative and we assume very little smoothness of the coefficients in the equation and the boundary condition

a bifurcation problem governed by the boundary condition ii we deal with positive solutions of u a x up in a bounded smooth domain omega subset mathbb r n subject to the boundary condition u v u a parameter p 1 we prove that this problem has a unique positive solution if and only if 0 0 and coincides with the first eigenvalue of an associated eigenvalue problem moreover we find the limit profile of the solution as 1

the influence of some fuzzy implication operators on the accuracy of a fuzzy model part ii abstract the influence of fuzzy implication operators and the connective also on the accuracy of a fuzzy model of a d c series motor is considered some typical fuzzy implication operators are applied to the construction of a fuzzy model of a d c series motor a root mean square error is used as the criterion of the fuzzy model s adequacy to the real system a number of mathematical operations necessary for the implementation of the fuzzy model are used as the criterion by which the fuzzy model s applicability if estimated from the point of view of computing techniques the best types of fuzzy relations representing fuzzy models of a real system are chosen in order to secure the least root mean square error with minimal number of mathematical operations necessary for computer implementation

construction of highly nonlinear 1 resilient boolean functions with optimal algebraic immunity and provably high fast algebraic immunity in 2013 tang carlet and tang ieee tit 59 1 653 664 2013 presented two classes of boolean functions the functions in the first class are unbalanced and the functions in the second one are balanced both of those two classes of functions have high nonlinearity high algebraic degree optimal algebraic immunity and high fast algebraic immunity however they are not 1 resilient which represents a drawback for their use as filter functions in stream ciphers in this paper we first propose a large family of 1 resilient boolean functions having high lower bound on nonlinearity optimal algebraic immunity and optimal algebraic degree that is meeting the siegenthaler bound most notably we can mathematically prove that every function in n variables belonging to this family has fast algebraic immunity no less than n 6 which is the first time that an infinite family of 1 resilient functions with provably high fast algebraic immunity has been invented furthermore we exhibit a subclass of the family which has higher lower bound on nonlinearity than all the known 1 resilient functions with potentially optimal algebraic immunity and potentially high fast algebraic immunity

the covering radius of the 2 15 16 reed muller code is at least 16276 two interesting cosets of the first order reed muller code of block length 2 15 are described they provide counterexamples to a conjecture on the covering radius

free boundary and mixed boundary value problems for quasilinear elliptic equations tangential oblique derivative and degenerate dirichlet boundary problems abstract we present holder estimates and holder gradient estimates for a class of free boundary problems with tangential oblique derivative boundary conditions provided the oblique vector does not vanish at any point on the boundary we also establish the existence result for a general class of quasilinear degenerate problems of this type including nonlinear wave systems and the unsteady transonic small disturbance equation

shock diffraction by convex cornered wedges for the nonlinear wave system we are concerned with rigorous mathematical analysis of shock diffraction by two dimensional convex cornered wedges in compressible fluid flow through the nonlinear wave system this shock diffraction problem can be formulated as a boundary value problem for second order nonlinear partial differential equations of mixed elliptic hyperbolic type in an unbounded domain it can be further reformulated as a free boundary problem for nonlinear degenerate elliptic equations of second order with a degenerate oblique derivative boundary condition we establish a global theory of existence and optimal regularity for this shock diffraction problem to achieve this we develop several mathematical ideas and techniques which are also useful for other related problems involving similar analytical difficulties

a proof of existence of perturbed steady transonic shocks via a free boundary problem we prove the existence of a solution of a free boundary problem for the transonic small disturbance equation the free boundary is the position of a transonic shock dividing two regions of smooth flow assuming inviscid irrotational flow as modeled by the transonic small disturbance equation the equation is hyperbolic upstream where the flow is supersonic and elliptic in the downstream subsonic region to study the stability of a uniform planar transonic shock we consider perturbation by a steady c1 upstream disturbance if the upstream disturbance is small in a c1 sense then there is a steady solution in which the downstream flow and the transonic shock are holder continuous perturbations of the uniform configuration this result provides a new use of inviscid perturbation techniques to demonstrate in two dimensions the stability of transonic shock waves of the type that appear for example over the wing of an airplane along an airfoil or as bow shocks in a flow with a supersonic free stream velocity 2000 john wiley sons inc

generalised fuzzy aggregation in estimating the risk of desertification of a burned forest this paper investigates two aspects of using fuzzy logic with a gis the use of non conventional aggregation operators for conjunctive and disjunctive reasoning and the use of weights when combining aggregates of different significance to the classification two methods of weighting are used weights as powers of the membership functions and the novel concept of membership functions that take values greater than 1 the two approaches are investigated in conjunction with 121 possible combinations of aggregation operators that are used to reason in the disjunctive and conjunctive level of the problem of assessing the risk of desertification after a forest fire

exploiting product distributions to identify relevant variables of correlation immune functions a boolean function f is correlation immune if each input variable is independent of the output under the uniform distribution on inputs for example the parity function is correlation immune we consider the problem of identifying relevant variables of a correlation immune function in the presence of irrelevant variables we address this problem in two different contexts first we analyze skewing a heuristic method that was developed to improve the ability of greedy decision tree algorithms to identify relevant variables of correlation immune boolean functions given examples drawn from the uniform distribution page and ray 2003 we present theoretical results revealing both the capabilities and limitations of skewing second we explore the problem of identifying relevant variables in the product distribution choice pdc learning model a model in which the learner can choose product distributions and obtain examples from them we prove a lemma establishing a property of boolean functions that may be of independent interest using this lemma we give two new algorithms for finding relevant variables of correlation immune functions in the pdc model

correlation immune functions over finite fields we give a series of constructions of correlation immune function over finite fields we prove that f sub 2 and f sub 3 are the only finite fields f sub q with the property that every n 1 th correlation immune function in n 2 variables over f sub q is linear we also show that by choosing larger finite fields one can alleviate the tradeoff between the length of the linear equivalent and the order of correlation immunity this is useful for the design of various cryptosystems

constructions of almost optimal resilient boolean functions on large even number of variables in this paper a technique on constructing nonlinear resilient boolean functions is described by using several sets of disjoint spectra functions on a small number of variables an almost optimal resilient function on a large even number of variables can be constructed it is shown that given any m one can construct infinitely many re variable n even m resilient functions with nonlinearity 2n 1 2n 2 a large class of highly nonlinear resilient functions which were not known are obtained then one method to optimize the degree of the constructed functions is proposed last an improved version of the main construction is given

further constructions of resilient boolean functions with very high nonlinearity one well known method of generating key stream sequences for stream ciphers is to combine the outputs of several linear feedback shift registers lfsr using a combining boolean function here we concentrate on the design of good combining boolean functions we provide resilient boolean functions with currently best known nonlinearity these functions were not known earlier and the issues related to their existence were posed as open questions in the literature some of the functions we construct here achieve the provable upper bound on nonlinearity for resilient boolean functions our technique interlinks mathematical results with classical computer search

a free boundary problem for a quasi linear degenerate elliptic equation regular reflection of weak shocks we prove the existence of a solution to the weak regular reflection problem for the unsteady transonic small disturbance utsd model for shock reflection by a wedge in weak regular reflection the state immediately behind the reflected shock is supersonic and constant the flow becomes subsonic further downstream the equation in self similar coordinates is degenerate at the sonic line the reflected shock becomes transonic and begins to curve there its position is the solution to a free boundary problem for the degenerate equation using the rankine hugoniot conditions along the reflected shock we derive an evolution equation for the transonic shock and an oblique derivative boundary condition at the unknown shock position by regularizing the degenerate problem we construct uniform bounds we apply local compactness arguments to extract a limit that solves the problem the solution is smooth in the interior and continuous up to the degenerate boundary this work completes a stage in our program to construct self similar solutions of two dimensional riemann problems in a series of papers we developed techniques for solving the degenerate elliptic equations that arise in self similar reductions of hyperbolic conservation laws in other papers especially in joint work with gary lieberman we developed techniques for solving free boundary problems of the type that arise from rankine hugoniot relations for the first time in this paper we combine these approaches and show that they are compatible although our construction is limited to a finite part of the unbounded subsonic region it suggests that this approach has the potential to solve a variety of problems in weak shock reflection including mach and von neumann reflection in the utsd equation and the analogous problems for the unsteady full potential equation 2002 john wiley sons inc

existence and stability of perturbed transonic shocks for compressible steady potential flows abstract we establish an existence theorem for perturbed transonic steady potential flows where the boundary of the subsonic region consists of a transonic shock and thus the governing equation becomes a free boundary problem we establish gradient estimates and use the fixed point theorem of caristi s which does not require a compactness of the map to establish the existence result we provide new techniques to handle the gradients and show that the flow is strictly elliptic inside of the subsonic region

the enhancement of the cell based gis analyses with fuzzy processing capabilities in order to store and process natural phenomena in geographic information systems gis it is necessary to model the real world to form computational representation since classical set theory is used in conventional gis softwares to model uncertain real world the natural variability in the environmental phenomena cannot be modeled appropriately because pervasive imprecision of the real world is unavoidably reduced to artificially precise spatial entities when the conventional crisp logic is used for modeling an alternative approach is the fuzzy set theory which provides a formal framework to represent and reason with uncertain information in addition linguistic variable concept in a fuzzy logic system is useful for communicating concepts and knowledge with human beings fuzzycell is a system designed and implemented to enhance commercial gis software namely arcmap r with fuzzy set theory fuzzycell allows users to a incorporate human knowledge and experience in the form of linguistically defined variables into gis based spatial analyses b handle imprecision in the decision making processes and c approximate complex ill defined problems in decision making processes and classification it provides eight membership functions inference methods methods for rule aggregation operators for set operations and methods for defuzzification the operation of fuzzycell is presented through case studies which demonstrate its application for classification and decision making processes this paper shows how fuzzy logic approach may contribute to a better representation and reasoning with imprecise concepts which are inherent characteristics of geographic data stored and processed in gis

high meets low construction of strictly almost optimal resilient boolean functions via fragmentary walsh spectra this paper considers the construction of resilient boolean functions on an odd number of variables with strictly almost optimal sao nonlinearity through introducing the fragmentary walsh transform a construction technique called high meets low is proposed the detailed design procedures of a 39 variable 3 resilient boolean function with sao nonlinearity 2 38 2 19 2 16 2 14 are given it is shown that the nonlinearity of an n variable t resilient boolean function can reach 2 n 1 2 n 1 2 5 cdot 2 n 11 2 or 2 n 1 2 n 1 2 2 n 7 2 which are the largest known values for the corresponding n and t values finally by constructing a 29 variable balanced boolean function with sao nonlinearity 2 28 2 14 2 10 2 9 we show an alternative method to realize the high meets low construction technique

evaluating structural and topological consistency of complex regions with broad boundaries in multi resolution spatial databases multi resolution or multi scale spatial databases store and manage multiple representations of spatial objects in the same area so consistency among multiple representations of the same objects should be evaluated and maintained although many approaches have been proposed to check inconsistencies in multi resolution databases there is still a lack of effective approaches working for complex objects especially for regions with broad boundaries which is a general model for representing various types of uncertainties this paper presents approaches for evaluating structural and topological consistency among multiple representations of complex regions with broad boundaries cbbrs based on map generalization operators merging dropping and hybrid of these two for evaluation of structural consistency all possible multiple representations of a cbbr are generated automatically and organized into a structured neighborhood graph and then correspondences and equivalences among the multiple representations are defined to determine whether two representations at different levels of detail are structurally consistent for evaluation of topological consistency the topological relations between all pairs of regions in two cbbrs are considered and their variation with change of spatial scale is analyzed since the approaches in this paper are built on a hiearchical representation of cbbrs with arbitrarily complex structure they will also work well for evaluating consistency among multiple representations of complex objects

the tricomi problem for a genuinely nonlinear lavrentiev bitsadze equation of mixed type abstract in this paper we consider the tricomi problem for a genuinely nonlinear lavrentiev bitsadze mixed type equation 2 u x 2 sgn y 1 u x 2 2 u y 2 0 whose coefficients depend on the first order derivative of an unknown function we prove the existence of a solution to this problem by a method which can be used to study more difficult problems for nonlinear mixed type equations arising in gas dynamics

the behavior of the principal eigenvalue of a mixed elliptic problem with respect to a parameter abstract in this paper we determine the exact asymptotic behavior of the principal eigenvalue of a mixed elliptic eigenvalue problem which depends on a positive parameter when we analyze the case in which the problem is considered in a smooth bounded domain of r n and also the case of planar domains which are smooth except for a finite number of corner points

a polyhedron comparison theorem for 3 manifolds with positive scalar curvature the study of comparison theorems in geometry has a rich history in this paper we establish a comparison theorem for polyhedra in 3 manifolds with nonnegative scalar curvature answering affirmatively a dihedral rigidity conjecture by gromov for a large collections of polyhedra with interior non negative scalar curvature and mean convex faces we prove the dihedral angles along its edges cannot be everywhere less or equal than those of the corresponding euclidean model unless it is isometric to a flat polyhedron

boundary value problem for a nonlinear equation of mixed type abstract in this paper we consider the boundary value problem for a nonlinear lavrentiev bitsadze equation of mixed type 2 u x 2 sgn y 1 u x 2 2 u y 2 0 whose coefficients depend on the first order derivatives of unknown function above y 0 and below y 0 the equation becomes the nonlinear elliptic equation and nonlinear hyperbolic equation respectively this is different from the equation studied in chen 2011 9 we prove the existence of solution to the problem by the method which can be used to study more difficult problems for nonlinear equations of mixed type arising in gas dynamics

on guess and determine cryptanalysis of lfsr based stream ciphers in this paper the complexity of applying a guess and determine attack to so called linear feedback shift register lfsr based stream ciphers is analyzed this family of stream ciphers uses a single or several lfsr and a filtering function f gf 2 n rarr gf 2 m to generate the blocks of m ges 1 keystream bits at the time in difference to a classical guess and determine attack a method based on guessing certain bits in order to determine the remaining secret key state bits our approach efficiently takes advantage of the reduced preimage space for relatively large m and at the same time employing the design structure of the cipher several variations of the algorithm are derived to circumvent the sensitivity of attack to the input data n m and the key length in certain cases our attack outperforms classical algebraic attacks these being considered as one of the most efficient cryptanalyst tools for this type of ciphers a superior performance of our attack over algebraic attacks is demonstrated in case the filtering function belongs to the extended maiorana mcfarland class

maximum nonlinearity of symmetric boolean functions on odd number of variables in this correspondence we establish that for odd n the maximum nonlinearity achievable by an n variable symmetric boolean function is 2 sup n 1 2 sup n 1 sup 2 and characterize the set of functions which achieve this value of nonlinearity in particular we show that for each odd n spl ges 3 there are exactly four possible symmetric boolean functions achieving the nonlinearity 2 sup n 1 2 sup n 1 2

a linear approximation for the regular reflection of a weak shock at a wedge satisfying sonic condition abstract the problem of shock reflection by a wedge which the flow is dominated by the unsteady potential flow equation is a important problem in weak regular reflection the flow behind the reflected shock is immediately supersonic and becomes subsonic further downstream the reflected shock is transonic its position is a free boundary for the unsteady potential equation which is degenerate at the sonic line in self similar coordinates applying the special partial hodograph transformation used in zhouping xin huicheng yin transonic shock in a nozzle i 2 d case comm pure appl math 57 2004 1 51 zhouping xin huicheng yin transonic shock in a nozzle ii 3 d case ims preprint 2003 we derive a nonlinear degenerate elliptic equation with nonlinear boundary conditions in a piecewise smooth domain when the angle which between incident shock and wedge is small we can see that weak regular reflection as the disturbance of normal reflection as in shuxing chen linear approximation of shock reflection at a wedge with large angle comm partial differential equations 21 78 1996 1103 1118 by linearizing the resulted nonlinear equation and boundary conditions with above viewpoint we obtain a linear degenerate elliptic equation with mixed boundary conditions and a linear degenerate elliptic equation with oblique boundary conditions in a curved quadrilateral domain by means of elliptic regularization techniques delicate a priori estimate and compact arguments we show that the solution of linearized problem with oblique boundary conditions is smooth in the interior and lipschitz continuous up to the degenerate boundary

a global subsonic solution to an interacting transonic shock for the self similar nonlinear wave equation abstract we present the existence of the subsonic solution to a two dimensional riemann problem governed by a self similar nonlinear wave equation where the boundary of the subsonic region consists of a transonic shock and the sonic circle thus the governing equation becomes a free boundary problem on the transonic shock and degenerates on the sonic circle by utilizing the barrier methods and iterative methods we show the well posedness of the transonic shock in the entire subsonic region and thus establish the global solution this result does not rely on any smallness of riemann data

global transonic conic shock wave for the symmetrically perturbed supersonic flow past a cone in this paper we are concerned with the global existence and stability of a steady transonic conic shock wave for the symmetrically perturbed supersonic flow past an infinitely long conic body the flow is assumed to be polytropic isentropic and described by a steady potential equation theoretically as indicated in r courant k o friedrichs supersonic flow and shock waves interscience publishers inc new york 1948 it follows from the rankine hugoniot conditions and the entropy condition that there will appear a weak shock or a strong shock attached at the vertex of the sharp cone in terms of the different pressure states at infinity behind the shock surface which correspond to the supersonic shock and the transonic shock respectively in the references shuxing chen zhouping xin huicheng yin global shock wave for the supersonic flow past a perturbed cone comm math phys 228 2002 47 84 dacheng cui huicheng yin global conic shock wave for the steady supersonic flow past a cone polytropic case preprint 2006 dacheng cui huicheng yin global conic shock wave for the steady supersonic flow past a cone isothermal case pacific j math 233 2 2007 257 289 and zhouping xin huicheng yin global multidimensional shock wave for the steady supersonic flow past a three dimensional curved cone anal appl 4 2 2006 101 132 the authors have established the global existence and stability of a supersonic shock for the perturbed hypersonic incoming flow past a sharp cone when the pressure at infinity is appropriately smaller than that of the incoming flow at present for the supersonic symmetric incoming flow we will study the global transonic shock problem when the pressure at infinity is appropriately large

constructions of resilient s boxes with strictly almost optimal nonlinearity through disjoint linear codes in this paper a novel approach of finding disjoint linear codes is presented the cardinality of a set of u m t 1 disjoint linear codes largely exceeds all the previous best known methods used for the same purpose using such sets of disjoint linear codes not necessarily of the same length we have been able to provide a construction technique of t resilient s boxes f f2n 2m n even with strictly almost optimal nonlinearity this is the first time that the bound 2n 1 2n 2 has been exceeded by multiple output resilient functions actually the nonlinearity of our functions is in many cases equal to the best known nonlinearity of balanced boolean functions a large class of previously unknown cryptographic resilient s boxes is obtained and several improvements of the original approach are proposed some other relevant cryptographic properties are also briefly discussed it is shown that these functions may reach siegenthaler s bound n t 1 and can be either of optimal algebraic immunity or of slightly suboptimal algebraic immunity which was confirmed by simulations

stability analysis for semilinear parabolic problems in general unbounded domains abstract we introduce several notions of generalised principal eigenvalue for a linear elliptic operator on a general unbounded domain under boundary condition of the oblique derivative type we employ these notions in the stability analysis of semilinear problems some of the properties we derive are new even in the dirichlet or in the whole space cases as an application we show the validity of the hair trigger effect for the fisher kpp equation on general uniformly smooth domains