large sets of disjoint spectra plateaued functions inequivalent to partially linear functions in this paper we give an efficient method for constructing a large set of disjoint spectra functions without linear structures which are not equivalent to partially linear functions this positively answers the open problem how to construct a large set of disjoint spectra functions which are not linearly equivalent to partially linear functions raised by zhang and xiao at the same time this significantly extends a recent result of zhang where a method of specifying four disjoint spectra functions was given it is demonstrated that such sets can be utilized in the design of highly nonlinear resilient functions in the second part based on a generalization of the indirect sum method we give an alternative approach for designing sets of disjoint spectra functions of even larger cardinality than already given ones but these functions then admit linear structures in addition it is shown that using suitable initial functions in the generalized indirect sum method we can specify highly nonlinear resilient boolean functions in odd number of input variables n whose nonlinearity in many cases exceeds the current best known values moreover we design some balanced functions for odd n that also achieve the highest nonlinearity known

secondary constructions of highly nonlinear boolean functions and disjoint spectra plateaued functions in this paper we modify a generalized indirect sum construction to construct functions with high nonlinearity by utilizing the modified construction highly nonlinear functions in n m variables can be obtained from known bent functions in n variables and highly nonlinear functions in m variables it is possible to obtain new n 15 variable functions with nonlinearity 2 n 1 5 1 2 n 1 5 1 2 20x2 n 2 and new 12 variable 2 resilient functions with nonlinearity 2000 and algebraic degree 8 which achieve optimal algebraic immunity moreover the modified construction can also be used as an iterative construction of a quadruple of disjoint spectra plateaued functions in addition we present sufficient conditions for a quadruple of disjoint spectra plateaued functions to have no nonzero linear structure

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

brief analysis of nonlinear time delay systems using modules over non commutative rings the theory of non commutative rings is introduced to provide a basis for the study of nonlinear control systems with time delays the left ore ring of non commutative polynomials defined over the field of meromorphic function is suggested as the framework for such a study this approach is then generalized to a broader class of nonlinear systems with delays that are called generalized roesser systems finally the theory is applied to analyze nonlinear time delay systems a weak observability is defined and characterized generalizing the well known linear result properties of closed submodules are then developed to obtain a result on the accessibility of such systems

generic constructions of five valued spectra boolean functions whereas the design and properties of bent and plateaued functions have been frequently addressed during the past few decades there are only a few design methods of the so called five valued spectra boolean functions whose walsh spectra take the values in 0 pm 2 lambda 1 pm 2 lambda 2 moreover these design methods mainly regard the specification of these functions in their algebraic normal form anf domain in this paper we give a precise characterization of this class of functions in their spectral domain using the concept of a dual of plateaued functions both necessary and sufficient conditions on the walsh support of these functions are given which then connects their design in the spectral domain to a family of the so called totally non overlap disjoint spectra plateaued functions we identify some suitable families of plateaued functions having this property thus providing some generic methods in the spectral domain furthermore we also provide an extensive analysis of their constructions in the anf domain and provide several generic design methods the importance of this class of functions is manifolded where apart from being suitable for some cryptographic applications we emphasize their property of being constituent functions in the so called four bent decomposition

on observation of time delay systems with unknown inputs causal and non causal observability are discussed in this technical note for nonlinear time delay systems with unknown inputs using the theory of non commutative rings and the algebraic framework introduced by xia the nonlinear time delay system is transformed into a suitable canonical form to solve the problem a necessary and sufficient condition is given to guarantee the existence of a change of coordinates leading to such a form

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

homoclinic orbits for second order hamiltonian systems possessing superquadratic potentials received by the editors november 27 1990 1991 mathematics subject classification primary 34c99 58e99 58f99 the first author was supported by ministero p i gruppo 40 calcolo delle variazioni the second author s research was sponsored in part by the u s army research office under contract daal03 87 k 0043 the national science foundation under grant mcs 8110556 and the office of naval research under grant n00014 88 ko134 any reproduction for the purpose of the united states govemment is permitted

new results for perturbed hamiltonian systems with impulses abstract in this paper we study the existence of three solutions for second order impulsive hamiltonian systems by using a variational method and some critical points theorems of b ricceri we obtain some new criteria for guaranteeing that the impulsive hamiltonian systems have three solutions some recent results are extended and improved some examples are presented to demonstrate the application of our main results

homoclinic orbits for a class of hamiltonian systems consider the second order hamiltonian system where q n and v c 1 n is t periodic in t suppose v q t 0 0 0 is a local maximum for v t and v t x x under these and some additional technical assumptions we prove that hs has a homoclinic orbit q emanating from 0 the orbit q is obtained as the limit as k of 2 kt periodic solutions i e subharmonics q k of hs the subharmonics q k are obtained in turn via the mountain pass theorem

existence of homoclinic solution for the second order hamiltonian systems abstract an existence theorem of homoclinic solution is obtained for a class of the nonautonomous second order hamiltonian systems u t l t u t w t u t 0 t r by the minimax methods in the critical point theory specially the generalized mountain pass theorem where l t is unnecessary uniformly positively definite for all t r and w t x satisfies the superquadratic condition w t x x 2 as x uniformly in t and need not satisfy the global ambrosetti rabinowitz condition

observability and related structural results for linear hereditary systems new results on the theory of observability and deterministic observers for linear time invariant systems with delays are presented the results have been established only for the case of point delays which are commensurable however most of the results can be generalized to the situation with distributed delays and to the ease with non commensurate delays

observability and observers for a class of linear systems with delays a brief description of observability detectability and spectral observability concepts for time delay systems is given and some results on relations between these concepts are presented another result of this correspondence is the derivation of constructive design procedures for dynamic observers for a large class of linear autonomous systems with time delays this class includes systems with arbitrary output measurement delays where the procedure is based on well known methods of spectrum assignment for a pair of real matrices it is also shown that the observer problem for general systems with delays can be reformulated so as to get an easier case without output delays

observability of linear systems with commensurate delays and unknown inputs this paper investigates the observability analysis for linear time systems whose outputs are affected by unknown inputs three different definitions of observability are proposed by introducing the smith form and comparing the invariant factors a sufficient condition is deduced for each proposed definition observability several examples are given for the purpose of highlighting the effectiveness of the proposed approach

infinitely many homoclinic solutions for second order hamiltonian systems with odd nonlinearities abstract in this paper we study the existence of homoclinic solutions for second order hamiltonian systems with odd nonlinearities u l t u w u t u 0 where l t and w t u are not assumed to be periodic in t we get under certain assumptions on l and w infinitely many homoclinic solutions for both subquadratic and superquadratic cases by using the fountain theorems in critical point theory

on plateaued functions the focus of this article is on nonlinear characteristics of cryptographic boolean functions first we introduce the notion of plateaued functions that have many cryptographically desirable properties second we establish a sequence of strengthened inequalities on some of the most important nonlinearity criteria including nonlinearity avalanche and correlation immunity and prove that critical cases of the inequalities coincide with characterizations of plateaued functions we then proceed to prove that plateaued functions include as a proper subset all partially bent functions that were introduced earlier by claude carlet 1993 this solves an interesting problem that arises naturally from previously known results on partially bent functions in addition we construct plateaued but not partially bent functions that have many properties useful in cryptography

cryptographically significant boolean functions with five valued walsh spectra we describe methods to construct balanced resp 1 resilient functions of odd number of variables n achieving the bent concatenation nonlinearity and having algebraic degree n1 resp n 2 the technique is to algebraically modify the concatenation of two properly chosen n 1 variable maiorana mcfarland bent functions the constructed functions can be used with certain recursive operators to provide higher order resilient functions with maximum possible degree and high nonlinearity such functions are well suited for stream cipher applications interestingly all the constructed functions have a five valued walsh spectr

on cryptographic properties of the cosets of r 1 m we introduce a new approach for the study of weight distributions of cosets of the reed muller code of order 1 our approach is based on the method introduced by kasami 1968 using pless 1963 identities by interpreting some equations we obtain a necessary condition for a coset to have a high minimum weight most notably we are able to distinguish such cosets which have three weights only we then apply our results to the problem of the nonlinearity of boolean functions we particularly study the links between this criterion and the propagation characteristics of a function

some results on connecting orbits for a class of hamiltonian systems abstract the existence of various kinds of connecting orbits is established for a certain hamiltonian system as well as its time dependent analogue for the autonomous case our main assumption is that v has a global maximum e g at x o and we find a various kinds of orbits terminating at o for the time dependent case v has a local but not global maximum at x o and we find a homoclinic orbit emanating from and terminating at o keywords periodic solution

infinitely many homoclinic solutions for second order hamiltonian systems abstract in this paper we study the existence of infinitely many homoclinic solutions for second order hamiltonian systems u l t u w u t u 0 t r where l t is unnecessarily positive definite for all t r and w t u is of subquadratic growth as u

generalized maiorana mcfarland construction of resilient boolean functions with high nonlinearity and good algebraic properties a new framework concerning the construction of small order resilient boolean functions whose nonlinearity is strictly greater than 2 n 1 2 n 2 is given first a generalized maiorana mcfarland construction technique is described which extends the current approaches by combining the usage of affine and nonlinear functions in a controllable manner it is shown that for any given m this technique can be used to construct a large class of n variable n both even and odd m resilient degree optimized boolean functions with currently best known nonlinearity this class may also provide functions with excellent algebraic properties measured through the resistance to fast algebraic attacks if the number of n 2 variable affine subfunctions used in the construction is relatively low due to a potentially low hardware implementation cost along with overall good cryptographic properties this class of functions is an attractive candidate for the use in certain stream cipher schemes

the disturbance decoupling problem for time delay nonlinear systems in this paper the disturbance decoupling problem ddp for a class of siso nonlinear systems with multiple delays in the input and the state is studied a pioneering mathematical approach is introduced for this class of systems and is claimed to be the cornerstone of the problem necessary and sufficient conditions are given for the existence of a bicausal feedback that solves the ddp sufficient conditions for the existence of a solution within other classes of compensators are included as well

homoclinic solutions for a class of second order hamiltonian systems with locally defined potentials abstract in this paper we study the existence of infinitely many homoclinic solutions for a class of second order hamiltonian systems u l t u w u t u 0 t r where l t is unnecessarily positive definite for all t r and w t u is only locally defined near the origin with respect to u and not assumed to be periodic with respect to t