information theoretic novelty detection we present a novel approach to online change detection problems when the training sample size is small the proposed approach is based on estimating the expected information content of a new data point and allows an accurate control of the false positive rate even for small data sets in the case of the gaussian distribution our approach is analytically tractable and closely related to classical statistical tests we then propose an approximation scheme to extend our approach to the case of the mixture of gaussians we evaluate extensively our approach on synthetic data and on three real benchmark data sets the experimental validation shows that our method maintains a good overall accuracy but significantly improves the control over the false positive rate

blow up phenomena and global existence for the nonuniform weakly dissipative b equation abstract we first establish the local well posedness for the nonuniform weakly dissipative b equation which includes both the weakly dissipative camassa holm equation and the weakly dissipative degasperis procesi equation as its special cases we then study the blow up phenomena and the long time behavior of the solutions two blow up results are established for certain initial profiles moreover two sufficient conditions for the decay of the solutions are presented

on the blow up phenomena of the periodic dullin gottwald holm equation we first present several new blow up results for the periodic dullin gottwald holm equation by using some new sobolev inequalities we then investigate the blow up rate for all nonglobal solutions and determine the blow up set of blowing up solutions to the equation for a large class of initial data we finally address the lower semicontinuity of the existence time of solutions with smooth initial data

blow up blow up rate and decay of the solution of the weakly dissipative camassa holm equation in this paper we mainly study several problems on the weakly dissipative periodic camassa holm equation at first the local well posedness of the equation is obtained by kato s theorem a necessary and sufficient condition of the blow up of the solution and some criteria guaranteeing the blow up of the solution are established then the blow up rate of the solution is discussed moreover we prove that the equation has global solutions and these global solutions decay to zero as time goes to infinite provided the potentials associated to their initial date are of one sign

on the weakly dissipative camassa holm degasperis procesi and novikov equations abstract we show that the weakly dissipative camassa holm degasperis procesi hunter saxton and novikov equations can be reduced to their non dissipative versions by means of an exponentially time dependent scaling hence up to a simple change of variables the non dissipative and dissipative versions of these equations are equivalent similar results hold also for the equations in the so called b family of equations as well as for the two component and versions of the above equations

wave breaking for shallow water models with time decaying solutions abstract a family of camassa holm type equations with a linear term and cubic and quartic nonlinearities is considered local well posedness results are established via kato s approach conserved quantities for the equation are determined and from them we prove that the energy functional of the solutions is a time dependent monotonically decreasing function of time and bounded from above by the sobolev norm of the initial data under some conditions the existence of wave breaking phenomenon is investigated and necessary conditions for its existence are obtained in our framework the wave breaking is guaranteed among other conditions when the coefficient of the linear term is sufficiently small which allows us to interpret the equation as a linear perturbation of some recent camassa holm type equations considered in the literature

on asymptotically equivalent shallow water wave equations abstract the integrable third order korteweg de vries kdv equation emerges uniquely at linear order in the asymptotic expansion for unidirectional shallow water waves however at quadratic order this asymptotic expansion produces an entire family of shallow water wave equations that are asymptotically equivalent to each other under a group of nonlinear non local normal form transformations introduced by kodama in combination with the application of the helmholtz operator these kodama helmholtz kh transformations are used to present connections between shallow water waves the integrable fifth order kdv equation and a generalization of the camassa holm ch equation that contains an additional integrable case the dispersion relation of the full water wave problem and any equation in this family agree to fifth order the travelling wave solutions of the ch equation are shown to agree to fifth order with the exact solution

well posedness and blow up phenomena for a higher order shallow water equation this paper deals with the cauchy problem for a higher order shallow water equation yt auxy buyx 0 where y 2ku i x2 ku and k 2 the local well posedness of solutions for the cauchy problem in sobolev space hs r with s 7 2 is obtained under some assumptions the existence and uniqueness of the global solutions to the equation are shown and conditions that lead to the development of singularities in finite time for the solutions are also acquired finally the weak solution for the equation is considered

symmetric boolean functions we present an extensive study of symmetric boolean functions especially of their cryptographic properties our main result establishes the link between the periodicity of the simplified value vector of a symmetric boolean function and its degree besides the reduction of the amount of memory required for representing a symmetric function this property has some consequences from a cryptographic point of view for instance it leads to a new general bound on the order of resiliency of symmetric functions which improves siegenthaler s bound the propagation characteristics of these functions are also addressed and the algebraic normal forms of all their derivatives are given we finally detail the characteristics of the symmetric functions of degree at most 7 for any number of variables most notably we determine all balanced symmetric functions of degree less than or equal to 7

conservation laws of the camassa holm equation we use the bi hamiltonian structure of the camassa holm equation to show that its conservation laws h n m are homogeneous with respect to the scaling m lambdam moreover a direct argument is presented proving that h 1 h 2 are of local character finally simple representations of the conservation laws in terms of their variational derivatives are derived and used to obtain a constructive scheme for computation of the h n s

well posedness and blow up solutions for an integrable nonlinearly dispersive model wave equation abstract we establish local well posedness in the sobolev space hs with any s 3 2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the camassa holm equation however unlike the more familiar korteweg devries model we demonstrate conditions on the initial data that lead to finite time blow up of certain solutions

well posedness global existence and blowup phenomena for a periodic quasi linear hyperbolic equation we establish the local well posedness of a recently derived model for small amplitude shallow water waves for a large class of initial data we prove global existence of the corresponding solution criteria guaranteeing the development of singularities in finite time for strong solutions with smooth initial data are obtained and an existence and uniqueness result for a class of global weak solutions is also given c 1998 john wiley sons inc

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

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

weakly damped forced korteweg de vries equations behave as a finite dimensional dynamical system in the long time abstract it is shown that a weak dissipation of order zero is sufficient to impose a finite dimensional behavior for korteweg de vries equations with periodic boundary conditions a universal attractor which captures all the trajectories is constructed its fractal dimension is proved to be finite

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

a note on symmetric boolean functions with maximum algebraic immunity in odd number of variables in this note it is proved that for each odd positive integer n there are exactly two n variable symmetric boolean functions with maximum algebraic immunity

on the weak solutions to a shallow water equation we obtain the existence of global in time weak solutions to the cauchy problem for a one dimensional shallow water equation that is formally integrable and can be obtained by approximating directly the hamiltonian for euler s equation in the shallow water regime the solution is obtained as a limit of viscous approximation the key elements in our analysis are some new a priori one sided supernorm and space time higher norm estimates on the first order derivatives 2000 john wiley sons inc

global existence and blow up phenomena for the degasperis procesi equation this paper is concerned with several aspects of the existence of global solutions and the formation of singularities for the degasperis procesi equation on the line global strong solutions to the equation are determined for a class of initial profiles on the other hand it is shown that the first blow up can occur only in the form of wave breaking a new wave breaking mechanism for solutions is described in detail and two results of blow up solutions with certain initial profiles are established

global weak solutions and blow up structure for the degasperis procesi equation in this paper we study several qualitative properties of the degasperis procesi equation we first established the precise blow up rate and then determine the blow up set of blow up strong solutions to this equation for a large class of initial data we finally prove the existence and uniqueness of global weak solutions to the equation provided the initial data satisfies appropriate conditions

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

symmetric boolean functions depending on an odd number of variables with maximum algebraic immunity to resist algebraic attacks boolean functions should possess high algebraic immunity in 2003 courtois and meier showed that the algebraic immunity of an n variable boolean function is upper bounded by spl lceil n 2 spl rceil and then several papers studied how to find symmetric boolean functions with maximum algebraic immunity in this correspondence we prove that for each odd n there is exactly one trivially balanced n variable symmetric boolean function achieving the maximum algebraic immunity

global existence and blow up phenomena for the weakly dissipative camassa holm equation abstract this paper is concerned with global existence and blow up phenomena for the weakly dissipative camassa holm equation a new global existence result and a new blow up result for strong solutions to the equation with certain profiles are presented the obtained results improve considerable the previous results