on codes matroids and secure multiparty computation from linear secret sharing schemes error correcting codes and matroids have been widely used in the study of ordinary secret sharing schemes in this paper the connections between codes matroids and a special class of secret sharing schemes namely multiplicative linear secret sharing schemes lssss are studied such schemes are known to enable multiparty computation protocols secure against general nonthreshold adversaries two open problems related to the complexity of multiplicative lssss are considered in this paper the first one deals with strongly multiplicative lssss as opposed to the case of multiplicative lssss it is not known whether there is an efficient method to transform an lsss into a strongly multiplicative lsss for the same access structure with a polynomial increase of the complexity a property of strongly multiplicative lssss that could be useful in solving this problem is proved namely using a suitable generalization of the well known berlekamp welch decoder it is shown that all strongly multiplicative lssss enable efficient reconstruction of a shared secret in the presence of malicious faults the second one is to characterize the access structures of ideal multiplicative lssss specifically the considered open problem is to determine whether all self dual vector space access structures are in this situation by the aforementioned connection this in fact constitutes an open problem about matroid theory since it can be restated in terms of representability of identically self dual matroids by self dual codes a new concept is introduced the flat partition that provides a useful classification of identically self dual matroids uniform identically self dual matroids which are known to be representable by self dual codes form one of the classes it is proved that this property also holds for the family of matroids that in a natural way is the next class in the above classification the identically self dual bipartite matroids

new mds self dual codes from generalized reed solomon codes both maximum distance separable and euclidean self dual codes have theoretical and practical importance and the study of mds self dual codes has attracted lots of attention in recent years in particular determining the existence of q ary mds self dual codes for various lengths has been investigated extensively the problem is completely solved for the case where q is even this paper focuses on the case where q is odd we construct a few classes of new mds self dual codes through generalized reed solomon codes more precisely we show that for any given even length n we have a q ary mds code as long as q equiv 1 bmod 4 and q is sufficiently large say q ge 4 n times n 2 furthermore we prove that there exists a q ary mds self dual code of length n if q r 2 and n satisfies one of the three conditions 1 n le r and n is even 2 q is odd and n 1 is an odd divisor of q 1 and 3 r equiv 3 mod 4 and n 2tr for any t le r 1 2

a priori estimates and weak solutions for the derivative nonlinear schrodinger equation on torus below h 1 2 abstract we propose a priori estimates for a weak solution to the derivative nonlinear schrodinger equation dnls on torus with small l 2 norm datum in low regularity sobolev spaces these estimates allow us to show the existence of solutions in h s t with some s 1 2 in a relatively weak sense furthermore we make some remarks on the error estimates arising from the finite dimensional approximation solutions of dnls using the fourier lesbesgue type as auxiliary spaces despite the fact that nahmod oh rey bellet and staffilani 12 have already seen them

periodic nonlinear schrodinger equation and invariant measures in this paper we continue some investigations on the periodic nlseiu u iu xx u u p 2 p 6 started in lrs we prove that the equation is globally wellposed for a set of data of full normalized gibbs measrue e beta h phi hd phi x h phi tfrac 1 2 int left phi right 2 tfrac 1 p int left phi right p after suitablel 2 truncation the set and the measure are invariant under the flow the proof of a similar result for the kdv and modified kdv equations is outlined the main ingredients used are some estimates from b1 on periodic nls and kdv type equations

multilinear estimates for periodic kdv equations and applications we prove an endpoint multilinear estimate for the xs b spaces associated to the periodic airy equation as a consequence we obtain sharp local well posedness results for periodic generalized kdv equations as well as some global well posedness results below the energy norm

optimal small data scattering for the generalized derivative nonlinear schrodinger equations abstract in this work we consider the following generalized derivative nonlinear schrodinger equation i t u x x u i u 2 x u 0 t x r r we prove that when 2 the solution is global and scattering when the initial data is small in h s r 1 2 s 1 moreover we show that when 0 2 there exist a class of solitary wave solutions c satisfying c h 1 r 0 when c tends to some endpoint which is against the small data scattering statement therefore in this model the exponent 2 is optimal for small data scattering we remark that this exponent is larger than the short range exponent and the strauss exponent

global well posedness for schrodinger equation with derivative in h 1 2 r abstract in this paper we consider the cauchy problem of the cubic nonlinear schrodinger equation with derivative in h s r this equation was known to be the local well posedness for s 1 2 takaoka 1999 27 ill posedness for s 1 2 biagioni and linares 2001 1 etc and global well posedness for s 1 2 i team 2002 10 in this paper we show that it is global well posedness in the endpoint space h 1 2 r which remained open previously the main approach is the third generation i method combined with a new resonant decomposition technique the resonant decomposition is applied to control the singularity coming from the resonant interaction

new constructions of mds euclidean self dual codes from grs codes and extended grs codes in this paper we consider the problem for which lengths a maximum distance separable mds euclidean self dual code over mathbb f q exists this problem is completely solved for the case where q is even for q is odd some q ary mds euclidean self dual codes were obtained in the literature in this paper we construct six new classes of q ary mds euclidean self dual codes by using generalized reed solomon grs for short codes and extended grs codes

on the derivative nonlinear schro dinger equation abstract in this paper we discuss the cauchy problem for the derivative nonlinear schrodinger equation i t 2i x 2 0 0 x x where 0 under an explicit smallness condition of the initial data we prove the unique global existence of solutions to this problem in the usual sobolev spaces in the weighted sobolev spaces and in the schwartz class we describe the smoothing effect in detail furthermore for the data decaying exponentially at infinity we prove that the above equation has unique local solutions which are analytic in the space direction

self excited oscillation under nonlinear feedback with time delay several important applications use nonlinear feedback methods for synthetically inducing self excited oscillations in mechanical systems the van der pol and saturation function type feedback methods are widely used the effects of time delay on the self excited oscillation of single and two degrees of freedom systems under nonlinear feedback have been studied in this paper it is shown that a single degree of freedom oscillator with the van der pol type nonlinear feedback can produce unbounded response in presence of time delay in general an uncontrolled time delay in the feedback changes the state of oscillations in an uncertain manner therefore a bounded saturation type feedback with controllable time delay is proposed for inducing self excited oscillations the feedback signal is essentially an infinite weighted sum of a nonlinear function of the state variables of the system measured at equal intervals in the past more recent is the measurement higher is the weight thus the feedback signal uses a large amount of information about the past history of the dynamics such a control signal can be realized in practice by a recursive means the control law allows three parameters to be varied namely the time delay feedback and recursive gains multiple time scale analysis is used to plot amplitude vs time delay curves time delay can be controlled to vary the amplitude of oscillation as well as to switch the oscillation from one mode to the other in a two degrees of freedom system it is shown that a higher recursive gain can exercise a better and a more robust control on the amplitude of oscillation of the system analytical results are compared with the results of numerical simulations

invariant measures for the periodic derivative nonlinear schrodinger equation we construct invariant measures associated to the integrals of motion of the periodic derivative nonlinear schrodinger equation dnls for small data in l 2 and we show these measures to be absolutely continuous with respect to the gaussian measure the key ingredient of the proof is the analysis of the gauge group of transformations associated to dnls as an intermediate step for our main result we prove quasi invariance with respect to the gauge maps of the gaussian measure on l 2 with covariance mathbb i delta k 1 for any k geqslant 2

the response of a duffing van der pol oscillator under delayed feedback control abstract the nonlinear dynamics of a duffing van der pol oscillator under linear plus nonlinear state feedback control with a time delay are investigated by means of the averaging method and taylor expansion two slow flow equations for the amplitude and phase of the primary resonance response are derived from which the relations between the amplitude and phase of the primary resonance response and all other parameters are obtained respectively the singularity analysis of the equation governing the amplitude of the primary resonance response shows that the bifurcation modes are perturbations of the pitchfork bifurcation conditions preventing multiple solutions corresponding to two different kinds of bifurcation modes are given since cases for which multiple solutions are available should be avoided the stable condition for steady state response is also given by the routh hurwitz criterion it is also shown that coupled nonlinear state feedback control can be replaced by uncoupled nonlinear state feedback control

global well posedness of the derivative nonlinear schrodinger equation with periodic boundary condition in h12 abstract we establish the global well posedness of the derivative nonlinear schrodinger equation with periodic boundary condition in the sobolev space h 1 2 provided that the mass of initial data is less than 4 this result matches the one by miao wu and xu and its recent mass threshold improvement by guo and wu in the non periodic setting below h 1 2 we show that the uniform continuity of the solution map on bounded subsets of h s does not hold for any gauge equivalent equation

construction of a gibbs measure associated to the periodic benjamin ono equation we define a finite borel measure of gibbs type supported by the sobolev spaces of negative indexes on the circle the measure can be seen as a limit of finite dimensional measures these finite dimensional measures are invariant by the ode s which correspond to the projection of the benjamin ono equation posed on the circle on the first n n 1 modes in the trigonometric bases

van der pol s oscillator under delayed feedback the effect of delayed feedback on oscillatory behaviour is investigated for the classical van der pol oscillator it is shown how the presence of delay can change the amplitude of limit cycle oscillations or suppress them altogether the result is compared to the conventional proportional and derivative feedback the derivative like effect of delay is also demonstrated in a modified equation where a delayed term provides the damping

explicit constructions of mds self dual codes in this paper we study self dual codes over finite fields using tools from algebraic function fields in one variable an algebraic geometry code of length n is defined using two divisors g and d p 1 cdots p n we characterize self orthogonality of the genus zero code in terms of the divisors g d and the value of a well chosen derivative polynomial at points p i 1 le i le n we explore the existence problem of mds self dual codes in the odd characteristic case and we explicitly construct families of new mds self dual codes

vibration control by recursive time delayed acceleration feedback this paper presents a theoretical basis of time delayed acceleration feedback control of linear and nonlinear vibrations of mechanical oscillators the control signal is synthesized by an infinite weighted sum of the acceleration of the vibrating system measured at equal time intervals in the past the proposed method is shown to have controlled linear resonant vibrations low frequency non resonant vibrations primary and 1 3 subharmonic resonances of a forced duffing oscillator the concept of an equivalent damping and natural frequency of the system is also introduced it is shown that a large amount of damping can be produced by appropriately selecting the control parameters for some combinations of the control parameters the effective damping factor of the system is shown to be inversely related to the time delay in the small delay limit selection of the optimum control parameters for controlling the forced and free vibrations is discussed it is shown that forced vibration is best controlled by unity recursive gain and smaller values of the time delay parameter however the transient response can be optimally controlled by suitably selecting the time delay depending upon the gain the delay values for the optimal forced response may be different from that required for the optimum transient response when both are important a suboptimal choice of the delay parameters with unity recursive gain is recommended

instability of solitary wave solutions for the nonlinear schrodinger equation of derivative type in degenerate case abstract we study the stability theory of solitary wave solutions for a type of derivative nonlinear schrodinger equation i t u x 2 u i u 2 x u b u 4 u 0 b 0 the equation has a two parameter family of solitary wave solutions of the form u c x t exp i t i c 2 x c t i 4 x c t c 2 d c x c t here c is some suitable function and 2 c 2 the stability in the frequency region of 2 c 2 for some 0 1 and the instability in the frequency region of 2 c 2 were proved by ohta 2014 recently in the endpoint case c 2 the instability of u c was proved by ning et al 2017 then the stability and instability region has been established except the degenerate case c 2 in this paper we address the problem and prove its instability in the degenerate case