injectivity of compressing maps on primitive sequences over bbz p e let zopf pe be the integer residue ring with odd prime p and integer eges2 for a sequence a over zopf pe one has a unique p adic expansion a a 0 a 1 p a e 1 pe 1 where a i can be regarded as a sequence over zopf p for 0lesilese 1 let f x be a strongly primitive polynomial over zopf pe and g f x pe be the set of all primitive sequences generated f x by over zopf pe recently the authors xuan yong zhu and wen feng qi have proved that for a function phi x0 xe 1 g xe 1 eta x0 xe 2 over zopf p and a b ising f x pe where 2lesdeg glesp 1 phi a 0 a 1 a e 1 phi b 0 b 1 b e 1 if and only if a b to further complete their work we show that such injectivity also holds for deg g 1 that is for a function phi x0 xe 1 xe 1 eta x0 xe 2 over zopf p and a b ising f x pe phi a 0 a 1 a e 1 phi b 0 b 1 b e 1 if and only if a b

distribution properties of compressing sequences derived from primitive sequences over bbz p e let z pe be the integer residue ring with odd prime p and integer e 2 any sequence a over z pe has a unique p adic expansion a a0 a1 p ae 1 pe 1 where ai can be regarded as a sequence over z p for 0 i e 1 let f x be a strongly primitive polynomial over z pe and a b be two primitive sequences generated by f x over z pe assume x0 xe 1 xe 1 x0 xe 2 is an e variable function over z p with the monomial p 1 2 xe 2 p 1 x1 p 1 not pearing in the expression of x0 x1 xe 2 it is shown that if there exists an s z p such that a0 t ae 1 t s if and only if b0 t be 1 t s for all nonnegative t with i 0 where is an m sequence determined by f x and a0 then a b this implies that for compressing sequences derived from primitive sequences generated by f x over z pe single element distribution is unique on all positions t with t 0 in particular when x0 x1 xe 2 0 it is a completion of the former result on the uniqueness of distribution of element 0 in highest level sequences

gain scheduled and nonlinear systems dynamic analysis by velocity based linearization families a family of velocity based linearizations is proposed for a nonlinear system in contrast to the conventional series expansion linearization a member of the family of velocity based linearizations is valid in the vicinity of any operating point not just an equilibrium operating point the velocity based linearizations facilitate dynamic analysis far from the equilibrium operating points and enable the transient behaviour of the nonlinear system to be investigated using velocity based linearizations stability conditions are derived for both smooth and non smooth nonlinear systems which avoid the restrictions to trajectories lying within an unnecessarily perhaps excessively small neighbourhood about the equilibrium operating points inherent in existing frozen input theory for systems where there is no restriction on the rate of variation the velocity based linearization analysis is global in nature the analysis techniques developed although quite general are motivated by the gain scheduling design

propagation of reactions in inhomogeneous media consider reaction diffusion equation ut u f x u with x d and general inhomogeneous ignition reaction 0 vanishing at u 0 1 typical solutions 0 u 1 transition from 0 to 1 as time progresses and we study them in the region where this transition occurs under fairly general qualitative hypotheses on f we show that in dimensions d 3 the hausdorff distance of the superlevel sets u e and u 1 e remains uniformly bounded in time for each e 0 1 thus u remains uniformly in time close to the characteristic function of u in the sense of hausdorff distance of superlevel sets we also show that each u e expands with average speed over any long enough time interval between the two spreading speeds corresponding to any x independent lower and upper bounds on f on the other hand these results turn out to be false in dimensions d 4 at least without further quantitative hypotheses on f the proof for d 3 is based on showing that as the solution propagates small values of u cannot escape far ahead of values close to 1 the proof for d 4 is via construction of a counterexample for which this fails such results were before known for d 1 but are new for general non periodic media in dimensions d 2 some are also new for homogeneous and periodic media they extend in a somewhat weaker sense to monostable bistable and mixed reaction types as well as to transitions between general equilibria u u of the pde and to solutions not necessarily satisfying u u u 2016 wiley periodicals inc

speed up of combustion fronts in shear flows this paper is concerned with the analysis of speed up of reaction diffusion advection traveling fronts in infinite cylinders with periodic boundary conditions the advection is a shear flow with a large amplitude and the reaction is nonnegative with either positive or zero ignition temperature the unique or minimal speeds of the traveling fronts are proved to be asymptotically linear in the flow amplitude as the latter goes to infinity solving an open problem from berestycki nonlinear pdes in condensed matter and reactive flows kluwer doordrecht 2003 the asymptotic growth rate is characterized explicitly as the unique or minimal speed of traveling fronts for a limiting degenerate problem and the convergence of the regular traveling fronts to the degenerate ones is proved for positive ignition temperatures under an additional hormander type condition on the flow

generalized transition waves and their properties in this paper we generalize the usual notions of waves fronts and propagation speeds in a very general setting these new notions which cover all usual situations involve uniform limits with respect to the geodesic distance to a family of hypersurfaces that are parametrized by time we prove the existence of new such waves for some time dependent reaction diffusion equations as well as general intrinsic properties some monotonicity properties and some uniqueness results for almost planar fronts the classification results which are obtained under some appropriate assumptions show the robustness of our general definitions 2012 wiley periodicals inc

front blocking versus propagation in the presence of drift term varying in the direction of propagation abstract in this paper we derive quantitative conditions under which a compactly supported drift term depending on the direction of propagation blocks a traveling wave solution or lets it pass almost unchanged we give explicit conditions on the drift term for blocking as well as almost unchanged propagation in one spatial dimension

bistable transition fronts in rn abstract this paper is chiefly concerned with qualitative properties of some reaction diffusion fronts the recently defined notions of transition fronts generalize the standard notions of traveling fronts in this paper we show the existence and the uniqueness of the global mean speed of bistable transition fronts in r n this speed is proved to be independent of the shape of the level sets of the fronts the planar fronts are also characterized in the more general class of almost planar fronts with any number of transition layers these qualitative properties show the robustness of the notions of transition fronts but we also prove the existence of new types of transition fronts in r n that are not standard traveling fronts thus showing that the notions of transition fronts are broad enough to include other relevant propagating solutions

nonlinear black box models in system identification mathematical foundations we discuss several aspects of the mathematical foundations of the nonlinear black box identification problem we shall see that the quality of the identification procedure is always a result of a certain trade off between the expressive power of the model we try to identify the larger the number of parameters used to describe the model the more flexible is the approximation and the stochastic error which is proportional to the number of parameters a consequence of this trade off is the simple fact that a good approximation technique can be the basis of a good identification algorithm from this point of view we consider different approximation methods and pay special attention to spatially adaptive approximants we introduce wavelet and neuron approximations and show that they are spatially adaptive then we apply the acquired approximation experience to estimation problems finally we consider some implications of these theoretical developments for the practically implemented versions of the spatially adaptive algorithms

front blocking in the presence of gradient drift abstract this paper tries to understand how a drift influences the wave propagation of a bistable reaction diffusion equation in straight cylinders in dimension n 3 we derive a quantitative condition under which a compactly supported drift term blocks the propagation of a traveling wave we assume for this that the drift has a potential

compression mappings on primitive sequences over z p sup e let z p sup e be the integer residue ring with odd prime p spl ges 5 and integer e spl ges 2 for a sequence a over z p sup e there is a unique p adic expansion a a sub 0 a spl middot p a sub e 1 spl middot p sup e 1 where each a sub i is a sequence over 0 1 p 1 and can be regarded as a sequence over the finite field gf p naturally let f x be a primitive polynomial over z p sup e and g f x p sup e the set of all primitive sequences generated by f x over z p sup e set spl phi sub e 1 x sub 0 x sub e 1 x sub e 1 sup k spl eta sub e 2 1 x sub 0 x sub 1 x sub e 2 spl psi sub e 1 x sub 0 x sub e 1 x sub e 1 sup k spl eta sub e 2 2 x sub 0 x sub 1 x sub e 2 where spl eta sub e 2 1 and spl eta sub e 2 2 are arbitrary functions of e 1 variables over gf p and 2 spl les k spl les p 1 then the compression mapping spl phi sub e 1 g f x p sup e spl rarr gf p sup spl infin a spl rarr spl phi sub e 1 a sub 0 a sub e 1 is injective that is a b if and only if spl phi sub e 1 a sub 0 a sub e 1 spl phi sub e 1 b sub 0 b sub e 1 for a b spl isin g f x p sup e furthermore if f x is a strongly primitive polynomial over z p sup e then spl phi sub e 1 a sub 0 a sub e 1 spl psi sub e 1 b sub 0 b sub e 1 if and only if a b and spl phi sub e 1 x sub 0 x sub e 1 spl psi sub e 1 x sub 0 x sub e 1 for a b spl isin g f x p sup e

existence of planar flame fronts in convective diffusive periodic media we prove the existence of planar travelling wave solutions in a reaction diffusion convection equation with combustion nonlinearity and self adjoint linear part in rn n 1 the linear part involves diffusion convection terms and periodic coefficients these travelling waves have wrinkled flame fronts propagating with constant effective speeds in periodic inhomogeneous media we use the method of continuation spectral theory and the maximum principle uniqueness and monotonicity properties of solutions follow from a previous paper these properties are essential to overcoming the lack of compactness and the degeneracy in the problem

existence and convergence to a propagating terrace in one dimensional reaction diffusion equations we consider one dimensional reaction diffusion equations for a large class of spatially periodic nonlinearities including multistable ones and study the asymptotic behavior of solutions with heaviside type initial data our analysis reveals some new dynamics where the profile of the propagation is not characterized by a single front but by a layer of several fronts which we call a terrace existence and convergence to such a terrace is proven by using an intersection number argument without much relying on standard linear analysis hence on top of the peculiar phenomenon of propagation that our work highlights several corollaries will follow on the existence and convergence to pulsating traveling fronts even for highly degenerate nonlinearities that have not been treated before

the most significant bit of maximum length sequences over spl zopf 2 sup l autocorrelation and imbalance the imbalance and the autocorrelation of the binary sequences in the title are explored by combining the local weil bound with spectral analysis recent estimates on these quantities are improved by a factor of order 2 sup l 2 for large l

identification of non linear system structure and parameters using regime decomposition abstract an off line algorithm for empirical modeling and identification of non linear dynamic systems is presented the minimal input to the algorithm is a sequence of empirical data and the model order using this information the algorithm searches for an optimal model structure and parameters within a rich non linear model set the model representation is based on the interpolation of a number of simple local models where each local model has a limited range of validity but the local models yield a complete global model when interpolated the method is illustrated using simulated data

on the distinctness of modular reductions of maximal length sequences modulo odd prime powers we discuss the distinctness problem of the reductions modulo m of maximal length sequences modulo powers of an odd prime p where the integer m has a prime factor different from p for any two different maximal length sequences generated by the same polynomial we prove that their reductions modulo m are distinct in other words the reduction modulo m of a maximal length sequence is proved to contain all the information of the original sequence

existence and nonexistence of traveling waves and reaction diffusion front propagation in periodic media we review the existence results of traveling wave solutions to the reaction diffusion equations with periodic diffusion convection coefficients and combustion bistable nonlinearities we prove that whenever traveling waves exist the solutions of the initial value problem with either frontlike or pulselike data propagate with the constant effective speeds of traveling waves in all suitable directions in the case of bistable nonlinearity and one space dimension we give an example of nonexistence of traveling waves which causes quenching localization of wavefront propagation quenching localization only occurs when the variations of the media from their constant mean values are large enough our related numerical results also provide evidence for this phenomenon in the parameter regimes not covered by the analytical example finally we comment on the role of the effective wave speeds in determining the effective wavefront equation hamilton jacobi equation of the reactiondiffusion equations under the small diffusion fast reaction limit with a formal geometric optics expansion

generalized traveling waves in disordered media existence uniqueness and stability we prove existence uniqueness and stability of transition fronts generalized traveling waves for reaction diffusion equations in cylindrical domains with general inhomogeneous ignition reactions we also show uniform convergence of solutions with exponentially decaying initial data to time translations of the front in the case of stationary ergodic reactions the fronts are proved to propagate with a deterministic positive speed our results extend to reaction advection diffusion equations with periodic advection and diffusion

further result of compressing maps on primitive sequences modulo odd prime powers let be the integer residue ring with odd prime and integer for a sequence over there is an unique adic expansion where each is a sequence over and can be regarded as a sequence over the prime field gf naturally let be a strongly primitive polynomial over and the set of all primitive sequences generated by over suppose that gf gf it is shown that any function in is an injective map from to gf and the derived sequences of different functions are also different that is if and only if and for and these injective functions in can be considered as good candidates for the keys of a stream cipher

further result on distribution properties of compressing sequences derived from primitive sequences over bf z p e let p be an odd prime number e an integer greater than 1 and z pe the integer residue ring modulo pe in this paper we obtain an improved result of the previous paper ieee trans inf theory 56 1 2010 555 563 on distribution properties of compressing sequences derived from primitive sequences over z pe it is shown that two primitive sequences and b generated by a strongly primitive polynomial f x over z pe are the same if there exist s z p and k z p such that the distribution of in their compressing sequences ae 1 a0 ae 2 and be 1 b0 be 2 is coincident at the positions t with t k where x0 xe 2 is an e variable polynomial over z p with the coefficient of xe 2p 1 x1p 1x0p 1 not equal to 1 e p 1 2 and is an m sequence over z p determined by f x and a compared with the previous result this gives a more precise characterization on the positions of a compressing sequence i e of the form ae 1 a0 ae 2 derived from a primitive sequence a over z pe that completely determines a in particular the result is also true for the highest level sequence ae 1 by taking x0 xe 2 0

generalized transition fronts for one dimensional almost periodic fisher kpp equations this paper investigates the existence of generalized transition fronts for fisher kpp equations in one dimensional almost periodic media assuming that the linearized elliptic operator near the unstable steady state admits an almost periodic eigenfunction we show that such fronts exist if and only if their average speed is above an explicit threshold this hypothesis is satisfied in particular when the reaction term does not depend on x or in some cases is small enough moreover except for the threshold case the fronts we construct and their speeds are almost periodic in a sense when our hypothesis is no longer satisfied such generalized transition fronts still exist for an interval of average speeds with explicit bounds our proof relies on the construction of sub and super solutions based on an accurate analysis of the properties of the generalized principal eigenvalues

inference of disjoint linear and nonlinear sub domains of a nonlinear mapping this paper investigates new ways of inferring nonlinear dependence from measured data the existence of unique linear and nonlinear sub spaces which are structural invariants of general nonlinear mappings is established and necessary and sufficient conditions determining these sub spaces are derived the importance of these invariants in an identification context is that they provide a tractable framework for minimising the dimensionality of the nonlinear modelling task specifically once the linear nonlinear sub spaces are known by definition the explanatory variables may be transformed to form two disjoint sub sets spanning respectively the linear and nonlinear sub spaces the nonlinear modelling task is confined to the latter sub set which will typically have a smaller number of elements than the original set of explanatory variables constructive algorithms are proposed for inferring the linear and nonlinear sub spaces from noisy data

transition fronts of time periodic bistable reaction diffusion equations in rn abstract this paper is concerned with the existence and qualitative properties of transition fronts for time periodic bistable reaction diffusion equations in r n we first show that any almost planar transition front is actually planar regardless of the number of transition layers then we prove that all transition fronts admit a global mean speed and it holds c where c is the speed of the planar traveling front finally we establish the existence of a transition front in r n that is not a standard traveling front such a front behaves like three moving time periodic planar fronts as time goes to and like a time periodic v shaped traveling front as time goes to

random properties of the highest level sequences of primitive sequences over z 2 sup e using the estimates of the exponential sums over galois rings we discuss the random properties of the highest level sequences spl alpha sub e 1 of primitive sequences generated by a primitive polynomial of degree n over z 2 sup e first we obtain an estimate of 0 1 distribution in one period of spl alpha sub e 1 on the other hand we give an estimate of the absolute value of the autocorrelation function c sub n h of spl alpha sub e 1 which is less than 2 sup e 1 2 sup e 1 1 spl radic 3 2 sup 2e 1 2 sup n 2 2 sup e 1 for h spl ne 0 both results show that the larger n is the more random spl alpha sub e 1 will be

bistable traveling waves around an obstacle we consider traveling waves for a nonlinear diffusion equation with a bistable or multistable nonlinearity the goal is to study how a planar traveling front interacts with a compact obstacle that is placed in the middle of the space n as a first step we prove the existence and uniqueness of an entire solution that behaves like a planar wave front approaching from infinity and eventually reaching the obstacle this causes disturbance on the shape of the front but we show that the solution will gradually recover its planar wave profile and continue to propagate in the same direction leaving the obstacle behind whether the recovery is uniform in space is shown to depend on the shape of the obstacle 2008 wiley periodicals inc

a heteroclinic orbit connecting traveling waves pertaining to different nonlinearities in a channel with decreasing cross section abstract in this paper we consider a semilinear parabolic equation in an infinite cylinder with shrinking cross section the portion where the domain is not a straight half cylinder is assumed to be compact the spatially varying nonlinearity is such that it connects two spatially independent bistable nonlinearities in a compact set in space we prove that given such a setting a traveling wave obeying the equation with the one bistable nonlinearity and starting at the respective side of the decreasing cylinder will converge to a traveling wave solution prescribed by the nonlinearity on the other side

orthogonal parameter estimation algorithm for non linear stochastic systems an orthogonal parameter estimation algorithm is derived which allows each parameter in a linear in the parameters non linear difference equation model to be estimated sequentially and quite independently of the other parameters in the model the algorithm can be applied for any persistently exciting input and provides both unbiased estimates in the presence of correlated noise and an indication of which terms to include in the model several simulated examples are included to demonstrate the effectiveness of the algorithm

regularity and stability of transition fronts in nonlocal equations with time heterogeneous ignition nonlinearity abstract the present paper is devoted to the investigation of various properties of transition fronts in one dimensional nonlocal equations in heterogeneous media of ignition type whose existence has been established by the authors of the present paper in a previous work it is first shown that transition fronts are continuously differentiable in space with uniformly bounded and uniformly lipschitz continuous space partial derivative this is the first time that space regularity of transition fronts in nonlocal equations is ever studied it is then shown that transition fronts are uniformly steep finally asymptotic stability in the sense of exponentially attracting front like initial data of transition fronts is studied

a heteroclinic orbit connecting traveling waves pertaining to different nonlinearities abstract in this paper we consider a semilinear parabolic equation in an infinite cylinder the spatially varying nonlinearity is such that it connects two spatially independent bistable nonlinearities in a compact set in space we prove that given such a setting a traveling wave obeying the equation with the one bistable nonlinearity and starting at the respective side of the cylinder will converge to a traveling wave solution prescribed by the nonlinearity on the other side

gain scheduled controller design an analytic framework directly incorporating non equilibrium plant dynamics a velocity based linearization framework is employed to develop a novel rigorous approach to gain scheduling design the proposed approach enables knowledge concerning the plant dynamics at non equilibrium operating points to be incorporated directly into the controller design since the velocity based linearization framework supports the analysis of the transient response performance considerations can be accommodated the approach retains continuity with linear methods which is central to the existing conventional gain scheduling methodology and since a single type of linearization is employed throughout the design procedure is both straightforward and conceptually appealing

nonlinear black box modeling in system identification a unified overview a nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics there has been considerable recent interest in this area with structures based on neural networks radial basis networks wavelet networks and hinging hyperplanes as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules this paper describes all these approaches in a common framework from a user s perspective it focuses on what are the common features in the different approaches the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques it is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space these mappings are discussed separately the latter mapping is usually formed as a basis function expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection

transition fronts in time heterogeneous and random media of ignition type abstract the current paper is devoted to the investigation of wave propagation phenomenon in reaction diffusion equations with ignition type nonlinearity in time heterogeneous and random media it is proven that such equations in time heterogeneous media admit transition fronts with time dependent profiles and that such equations in time random media admit transition fronts with random profiles important properties of transition fronts including the boundedness of propagation speeds and the uniform decaying estimates of the propagation fronts are also obtained