gaussian filter for nonlinear systems with correlated noises at the same epoch this paper proposes a general framework solution of gaussian filter gf for both linear and nonlinear dynamic systems with correlated noises at the same epoch detailed discussions and simulation comparisons with existing gaussian approximation recursive filter and existing de correlating gf are provided which show advantages of estimation accuracy of the proposed method in some applications

iterative regularization for elliptic inverse problems elliptic inverse problems can be formulated using coefficient dependent energy least squares functionals resulting in a smooth convex objective functional a variational inequality emerges as a necessary and sufficient optimality condition the principle of iterative regularization when coupled with the auxiliary problem principle results in a strongly convergent scheme for the solution of elliptic inverse problems

initial monomial invariants of holomorphic maps we study a new biholomorphic invariant of holomorphic maps between domains in different dimensions based on generic initial ideals we start with the standard generic monomial ideals to find invariants for rational maps of spheres and hyperquadrics giving a readily computable invariant in this important case for example the generic initial monomials distinguish all four inequivalent rational proper maps from the two to the three dimensional ball next we associate to each subspace x subset mathcal o u a generic initial monomial subspace which is invariant under biholomorphic transformations and multiplication by nonzero functions the generic initial monomial subspace is a biholomorphic invariant for holomorphic maps if the target automorphism is linear fractional as in the case of automorphisms of spheres or hyperquadrics

locating the least 2 norm solution of linear programs via a path following method a linear program has a unique least 2 norm solution provided that the linear program has a solution to locate this solution most of the existing methods were devised to solve certain equivalent perturbed quadratic programs or unconstrained minimization problems we provide in this paper a new theory which is different from these traditional methods and is an effective numerical method for seeking the least 2 norm solution of a linear program the essence of this method is a interior point like path following algorithm that traces a newly introduced regularized central path that is fairly different from the central path used in interior point methods one distinguishing feature of our method is that it imposes no assumption on the problem the iterates generated by this algorithm converge to the least 2 norm solution whenever the linear program is solvable otherwise the iterates converge to a point which gives a minimal kkt residual when the linear program is unsolvable

regularized auxiliary problem principle for variational inequalities abstract this paper is devoted to the unification of the auxiliary problem principle and the principle of iterative regularization for the approximate solution of variational inequalities this unification permits the extension of the principle of iterative regularization to real reflexive banach spaces on the basis of this unification an algorithm is proposed and the strong convergence of the proposed algorithm is depicted

uniqueness of certain polynomials constant on a line abstract we study a question with connections to linear algebra real algebraic geometry combinatorics and complex analysis let p x y be a polynomial of degree d with n positive coefficients and no negative coefficients such that p 1 when x y 1 a sharp estimate d 2 n 3 is known in this paper we study the p for which equality holds we prove some new results about the form of these sharp polynomials using these new results and using two independent computational methods we give a complete classification of these polynomials up to d 17 the question is motivated by the problem of classification of cr maps between spheres in different dimensions

a gaussian approximation recursive filter for nonlinear systems with correlated noises this paper proposes a gaussian approximation recursive filter gasf for a class of nonlinear stochastic systems in the case that the process and measurement noises are correlated with each other through presenting the gaussian approximations about the two step state posterior predictive probability density function pdf and the one step measurement posterior predictive pdf a general gasf framework in the minimum mean square error mmse sense is derived based on the framework the gasf implementation is transformed into computing the multi dimensional integrals which is solved by developing a new divided difference filter ddf with correlated noises simulation results demonstrate the superior performance of the proposed ddf as compared to the standard ddf the existing ukf and ekf with correlated noises

correspondence comments on a gaussian approximation recursive filter for nonlinear systems with correlated noises automatica 48 2012 2290 2297 this note points out that the framework proposed in wang et al 2012 is equivalent to the conventional de coupling framework introduced in some textbooks see e g bar shalom et al 2001

general equivalence between two kinds of noise correlation filters a recent comment chang 2014 theoretically demonstrated that for the linear system with the correlated process and measurement noises the gasf framework proposed in the paper wang et al 2012 was equivalent to the conventional de coupling filtering framework in this note we would further show that such equivalence between the two frameworks can be justified in a more general way even for the nonlinear system

extending proper holomorphic mappings of positive codimension in this paper we obtain results on holomorphic continuation of proper holomorphic mappings between pseudoconvex domains with real analytic boundaries in complex spaces of different dimensions equivalently we obtain results concerning the analyticity of cauchy riemann mappings between real analytic pseudoconvex hypersurfaces in complex spaces of different dimensions to begin with we recall the corresponding results for mappings of equidimensional domains let d and d be bounded pseudoconvex domains with smooth boundaries in c if the boundaries of d and d are strictly pseudoconvex or more generally of finite type in the sense of d angelo 15 then every proper holomorphic map of d onto d extends smoothly t o according to the results of bell and catlin 7 8 and diederich and forn ess 19 for mappings between strictly pseudoconvex domains this was proved by fefferman 26 and nirenberg webster and yang 37 if the boundaries of the pseudoconvex domains d d c c are real analytic then every proper holomorphic mapping of d onto d extends holomorphically to a neighborhood of 3 according to baouendi and rothschild 2 and diederich and forn ess 21 this reflection principle was first discovered by lewy 34 and pin6uk 38 for mappings between strictly pseudoconvex domains in the case of biholomorphic mappings between weakly pseudoconvex domains with realanalytic boundaries the result follows from the work of baouendi jacobowitz and treves 5 results in this direction were obtained in recent years by several authors see the papers 4 6 18 22 33 47 49 in this paper we are treating the case when the domains d and d have different dimensions to be specific we assume that d e c and d c c n are bounded pseudoconvex domains with real analytic boundaries and n n l in this situation a proper holomorphic map f d d need not be regular at the boundary for instance there exist proper holomorphic maps of balls of different dimensions

monotonicity of fixed point and normal mappings associated with variational inequality and its application we prove sufficient conditions for the monotonicity and the strong monotonicity of fixed point and normal maps associated with variational inequality problems over a general closed convex set sufficient conditions for the strong monotonicity of their perturbed versions are also shown these results include some well known in the literature as particular instances inspired by these results we propose a modified solodov and svaiter iterative algorithm for the variational inequality problem whose fixed point map or normal map is monotone

a reflection principle with applications to proper holomorphic mappings j l holomorphic mappings from b into b k we then apply this principle to the problem of characterizing the proper holomorphic mappings from b into b k two such mappings f and g are said to be equivalent if there exist holomorphic automorphisms b and p of b and bk respectively such that f pogo49 there are at present three significant papers on the subject the first by alexander 1 proves that i f f is a proper holomorphic mapping of b into b then f is a holomorphic automorphism of b webster i 5 proved that for n 3 i f f is a proper holomorphic mapping of b into b 1 which is c3 then f maps b into a hyperplane in r hence using alexander s result and properties of the holomorphic automorphisms f is equivalent to the mapping zl z2 z zi z2 zn o alexander s example zl z2 z2 zlz2 z 2 shows that webster s result does not hold for n 2 in a recent paper faran 2 has characterized all proper holomorphic mappings f from b 2 to b 3 that satisfy the additional smoothness condition fec3 2 he proves that such mappings are equivalent to one of the four mappings z w z w 0 z w z zw w2 z w r z 2 l zw w2

on a new homotopy continuation trajectory for nonlinear complementarity problems most known continuation methods for p 0 complementarity problems require some restrictive assumptions such as the strictly feasible condition and the properness condition to guarantee the existence and the boundedness of certain homotopy continuation trajectory to relax such restrictions we propose a new homotopy formulation for the complementarity problem based on which a new homotopy continuation trajectory is generated for p 0 complementarity problems the most promising feature of this trajectory is the assurance of the existence and the boundedness of the trajectory under a condition that is strictly weaker than the standard ones used widely in the literature of continuation methods particularly the often assumed strictly feasible condition is not required here when applied to p complementarity problems the boundedness of the proposed trajectory turns out to be equivalent to the solvability of the problem and the entire trajectory converges to the unique least element solution provided that it exists moreover for monotone complementarity problems the whole trajectory always converges to a least 2 norm solution provided that the solution set of the problem is nonempty the results presented in this paper can serve as a theoretical basis for constructing a new path following algorithm for solving complementarity problems even for the situations where the solution set is unbounded

super rigidity for cr embeddings of real hypersurfaces into hyperquadrics we consider holomorphic mappings sending a given levi nondegenerate pseudoconcave hypersurface m in into a nondegenerate hyperquadric of the same signature in and show that if m is sufficiently close to a hyperquadric in a certain sense then any two such mappings differ only by an automorphism of the hyperquadric

maps from the two ball to the three ball in 4 webster proved the following theorem let b z e c 7 2 3 is a proper holomorphic map which is c a up to the boundary of b then f is linear fractional the purpose of this paper is to extend this result to the case n 2 however the theorem is false when n 2 f need not be linear fractional so instead of trying to prove this false theorem we shall instead try to make a list of maps f bz b a which are c 3 up to the boundary of course given such an f we can get another such by composing f with an automorphism of b 2 and an automorphism of b a so we make the

a regularization approach for variational inequalities abstract this paper is devoted to a regularization approach for variational inequalities a general method based on the theory of linear continuous and linear compact operators is developed for the stable approximation of ill posed variational inequalities variational inequalities are considered for noncoercive monotone and pseudo monotone operators the approach is shown to be successful in handling variational inequalities formulated in reflexive as well as in nonreflexive spaces

embedding strictly pseudoconvex domains into balls every relatively compact strictly pseudocc nvex domain d with c2 boundary in a stein manifold can be embedded as a closed complex submanifold of a finite dimensional ball however for each n 2 there exist bounded strictly pseudoconvex domains d in cn with real analytic boundary such that no proper holomorphic map from d into any finite dimensional ball extends smoothly to d 0 introduction in this paper we study the representations of bounded strictly pseudoconvex domains d c cn if the boundary of d is of class ck k e 2 3 oo then by a theorem of fornaess 8 and khenkin 13 d can be mapped biholomorphically onto the intersection xn q of a bounded strictly convex domain q c cn with ck boundary and a closed complex submanifold x defirxed in a neighborhood of q in cn x intersecting the boundary of q transversally moreover the map f d x n q extends to a holomorphic map on a neighborhood of d the convex domain q depends on d hence a natural question is whether a similar result holds with q replaced by the unit ball b z z1l zn e cn z 2 e zjl2 n that intersects bbn transversally such that d is biholomorphically equivalent to xn e3ff this question has been mentioned by lempert 14 pinduk 20 bedford 2 and others our main result is that the answer to this question is negative in general if d is as above then every biholomorphism of d onto xne3n extends smoothly to d according to 3 however we will show that not all such domains d admit a proper holomorphic map into a finite dimensional ball that is smooth on d theorem 1 1 a similar local result was obtained independently by faran 7 we shall show that the answer to the question q is positive if we allow the intersections of complex submanifolds with strictly convex domains q c cn with real analytic boundaries theorem 1 2 thetheoremsoffornaess 8 andkhenkin 13 onlygiveanqwith smooth boundary received by the editors april 4t 1985 1980 mathematics subject classification primary 32h05 1research supported by a fellowship from the alfred p sloan foundation t 1986 american mathematical society 0002 9947 86 1 00 25 per page