This study attempts to characterize and predict stock index series in Shenzhen stock market using the concepts of multivariate local polynomial regression. Based on nonlinearity and chaos of the stock index time series, multivariate local polynomial prediction methods and univariate local polynomial prediction method, all of which use the concept of phase space reconstruction according to Taken...

In this paper, we study the local polynomial composite quantile regression (CQR) smoothing method for the nonlinear and nonparametric models under the Harris recurrent Markov chain framework. The local polynomial CQR regression method is a robust alternative to the widely-used local polynomial method, and has been well studied in stationary time series. In this paper, we relax the stationarity ...

— A compressive sensing (CS) reconstruction method for polynomial phase signals is proposed in this paper. It relies on the Polynomial Fourier transform, which is used to establish a relationship between the observation and sparsity domain. Polynomial phase signals are not sparse in commonly used domains such as Fourier or wavelet domain. Therefore, for polynomial phase signals standard CS algo...

We give a polynomial time algorithm for computing the Igusa local zeta function Z(s, f) attached to a polynomial f(x) ∈ Z[x], in one variable, with splitting field Q, and a prime number p. We also propose a new class of linear feedback shift registers based on the computation of Igusa’s local zeta function.

We consider the concept of a local set of inference rules. A local rule set can be automatically transformed into a rule set for which bottom up evaluation terminates in polynomial time. The local rule set transformation gives polynomial time evaluation strategies for a large variety of rule sets that can not be given terminating evaluation strategies by any other known automatic technique. Thi...

We analyze the spatial discretization errors associated with solutions of onedimensional hyperbolic conservation laws by discontinuous Galerkin methods in space. We show that the leading term of the spatial discretization error with piecewise polynomial approximations of degree p is proportional to a Radau polynomial of degree p+1 on each element. We also prove that the local and global discret...

In this paper we will prove saturation estimates for the adaptive hp-finite element method for linear, second order partial differential equations. More specifically we will consider a sequence of nested finite element discretizations where we allow for both, local mesh refinement and locally increasing the polynomial order. We will prove that the energy norm of the error on the finer level can...

Let M be a compact complex manifold of real dimension m = 2m̄ with a Hermitian metric. Let an(x,∆) be the heat equation asymptotics of the complex Laplacian ∆. Then TrL2(fe−t∆ p,q ) ∼ Σn=0t ∫ M fan(x,∆) for any f ∈ C∞(M); the an vanish for n odd. Let ag(M) be the arithmetic genus and let an(x, ∂̄) := Σq(−1)an(x,∆) be the supertrace of the heat equation asymptotics. Then ∫ M an(x, ∂̄)dx = 0 if n 6=...

To a polynomial f over a p{adic eld K and a character of the group of units of the valuation ring of K one associates Igusa's local zeta function Z(s; f;), which is a meromorphic function on C. Several theorems and conjectures relate the poles of Z(s; f;) to the monodromy of f; the so{called holomorphy conjecture states roughly that if the order of does not divide the order of any eigenvalue of...

Let k be a field, possibly of finite characteristic, V a finite dimensional vector space over k of dimension r, and W ⊂ Autk(V ) a finite subgroup. There is a natural action of W on the k-dual V # of V , as well as on the symmetric algebra S = S(V ). The algebra S is isomorphic to a polynomial algebra over k on r generators, and we are interested in the question of when the invariant algebra R ...