and Applied Analysis 3 2. Preliminaries 2.1. Notations Throughout this paper, R shall denote the n-dimensional Euclidean space and Rn×n the set of all n × n real matrices. The superscript T shall denote the transpose of a matrix or a vector, Tr · the trace of the corresponding matrix A A A /2 and 1n 1, 1, . . . , 1 T ∈ R and In the n-dimensional identity matrix. For square matrices M, the notat...

In this paper, a computational algorithm for solving sign-indefinite general multiparameter algebraic Riccati equation (SIGMARE) that arises in the H∞ filtering problem is investigated. After establishing the asymptotic structure of the solution of the SIGMARE, in order to solve the SIGMARE, Newton’s method and two fixed point algorithms are combined. As a result, the new iterative algorithm ac...

where (εi)i=1,...,n are i.i.d. random variables. The unknown autoregression function f is then the target of statistical inference and the development of efficient estimators is a natural task for theoretically oriented statisticians. On the one hand, it has been recognized for a long time that commonly used estimators in model (1) have the same asymptotic behavior as corresponding estimators i...

This brief article provides an independent derivation of a formula given by Kafadar and Eringen (1971) connecting two distinct Cosserat spins. The first of these, the logarithmic spin represents the time rate of change of the vector defining finite Cosserat rotation, whereas the second, the instantaneous spin, gives the local angular velocity representing the infinitesimal generator of that rot...

This work studies the electrical properties for pure epoxy, and epoxy with (0, 1, 1.5, 2 wt%) titanium dioxide powder composites. The effects of contents on optical dielectrically epoxy/ have investigated by several techniques were used to characterize epoxy/titanium dioxide: UV-visible spectrophotometer reveals a new absorption band in wavelength range (350-600) nm. findings this investigation...

∞ i=1 aiεn−i, where the εi are i.i.d. with mean 0 and at least finite second moment, and the ai are assumed to satisfy |ai| = O(i) with β > 1/2. When 1/2 < β < 1, Xn is usually called a long-range dependent or long-memory process. For a certain class of Borel functions K(x1, . . . , xd+1), d≥ 0, from R to R, which includes indicator functions and polynomials, the stationary sequence K(Xn,Xn+1, ...

In this paper, we study the problem of non parametric estimation of the mean and variance functions b and σ2 in a model: Xi+1 = b(Xi) + σ(Xi)εi+1. For this purpose, we consider a collection of finite dimensional linear spaces . We estimate b using a mean squares estimator built on a data driven selected linear space among the collection. Then an analogous procedure estimates σ2, using a possibl...

whose distribution we may hope to be close to Gaussian. T1 can be bootstrapped (potentially with standard biascorrection and acceleration) to obtain bootstrap CIs, nonparametrically dealing with the unknown variance v1. We ran simulations with n = 800, p = 1500, X having i.i.d. Bernoulli(0.05) entries (the columns of X were then standardized to have mean 0 and variance 1), θ = σ = 10, and εi i....

This paper presents an algorithm for computing a GPS receiver's position and the current time from C/A-code phase measurements to at least six satellites and a set of valid satellite ephemerides. Reference position and reference time are not necessary. The process uses a cost function having numerous local minima in addition to the global minimum. An exhaustive search over the 5dimensional time...

The εi are called the elementary divisors of A and à is called the Smith normal form or elementary divisors form of A. In Section 3 we give an algorithm for computing for a given matrix A, its rank r and a prime p the p-parts of the elementary divisors of A. During the algorithm we perform row operations on the matrix A which are driven by only considering certain reductions of row vectors modu...