We present a simple formula for the expected number of times that a complex-valued Gaussian stochastic process has a zero imaginary part and the absolute value of its real part is bounded by a constant value M. We show that only some mild conditions on the stochastic process are needed for our formula to remain valid. We further apply this formula to a random algebraic polynomial with complex c...

let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...

in this paper, we introduce the notions of c-numerical range and c-spectrum of matrix polynomials. some algebraic and geometrical properties are investigated. we also study the relationship between the c-numerical range of a matrix polynomial and the joint c-numerical range of its coefficients.

In this paper we study the complexity of constructing a hitting set for VP, the class of polynomials that can be infinitesimally approximated by polynomials that are computed by polynomial sized algebraic circuits, over the real or complex numbers. Specifically, we show that there is a PSPACE algorithm that given n, s, r in unary outputs a set of inputs from Qn of size poly(n, s, r), with poly(...

An algebraic source is a random variable distributed uniformly over the set of common zeros of one or more multivariate polynomials defined over a finite field F. Our main result is the construction of an explicit deterministic extractor for algebraic sources over exponentially large prime fields. More precisely, we give an explicit (and arguably simple) function E : Fn 7→ {0, 1}m such that the...

variace / covariance components of 227118 first lactaiom test-day milk yield records belonged to 31258 iranian holstein cows were estimated using nine random regression models. afterwards, different measures of persistency based on estimation breeding value were evaluated. three functions were used to adjust fixed lactation curve: ali and schaeffer (as), quadratic (le3) and cubic (le4) order of...

Let Qn(x) = ∑n i=0 Aix i be a random algebraic polynomial where the coefficients A0, A1, · · · form a sequence of centered Gaussian random variables. Moreover, assume that the increments ∆j = Aj − Aj−1, j = 0, 1, 2, · · · are independent, A−1 = 0. The coefficients can be considered as n consecutive observations of a Brownian motion. We study the asymptotic behaviour of the expected number of lo...

 Let $P(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. In this paper, some algebraic and geometrical properties of the $k$-numerical range of $P(lambda)$ are investigated. In particular, the relationship between the $k$-numerical range of $P(lambda)$ and the $k$-numerical range of its companion linearization is stated. Moreover, the $k$-numerical...

In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.