We present measurements of the production cross sections times leptonic branching fractions and the transverse momentum distributions of W and Z bosons in p p collisions at p s = 1:8 TeV using data collected with the DD detector at the Fermilab Tevatron p p collider. A preliminary measurement of the W charge asymmetry is also presented. At p s = 1:8 TeV, production of W and Z bosons in p p coll...

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Let P (z) be a formal power series in z = (z1, · · · , zn) with o(P (z)) ≥ 2 and t a formal parameter which commutes with z. We say P (z) is HN (Hessian nilpotent) if its Hessian matrix HesP (z) = ( ∂ 2 P ∂zi∂zj ) is nilpotent. The deformed inversion pair Qt(z) of P (z) by definition is the unique Qt(z) ∈ C[[z, t]] with o(Qt(z)) ≥ 2 such that the formal maps Gt(z) = z + t∇Q(z) and Ft(z) = z − t...

K e y w o r d s O p t i m a l control of dams, Diffusion processes, Potential, Infinitesimal generator, Control policies, Total discounted cost, Long-run average cost. 1. I N T R O D U C T I O N A N D S U M M A R Y A b d e l H a m e e d a n d N a k h i [1] d i scuss t h e o p t i m a l con t ro l of a f in i te d a m us ing P~,I r pol ic ies (def ined be low) . T h e y use b o t h t h e t o t a...

Suppose $p$ is a prime, $t$ is a positive integer, and $f\!\in\!\mathbb{Z}[x]$ is a univariate polynomial of degree $d$ with coefficients of absolute value $<\!p^t$. We show that for any fixed $t$, we can compute the number of roots in $\mathbb{Z}/(p^t)$ of $f$ in deterministic time $(d+\log p)^{O(1)}$. This fixed parameter tractability appears to be new for $t\!\geq\!3$. A consequence for arit...

Let be a positive measure on the real line, with orthogonal polynomials fpng and leading coe¢ cients f ng. The Geronimus type identity 1 jIm zj Z 1 1 P (t) jzpn (t) pn 1 (t)j dt = n 1 n Z P (t) d (t) ; valid for all polynomials P of degree 2n 2 has known analogues within the theory of orthogonal rational functions, though apparently unknown in the theory of orthogonal polynomials. We present ne...

and Applied Analysis 3 2. Proof of Theorem 1 We need the following lemmas for the proof of Theorem 1. The difference analogue of the logarithmic derivative lemma was given by Halburd-Korhonen [8, Corollary 2.2] and Chiang-Feng [7, Corollary 2.6], independently. The following Lemma 8 is a variant of [8, Corollary 2.2]. Lemma 8. Let f(z) be a nonconstant meromorphic function of finite order, and ...

Let p(z) = a0 + ∑n j=t ajz be a polynomial of degree n, having no zeros in |z| < k, k ≥ 1, then it has been shown that for R > 1 and |z| = 1, |p(Rz)−p(z)| ≤ (Rn− 1)(1+AtBtkt+1)/(1+kt+1+AtBt(kt+1+k2t))max|z|=1 |p(z)|−{1− (1+AtBtkt+1)/(1+ kt+1 +AtBt(kt+1 + k2t))}((Rn − 1)m/kn), where m = min|z|=k |p(z)|, 1 ≤ t < n, At = (Rt−1)/(Rn−1), and Bt = |at/a0|. Our result generalizes and improves some wel...

[12] N. Takayama, Computation of intersection numbers of a twisted homology group of a locally constant sheaf of more than 1 dimension, 1995, preprint. Corollary 5.2. The monodromy matrices of solutions of the dierential equation (z d dz p Y k=2 z d dz + b k 0 1 0 z p Y k=1 z d dz + a k) y = 0 which correspond to the compact chambers of the hyperplane arrangement ((1 0 t 1)(z 0 t p01) p02 Y i=1...

Abstract. We extend Aziz and Mohammad’s result that the zeros, of a polynomial P (z) = ∑n j=0 ajz , taj > aj−1 > 0, j = 2, 3, . . . , n for certain t ( > 0), with moduli greater than t(n − 1)/n are simple, to polynomials with complex coefficients. Then we improve their result that the polynomial P (z), of degree n, with complex coefficients, does not vanish in the disc |z − ae| < a/(2n); a > 0,...