Distribution of zeros polynomials constitute a classic analytic problem. In the paper, distribution zeroes to generalized Hermite Hm,n(z) is approximated as m, n → ∞, m/n = O(1). These defined Wronskians appear in number mathematical physics problems well theory random matrices. The calcualation based on scaling reduction Painlevé IV equation which has solutions u(z) −2z + ∂z ln Hm,n+1(z)/Hm+1,...

we consider the number of zeros of the integral $i(h) = oint_{gamma_h} omega$ of real polynomial form $omega$ of degree not greater than $n$ over a family of vanishing cycles on curves $gamma_h:$ $y^2+3x^2-x^6=h$, where the integral is considered as a function of the parameter $h$. we prove that the number of zeros of $i(h)$, for $0 < h < 2$, is bounded above by $2[frac{n-1}{2}]+1$.

In this paper, damping of interarea oscillations using simultaneous coordination of static Var compensator (SVC) and power system stabilizer (PSS) is considered.&nbsp; To be effective in damping of oscillations, the best-input signal of power oscillation damper (POD) associated with SVC is selected using Hankel singular values (HSVs), and right-hand plane zeros (RHP-zeros). The 4-machine-2 area...

Abstract. We discuss the multiplicity of the non-trivial zeros of the Riemann zetafunction and the summatory function M(x) of the Möbius function. The purpose of this paper is to consider two open problems under some conjectures. One is that whether all zeros of the Riemann zeta-function are simple or not. The other problem is that whether M(x) ≪ x holds or not. First, we consider the former pr...

We study the imaginary quadratic fields such that the Iwasawa λ2-invariant equals 1, obtaining information on zeros of 2-adic L-functions and relating this to congruences for fundamental units and class numbers. This paper explores the interplay between zeros of 2-adic L-functions and congruences for fundamental units and class numbers of quadratic fields. An underlying motivation was to study ...

Of the many methods which have been proposed for solving algebraic equations the most practical one, where complex roots are concerned, is the well known "root-squaring" method usually referred to as the Graeffe1 process. Nearly all accounts of the method show by examples how all the roots of an equation may be found by first finding all the absolute values of the roots, and later by various de...

We prove that if f ( x ) = ∑ k 0 ∞ a , > is an entire function such the sequence Q : 2 − 1 + non-decreasing and ≥ 3 then all but finite number of zeros are real simple. also present criterion in terms closest to zero roots for have only (in other words, belonging Laguerre–Pólya class type I) under additional assumption on .

Relative t-designs in the n-dimensional hypercube Qn are equivalent to weighted regular t-wise balanced designs, which generalize combinatorial t-(n, k, ?) designs by allowing multiple block sizes as well weights. Partly motivated recent study on tight Euclidean two concentric spheres, this paper we discuss relative supported shells. We show under a mild condition that such t-design induces str...

Of the many methods which have been proposed for solving algebraic equations the most practical one, where complex roots are concerned, is the well known "root-squaring" method usually referred to as the Graeffe1 process. Nearly all accounts of the method show by examples how all the roots of an equation may be found by first finding all the absolute values of the roots, and later by various de...

The solution of a problem arising in integrable systems [10] requires the asymptotics as α → ∞, with very small error, of the inverses and determinants of truncated Wiener-Hopf operators Wα(σ) acting on L (0, α), both in the regular case (where the Wiener-Hopf operator W (σ) on L2(R) is invertible) and in singular cases. This paper treats two cases where σ has simple Fisher-Hartwig singularitie...