We study entropy travelling wave solutions for rst order hyperbolic balance laws. Results concerning existence, regularity and asymptotic stability of such solutions are proved for convex uxes and source terms with simple isolated zeros.

‎let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$‎. ‎in this paper we obtain some new results about the dependence of $|p(rz)|$ on $|p(rz)| $ for $r^2leq rrleq k^2$‎, ‎$k^2 leq rrleq r^2$ and for $rleq r leq k$‎. ‎our results refine and generalize certain well-known polynomial inequalities‎.

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 $2[frac{n-1}{2}]+1$.

We study divisibility by eight of exponential sums of several classes of functions over finite fields of characteristic two. For the binary classical Kloosterman sums K(a) over such fields we give a simple recurrent algorithm for finding the largest k, such that 2 divides the Kloosterman sum K(a). This gives a simple description of zeros of such Kloosterman sums.

This paper contains results on the design of optimum equalizers to eliminate intersymbol interference in linear non-minimum phase channels conveying binary signals. The optimization is with respect to an open eye condition with a given delay. For causal stable channels with non-minimum phase zeros, we argue that this problem requires only the consideration of the FIR modified channel that has a...

The common zeros of two bivariate functions can be computed by finding the common zeros of their polynomial interpolants expressed in a tensor Chebyshev basis. From here we develop a bivariate rootfinding algorithm based on the hidden variable resultant method and Bézout matrices with polynomial entries. Using techniques including domain subdivision, Bézoutian regularization and local refinemen...

We study the divisibility by 3 of Kloosterman sums K(a) over finite fields of characteristic 3. We give a simple recurrent algorithm for finding the largest k, such that 3 divides the Kloosterman sum K(a). This gives a simple description of zeros of such Kloosterman sums.

We describe new zero-free regions for the derivatives ζ(s) of the Riemann zeta function: they take form of vertical strips in the right half-plane; and we show that the zeros located in the narrow complements of these zero-free regions – which, in analogy with the classical case, we call “critical strips” – tend to converge to their central “critical lines” and exhibit surprising vertical perio...