A novel multivariable laboratory process that consists of four interconnected water tanks is presented. The linearized dynamics of the system have a multivariable zero that is possible to move along the real axis by changing a valve. The zero can be placed in both the lefr and the right half-plane. I n this way the quadrupletank process is ideal for illustrating many concepts in multivariable c...

Design of the leading zero anticipator ( L a ) or detector (LZD) is pivotal to the normalization of results for addition and fused multiplication-addition in highperjormance floating point processors. This paper formalizes the analysis and describes some alternative organizations and implementations from the known art. It shows how choices made in the design are o fen dependent on the overall d...

admits a meromorphic continuation to the entire complex plane, with the unique and simple pole of residue 1 at s = 1. In the half-plane {s : Rs ≤ 0}, the Riemann zeta function has simple zeros at −2,−4,−6, . . ., and only at these points which are called trivial zeros. There exist also non-trivial zeros in the band {s : 0 < Rs < 1}. We refer for these basic facts for instance to [Bl] (Propositi...

An experimental investigation of near field aerodynamics of wind dispersed rotary seeds has been performed using stereoscopic digital particle image velocimetry (DPIV). The detailed three-dimensional flow structure of the leading-edge vortex (LEV) of autorotating mahogany seeds (Swietenia macrophylla) in a low-speed vertical wind tunnel is revealed for the first time. The results confirm that t...

We show that the equation φ(a) = σ(b) has infinitely many solutions, where φ is Euler’s totient function and σ is the sum-of-divisors function. This proves a fifty-year-old conjecture of Erdős. Moreover, we show that, for some c > 0, there are infinitely many integers n such that φ(a) = n and σ(b) = n, each having more than n solutions. The proofs rely on the recent work of the first two author...

J. Jonek-Kowalska, Silesian University of Technology, Faculty of Organization and Management, Zabrze, Poland The purpose of the article is an assessment of risk, profitability and value as well as the relationships between these parameters for fifteen leading steel producers in the world. The research methodology uses return on assets, beta coefficient and price/book value ratio (P/BV). The res...

This paper presents a high-speed method for accurate function approximations. This method employs parallel table lookups followed by multi-operand addition. It takes advantage of leading zeros and symmetry in the table entries to reduce the table sizes. By increasing the number of tables and the number of operands in the multi-operand addition, the amount of memory is signiicantly reduced. This...

We derive the large n asymptotics of zeros of sections of a generic exponential sum. We divide all the zeros of the nth section of the exponential sum into “genuine zeros,” which approach, as n → ∞, the zeros of the exponential sum, and “spurious zeros,” which go to infinity as n → ∞. We show that the spurious zeros, after scaling down by the factor of n, approach a “rosette,” a finite collecti...

Let f(x) be a differentiable function on the real line R, and let P be a point not on the graph of f(x). Define the illumination index of P to be the number of distinct tangents to the graph of f which pass through P . We prove that if f ′′ is continuous and nonnegative on R, f ′′ ≥ m > 0 outside a closed interval of R, and f ′′ has finitely many zeros onR, then any point P below the graph of f...