Fiber lengths were analyzed for random samples of medium-density fiberboard (MDF) fibers and wood particles taken from eleven different populations. For six of the samples, the lognormal distribution fit the data, while the Weibull distribution did not. For three of the samples, the Weibull fit the data, while the lognormal did not. For two of the samples, both the lognormal and Weibull fit the...

The normal curve has been used to fit the rate of both world and US oil production. In this article we give the first theoretical basis for these curve fittings. It is well known that oil field sizes can be modeled by independent samples from a lognormal distribution. We show that when field sizes are lognormally distributed, the starting time of the production of a field is approximately a lin...

This paper presents a method for producing hardware designs for Elliptic Curve Cryptography (ECC) systems over the finite field GF(2), using the optimal normal basis for the representation of numbers. A design generator has been developed which can automatically produce a customised ECC hardware design that meets user-defined requirements. This method enables designers to rapidly explore and im...

In the present paper we investigate a special class of two-dimensional rational surfaces Φ in R whose tangent planes satisfy the following property: For any threespace E in R there exists a unique tangent plane T (u, v) of Φ which is parallel to E. For all possible varieties of tangent planes T (u, v) the corresponding families of surfaces in R are constructed explicitly. Quadratic triangular B...

This article presents a damage detection method for prestressed reinforced concrete (PRC) elements based on free vibration tests and nonlinear damping identification. Integrated static and dynamic experiments were carried out on three precast PRC beam specimens. The static loading induced different levels of damage to the beams. At each damage level, impulsive loading was applied to the beams a...

For a given high-speed machinery, a significant source of the internally induced vibrational excitation is the presence of high frequency harmonics in the trajectories that the system is forced to follow. In this paper a special class of rational Brzier curves is presented that correspond to low-harmonic trajectory patterns. Harmonic Bernstein polynomials and harmonic deCasteljau algorithm are ...

We analyze four recently proposed normal forms for elliptic curves. Though these forms are mathematically appealing and exhibit some cryptographically desirable properties, they nonetheless fall short of cryptographic viability, especially when compared to various types of Edwards Curves. In this paper, we present these forms and demonstrate why they fail to measure up to the standards set by E...

We present normal forms for elliptic curves over a field of characteristic 2 analogous to Edwards normal form, and determine bases of addition laws, which provide strikingly simple expressions for the group law. We deduce efficient algorithms for point addition and scalar multiplication on these forms. The resulting algorithms apply to any elliptic curve over a field of characteristic 2 with a ...

background identification of a normal range for biomarkers, based on pregnancy outcomes (caused by their high or low values) is of special importance in clinical studies. as some pregnancy outcomes can happen in both high and low levels of biomarkers, the receiver-operating characteristic (roc) curve is unsuitable for identifying these levels separately; rather, a statistical method is preferab...