This paper presents a new method for solving the direct kinematics problem of a general Stewart Platform by using three linear extra sensors. The sensors are disposed at a most general way, connecting the non-planar base and the planar mobile platform at distinct points. The extra sensory data enables to reduce the problem to the solution of an overdetermined system of 6 quadratic equations in ...

In this survey, I describe some applications of LLL in number theory. I show in particular how it can be used to solve many different linear problems, to solve quadratic equations, to compute efficiently in number fields...

The period of circadian rhythms often fluctuates around 24 h due to the changes of environmental factors. Actually, the period varies directly with the ambient stimuli which could be expressed as different values of the kinetic parameters included in the circadian models. Therefore, to study the relationships between kinetic parameters and period, which is also known as sensitivity analysis, is...

In this paper we introduce the notion of orthogonally constant mapping in an isosceles orthogonal space and establish stability of orthogonally constant mappings. As an application, we discuss the orthogonal stability of the Pexiderized quadratic equation f(x + y) + g(x + y) = h(x) + k(y).

It has been observed that for most classes of planar maps, the number of maps of size n grows asymptotically like c · n−5/2γn, for suitable positive constants c and γ. It has also been observed that, if dk is the limit probability that the root vertex in a random map has degree k, then again for most classes of maps the tail of the distribution is asymptotically of the form dk ∼ c·kq as k →∞, f...

Revealed preference of the weighted utility theory of Chew (1983) is investigated in the same set-up as Green and Osband (1991) for expected utility theory; the structure of the partition of the state simplex according to the chosen act is examined. It is shown that the boundary between two partition elements generated by a weighted utility is the solution set to a quadratic equation. Moreover,...

Updating a system modeled as a real symmetric quadratic eigenvalue problem to match observed spectral information has been an important task for practitioners in different disciplines. It is often desirable in the process to match only the newly measured data without tampering with the other unmeasured and often unknown eigenstructure inherent in the original model. Such an updating, known as n...

Abstract. The Spitzer Infrared Spectrograph (IRS) data are taken via readwithout-reset measurements to obtain multiple samples forming a photometric “ramp” for each pixel in an echellogram. Each ramp is linearized via a quadratic model. After linearization, a quality-assurance test is performed to determine how linear each pixel’s ramp has become. This is accomplished by fitting a straight line...

Screening designs are attractive for assessing the relative impact of a large number of factors on a response of interest. Experimenters often prefer quantitative factors with three levels over two-level factors because having three levels allows for some assessment of curvature in the factor–response relationship. Yet, the most familiar screening designs limit each factor to only two levels. W...