Algebraic approach to stretching vibrational spectrum of H2S

The stretching vibrational spectra of H2S have been calculated by using the algebraic model, and the local mode characteristics have been analyzed. Within the vibrational quanta v=5, the standard deviation is 1.71 cm(-1), which is better than that from the local model HCAO model calculation.

Algebraic Functions For Recognition

In the general case, a trilinear relationship between three perspective views is shown to exist. The trilinearity result is shown to be of much practical use in visual recognition by alignment --- yielding a direct method that cuts through the computations of camera transformation, scene structure and epipolar geometry. The proof of the central result may be of further interest as it demonstrates certain regularities across homographies of the plane and introduces new view invariants. Experiments on simulated and real image data were conducted, including a comparative analysis with epipolar intersection and the linear combination methods, with results indicating a greater degree of robustness in practice and a higher level of performance in re-projection tasks.

Extracting Salient Curves from Images: An Analysis of the Saliency Network

The Saliency Network proposed by Shashua and Ullman is a well-known approach to the problem of extracting salient curves from images while performing gap completion. This paper analyzes the Saliency Network. The Saliency Network is attractive for several reasons. First, the network generally prefers long and smooth curves over short or wiggly ones. While computing saliencies, the network also fills in gaps with smooth completions and tolerates noise. Finally, the network is locally connected, and its size is proportional to the size of the image. Nevertheless, our analysis reveals certain weaknesses with the method. In particular, we show cases in which the most salient element does not lie on the perceptually most salient curve. Furthermore, in some cases the saliency measure changes its preferences when curves are scaled uniformly. Also, we show that for certain fragmented curves the measure prefers large gaps over a few small gaps of the same total size. In addition, we analyze the time complexity required by the method. We show that the number of steps required for convergence in serial implementations is quadratic in the size of the network, and in parallel implementations is linear in the size of the network. We discuss problems due to coarse sampling of the range of possible orientations. We show that with proper sampling the complexity of the network becomes cubic in the size of the network. Finally, we consider the possibility of using the Saliency Network for grouping. We show that the Saliency Network recovers the most salient curve efficiently, but it has problems with identifying any salient curve other than the most salient one.

Application of dynamical Lie algebraic method to atom-diatomic molecule scattering

The dynamical Lie algebraic approach developed by Alhassid and Levine combined with intermediate picture is applied to the study of translational-vibrational energy transfer in the collinear collision between an atom and an anharmonic oscillator. We find that the presence of the anharmonic terms indeed has an effect on the vibrational probabilities of the oscillator. The computed probabilities are in good agreement with those obtained using exact quantum method. It is shown that the approach of dynamical Lie algebra combining with intermediate picture is reasonable in the treating of atom-anharmonic oscillator scattering.

Winkler springs (p-y curves) for liquefied soil from element tests.

In practice, piles are most often modelled as "Beams on Non-Linear Winkler Foundation" (also known as “p-y spring” approach) where the soil is idealised as p-y springs. These p-y springs are obtained through semi-empirical approach using element test results of the soil. For liquefied soil, a reduction factor (often termed as p-multiplier approach) is applied on a standard p-y curve for the non-liquefied condition to obtain the p-y curve liquefied soil condition. This paper presents a methodology to obtain p-y curves for liquefied soil based on element testing of liquefied soil considering physically plausible mechanisms. Validation of the proposed p-y curves is carried out through the back analysis of physical model tests.

Reproduction of algebraic structures by 16-18 year old students

In this exploratory research we analyze the structure sense evidenced by 33 secondary students (16-18 years old) in tasks requiring to reproduce the structure of given algebraic expressions. The expressions used were algebraic fractions related to algebraic identities. There were big differences between the students performance which allowed differencing levels in students´ structure sense. Questions and conjectures to be addressed in future research are presented.

Maximum curves and isolated points of entire functions

Given M(r; f) =maxjzj=r (jf(z)j) , curves belonging to the set of points M = fz : jf(z)j = M(jzj; f)g were de�ned by Hardy to be maximum curves. Clunie asked the question as to whether the set M could also contain isolated points. This paper shows that maximum curves consist of analytic arcs and determines a necessary condition for such curves to intersect. Given two entire functions f1(z) and f2(z), if the maximum curve of f1(z) is the real axis, conditions are found so that the real axis is also a maximum curve for the product function f1(z)f2(z). By means of these results an entire function of in�nite order is constructed for which the set M has an in�nite number of isolated points. A polynomial is also constructed with an isolated point.