Knowledge Tracing is an extremely popular method for student modeling because of its capability to infer a student’s dynamic knowledge state in real time as the student is observed solving a series of problems (Corbett & Anderson, 1995). After its introduction in 1995, many extensions to the original technique have been proposed to improve its predictive accuracy. Variants include: fitting mode...

In this paper we consider the nonexistence of global solutions of a Klein-Gordon equation of the form utt −∆u+mu = f(u), (t, x) ∈ [0, T )× Rn. Here m = 0 and the nonlinear power f(u) satisfies some assumptions which will be stated later. We give a sufficient condition on the initial datum with arbitrarily high initial energy such that the solution of the above Klein-Gordon equation blows up in ...

The supersymmetric sinh-Gordon model on a half-line with integrable boundary conditions is considered perturbatively to verify conjectured exact reflection factors to one loop order. Propagators for the boson and fermion fields restricted to a half-line contain several novel features and are developed as prerequisites for the calculations.

The sine-Gordon equation has hyperelliptic al function solutions over a hyperelliptic Jacobian for y = f(x) of arbitrary genus g. This article gives an extension of the sine-Gordon equation to that over subvarieties of the hyperelliptic Jacobian. We also obtain the condition that the sine-Gordon equation in a proper subvariety of the Jacobian is defined.

We study the scattering theory for the coupled KleinGordon-Schrödinger equation with the Yukawa type interaction in two space dimensions. The scattering problem for this equation belongs to the borderline between the short range case and the long range one. We show the existence of the wave operators to this equation without any size restriction on the Klein-Gordon component of the final state ...

This paper investigates the occurrence of 'technology acceleration' across a range of information technologies. The prospect of technology was broached by Gordon Moore of Intel in 1965. His anecdotal 'law' – i.e. performance / price doubles every 18 months – has become received wisdom in many technology industries. Gilder popularized it as Moore’s law and proposed Gilder’s law and a number of s...

M. Venturoli,1, 2, ∗ M. J. Harvey,1 G. Giupponi,1 P.V. Coveney,1, † R. L. Pinning,3 A. R. Porter,3 and S. M. Pickles3 1Centre for Computational Science, Department of Chemistry, University College London, Christopher Ingold Laboratories, 20 Gordon Street, London WC1H 0AJ, United Kingdom 2 Schlumberger Cambridge Research, High Cross, Madingley Road, Cambridge CB3 0EL, United Kingdom 3 Manchester...

T. Skajaa, D. P. Cormode, P. Jarzyna, A. Barazza, E. A. Fisher, R. E. Gordon, Z. A. Fayad, and W. J. Mulder Translational and Molecular Imaging Institute, Mount Sinai School of Medicine, New York, NY, United States, Faculty of Health Sciences, Aarhus, Denmark, School of Medicine, New York University, New York, NY, United States, Department of Pathology, Mount Sinai School of Medicine, New York,...

We study Klein-Gordon chains with attractive nearest neighbour forces and convex on-site potential, and show that there exists a two-parameter family of periodic travelling waves (wave trains) with unimodal and even profile functions. Our existence proof is based on a saddle-point problem with constraints and exploits the invariance properties of an improvement operator. Finally, we discuss the...

BACKGROUND AND OBJECTIVES: Sleep is important to child development, but there is limited understanding of individual developmental patterns of sleep, their underlying determinants, and how these influence health and well-being. This article explores the presence of various sleep patterns in children and their implications for healthrelated quality of life. METHODS: Data were collected from the ...