We propose a modular approach to development of a computerized adaptive practice system for learning of facts in areas with widely varying prior knowledge: decomposing the system into estimation of prior knowledge, estimation of current knowledge, and selection of questions. We describe specific realization of the system for geography learning and use data from the developed system for evaluati...

In this paper, a mathematical model is presented to identify the direct dynamic coefficients (kxx, kzz, cxx, czz) of pressurized bearing in rotor-bearing system. The for online identification result application algebraic approach two-degree-of-freedom model. proposed requires only vibration response as input data. performance was assessed by theoretically and experimentally testing identifier a...

Integrable equations in (1 + 1) dimensions have their own higher order integrable equations, like the KdV, mKdV and NLS hierarchies etc. In this paper we consider whether integrable equations in (2 + 1) dimensions have also the analogous hierarchies to those in (1 + 1) dimensions. Explicitly is discussed the Bogoyavlenskii-Schiff(BS) equation. For the BS hierarchy, there appears an ambiguity in...

Fermat's Last Theorem—which we shall abbreviate to FLT—is the (as yet unproved) assertion that the Diophantine equation x" + y" — z" has no solutions in positive integers if 11 ^ 3. It would suffice to deal with the case in which n is prime, and this is where the most significant work has been done. None the less it is not yet known even whether FLT is true for infinitely many prime exponents. ...