Cognitive assessment is a growing area in psychological and educational measurement, where tests are given to assess mastery/deficiency of attributes or skills. A key issue is the correct identification of attributes associated with items in a test. In this paper, we set up a mathematical framework under which theoretical properties may be discussed. We establish sufficient conditions to ensure...

A mathematical and graphical treatment of the Q-theory extension of the Basic Real Business Cycle model of Prescott indicates that several key results are robust to both investment adjustment costs and to variation in the shape of the utility function and the production function while other customary results are fragile. It also demonstrates some of the richness of general equilibrium analysis....

We propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff’s classification scheme with the connection matrix to define and describe their Galois groups. Then we describe fundamental subgroups that give rise to a Riemann-Hilbert correspondence and to a density theorem of Schlesinger’s type.

We study Chern-Simons theory on 3-manifolds M that are circle-bundles over 2dimensional surfaces Σ and show that the method of Abelianisation, previously employed for trivial bundles Σ× S, can be adapted to this case. This reduces the non-Abelian theory onM to a 2-dimensional Abelian theory on Σ which we identify with q-deformed Yang-Mills theory, as anticipated by Vafa et al. We compare and co...

Part I of this paper develops various general concepts in generic representation and cohomology theories. Roughly speaking, we provide a general theory of orders in non-semisimple algebras applicable to problems in the representation theory of nite and algebraic groups, and we formalize the notion of a \generic" property in representation theory. Part II makes new contributions to the non-descr...

We examine the energetics of Q-balls in Maxwell-Chern-Simons theory in two space dimensions. Whereas gauged Q-balls are unallowed in this dimension in the absence of a Chern-Simons term due to a divergent electromagnetic energy, the addition of a Chern-Simons term introduces a gauge field mass and renders finite the otherwise-divergent electromagnetic energy of the Q-ball. Similar to the case o...

The interest in q-analogs of codes and designs has been increased in the last few years as a consequence of their new application in error-correction for random network coding. There are many interesting theoretical, algebraic, and combinatorial coding problems concerning these q-analogs which remained unsolved. The first goal of this paper is to make a short summary of the large amount of rese...

We give an introductory account of functional determinants of elliptic operators on manifolds and Polyakov-type formulas for their infinitesimal and finite conformal variations. We relate this to extremal problems and to the Q-curvature on even-dimensional conformal manifolds. The exposition is self-contained, in the sense of giving references sufficient to allow the reader to work through all ...

Ž . ABSTRACT: Density Functional Theory DFT calculations at the B3LYPr631G level have been performed on four bowl-shaped polyaromatic Ž . Ž . Ž . hydrocarbons of C H molecular formula 1]4 showing C 1 , C 2 and 4 , 30 12 3 2 v Ž . and C 3 symmetries. The geometrical and electronic properties of the 2 h compounds studied have been analyzed to explain their relative stability. NMR chemical shifts ...

We compute analytically the tetrahedron graph in Liouville theory on the pseudosphere. The result allows to extend the check of the bootstrap formula of Zamolodchikov and Zamolodchikov to third order perturbation theory of the coefficient G3. We obtain complete agreement. A.B. Zamolodchikov and Al.B. Zamolodchikov [1] proposed an exact non perturbative formula for the one-point function 〈 Va(z1...