Schaefer proved in 1978 that the Boolean constraint satisfaction problem for a given constraint language is either in P or is NPcomplete, and identified all tractable cases. Schaefer’s dichotomy theorem actually shows that there are at most two constraint satisfaction problems, up to polynomial-time isomorphism (and these isomorphism types are distinct if and only if P 6= NP). We show that if o...

Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the well-known isomorphism between completely positive maps and bipartite density operators is derived, which makes this connection much more explicit. The new isomor...

Let M be a closed orientable 3-manifold of Heegaard genus two with a non-trivial JSJ-decomposition and G be a finite group of orientation-preserving smooth actions on M which preserves each handlebody of Heegaard splitting and each piece of the JSJ-decomposition of M . We will call some specific conditions of the Heegaard splitting and the JSJ-tori the condition A, . . . , and the condition F. ...

We construct a numeric algorithm for completing the proof of conjecture asserting that all deformed preprojective algebras generalized Dynkin type are periodic. In particular, we obtain an algorithmic procedure showing non-trivial types E7 and E8 exist only in characteristic 2. As consequence, show E6, periodic classification such algebras, up to algebra isomorphism. do it by reduction solution...

We mix together the Kontsevich integral, chord diagrams, Chinese characters, the Reshetikhin-Turaev knot invariants, the Poincare-Birkhoo-Witt theorem, the Harish-Chandra isomorphism, the Duuo isomorphism, the Kirillov formula and some minor Fourier-analysis computations. This enables us to make an intelligent guess for an exact formula for the Kontsevich integral of the unknot, and to conjectu...

In this paper, we show that a class of 2-dimensional locally CAT(-1) spaces is topologically rigid: isomorphism of the fundamental groups is equivalent to the spaces being homeomorphic. An immediate application of this result is a diagram rigidity theorem for certain amalgamations of free groups. The direct limits of two such amalgamations are isomorphic if and only if there is an isomorphism b...

We mix together the Kontsevich integral, chord diagrams, Chinese characters, the Reshetikhin-Turaev knot invariants, the Poincare-Birkhoff-Witt theorem, the HarishChandra isomorphism, the Duflo isomorphism, the Kirillov formula and some minor Fourieranalysis computations. This enables us to make an intelligent guess for an exact formula for the Kontsevich integral of the unknot, and to conjectu...

Unanticipated connections between different fragments of lambda calculus and different families of embedded graphs (a.k.a. “maps”) motivate the problem of enumerating β-normal linear lambda terms. In this brief note, it is shown (by appeal to a theorem of Arquès and Beraud) that the sequence counting isomorphism classes of β-normal linear lambda terms up to free exchange of adjacent lambda abst...

In this article, we investigate the plus space of levelN , where 4−1N is a square-free (not necessarily odd) integer. This is a generalization of Kohnen’s work. We define a Hecke isomorphism ℘k of Mk+1/2(4M) onto M k+1/2(8M) for any odd positive integer M . The methods of the proof of the newform theory are this isomorphism, Waldspurger’s theorem, and the dimension identity.

In this paper, we show that a class of 2-dimensional locally CAT(-1) spaces is topologically rigid: isomorphism of the fundamental groups is equivalent to the spaces being homeomorphic. An immediate application of this result is a diagram rigidity theorem for certain amalgamations of free groups. The direct limit of two such amalgamations are isomorphic if and only if there is an isomorphism be...