We introduce a Reversible Programmable Gate Array (RPGA) based on regular structure to realize binary functions in reversible logic. This structure, called a 2 * 2 Net Structure, allows for more efficient realization of symmetric functions than the methods shown by previous authors. In addition, it realizes many non-symmetric functions even without variable repetition. Our synthesis method to R...

We discuss and compare the notions of braided and coboundary monoidal categories. Coboundary monoidal categories are analogues of braided monoidal categories in which the role of the braid group is replaced by the cactus group. We focus on the categories of representations of quantum groups and crystals and explain how while the former is a braided monoidal category, this structure does not pas...

The density and pressure are positive physical quantities in magnetohydrodynamics (MHD). Design of provably positivity-preserving (PP) numerical schemes for ideal compressible MHD is highly desired, but remains a challenge especially in the multi-dimensional cases. In this paper, we develop uniformly high-order discontinuous Galerkin (DG) schemes which provably preserve the positivity of densit...

A simple, compact, and systematic derivation is given of the characteristic properties of the magnetohydrodynamic ~MHD! equations with two independent variables ~time-dependent MHD in the xt plane and steady MHD in the xy plane!, based on the symmetrizable Galilean invariant form of the equations and using a matrix approach. A numerically obtained stationary planar field-aligned MHD bow shock f...

It is well-known that translation schemes on prime number of vertices are exactly the cyclotomic schemes. In this current paper, we show that there are no nonsymmetric primitive translation schemes on prime square vertices with at most four classes. On the other hand, we find new non-symmetric fourand five-class association schemes from cyclotomy as fission schemes of certain symmetric three-cl...

The paper deals with difference schemes for the heat-conduction equation with nonlocal boundary conditions containing two real parameters, α and γ. Such schemes have been investigated for some special parameter values, but the general case was not considered previously. The eigenvalue problem arises as a result of variable division and is solved here explicitly. The so-called reality domains we...

The present paper is a survey of a simple combinatorial model for the irreducible characters of complex semisimple Lie algebras, and, more generally, of complex symmetrizable Kac-Moody algebras. This model, which will be referred to as the alcove path model, can be viewed as a discrete counterpart to the Littelmann path model. It allows us to give character formulas and a LittlewoodRichardson r...

Today I’ll define crystal bases, and discuss their basic properties. This will include the tensor product rule and the relationship between the crystals B(λ) of highest weight modules and the infinity crystal B(∞). I’ll then discuss an intrinsic characterization of crystal lattices and crystal bases in terms of a natural bilinear form (sometimes called “polarization”). Unless otherwise stated, ...

Let Gm resp. Gf be the minimal resp. formal Kac-Moody group, associated to a symmetrizable generalized Cartan matrix, over a field F of characteristic 0. Let F [Gm] be the algebra of strongly regular functions on Gm. We denote by Ĝm resp. Ĝf certain monoid completions of Gm resp. Gf , build by using the faces of the Tits cone. We show that there is an action of Ĝf × Ĝf on the spectrum of F-valu...