The purpose of this paper is to provide a construction to model shared-variable systems using higher-dimensional automata which is compositional in the sense that the parallel composition of completely independent systems is modeled by the standard tensor product of HDAs and nondeterministic choice is represented by the coproduct.

We define a faithful linear monoidal functor from the partition category, and hence Deligne’s category $\mathrm{\underline{Re}p}(S\_t)$, to additive Karoubi envelope of Heisenberg category. show that induced map on Grothendieck rings is injective corresponds Kronecker coproduct symmetric functions.

In this paper, we studied the boost operator in setting of su ( 1 | ) 2 . We find a family different algebras where such an can consistently appear, which classify according to how two copies interact with each other. Finally, construct coproduct maps for these and discuss algebraic relationships among them.

By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain Drinfeld current realization for quantum affine superalgebra Uq[gl(m|n) ]. We find a simple coproduct for the quantum current generators and establish the Hopf algebra structure of this super current algebra. Queen Elizabeth II Fellow; Email: [email protected]

This paper is an initial inquiry into the structure of the Hopf algebra of matroids with restriction-contraction coproduct. Using a family of matroids introduced by Crapo in 1965, we show that the subalgebra generated by a single point and a single loop in the dual of this Hopf algebra is free.

We construct algebra homomorphisms from affine Yangians to the current algebras of rectangular W-algebras both in type A. The construction is given via coproduct and evaluation map for Yangians. As a consequence, we show that parabolic inductions representations can be regarded as tensor product under homomorphisms. same method applicable also super-setting.

This article is essentially an appendix to [4]. We gather here some useful properties of the algebra FQSym of free quasi-symmetric functions which were overlooked in [4]. Recall that FQSym is a subalgebra of the algebra of noncommutative polynomials in infinitely many variables ai which is mapped onto Gessel’s algebra of quasi-symmetric functions QSym by the commutative image ai 7→ xi of K〈A〉. ...

Angus×Simmental crossbred heifers (n=150) and steers (n=100) were used to evaluate 1 of 5 growing diets: 1) a corn-based growing diet (CRN); 2) a high-fat, high-protein coproduct blend; 3) a high-fat, low-protein coproduct blend; 4) a low-fat, high-protein coproduct blend; and 5) a low-fat, low-protein coproduct blend in a 2×2+1 factorial arrangement. Low-protein and low-fat diets were formulat...