A Cu–Co–P
electrocatalyst for hydrogen evolution
reaction (HER) was designed with a dendritic and porous foam structure.
Fabricated by one-step electrodeposition with binary alloy on a hydrogen
bubble template, the porous foam exhibited remarkable HER activity
in alkaline conditions. Cu was the dominant element in the core and
shell region and acted for 3D structure formation. Cu–Co formed
in the shell part and acted as an active region for hydrogen evolution
reaction. Also, as the amount of P increased in the Cu–Co–P
foams, the pore numbers, the electrochemical surface area (ECSA),
and the HER activity were enhanced. The improved activity is believed
to originate from the charge separation between the negatively charged
P (δ–) and positively charged Cu and Co (δ+), the larger ECSA, and increased porosity.
We determine the Gröbner-Shirshov bases for finite-dimensional irreducible representations of the special linear Lie algebra sl n+1 and construct explicit monomial bases for these representations. We also show that each of these monomial bases is in 1-1 correspondence with the set of semistandard Young tableaux of a given shape.
We show that a set of monic polynomials in a free Lie superalgebra is a Grobner᎐Shirshov basis for a Lie superalgebra if and only if it is ä Grobner᎐Shirshov basis for its universal enveloping algebra. We investigate thë structure of Grobner᎐Shirshov bases for Kac᎐Moody superalgebras and givë explicit constructions of Grobner᎐Shirshov bases for classical Lie superalgebras.
In this paper, we study the structure of Specht modules over Hecke algebras using the Gröbner-Shirshov basis theory for the representations of associative algebras. The Gröbner-Shirshov basis theory enables us to construct Specht modules in terms of generators and relations. Given a Specht module S λ q , we determine the Gröbner-Shirshov pair (R q , R λ q ) and the monomial basis G(λ) consisting of standard monomials. We show that the monomials in G(λ) can be parameterized by the cozy tableaux. Using the division algorithm together with the monomial basis G(λ), we obtain a recursive algorithm of computing the Gram matrices. We discuss its applications to several interesting examples including Temperley-Lieb algebras.
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