Fermionic formulae originate in the Bethe ansatz in solvable lattice models. They are specific expressions of some q-polynomials as sums of products of q-binomial coefficients. We consider the fermionic formulae associated with general non-twisted quantum affine algebra Uq(X (1) n ) and discuss several aspects related to representation theories and combinatorics. They include crystal base theor...

Let H be Monge-Ampère singular integral operator, [Formula: see text], and [Formula: see text]. It is proved that the commutator [Formula: see text] is bounded from [Formula: see text] to [Formula: see text] for [Formula: see text] and from [Formula: see text] to [Formula: see text] for [Formula: see text]. For the extreme case [Formula: see text], a weak estimate is given.

In this paper, by means of the q-Rice formula we obtain a general q-identity which is a unified generalization of three kinds of identities. Some known results are special cases of ours. Meanwhile, some identities on q-generalized harmonic numbers are also derived.

In this paper, we develop conditions under which the Sherman–Morrison–Woodbury formula can be represented in the Moore–Penrose inverse and the generalized Drazin inverse forms. These results generalize the original Sherman–Morrison–Woodbury formula. © 2011 Elsevier Ltd. All rights reserved.

In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if A, B, X are [Formula: see text] matrices, then [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are non-negative continuous functions such that [Formula: see text] and [Formula: see...