This paper gives an application of so-called connected sums, introduced recently by Seki and Yamamoto [SY]. Special about our approach is that it proves a duality for the Schlesinger–Zudilin Bradley–Zhao model qMZVs simultaneously. The latter implies MZVs former can be used to prove shuffle product formula MZVs. Furthermore, $q$-Ohno relation, generalization duality, also obtained.

The duality relation of one-variable multiple polylogarithms was proved by Hirose, Iwaki, Sato and Tasaka means iterated integrals. In this paper, we give a new proof using the method connected sums, which recently invented Seki author. Interestingly, sum involves hypergeometric function in its connector. Moreover, introduce two kinds $q$-analogues generalize to them.

We introduce a new family of superalgebras, the quantum walled Brauer-Clifford superalgebras BCr,s(q). The superalgebra BCr,s(q) is a quantum deformation of the walled BrauerClifford superalgebra BCr,s and a super version of the quantum walled Brauer algebra. We prove that BCr,s(q) is the centralizer superalgebra of the action of Uq(q(n)) on the mixed tensor space V q = V ⊗r q ⊗ (V∗ q) when n ≥...

Let Gp be p -series field. We prove the restricted two-parameter Sunouchi operator T χ h is bounded from H q to Lq for 0 < q 1 . By means of interpolation and duality argument, this theorem can be extended to Hardy-Lorentz spaces. As a consequence, we prove the restricted Sunouchi operator is of weak type (L1,L1) . Mathematics subject classification (2010): 42C10.

The QCD effective charge αg1(Q) is an observable that characterizes the magnitude of strong interaction. At high momentum Q, it coincides with running coupling αs(Q). low offers a nonperturbative definition coupling. We have extracted from measurements carried out at Jefferson Lab span very to moderately Q domain, 0.14≤Q≤2.18 GeV. precision new results much improved over previous extractions an...

We interpret a recent formula for counting orbits of GL(d, Fq) in terms of counting fixed points as addition in the affine braided line. The theory of such braided groups (or Hopf algebras in braided categories) allows us to obtain the inverse relationship, which turns out to be the same formula but with q and q interchanged (a perfect duality between counting orbits and counting fixed points)....

In this paper, we show the second part of Schur-Weyl duality for mixed tensor space. The quantum group U = U(gln) of the general linear group and a q-deformation Br,s(q) of the walled Brauer algebra act on V ⊗r ⊗V ∗⊗s where V = R is the natural U-module. We show that EndBnr,s(q)(V ⊗r ⊗ V ∗) is the image of the representation of U, which we call the rational q-Schur algebra. As a byproduct, we o...

We prove stable versions of trace theorems on the sphere in L with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into L for q > 2, by combining a refined Hardy–Littlewood–Sobolev inequality on the sphere with a duality-stability result proved very recently by Carlen. Finally, we extend a local version of C...