Shifting by ±1 powers sums: pi → pi± 1 induces a transformation on symmetric functions that we detail in the case of Hall-Littlewood polynomials. By iteration, this gives a description of these polynomials in terms of plane partitions, as well as some generating functions. We recover in particular an identity of Warnaar related to RogersRamanujan identities. ’ ooo oo o ’ ooo oo o ’ ooo oo o ’ o...

Pfaffians of matrices with entries z[i, j]/(xi + xj), or determinants of matrices with entries z[i, j]/(xi−xj), where the antisymmetrical indeterminates z[i, j] satisfy the Plücker relations, can be identified with a trace in an irreducible representation of a product of two symmetric groups. Using Young’s orthogonal bases, one can write explicit expressions of such Pfaffians and determinants, ...

LEMMA L 1 When Kp< oo, then &fis a continuous (bounded) linear transformation with both domain and range Lp( — <*> , oo ), and § 2 / = — ƒ. LEMMA 2. Whenf(t)ÇzLi(— <*>, oo), then §ƒ exists for almost all x in ( — oo , co ), but does not necessarily belong to Li(a, b), where a, b are arbitrary numbers(— oo ^a<b^ oo) ; however (l+x)~\ &f\ÇzLi(— oo , co) when 0<q<l. When f and ^f belong to Li(— oo...

Pfaffians of matrices with entries z[i, j]/(xi + xj), or determinants of matrices with entries z[i, j]/(xi−xj), where the antisymmetrical indeterminates z[i, j] satisfy the Plücker relations, can be identified with a trace in an irreducible representation of a product of two symmetric groups. Using Young’s orthogonal bases, one can write explicit expressions of such Pfaffians and determinants, ...

Pfaffians of matrices with entries z[i, j]/(xi + xj), or determinants of matrices with entries z[i, j]/(xi−xj), where the antisymmetrical indeterminates z[i, j] satisfy the Plücker relations, can be identified with a trace in an irreducible representation of a product of two symmetric groups. Using Young’s orthogonal bases, one can write explicit expressions of such Pfaffians and determinants, ...

Dioxygen reacts with the gold(I) hydride (IPr)AuH under insertion to give the hydroperoxide (IPr)AuOOH, a long-postulated reaction in gold catalysis and the first demonstration of O2 activation by Au-H in a well-defined system. Subsequent condensation gave the peroxide (IPr)Au-OO-Au(IPr) (IPr = 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene). The reaction kinetics are reported, as well as the...

We demonstrate that oxygen-oxygen (OO) collisions at the LHC provide unprecedented sensitivity to parton energy loss in a system whose size is comparable those created very peripheral heavy-ion collisions. With leading and next-to-leading order calculations of nuclear modification factors, we show baseline absence partonic rescattering known with up 2% theoretical accuracy inclusive OO Surprisi...