First results on quark-hadron duality in the spin sector from the HERMES experiment are reported in the range 1.2 ≤ Q ≤ 12 GeV and 1 ≤ W 2 ≤ 4 GeV. A complete set of measurements of the generalised GDH integrals for the deuteron, proton and neutron is also shown in the same Q range and in the full W 2 range. PACS. 13.60.Hb Total and inclusive cross-sections (including deep-inelastic processes) ...

The q-state Potts model on the triangular lattice with nearest-neighbour interactions and three-site interactions in half of the triangular faces is considered. The exact duality relation is re-examined from the point of view of determining its critical point. Using the continuity and uniqueness arguments we determine the exact critical point in the ferromagnetic model. It is argued that a tran...

We show that for any C∗-algebra A, a sufficiently large Hilbert space H and a unit vector ξ ∈ H, the natural application rep(A:H) θξ −−→ Q(A), π 7→ 〈π(−)ξ, ξ〉 is a topological quotient, where rep(A:H) is the space of representations on H and Q(A) the set of quasi-states, i.e. positive linear functionals with norm at most 1. This quotient might be a useful tool in the representation theory of C∗...

On the predual of a von Neumann algebra, we define a dif-ferentiable manifold structure and affine connections by embeddings into non-commutative L p –spaces. Using the geometry of uniformly convex Ba-nach spaces and duality of the L p and L q spaces for 1/p + 1/q = 1, we show that we can introduce the α-divergence, for α ∈ (−1, 1), in a similar manner as Amari in the classical case. If restric...

Let P be a finite poset and G a group of automorphisms of P. The action of G on P can be used to define various linear representations of G, and we investigate how these representations are related to one another and to the structure of P. Several examples are analyzed in detail, viz., the symmetric group G, acting on a boolean algebra, CL,(q) acting on subspaces of an n-dimensional vector spac...

We investigate the complete phase diagram of the decoupled world-sheet theory of (P,Q) strings. These theories include 1+1 dimensional super Yang-Mills theory and non-commutative open string theory. We find that the system exhibits a rich fractal phase structure, including a cascade of alternating supergravity, gauge theory, and matrix string theory phases. The cascade proceeds via a series of ...

We prove polynomial boson-fermion identities for the generating function of the number of partitions of n of the form n = ∑L−1 j=1 jfj, with f1 ≤ i−1, fL−1 ≤ i ′−1 and fj+fj+1 ≤ k. The bosonic side of the identities involves q-deformations of the coefficients of xa in the expansion of (1 + x + · · · + xk)L. A combinatorial interpretation for these q-multinomial coefficients is given using Durfe...

We construct a commutative algebra Az , generated by d algebraically independent q-difference operators acting on variables z1, z2, . . . , zd, which is diagonalized by the multivariable Askey-Wilson polynomials Pn(z) considered by Gasper and Rahman [6]. Iterating Sears’ 4φ3 transformation formula, we show that the polynomials Pn(z) possess a certain duality between z and n. Analytic continuati...

We present a general result of simultaneous approximation to several transcendental real, complex or p-adic numbers ξ1, ..., ξt by conjugate algebraic numbers of bounded degree over Q, provided that the given transcendental numbers ξ1, ..., ξt generate over Q a field of transcendence degree one. We provide sharper estimates for example when ξ1, ..., ξt form an arithmetic progression with non-ze...

For a birth and death chain on the nonnegative integers with birth and death probabilities p i and q i 1 ? p i and reeecting barrier at 0, it is shown that the right tails of the probability of the rst return from state 0 to state 0 are simple transition probabilities of a dual birth and death chain obtained by switching p i and q i. Combinatorial and analytical proofs are presented. Extensions...