The Lifting Problem for Commuting Subnormals (LPCS) asks for necessary and sufficient conditions for a pair of subnormal operators on Hilbert space to admit commuting normal extensions. Given a 2-variable weighted shift T with diagonal core, we prove that LPCS is soluble for T if and only if LPCS is soluble for some power Tm (m ∈ Z+,m ≡ (m1,m2),m1,m2 ≥ 1). We do this by first developing the bas...

In this paper a non-diagonal regulator, based on the QFT method, is synthesized for an uncertain MIMO plant whose output and control signals are subjected to hard time-domain constraints. This procedure includes the design of a non-diagonal pre-controller based on a new simple approach, followed by the sequential design of a diagonal QFT controller. We present a new formulation for the latter s...

It is shown that the numbers of off-diagonal solutions to the Uq(X (r) N ) Bethe equation at q = 0 coincide with the coefficients in the recently introduced canonical power series solution of the Q-system. Conjecturally the canonical solutions are characters of the KR (Kirillov-Reshetikhin) modules. This implies that the numbers of off-diagonal solutions agree with the weight multiplicities, wh...

If f = EW:-, a,,t” is a formal Laurent series with certain restrictions on the a,, then f = f-fof+ , where fcontains only negative powers of t, f+ contains only positive powers of t, and f. is independent of t. Applications include Lagrange’s formula for series reversion, the problem of counting lattice paths below a diagonal, and a theorem of Furstenberg that the diagonal of a rational power s...

We describe non-conventional localization of the midband E = 0 state in square and cubic finite bipartite lattices with off-diagonal disorder by solving numerically the linear equations for the corresponding amplitudes. This state is shown to display multifractal fluctuations, having many sparse peaks, and by scaling the participation ratio we obtain its disorder-dependent fractal dimension D2....

Abstract Diagonal (multiplication) operators acting between a particular class of countable inductive spectra Fréchet sequence spaces, called (LF)-spaces, are investigated. We prove results concerning boundedness, compactness, power and mean ergodicity. Furthermore, we determine when diagonal operator is Montel reflexive. analyze the in terms system weights defining spaces.

CONTEXT Assessment techniques used to measure functional tasks involving active trunk control are restricted to linear movements that lack the explosive movements and dynamic tasks associated with activities of daily living and sport. Reliable clinical methods used to assess the diagonal and ballistic movements about the trunk are lacking. OBJECTIVE To assess the interday reliability of peak ...