The two parameter family of coefficients Kλμ(q, t) introduced by Macdonald are conjectured to (q, t) count the standard tableaux of shape λ. If this conjecture is correct, then there exist statistics aμ(T ) and bμ(T ) such that the family of symmetric functions Hμ[X; q, t] = ∑ λKλμ(q, t)sλ[X] are generating functions for the standard tableaux of size |μ| in the sense that Hμ[X; q, t] = ∑ T q aμ...

Let Ω be a bounded domain in IR with a Lipschitz boundary, ∂Ω ∈ | C and let Γ1, Γ2 be open disjoint subsets of ∂Ω such that ∂Ω = Γ1 ∪ Γ2, Γ1 6= ∅ and the 1-dimensional measure of ∂Ω − (Γ1 ∪ Γ2) is zero. The domain Ω represents a channel filled up with a fluid, Γ1 is a fixed wall and Γ2 is both the input and the output of the channel. Let T ∈ (0,∞], Q = Ω×(0, T ). The classical formulation of ou...

In this paper we discuss a relationship between the following two algebras: (i) the subconstituent algebra T of a distance-regular graph that has q-Racah type; (ii) the q-tetrahedron algebra ⊠q which is a q-deformation of the three-point sl2 loop algebra. Assuming that every irreducible T -module is thin, we display an algebra homomorphism from ⊠q into T and show that T is generated by the imag...

Using the modern time-series analysis method in the time domain, based on the autoregressive moving average (ARMA) innovation model and white noise estimator, non-regular descriptor discrete-time stochastic linear systems are researched. Under assumption 1~3, an asymptotically stable reduced-order Wiener state estimator for descriptor systems is given by using projection and block matrix theori...

30 b 0 = pl(T new ; b), and q 0 = pl(T new ; v). We now construct ZST T 0 for S by cutting oo the subtree of T rooted at q and replacing it with T new minus the edge between q and z. Since t LD (T 0 ; q) = d(q; s i), it must be that t LD (T 0 ; q) t LD (T; q). If the strict inequality holds, we add extra wire between q and q 0 to enforce equality, and thereby retain zero skew. For convenience, ...

In this study, we construct q-analog C(q) of Catalan matrix and study the sequence spaces c0(C(q)) c(C(q)) defined as domain q-Catalan in c0 c, respectively. We exhibit some topological properties, obtain Schauder bases determine ?-, ?-duals c(C(q)). Finally, characterize certain class mappings from to space ? = {??, c0, ?1} give necessary sufficient conditions for a operator be compact.

We give a reformulation of a six-parameter family of coupled Painlevé VI systems with affine Weyl group symmetry of type D (1) 6 . We also study some Hamiltonian structures of this system. 0. Introduction In [4], we proposed a 6-parameter family of four-dimensional coupled Painlevé VI systems with affine Weyl group symmetry of type D (1) 6 . This system can be considered as a genelarization of ...

Attenuation is often significant during seismic wave propagation in the subsurface, leading to reduced resolution and narrower bandwidth of images. Traditional corrections for such effects are inverse-Q filtering deconvolution, which require a high signal-to-noise ratio (SNR) avoid noise boost-up. Here, we propose time-domain method offering advantages interpretational quality resulting Similar...

This paper describes the passive Qswitch, based on polymer and organic dye BDN, of a pulsed Nd:YAG laser. Pulses of 27ns duration and peak power of 1.7MW for initial transmission of Q-switch 18.4% 0 T = have been obtained. We have obtained Q-switching efficiency of 77% for train of pulses of 31 and 76.2% 0 T = at the pump energy of 98J. We have also obtained the dependency of laser pulse charac...