Let K denote a field and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A∗ : V → V that satisfy the following conditions: (i) each of A,A∗ is diagonalizable; (ii) there exists an ordering {Vi} d i=0 of the eigenspaces of A such that A ∗Vi ⊆ Vi−1+Vi+Vi+1 for 0 ≤ i ≤ d, where V−1 = 0 and Vd+1 = 0; (iii) there exists an...

and Applied Analysis 3 Remark 5. Assumption (13) holds if the system has a unique solution. For brevity, we rewrite system (2)∼(5) in the vector form by introducing W(x, t) = (u(x, t), n(x, t)) and Y(x, t) = (a(x, t), b(x, t)). We denote by E 0 = H 2 ⋂H 1 0 (Ω) × H 1 0 (Ω) the space of vector functionsW(x, t) = (u(x, t), n(x, t)) with norm E0 = {‖u‖ 2 H 2 + ‖n‖ 2 H 1} 1/2 . (14) Similarly, we d...

This paper builds on the previous paper by the author, where a relationship between Zhedanov’s algebra AW (3) and the double affine Hecke algebra (DAHA) corresponding to the Askey-Wilson polynomials was established. It is shown here that the spherical subalgebra of this DAHA is isomorphic to AW (3) with an additional relation that the Casimir operator equals an explicit constant. A similar resu...

background: cardiovascular diseases are viewed worldwide as one of the main causes of death.this study aims to report the burden of ischemic heart diseases (ihds) in iran by using data of the global burden of disease (gbd) study, 1990-2010. materials and methods: the gbd study 2010 was a systematic eff ort to provide comprehensive data to calculate disability-adjusted life years (dalys) for dis...