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...

BACKGROUND Identification of patients at risk of death from cancer surgery should aid in preoperative preparation. The purpose of this study is to assess and adjust the age-adjusted Charlson comorbidity index (ACCI) to identify cancer patients with increased risk of perioperative mortality. METHODS We identified 156,151 patients undergoing surgery for one of the ten common cancers between 200...

objectives: the aims of this study were to investigate the association of mini-nutritional assessment and activities of daily living as well as examining mini nutritional assessment as a good prognostic tool ofactivities of daily living in elderly residents of nursing home. methods & materials: in a cross-sectional study, among 1200 recorded files, 247 subjects completed mini nutritional assess...

Objectives The objective of this study was to evaluate the association between weight-adjusted waist index (WWI) and prevalence kidney stones among adults in United States. Methods cross-sectional utilized data from National Health Nutrition Examination Survey (NHANES) spanning years 2007-2018. A total 31,344 participants were categorized into two groups: those with without. WWI determined by d...

So long as both goods are produced and factor intensity reversals do not occur, each price vector (pX , pY ) corresponds to a unique factor price vector. This should be pretty obvious from both the Woodland-Mussa and the Lerner-Pearce diagram. With the same technology and given prices, there is a unique intersection between the zero profit lines in the Woodland-Mussa diagram. Similarly, for giv...

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...