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 uses the Banzhaf power measure to calculate the a priori voting power of individual voters under the existing Electoral College system for electing the President of the United States, as well as under variants of this system in which electoral votes are either apportioned among the states in a different manner or cast by the states in a different manner. While the present winner-take...

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...

We provide a natural extension of the Borda count to the n-dimensional spatial context, an algorithm to find the spatial Borda winner based on the notion of an inverse Borda count, the result that the Borda winner and the Condorcet winner coincide in unidimensional space when all alternatives on a line are feasible, results that show that in multi-dimensional space the Borda winner and the Cond...

Purpose Many phase II clinical trials evaluate unique experimental drugs/combinations through multi-arm design to expedite the screening process (early termination of ineffective drugs) and to identify the most effective drug (pick the winner) to warrant a phase III trial. Various statistical approaches have been developed for the pick-the-winner design but have been criticized for lack of obje...

AbstractAccuracy in identifying the subjects’ intentions for moving their different limbs from EEG signals is regarded as an important factor in the studies related to BCI. In fact, the complexity of motor-imagination and low amount of signal-to-noise ratio for EEG signal makes this identification as a difficult task. In order to overcome these complexities, many techniques such as variou...