We define a centrally symmetric analogue of the cyclic polytope and study its facial structure. We conjecture that our polytopes provide asymptotically the largest number of faces in all dimensions among all centrally symmetric polytopes with n vertices of a given even dimension d = 2k when d is fixed and n grows. For a fixed even dimension d = 2k and an integer 1 ≤ j < k we prove that the maxi...

We prove that every polarity of PG(2k − 1, q), where k ≥ 2, gives rise to a design with the same parameters and the same intersection numbers as, but not isomorphic to PGk(2k, q). In particular, the case k = 2 yields a new family of quasi-symmetric designs. We also show that our construction provides an infinite family of counterexamples to Hamada’s conjecture, for any field of prime order p. P...

Consider y" (t) + A (t)y (t) + 0, y is a real n-dimensinal vector and A(t) is a real nxn matrix, continuous on some interval. Some positivity properties of solutions and conjugate points of y"(t) + A(t)y (t) = 0 appeared in literature. We prove similar results for focal points

In this preliminary work, left and right conjugate vectors are deened for nonsymmetric, nonsin-gular matrices A and some properties of these vectors are studied. A left conjugate direction (LCD) method for solving nonsymmetric systems of linear equations is proposed. The method reduces to the usual conjugate gradient method when A is symmetric positive deenite. A nite termination property of th...

We define a quantum model for multiparty communication complexity and prove a simulation theorem between the classical and quantum models. As a result, we show that if the quantum k-party communication complexity of a function f is Ω( n 2k ), then its classical k-party communication is Ω( n 2k/2 ). Finding such an f would allow us to prove strong classical lower bounds for k ≥ log n players and...