In this paper we prove the conjecture of Korevaar and Meyers: for each N â‰¥ cdt there exists a spherical t-design in the sphere S consisting of N points, where cd is a constant depending only on d.

We estimate the degree of comonotone polynomial approximation of continuous functions f , on [âˆ’1,1], that change monotonicity s â‰¥ 1 times in the interval, when the degree of unconstrained polynomialâ€¦ (More)

she announced her spectacular result in the paper titled â€˜The sphere packing problem in dimension 8â€™ [10] on the arXiv-preprint server. Only one week later, on 21 March 2016, Henry Cohn, Abhinavâ€¦ (More)

An N -dimensional parallelepiped will be called a bar if and only if there are no more than k different numbers among the lengths of its sides (the definition of bar depends on k). We prove that aâ€¦ (More)