The Levi graph of a balanced incomplete block design is the bipartite graph whose vertices are the points and blocks of the design, with each block adjacent to those points it contains. We derive upper and lower bounds on the isoperimetric numbers of such graphs, with particular attention to the special cases of finite projective planes and Hadamard designs.

This paper is focused on the applications of Schur complements to determinant inequalities. It presents a monotonic characterization of Schur complements in the L öwner partial ordering sense such that a new proof of the Hadamard-Fischer-Koteljanski inequality is obtained. Meanwhile, it presents matrix identities and determinant inequalities involving positive semidefinite matrices and extends ...

The Hermite-Hadamard inequality is used to develop an approximation to the logarithm of the gamma function which is more accurate than the Stirling approximation and easier to derive. Then the concavity of the logarithm of gamma of logarithm is proved and applied to the Jensen inequality. Finally, the Wallis ratio is used to obtain the additional term in Stirling’s approximation formula. Mathem...

We show that for any unitarily invariant norm k k on M n (the space of n-by-n complex matrices) where denotes the Hadamard (entrywise) product. These results are a consequence of an inequality for absolute norms on C n kx yk 2 kx xk ky yk for all x; y 2 C n : (2) We also characterize the norms on C n that satisfy (2), characterize the unitary similarity invariant norms on M n that satisfy (1), ...

We show that certain statements related to the Fourier-Walsh expansion of functions with respect to a biased measure on the discrete cube can be deduced from the respective results for the uniform measure by a simple reduction. In particular, we present simple generalizations to the biased measure μp of the Bonami-Beckner hypercontractive inequality, and of Talagrand’s lower bound on the size o...

The aim of this paper is to establish some new Hermite–Hadamard type inequalities for harmonic h-convex functions involving hypergeometric functions. We also discuss some new and known special cases, which can be deduced from our results. The ideas and techniques of this paper may inspire further research in this field. In recent years, much attention have been given to theory of convexity beca...