We consider the Brascamp–Lieb inequalities concerning multilinear integrals of products of functions in several dimensions. We give a complete treatment of the issues of finiteness of the constant, and of the existence and uniqueness of centred gaussian extremals. For arbitrary extremals we completely address the issue of existence, and partly address the issue of uniqueness. We also analyse th...

We prove global versions of certain known nonlinear Brascamp– Lieb inequalities under a natural homogeneity assumption. We also establish a conditional theorem allowing one to generally pass from local to global nonlinear Brascamp–Lieb estimates under such a homogeneity assumption.

The separated electromagnetic responses RL(q, ω) and RT (q, ω) for inclusive electron scattering off nuclei are studied within a functional scheme.

The stochastic dynamics of networks of biochemical reactions in living cells are typically modelled using chemical master equations (CMEs). The stationary distributions of CMEs are seldom solvable analytically, and few methods exist that yield numerical estimates with computable error bounds. Here, we present two such methods based on mathematical programming techniques. First, we use semidefin...

Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever distribution of samples under null hypothesis is invariant to some rearrangement. Despite its increasing popularity and empirical success, theoretical properties permutation test, especially power, have not been fully explored beyond simple cases. In this paper, we attempt part...

In this paper we present a systematic approach for the construction of bounds for the average cost in Markov chains with innnitely many states. The technique to prove the bounds is based on dynamic programming. Most performance characteristics of Marko-vian systems can be represented by the average cost for some appropriately chosen cost structure. Therefore, the approach can be used to generat...

A function is said to be bi-univalent on the open unit disk D if both the function and its inverse are univalent in D. Not much is known about the behavior of the classes of bi-univalent functions let alone about their coefficients. In this paper we use the Faber polynomial expansions to find coefficient estimates for four well-known classes of bi-univalent functions which are defined by subord...