We compare the volumes of projections of convex bodies and the volumes of the projections of their sections, and, dually, those of sections of convex bodies and of sections of their circumscribed cylinders. For L ⊂ R a convex body, we take n random segments in L and consider their ‘Minkowski average’ D. For fixed n, the pth moments of V (D) (1 ≤ p < ∞) are minimized, for V (L) fixed, by the ell...

The effect of angular momentum conservation in microcanonical thermodynamics is considered. This is relevant in gravitating systems, where angular momentum is conserved and the collapsing nature of the forces makes the microcanonical ensemble the proper statistical description of the physical processes. The microcanonical distribution function with non-vanishing angular momentum is obtained as ...

By a result of Helton and McCullough [HM12], open bounded convex free semialgebraic sets are exactly open (matricial) solution sets D◦ L of a linear matrix inequality (LMI) L(X) 0. This paper gives a precise algebraic certificate for a polynomial being nonnegative on a convex semialgebraic set intersect a variety, a so-called “Perfect” Positivstellensatz. For example, given a generic convex fre...

This paper presents new adaptive filtering techniques used in speech enhancement system. Adaptive filtering schemes are subjected to different trade-offs regarding their steady-state misadjustment, speed of convergence, and tracking performance. Fractional Least-Mean-Square (FLMS) is a new adaptive algorithm which has better performance than the conventional LMS algorithm. Normalization of LMS ...

This paper will define the random walk on an integer lattice and will approximate the probability that the random walk is at a certain point after a certain number of steps by using a modified version of the Central Limit Theorem. To accomplish this, we will define the characteristic function of the random walk, find the Taylor expansion of this function, and bound the difference between this f...

The cross covariogram gK,L of two convex sets K and L in R n is the function which associates to each x ∈ R the volume of K ∩ (L + x). Very recently Averkov and Bianchi [AB] have confirmed Matheron’s conjecture on the covariogram problem, that asserts that any planar convex body K is determined by the knowledge of gK,K . The problem of determining the sets from their covariogram is relevant in ...

Non-deterministic programs can represent specifications, and non-determinism arises naturally in concurrent programming languages. In this dissertation, λ-calculi exhibiting erratic nondeterminism are studied in order to identify definitions and techniques that may be applicable to higher-order programming languages for specification or concurrency. The non-deterministic λ-calculi arise as frag...

1. The concept of arcwise convex set is a natural generalization of the notion of L set. The latter was studied by Horn and Valentine [2]1. It is especially interesting to observe how the theorem about the complement of an arcwise convex continuum sheds light on the corresponding theorem for L sets. In order to make this precise, the following definitions are used. Definition 1. An arc C is sai...

We give a description of an affine mapping T involving contact pairs of two general convex bodies K and L, when T (K) is in a position of maximal volume in L. This extends the classical John’s theorem of 1948, and is applied to the solution of a problem of Grünbaum; namely, any two convex bodies K and L in Rn have non-degenerate affine images K ′ and L′ such that K ′ ⊂ L′ ⊂ −nK ′. As a corollar...