The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai [1] seeks to relate two fundamental measures of Boolean function complexity: it states that H[f ] ≤ C · Inf [f ] holds for every Boolean function f , where H[f ] denotes the spectral entropy of f , Inf [f ] is its total influence, and C > 0 is a universal constant. Despite significant interest in the conjecture it has only bee...

we investigate the classical h.~zassenhaus conjecture‎ ‎for integral group rings of alternating groups $a_9$ and $a_{10}$ of degree‎ ‎$9$ and $10$‎, ‎respectively‎. ‎as a consequence of our‎ ‎previous results we confirm the prime graph‎ ‎conjecture for integral group rings of $a_n$ for all $n leq 10$‎.

This paper presents and proves an extension of Meek’s conjecture to chain graphs under the Lauritzen-Wermuth-Frydenberg interpretation. The proof of the conjecture leads to the development of a structure learning algorithm that finds an inclusion optimal chain graph for any given probability distribution satisfying the composition property. Finally, the new algorithm is experimentally evaluated.

Brennan’s conjecture in univalent function theory states that if τ is any analytic univalent transform of the open unit disk D onto a simply connected domain G and −1/3 < p < 1, then 1/(τ ′)p belongs to the Hilbert Bergman space of all analytic square integrable functions with respect to the area measure. We introduce a class of analytic function spaces La(μp) on G and prove that Brennan’s conj...

We study the analogue of classical infinitesimal center problem in plane, but for zero cycles. define displacement function this context and prove that it is identically if only deformation has a composition factor. That is, we here conjecture true, contrast with tangential on Finally, give examples applications our results.

This note introduces a new general conjecture correlating the dimensionality dT of an infinite lattice with N nodes to the asymptotic value of its Wiener Index W(N). In the limit of large N the general asymptotic behavior W(N)≈Ns is proposed, where the exponent s and dT are related by the conjectured formula s=2+1/dT allowing a new definition of dimensionality dW=(s-2)-1. Being related to the t...

To study finite-dimensional modules of the Lie superalgebras, Kac introduced the Kac-modules V(Λ) and divided them into typical or atypical modules according as they are simple or not. For Λ being atypical, Hughes et al have an algorithm to determine all the composition factors of a Kac-module; they conjectured that there exists a bijection between the composition factors of a Kac-module and th...

The following conjecture generalizing the Contraction Mapping Theorem was made by Stein in [9]: Let (X, ρ) be a complete metric space and let F = {T1, . . . , Tn} be a finite family of self-maps of X. Suppose there is a constant γ ∈ (0, 1) such that for any x, y ∈ X there exists T ∈ F with ρ(T (x), T (y)) ≤ γρ(x, y). Then some composition of members of F has a fixed point. In this paper we disp...

We determine the spectra of weighted composition operators acting on the weighted Banach spaces of analytic functions H∞ vp when the symbol φ has a fixed point in the open unit disk. Further, we apply this result to give the spectra of composition operators on Bloch type spaces. In particular, we answer in the affirmative a conjecture by MacCluer and Saxe.