Related papers: Analytical results for the C-angularity soft funct…
This four-pages note is an invitation to explore explicit K-stability for arbitrary K\"ahler classes of low dimension and low rank spherical varieties. We apply our simple combinatorial criterion of K-stability of rank one spherical…
Conformal symmetry of QCD is restored at the Wilson-Fisher critical point in noninteger $4-2\epsilon$ space-time dimensions. Correlation functions of multiplicatively renormalizable operators with different anomalous dimensions at the…
In this note we define a $C^1$ function $F:[0,M]^2\to [0,2]$ that satisfies that its set of critical values has positive measure. This function provides an example, easier than those that usually appear in the literature, of how the order…
We consider a family of Caffarelli-Kohn-Nirenberg interpolation inequalities and weighted logarithmic Hardy inequalities which have been obtained recently as a limit case of the first ones. We discuss the ranges of the parameters for which…
We study scaling function geometry. We show the existence of the scaling function of a geometrically finite one-dimensional mapping. This scaling function is discontinuous. We prove that the scaling function and the asymmetries at the…
We calculate the one-loop corrections to the soft anomalous dimension matrices for the production of a top-antitop quark pair in association with a jet at hadron colliders. This is a step forward towards implementing a procedure for the…
At high values of the pair invariant mass the differential cross section for top-quark pair production at hadron colliders factorizes into soft, hard, and fragmentation functions. In this paper we calculate the next-to-next-to-leading-order…
In the study of the amplitudes for many-particle processes, and also for processes involving particles with spin, the use is made of matrix elements of the rotation group d^j_{\mu\nu}(z). In this paper the generalization of the functions…
We formally extend the CFT techniques introduced in arXiv:1505.00963, to $\phi^{\frac{2d_0}{d_0-2}}$ theory in $d=d_0-\epsilon$ dimensions and use it to compute anomalous dimensions near $d_0=3, 4$ in a unified manner. We also do a similar…
In paper I of this series on fluid turbulence we showed that exact resummations of the perturbative theory of the structure functions of velocity differences result in a finite (order by order) theory. These findings exclude any known…
We discuss some aspects of approximating functions on high-dimensional data sets with additive functions or ANOVA decompositions, that is, sums of functions depending on fewer variables each. It is seen that under appropriate smoothness…
We extend the notion of Ulam floating sets from convex bodies to Ulam floating functions. We use the Ulam floating functions to derive a new variational formula for the affine surface area of log-concave functions.
We present efficient algorithms for computing the $N$-point correlation functions (NPCFs) of random fields in arbitrary $D$-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences, and provide a…
In a prior paper \cite{EFRST20}, two of us, along with P. Ellingsen, P. Felke and A. Tkachenko, 1defined a new (output) multiplicative differential, and the corresponding $c$-differential uniformity, which has the potential of extending…
We define a family of $C^1$ functions which we call "nowhere coexpanding functions" that is closed under composition and includes all $C^3$ functions with non-positive Schwarzian derivative. We establish results on the number and nature of…
We derive the hard functions for all 2->2 processes in massless QCD up to next-to-next-to-leading order (NNLO) in the strong coupling constant. By employing the known one- and two-loop helicity amplitudes for these processes, we obtain…
We establish the global $C^{1, \alpha}$-regularity for functions in solution classes, whenever ellipticity constants are sufficiently close. As an application, we derive the global regularity result concerning the parabolic normalized…
This work focuses on angular values of nonautonomous dynamical systems which have been introduced for general random and (non)autonomous dynamical systems in a previous publication [W.-J. Beyn, G. Froyland, and T. H\"uls, SIAM J. Appl. Dyn.…
This paper is devoted to the analysis of the distribution of the total angular momentum in a relativistic configuration. Using cumulants and generating function formalism this analysis can be reduced to the study of individual subshells…
The entanglement entropy of spacetime regions $A$ in odd-dimensional conformal field theories (CFTs) contains a universal constant term, $(-1)^{\frac{d-1}{2}}F(A)$. This quantity can be robustly defined by considering the mutual information…