Related papers: The Brjuno and Wilton Functions
We derive one-point functions in 4d $\mathcal N=4$ SYM with $\tfrac{1}{2}$-BPS boundaries, defects and interfaces which host large numbers of defect degrees of freedom. The theories are engineered by Gaiotto-Witten D3/D5/NS5 brane setups…
We consider two natural gradings on the space of symmetric functions: by degree and by length. We introduce a differential operator $T$ that leaves the components of this double grading invariant and exhibit a basis of bihomogeneous…
We relate the fragmentation functions of partons into mesons and baryons in the framework of recombination of shower partons. The results are in reasonable agreement with the data. The implication is that the meson and baryon fragmentation…
We introduce a "Hamiltonian"-like function, called the volume function, indispensable to describe the ensemble of jammed matter such as granular materials and emulsions from a geometrical point of view. The volume function represents the…
We study the b-functions of relative invariants of the prehomogeneous vector spaces associated with quivers of type A. By applying the decomposition formula for b-functions, we determine explicitly the b-functions of one variable for each…
Slice-regular functions of a quaternionic variable have been studied extensively in the last 12 years, resulting, in many ways, quite close to classical holomorphic functions of a complex variable; indeed, there is a correspondence between…
We define Bernstein-Sato polynomials for meromorphic functions and study their basic properties. In particular, we prove a Kashiwara-Malgrange type theorem on their geometric monodromies, which would be useful also in relation with the…
The Lambert W function, implicitly defined by W(x) exp{W(x)}=x, is a "new" special function that has recently been the subject of an extended upsurge in interest and applications. In this note, I point out that the Lambert W function can…
This paper develops theory for a newly-defined bicomplex hyperbolic harmonic function with four real-dimensional inputs, in a way that generalizes the connection between real harmonic functions with two real-dimensional inputs and complex…
In this article, we define a special function called the Bigamma function. It provides a generalization of Euler's gamma function. Several algebraic properties of this new function are studied. In particular, results linking this new…
One of the main purposes of this article is to give functional equations and differential equations between Bernstein basis functions and generating functions of B-spline curves. Using these equations, very useful formulas containing the…
Let $\Delta_m$ be the standard $m$-dimensional simplex of non-negative $m+1$ tuples that sum to unity and let $S$ be a nonempty subset of $\Delta_m$. A real valued function $h$ defined on a convex subset of a real vector space is $S$-almost…
In this paper we study the Bremsstrahlung functions for the 1/6 BPS and the 1/2 BPS Wilson lines in ABJM theory. First we use a superconformal defect approach to prove a conjectured relation between the Bremsstrahlung functions associated…
Computations in high-dimensional spaces can often be realized only approximately, using a certain number of projections onto lower dimensional subspaces or sampling from distributions. In this paper, we are interested in pairs of…
An analogue of Brylinski's knot beta function is defined for a submanifold of d-dimensional Euclidean space. This is a meromorphic function on the complex plane. The first few residues are computed for a surface in three dimensional space.
The main goal of this article is to analyze some peculiar features of the global (and local) minima of $\alpha$-Brjuno functions $B_\alpha$ where $\alpha\in(0,1].$ Our starting point is the result by Balazard--Martin (2020), who showed that…
A space-filling function is a bijection from the unit line segment to the unit square, cube, or hypercube. The function from the unit line segment is continuous. The inverse function, while well-defined, is not continuous. Space-filling…
Let $f(z)=\sum_{n=0}^{+\infty} a_nz^n$\ $(z\in\mathbb{C})$\ be an analytic function in the unit disk and $f_t$ be an analytic function of the form $f_t(z)=\sum_{n=0}^{+\infty} a_ne^{i\theta_nt}z^n,$ where $t\in\mathbb{R},$…
In this article, by comparing the characteristic functions, we prove that for any $\nu$-valued algebroid function $w(z)$ defined in the unit disk with $\limsup_{r\to1-}T(r,w)/\log\frac{1}{1-r}=\infty$ and the hyper order $\rho_2(w)=0$, the…
We study the existence of Gabor orthonormal bases with window the characteristic function of the set W=[0,a] U [b+a, b+1] of measure 1, with a, b>0. By the symmetries of the problem, we can restrict our attention to the case a<=1/2. We…