Related papers: Bifurcation values of $C^{\infty} functions
We prove a new upper bound on the generalization gap of classifiers that are obtained by first using self-supervision to learn a representation $r$ of the training data, and then fitting a simple (e.g., linear) classifier $g$ to the labels.…
Let $F$ be a local field and $n\ge 2$ an integer. We study the Radon transform as an operator $M : \mathcal C_+ \to \mathcal C_-$ from the space of smooth $K$-finite functions on $F^n \setminus \{0\}$ with bounded support to the space of…
We classify simple singularities of functions on space curves. We show that their bifurcation sets have properties very similar to those of functions on smooth manifolds and complete intersections [1,2]: the k(pi, 1)-theorem for the…
We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
A general class of singular real hypersurfaces, called subanalytic, is defined. For a subanalytic hypersurface M in C^n, Cauchy-Riemann (or simply CR) functions on M are defined, and certain properties of CR functions discussed. In…
It is common to have to process signals or images whose values are cyclic and can be represented as points on the complex circle, like wrapped phases, angles, orientations, or color hues. We consider a Tikhonov-type regularization model to…
In the context of global optimization of mixed-integer nonlinear optimization formulations, we consider smoothing univariate functions $f$ that satisfy $f(0)=0$, $f$ is increasing and concave on $[0,+\infty)$, $f$ is twice differentiable on…
We present a class of multiplicative functions $f:\mathbb{N}\to\mathbb{C}$ with bounded partial sums. The novelty here is that our functions do not need to have modulus bounded by $1$. The key feature is that they pretend to be the constant…
We establish the theorems that give necessary and sufficient conditions for an arbitrary function defined in the unit disk of complex plane in order to has boundary values along classes of equivalencies of simple curves. Our results…
We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. We use the results to calculate the renormalization functions $\beta$, $\gamma$, $\gamma_m$ of…
In this paper, some sufficient conditions for the differentiability of the $n$-variable real-valued function are obtained, which are given based on the differentiability of the $n-1$-variable real-valued function and are weaker than…
We present criteria for deciding whether a bivariate rational function in two variables can be written as a sum of two (q-)differences of bivariate rational functions. Using these criteria, we show how certain double sums can be evaluated,…
The object of this paper is studying some properties of meromorphic functions which satisfy in the condition \[Re(zf(z)) > \alpha|z^2f'(z)+zf(z)| .\] Parallel results for some related classes are also obtained.
Let R+ = (0,infinity) and let M be the family of all mean values of two numbers in R+ (some examples are the arithmetic, geometric, and harmonic means). Given m1, m2 in M, we say that a function f : R+ to R+ is (m1,m2)-convex if f(m1(x,y))…
We prove semi-rationalification and semi-log-canonicalization for Gorenstein demi-normal surfaces. That is, given a Gorenstein demi-normal surface X with semi-rational (respectively, semi-log canonical) singularities in an open set U with…
Let F and G be two families of meromorphic functions on a domain D, and let a, b and c be three distinct points in the extended complex plane. Let G be a normal family in D such that all limit functions of G are non-constant. If for each f…
Suppose that $F$ is a smooth and connected complex surface (not necessarily compact) containing a smooth rational curve $C$ with positive self-intersection. We prove that there exists a neighborhood $U\supset C$ such that any meromorphic…
In this paper we introduce the class of infinite infimal convolution functionals and apply these functionals to the regularization of ill-posed inverse problems. The proposed regularization involves an infimal convolution of a continuously…
General-purpose Markov Chain Monte Carlo sampling algorithms suffer from a dramatic reduction in efficiency as the system being studied is driven towards a critical point. Recently, a series of seminal studies suggested that normalizing…