Related papers: A Maximum Modulus Theorem for functions admitting …
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
We derive modular parametrizations for certain infinite series whose summands involve central binomial coefficients and higher-order harmonic numbers. When the rates of convergence are certain rational numbers, modularity allows us to…
In this paper we consider a class of planar autonomous systems having an isolated limit cycle x_0 of smallest period T>0 such that the associated linearized system around it has only one characteristic multiplier with absolute value 1. We…
For a (not necessarily locally convex) topological vector space $\mathcal{X}$ of holomorphic functions in one complex variable, we show that the shift invariant subspace generated by a set of polynomials is $\mathcal{X}$ if and only if…
We consider the multiplicity of limit cycles that appear when a hyperbolic polycycle is perturbed. We prove, in particular, that if such unfolding happens in generic finite-parameter families, the multiplicity of every new limit cycle does…
A functional limit theorem is established for the partial-sum process of a class of stationary sequences which exhibit both heavy tails and long-range dependence. The stationary sequence is constructed using multiple stochastic integrals…
A new class of regular quaternionic functions, defined by power series in a natural fashion, has been introduced in recent years. Several results of the theory recall the classical complex analysis, whereas other results reflect the…
We construct a (bi)cyclic sieving phenomenon on the union of dominant maximal weights for level $\ell$ highest weight modules over an affine Kac-Moody algebra with exactly one highest weight being taken for each equivalence class, in a way…
A simple but rigorous proof of the Fundamental Theorem of Calculus is given in geometric calculus, after the basis for this theory in geometric algebra has been explained. Various classical examples of this theorem, such as the Green's and…
A number of recent results on optimization problems involving submodular functions have made use of the multilinear relaxation of the problem. These results hold typically in the value oracle model, where the objective function is…
Let $X$ be a planar smooth vector field with a polycycle $\Gamma^n$ with $n$ sides and all its corners, that are at most $n$ singularities, being hyperbolic saddles. In this paper we study the cyclicity of $\Gamma^n$ in terms of the…
We introduce, develop, and apply a new approach for dealing with the intuitive notion of function, called Flow Theory. Within our framework all functions are monadic and none of them has any domain. Sets, proper classes, categories,…
We consider a class of weighted harmonic functions in the open upper half-plane known as $\alpha$-harmonic functions. Of particular interest is the uniqueness problem for such functions subject to a vanishing Dirichlet boundary value on the…
We recast the well-known axiom system of quantum mechanics used by physicists (the Dirac calculus) in the language of Continuous Logic. For the basic version of the axiomatic system we prove that along with the canonical continuous model…
A large class of real $3$-dimensional nilpotent polynomial vector fields of arbitrary degree is considered. The aim of this work is to present general properties of the discrete and continuous dynamical systems induced by these vector…
We describe several infinite series of rational conformal field theories whose conformal characters are modular units, i.e. which are modular functions having no zeros or poles in the upper complex half plane, and which thus possess simple…
The multilinear framework has achieved the breakthrough $1-1/e$ approximation for maximizing a monotone submodular function subject to a matroid constraint. This framework has a continuous optimization part and a rounding part. We extend…
Using the Dirichlet theorem on the equidistribution of residue classes modulo $q$ and the Lemke Oliver-Soundararajan conjecture on the distribution of pairs of residues on consecutive primes, we show that the domain of convergence of the…
We prove that the maximal number of limit cycles which bifurcate from an open period annulus under a given multi-parameter analytic deformation of a given analytic vector field is the same as in an appropriate one-parameter analytic…
Let M be a meromorphic connection with poles along a smooth divisor D in a smooth algebraic variety. Let Sol M be the solution complex of M. We prove that the good formal decomposition locus of M coincides with the locus where the…