Related papers: The Three Gap Theorem and Periodic Functions
Some fixed point results are given for a class of functional contractions acting on (reflexive) triangular symmetric spaces. Technical connections with the corresponding theories over (standard) metric and partial metric spaces are also…
If a function $f:\mathbb{R}\to\mathbb{R}$ can be represented as the sum of $n$ periodic functions as $f=f_1+\dots+f_n$ with $f(x+\alpha_j)=f(x)$ ($j=1,\dots,n$), then it also satisfies a corresponding $n$-order difference equation…
Two measures of how near an arbitrary function between groups is to being a homomorphism are considered. These have properties similar to conjugates and commutators. The authors show that there is a rich theory based on these structures,…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc.…
There exist small perturbations of L-functions, satisfying the appropriate functional equation, for which the analogue of the Riemann hypothesis fails radically. Moreover, this phenomenon is generic. However, there also exist small…
We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein-Uhlenbeck process, providing the foundation for the fluctuation theory of slow/fast systems driven by such a noise. Our main contribution is on the…
In this work, a functional variant of the polynomial analogue of the classical Gandy's fixed point theorem is obtained. Sufficient conditions have been found to ensure that the complexity of the recursive function does not go beyond the…
In this paper, we establish three Landau-type theorems for certain bounded poly-analytic functions, which generalize the corresponding result for bi-analytic functions given by Liu and Ponnusamy [Canad. Math. Bull. 67(1): 2024, 152-165].…
We prove the existence of gaps between all the different classes of matrix monotone functions defined on an interval, provided the interval is non trivial and different from the whole real line. We then show how matrix monotone functions…
In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…
We investigate thermodynamics of general nonequilibrium processes stopped at stochastic times. We propose a systematic strategy for constructing fluctuation-theorem-like martingales for each thermodynamic functional, yielding a family of…
With the help of a new type of functionals we study manifolds diffeomorphic to $S^2\times S^2$ and establish, in particular, the Hopf conjecture.
The Collatz function is defined as C(n) = n / 2 if n is even and C(n) = 3n + 1 if n is odd. The Collatz conjecture states that every sequence generated by the Collatz function ends with the cycle (4, 2, 1) after a finite number of…
By restricting the variables running over various (possibly different) subfields, we introduce the notion of a partial zeta function. We prove that the partial zeta function is rational in an interesting case, generalizing Dwork's well…
A numeral system is an infinite sequence of different closed normal $\lambda$-terms intended to code the integers in $\lambda$-calculus. H. Barendregt has shown that if we can represent, for a numeral system, the functions : Successor,…
We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…
The Weil conjecture is a delightful theorem for algebraic varieties on finite fields and an important model for dynamical zeta functions. In this paper, we prove a functional equation of Lefschetz zeta functions for infinite cyclic…
The study of the diameter of the graph of polyhedra is a classical problem in the theory of linear programming. While transportation polytopes are at the core of operations research and statistics it is still open whether the Hirsch…
We present an illustrative application of the two famous mathematical theorems in differential topology in order to show the existence of periodic orbits with arbitrary given period for a class of hamiltonians .This result point out for a…
Given two quasi-definite moment functionals, the corresponding orthogonal polynomial systems satisfy an algebraic differential relation(called an extended coherent pair). We study generalizing extended coherent pairs that unify extended…