Related papers: Sharp Constants of Approximation Theory. IV. Asymp…
We prove almost Strichartz estimates found after adding regularity in the spherical coordinates for Schr\"odinger-like equations. The estimates are sharp up to endpoints. The proof relies on estimates involving spherical averages. Sharpness…
String theory axions appear to be promising candidates for explaining cosmological constant via quintessence. In this paper, we study conditions on the string compactifications under which axion quintessence can happen. For sufficiently…
Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…
This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems. In many instances, it is possible to efficiently find an…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
In many combinatorial problems one may need to model the diversity or similarity of assignments in a solution. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this…
We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one…
This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers $\zeta_{1},\zeta_{2},...,\zeta_{k}$. The approach relies on results on the connection between the set of all…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
The quantum measurement problem is formulated in the form of an insolubility theorem that states the impossibility of obtaining, for all available object preparations, a mixture of states of the compound object and apparatus system that…
A quasi-schemoid is a small category with a particular partition of the set of morphisms. We define a homotopy relation on the category of quasi-schemoids and study its fundamental properties. As a homotopy invariant, the homotopy set of…
We define a generalization of the fixed point set, called the bounded fixed set, for a group acting by isometries on a metric space. An analogue of the P. A. Smith theorem is proved for metric spaces of finite asymptotic dimension, which…
Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…
We study the relative entropy between the empirical estimate of a discrete distribution and the true underlying distribution. If the minimum value of the probability mass function exceeds an $\alpha > 0$ (i.e. when the true underlying…
A theory of gravity with a generic action functional and minimally coupled to N matter fields has a nontrivial fixed point in the leading large N approximation. At this fixed point, the cosmological constant and Newton's constant are…
We present a generalization of first-order unification to a term algebra where variable indexing is part of the object language. We exploit variable indexing by associating some sequences of variables ($X_0,\ X_1,\ X_2,\dots$) with a…
Self-similar approximation theory is shown to be a powerful tool for describing phase transitions in quantum field theory. Self-similar approximants present the extrapolation of asymptotic series in powers of small variables to the…
We prove optimal convergence estimates for eigenvalues and eigenvectors of a class of singular/stiff perturbed problems. Our profs are constructive in nature and use (elementary) techniques which are of current interest in computational…
We compare the usual operator modulus with two symmetrized variants, the arithmetic symmetric modulus and the quadratic symmetric modulus. For every unitarily invariant norm, we determine sharp equivalence constants among these three…
Perturbation theory is a powerful tool in manipulating dynamical system. However, it is legal only for infinitesimal perturbations. We propose to dispose this problem by means of perturbation group, and find that the coupling constant…