Related papers: On Absolute and Relative Change

We show that if one or more of the `constants' of Nature can vary then their values, as measured in the laboratory, should oscillate over the year in a very particular way. These seasonal changes in the constants could well be detected, in…

Ranking entities such as algorithms, devices, methods, or models based on their performances, while accounting for application-specific preferences, is a challenge. To address this challenge, we establish the foundations of a universal…

In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…

With increasing demand for accurate calculation of isotope shifts of atomic systems for fundamental and nuclear structure research, an analytic energy derivative approach is presented in the relativistic coupled-cluster theory framework to…

Relative algebroids provide a framework that unifies Lie algebroids with partial differential equations. In this set of notes, we explain how relative algebroids arise from geometric problems, and give an introduction to their structural…

We prove relative versions of many earlier results about almost invariant sets and splittings of groups. In particular, we prove a relative version of the algebraic torus theorem, and we prove the existence and uniqueness of relative…

In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].

Using Morse theory and a new relative homological linking of pairs, we prove a ``homological linking principle'', thereby generalizing many well known results in critical point theory.

We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…

A general organizing principle is proposed that can be used to derive the equations of motion describing the near-equilibrium dynamics of causal and thermodynamically stable relativistic systems. The latter are found to display some new…

The notion that any physical quantity is defined and measured relative to a reference frame is traditionally not explicitly reflected in the theoretical description of physical experiments where, instead, the relevant observables are…

We give a new heuristic for all of the main terms in the quotient of products of L-functions averaged over a family. These conjectures generalize the recent conjectures for mean values of L-functions. Comparison is made to the analogous…

Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms of Group Theory; but some systems are much deeper, such as the axioms of…

Hutchins, Yuan, M., and Santangelo (2015) proposed the Relative Citation Ratio (RCR) as a new field-normalized impact indicator. This study investigates the RCR by correlating it on the level of single publications with established…

We present two possible criteria quantifying the degree of classicality of an arbitrary (finite dimensional) dynamical system. The inputs for these criteria are the classical dynamical structure of the system together with the quantum and…

Various properties of relative entropy have led to its widespread use in information theory. These properties suggest that relative entropy has a role to play in systems that attempt to perform inference in terms of probability…

Composites are often created to facilitate the work of decision-makers. Therefore, practical or theoretical considerations may lead to a priori weights of the indicators forming a composite. Composites that are created a weighted aggregates…

We introduce and axiomatize the notion of a reflective cardinal, use it to give semantics to higher order set theory, and explore connections between the notion of reflective cardinals and large cardinal axioms.

In this note we give a characterization of a family of relative entropies on open domain depending on a real parameter $\alpha$ based on recursivity and symmetry. In the cases $\alpha=1$ and $\alpha=0$ we use additionally a weak regularity…

A new approach to special relativity is presented which introduces coordinate systems with imaginary time axes, observation systems, and coordinate bases.