Related papers: What is Cost?
A survey of recent results concerning cardinal invariants of measure and category. Submitted as a chapter of the upcoming Handbook of Set Theory.
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
In this paper, we explore a quantitative approach to querying inconsistent description logic knowledge bases. We consider weighted knowledge bases in which both axioms and assertions have (possibly infinite) weights, which are used to…
There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This…
Experimentation and Measurement (E&M) capabilities allow organizations to accurately assess the impact of new propositions and to experiment with many variants of existing products. However, until now, the question of measuring the…
This paper describes a mathematical formulation for measuring how one system can estimate the consciousness of another. This consciousness estimate is always relative to the observer. The paper shows how this formulation leads to simple…
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
The measurement apparatus proposed in the titled paper, "Energy-Time Uncertainty Relations in Quantum Measurements" [Found. Phys. 46, 1522-1550 (2016)] was examined. A simple proof was presented for the non-existence of the apparatus.
The paper deals with the problem of identifying the internal dependencies and similarities among a large number of random processes. Linear models are considered to describe the relations among the time series and the energy associated to…
We define graph products of families of pairs of groups and study the question when two such graph products are commensurable. As an application we prove linearity of certain graph products.
We develop an axiomatic theory of information acquisition that captures the idea of constant marginal costs in information production: the cost of generating two independent signals is the sum of their costs, and generating a signal with…
The paper describes methodology of math education for students interested in chemistry. Suppose we have mathematical circle 2 hours per week. What can be done? We can not provide any systematic study, but we can choose one subject and show…
How much do financial management fees cost investors? This article studies an approximate formula for the cumulative costs of annual Assets Under Management (AUM) fees. The formula states that an investment paying an annual fee of…
We present empirical evidence on the relationship between demand shocks and price changes, conditional on returns to scale. We find that in industries with decreasing returns to scale, demand increases (which raise costs) correspond to…
The status of our understanding of relativistic sum rules is reviewed. The recent development of new theoretical methods for the evaluation of these sum rules offers hope for further advances in this challenging field. These new techniques…
We give a survey on results regarding self-similar and automaton presentations of free groups and semigroups and related products. Furthermore, we discuss open problems and results with respect to algebraic decision problems in this area.
These are notes for a graduate-level introductory course on singularity categories.
We develop almost ring theory, which is a domain of mathematics somewhere halfway between ring theory and category theory (whence the difficulty of finding appropriate MSC-class numbers). We apply this theory to valuation theory and to…
We introduce the concepts of a pair of valuations and a good generating set and show how they can be used to prove geometric properties of soluble groups.
GGR News: we hear that... GR Centenial Speakers Bureau GGR $\to$ DGR GGR program at the APS meeting in Baltimore, MD Conference reports: New Frontiers in Dynamical Gravity Frontiers of Neutron Star Astrophysics Quantum Information in…