Related papers: Irrational centers
This is a 20-year old review on singularities and singularity theorems. The main reason to submit it now is -apart from increasing its availability- to correct a very strange error that appears in the journal's online version: it contains…
The majority of experiments in fundamental science today are designed to be multi-purpose: their aim is not simply to measure a single physical quantity or process, but rather to enable increased precision in the measurement of a number of…
The object of our investigation is a point that gives the maximum value of a potential with a strictly decreasing radially symmetric kernel. It defines a center of a body in Rm. When we choose the Riesz kernel or the Poisson kernel as the…
Contradiction is often seen as a defect of intelligent systems and a dangerous limitation on efficiency. In this paper we raise the question of whether, on the contrary, it could be considered a key tool in increasing intelligence in…
The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…
The basic formalism of a novel scale invarinat nonlinear analysis is presented. A few analytic number theoretic results are derived independent of standard approaches.
This is a survey on (lack of) stable rationality over arbitrary fields (including algebraically closed fields). Topics addressed include: Rationality and unirationality, R-equivalence on rational points, Chow groups of zero-cycles, Galois…
Recently developed supersymmetric perturbation theory has been successfully employed to make a complete mathematical analysis the reason behind exact solvability of some non-central potentials. This investigation clarifies once more the…
The argument of physical dimension/units is applied to electrical switched circuits, making the topic of the nonlinearity of such circuits simpler. This approach is seen against the background of a more general outlook (IEEE CAS MAG, III,…
In this note, basing on a certain functional equation of the dilogarithm function, we establish nontrivial lower bounds for the $p$-adic valuation (where $p$ is a given prime number) of some type of rational numbers involving harmonic…
In this paper I consider some logical and mathematical aspects of the discussion of the identity and individuality of quantum entities. I shall point out that for some aspects of the discussion, the logical basis cannot be put aside; on the…
The kernel of analysis, to me anyway, is the following idea: A point is arbitrarily close to a set if every neighborhood of the point intersects the set. Defining ``arbitrarily close'' in this way provides a foundation for classical results…
We show remnants of chiral symmetry breaking in the center-projected theory. We construct and study an unambiguous definition of center vortices.
Rationality has been an intriguing topic for several decades. Even the scope of definition of rationality across different subjects varies. Several theories (e.g., game theory) initially evolved on the basis that agents (e.g., humans) are…
A new definition of a real number is that it is a rule which says Yes or No based on whether the real number ought to be in a given rational interval. This is a teaser paper for formalizing, exploring, and generalizing this definition. The…
The notions of potential infinity (understood as expressing a direction) and actual infinity (expressing a quantity) are investigated. It is shown that the notion of actual infinity is inconsistent, because the set of all (finite) natural…
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.
This paper uses an axiomatic foundation to create a new measure for the cost of learning that allows for multiple perceptual distances in a single choice environment so that some events can be harder to differentiate between than others.…
Our understanding of intelligence is directed primarily at the human level. This paper attempts to give a more unifying definition that can be applied to the natural world in general and then Artificial Intelligence. The definition would be…
We consider networks in which random walkers are removed because of the failure of specific nodes. We interpret the rate of loss as a measure of the importance of nodes, a notion we denote as failure-centrality. We show that the degree of…