scholarly journals An open problem on inverse matrices from industrial organization, and a partial solution

2012 ◽  
Vol 437 (1) ◽  
pp. 294-306
Author(s):  
Jingang Zhao
Keyword(s):  
Industrial Organization ◽  
Open Problem ◽  
Partial Solution

A partial solution to an open problem of Amadio and Curien

2018 ◽  
Vol 260 ◽  
pp. 126-134
Author(s):  
Xiaoyong Xi ◽  
Jinbo Yang ◽  
Hui Kou
Keyword(s):  
Open Problem ◽  
Partial Solution

Extensional quotients for type theory and the consistency problem for NF

1998 ◽  
Vol 63 (1) ◽  
pp. 247-261
Author(s):  
Gian Aldo Antonelli
Keyword(s):  
Equivalence Relation ◽  
Open Problem ◽  
Type Theory ◽  
Partial Solution ◽  
Weak Version ◽  
New Foundations ◽  
Multiple Copies ◽  
Consistency Problem ◽  
Membership Relation ◽  
Main Ideas

Quine's “New Foundations” (NF) was first presented in Quine [10] and later on in Quine [11]. Ernst Specker [15, 13], building upon a previous result of Ehrenfeucht and Mostowski [5], showed that NF is consistent if and only if there is a model of the Theory of Negative (and positive) Types (TNT) with full extensionality that admits of a “shifting automorphism,” but the existence of such a model remains an open problem.In his [8], Ronald Jensen gave a partial solution to the problem of the consistency of Quine's NF. Jensen considered a version of NF—referred to as NFU—in which the axiom of extensionality is weakened to allow for Urelemente or “atoms.” He showed, modifying Specker's theorem, that the existence of a model of TNT with atoms admitting of a “shifting automorphism” implies the consistency of NFU, proceeding then to exhibit such a model.This paper presents a reduction of the consistency problem for NF to the existence of a model of TNT with atoms containing certain “large” (unstratified) sets and admitting a shifting automorphism. In particular we show that such a model can be “collapsed” to a model of pure TNT in such a way as to preserve the shifting automorphism. By the above-mentioned result of Specker's, this implies the consistency of NF.Let us take the time to explain the main ideas behind the construction. Suppose we have a certain universe U of sets, built up from certain individuals or “atoms.” In such a universe we have only a weak version of the axiom of extensionality: two objects are the same if and only if they are both sets having the same members. We would like to obtain a universe U′ that is as close to U as possible, but in which there are no atoms (i.e., the only memberless object is the empty set). One way of doing this is to assign to each atom ξ, a set a (perhaps the empty set), inductively identifying sets that have members that we are already committed to considering “the same.” In doing this we obtain an equivalence relation ≃ over U that interacts nicely with the membership relation (provided we have accounted for multiplicity of members, i.e., we have allowed sets to contain “multiple copies” of the same object). Then we can take U′ = U/≃, the quotient of U with respect to ≃. It is then possible to define a “membership” relation over U′ in such a way as to have full extensionality. Relations such as ≃ are referred to as “contractions” by Hinnion and “bisimulations” by Aczel.

The New Cycle in Industrial Organization

1918 ◽  
Vol 119 (12) ◽  
pp. 229-229
Author(s):  
Mark M. Jones
Keyword(s):  
Industrial Organization

Business-groups in Russian industries

2004 ◽  
pp. 121-134 ◽  
Author(s):  
S. Avdasheva
Keyword(s):  
Industrial Organization ◽  
Economic System ◽  
Institutional Economics ◽  
Business Groups ◽  
Control Rights ◽  
Organization And Management ◽  
Russian Economy ◽  
Main Determinants ◽  
Soviet Economic System

The chapter of “Institutional Economics” textbook is devoted to the development of business-groups as a specific feature of industrial organization in the Russian economy. The main determinants of forming and functioning of business-groups such as allocation of property rights in Soviet enterprises, networks of directors and executive authorities in the Soviet economic system as well as import of new institutes and inefficient state enforcement are in the center of analysis. Origins, structure, organization and management within the groups and the role of shareholding and informal control rights are considered.

The Yukawa Potential Function and Reciprocal Univalent Function

2013 ◽  
Vol 3 (2) ◽  
pp. 197-202
Author(s):  
Amir Pishkoo ◽  
Maslina Darus
Keyword(s):  
Mathematical Model ◽  
Unit Disk ◽  
Potential Function ◽  
Univalent Function ◽  
Open Problem ◽  
Yukawa Potential ◽  
Reciprocal Theorem ◽  
Problem Statement ◽  
Fundamental Forces

This paper presents a mathematical model that provides analytic connection between four fundamental forces (interactions), by using modified reciprocal theorem,derived in the paper, as a convenient template. The essential premise of this work is to demonstrate that if we obtain with a form of the Yukawa potential function [as a meromorphic univalent function], we may eventually obtain the Coloumb Potential as a univalent function outside of the unit disk. Finally, we introduce the new problem statement about assigning Meijer's G-functions to Yukawa and Coloumb potentials as an open problem.

Sign in / Sign up

Export Citation Format

Share Document