scholarly journals Homogeneous models and almost decidability

1989 ◽  
Vol 46 (3) ◽  
pp. 343-355 ◽  
Author(s):  
Terry Millar
Keyword(s):  
Elementary Theory ◽  
Homogeneous Model ◽  
Point Of View ◽  
Type Spectrum ◽  
Homogeneous Models ◽  
Theoretic Point

AbstractCountable homogeneous models are ‘simple’ objects from a model theoretic point of view. From a recursion theoretic point of view they can be complex. For instance the elementary theory of such a model might be undecidable, or the set of complete types might be recursively complex. Unfortunately even if neither of these conditions holds, such a model still can be undecidable. This paper investigates countable homogeneous models with respect to a weaker notion of decidability called almost decidable. It is shown that for theories that have only countably many type spectra, any countable homogeneous model of such a theory that has a Σ2 type spectrum is almost decidable.

On the validity of hilbert's nullstellensatz, artin's theorem, and related results in grothendieck toposes

1988 ◽  
Vol 53 (4) ◽  
pp. 1177-1187
Author(s):  
W. A. MacCaull
Keyword(s):  
Intuitionistic Logic ◽  
Main Idea ◽  
Rational Functions ◽  
Completeness Theorem ◽  
Point Of View ◽  
Polynomial Rings ◽  
Von Neumann ◽  
Ordered Fields ◽  
Von Neumann Regular ◽  
Theoretic Point

Using formally intuitionistic logic coupled with infinitary logic and the completeness theorem for coherent logic, we establish the validity, in Grothendieck toposes, of a number of well-known, classically valid theorems about fields and ordered fields. Classically, these theorems have proofs by contradiction and most involve higher order notions. Here, the theorems are each given a first-order formulation, and this form of the theorem is then deduced using coherent or formally intuitionistic logic. This immediately implies their validity in arbitrary Grothendieck toposes. The main idea throughout is to use coherent theories and, whenever possible, find coherent formulations of formulas which then allow us to call upon the completeness theorem of coherent logic. In one place, the positive model-completeness of the relevant theory is used to find the necessary coherent formulas.The theorems here deal with polynomials or rational functions (in s indeterminates) over fields. A polynomial over a field can, of course, be represented by a finite string of field elements, and a rational function can be represented by a pair of strings of field elements. We chose the approach whereby results on polynomial rings are reduced to results about the base field, because the theory of polynomial rings in s indeterminates over fields, although coherent, is less desirable from a model-theoretic point of view. Ultimately we are interested in the models.This research was originally motivated by the works of Saracino and Weispfenning [SW], van den Dries [Dr], and Bunge [Bu], each of whom generalized some theorems from algebraic geometry or ordered fields to (commutative, von Neumann) regular rings (with unity).

scholarly journals On the Graph of Divisibility of an Integral Domain

2015 ◽  
Vol 58 (3) ◽  
pp. 449-458 ◽  
Author(s):  
Jason Greene Boynton ◽  
Jim Coykendall
Keyword(s):  
Topological Space ◽  
Integral Domain ◽  
Point Of View ◽  
Current Understanding ◽  
Main Theme ◽  
Topological Graph ◽  
Integral Domains ◽  
Graph Theoretic ◽  
Theoretic Point ◽  
Group Of Divisibility

AbstractIt is well known that the factorization properties of a domain are reflected in the structure of its group of divisibility. The main theme of this paper is to introduce a topological/graph-theoretic point of view to the current understanding of factorization in integral domains. We also show that connectedness properties in the graph and topological space give rise to a generalization of atomicity.

scholarly journals Intima heterogeneity in stress assessment of atherosclerotic plaques

2017 ◽  
Vol 8 (1) ◽  
pp. 20170008 ◽  
Author(s):  
Ali C. Akyildiz ◽  
Lambert Speelman ◽  
Bas van Velzen ◽  
Raoul R. F. Stevens ◽  
Antonius F. W. van der Steen ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Plaque Rupture ◽  
Homogeneous Model ◽  
Sensitivity Analyses ◽  
Homogeneous Material ◽  
Sensitivity Index ◽  
Stress Assessment ◽  
Heterogeneous Models ◽  
Homogeneous Models ◽  
Accuracy Stress

Atherosclerotic plaque rupture is recognized as the primary cause of cardiac and cerebral ischaemic events. High structural plaque stresses have been shown to strongly correlate with plaque rupture. Plaque stresses can be computed with finite-element (FE) models. Current FE models employ homogeneous material properties for the heterogeneous atherosclerotic intima. This study aimed to evaluate the influence of intima heterogeneity on plaque stress computations. Two-dimensional FE models with homogeneous and heterogeneous intima were constructed from histological images of atherosclerotic human coronaries ( n = 12). For homogeneous models, a single stiffness value was employed for the entire intima. For heterogeneous models, the intima was subdivided into four clusters based on the histological information and different stiffness values were assigned to the clusters. To cover the reported local intima stiffness range, 100 cluster stiffness combinations were simulated. Peak cap stresses (PCSs) from the homogeneous and heterogeneous models were analysed and compared. By using a global variance-based sensitivity analysis, the influence of the cluster stiffnesses on the PCS variation in the heterogeneous intima models was determined. Per plaque, the median PCS values of the heterogeneous models ranged from 27 to 160 kPa, and the PCS range varied between 43 and 218 kPa. On average, the homogeneous model PCS values differed from the median PCS values of heterogeneous models by 14%. A positive correlation ( R 2 = 0.72) was found between the homogeneous model PCS and the PCS range of the heterogeneous models. Sensitivity analysis showed that the highest main sensitivity index per plaque ranged from 0.26 to 0.83, and the average was 0.47. Intima heterogeneity resulted in substantial changes in PCS, warranting stress analyses with heterogeneous intima properties for plaque-specific, high accuracy stress assessment. Yet, computations with homogeneous intima assumption are still valuable to perform sensitivity analyses or parametric studies for testing the effect of plaque geometry on PCS. Moreover, homogeneous intima models can help identify low PCS, stable type plaques with thick caps. Yet, for thin cap plaques, accurate stiffness measurements of the clusters in the cap and stress analysis with heterogeneous cap properties are required to characterize the plaque stability.

Universal recursion theoretic properties of r.e. preordered structures

1985 ◽  
Vol 50 (2) ◽  
pp. 397-406 ◽  
Author(s):  
Franco Montagna ◽  
Andrea Sorbi
Keyword(s):  
Equivalence Relation ◽  
Point Of View ◽  
Main Concern ◽  
Natural Numbers ◽  
Axiomatic Theory ◽  
Recursive Functions ◽  
Theoretic Point

When dealing with axiomatic theories from a recursion-theoretic point of view, the notion of r.e. preordering naturally arises. We agree that an r.e. preorder is a pair = 〈P, ≤P〉 such that P is an r.e. subset of the set of natural numbers (denoted by ω), ≤P is a preordering on P and the set {〈;x, y〉: x ≤Py} is r.e.. Indeed, if is an axiomatic theory, the provable implication of yields a preordering on the class of (Gödel numbers of) formulas of .Of course, if ≤P is a preordering on P, then it yields an equivalence relation ~P on P, by simply letting x ~Py iff x ≤Py and y ≤Px. Hence, in the case of P = ω, any preordering yields an equivalence relation on ω and consequently a numeration in the sense of [4]. It is also clear that any equivalence relation on ω (hence any numeration) can be regarded as a preordering on ω. In view of this connection, we sometimes apply to the theory of preorders some of the concepts from the theory of numerations (see also Eršov [6]).Our main concern will be in applications of these concepts to logic, in particular as regards sufficiently strong axiomatic theories (essentially the ones in which recursive functions are representable). From this point of view it seems to be of some interest to study some remarkable prelattices and Boolean prealgebras which arise from such theories. It turns out that these structures enjoy some rather surprising lattice-theoretic and universal recursion-theoretic properties.After making our main definitions in §1, we examine universal recursion-theoretic properties of some r.e. prelattices in §2.

AN OVERVIEW ON GAME THEORY APPLICATIONS TO ENGINEERING

2013 ◽  
Vol 15 (03) ◽  
pp. 1340019 ◽  
Author(s):  
JOAQUIN SANCHEZ-SORIANO
Keyword(s):  
Game Theory ◽  
State Of The Art ◽  
Point Of View ◽  
Sole Purpose ◽  
Engineering Problems ◽  
Theoretic Point ◽  
Game Theoretic

In this paper, we review some of the literature in which different applications to engineering problems are analyzed from a game-theoretic point of view. The revision is far from exhaustive and the sole purpose of this paper is to provide an approximate state-of-the-art on this topic. Likewise, we try throughout the paper to highlight what game theory could contribute to the study of engineering problems.

SHORT- AND LONG-TERM EFFECTS OF THE 9/11 EVENT: THE INTERNATIONAL EVIDENCE

2005 ◽  
Vol 08 (07) ◽  
pp. 947-958 ◽  
Author(s):  
VINCENT RICHMAN ◽  
MICHAEL R. SANTOS ◽  
JOHN T. BARKOULAS
Keyword(s):  
Stock Market ◽  
Capital Markets ◽  
Systematic Risk ◽  
Point Of View ◽  
Long Term Effects ◽  
Market Reactions ◽  
Theoretic Point ◽  
Short And Long Term ◽  
Stock Market Reactions

This paper analyzes the short- and long-term effects of the September 11, 2001 terrorist attacks on a comprehensive sample of stock market indices from 33 industrial and emerging economies. From a finance-theoretic point of view, we employ the international capital asset pricing model (ICAPM) to analyze the incidence of the 9/11 event. Consistent with expectations, we document statistically negative short-term stock market reactions to the 9/11 event for 28 countries. More importantly, we find increases in the level of systematic risk for 10 stock markets which attest to the presence of negative permanent effects emanating for the 9/11 event. However, a great many capital markets (including the US, Canada, Japan, China, Russia, and the largest European economies) did not experience statistically significant increases in systematic risk in the post-9/11 period. The decisiveness of the evidence clearly points in the direction of resilience and flexibility of the world capital markets.

scholarly journals On Turnbull identity for skew-symmetric matrices

2000 ◽  
Vol 43 (2) ◽  
pp. 379-393 ◽  
Author(s):  
Tôru Umeda ◽  
Takeshi Hirai
Keyword(s):  
Differential Operators ◽  
Symmetric Matrix ◽  
Point Of View ◽  
Symmetric Matrices ◽  
Invariant Differential Operators ◽  
Type Identity ◽  
Central Elements ◽  
Theoretic Point ◽  
Invariant Differential ◽  
Matrix Spaces

AbstractIn the last six lines of Turnbull's 1948 paper, he left an enigmatic statement on a Capelli-type identity for skew-symmetric matrix spaces. In the present paper, on Turnbull's suggestion, we show that certain Capelli-type identities hold for this case. Our formulae connect explicitly the central elements inU(gln) to the invariant differential operators, both of which are expressed with permanent. This also clarifies the meaning of Turnbull's statement from the Lie-theoretic point of view.

Sign in / Sign up

Export Citation Format

Share Document