scholarly journals THE BOREL COMPLEXITY OF ISOMORPHISM FOR O-MINIMAL THEORIES

2017 ◽  
Vol 82 (2) ◽  
pp. 453-473 ◽  
Author(s):  
RICHARD RAST ◽  
DAVENDER SINGH SAHOTA
Keyword(s):  
Lower Bounds ◽  
General Model ◽  
Isomorphism Problem ◽  
Linear Orders ◽  
Minimal Theory ◽  
Borel Complexity ◽  
Image Position ◽  
Countable Models

AbstractGiven a countable o-minimal theory T, we characterize the Borel complexity of isomorphism for countable models of T up to two model-theoretic invariants. If T admits a nonsimple type, then it is shown to be Borel complete by embedding the isomorphism problem for linear orders into the isomorphism problem for models of T. This is done by constructing models with specific linear orders in the tail of the Archimedean ladder of a suitable nonsimple type.If the theory admits no nonsimple types, then we use Mayer’s characterization of isomorphism for such theories to compute invariants for countable models. If the theory is small, then the invariant is real-valued, and therefore its isomorphism relation is smooth. If not, the invariant corresponds to a countable set of reals, and therefore the isomorphism relation is Borel equivalent to F2.Combining these two results, we conclude that $\left( {{\rm{Mod}}\left( T \right), \cong } \right)$ is either maximally complicated or maximally uncomplicated (subject to completely general model-theoretic lower bounds based on the number of types and the number of countable models).

scholarly journals ON CUTS IN ULTRAPRODUCTS OF LINEAR ORDERS II

2018 ◽  
Vol 83 (1) ◽  
pp. 29-39
Author(s):  
MOHAMMAD GOLSHANI ◽  
SAHARON SHELAH
Keyword(s):  
Linear Order ◽  
Linear Orders ◽  
Combinatorial Characterization ◽  
Image Position

AbstractWe continue our study of the class ${\cal C}\left( D \right)$, where D is a uniform ultrafilter on a cardinal κ and ${\cal C}\left( D \right)$ is the class of all pairs $\left( {{\theta _1},{\theta _2}} \right)$, where $\left( {{\theta _1},{\theta _2}} \right)$ is the cofinality of a cut in ${J^\kappa }/D$ and J is some ${\left( {{\theta _1} + {\theta _2}} \right)^ + }$-saturated dense linear order. We give a combinatorial characterization of the class ${\cal C}\left( D \right)$. We also show that if $\left( {{\theta _1},{\theta _2}} \right) \in {\cal C}\left( D \right)$ and D is ${\aleph _1}$-complete or ${\theta _1} + {\theta _2} > {2^\kappa }$, then ${\theta _1} = {\theta _2}$.

scholarly journals Singular perturbations of the unicritical polynomials with two parameters

2016 ◽  
Vol 37 (6) ◽  
pp. 1997-2016 ◽  
Author(s):  
YINGQING XIAO ◽  
FEI YANG
Keyword(s):  
Julia Set ◽  
Dynamical Behavior ◽  
Rational Maps ◽  
Topological Properties ◽  
Fatou Set ◽  
The Family ◽  
Image Position ◽  
Two Parameters ◽  
Unicritical Polynomials

In this paper, we study the dynamics of the family of rational maps with two parameters $$\begin{eqnarray}f_{a,b}(z)=z^{n}+\frac{a^{2}}{z^{n}-b}+\frac{a^{2}}{b},\end{eqnarray}$$ where $n\geq 2$ and $a,b\in \mathbb{C}^{\ast }$. We give a characterization of the topological properties of the Julia set and the Fatou set of $f_{a,b}$ according to the dynamical behavior of the orbits of the free critical points.

Stochastic inequalities for an overflow model

1987 ◽  
Vol 24 (3) ◽  
pp. 696-708 ◽  
Author(s):  
Arie Hordijk ◽  
Ad Ridder
Keyword(s):  
Failure Rate ◽  
Lower Bounds ◽  
Approximation Method ◽  
Queueing Networks ◽  
Upper And Lower Bounds ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Decreasing Failure Rate ◽  
General Method

A general method to obtain insensitive upper and lower bounds for the stationary distribution of queueing networks is sketched. It is applied to an overflow model. The bounds are shown to be valid for service distributions with decreasing failure rate. A characterization of phase-type distributions with decreasing failure rate is given. An approximation method is proposed. The methods are illustrated with numerical results.

The randomized communication complexity of revenue maximization

2021 ◽  
Vol 19 (2) ◽  
pp. 75-83
Author(s):  
Aviad Rubinstein ◽  
Junyao Zhao
Keyword(s):  
Lower Bounds ◽  
Communication Complexity ◽  
Social Choice Rule ◽  
Valuation Function ◽  
Optimal Auctions ◽  
Incentive Compatible ◽  
First Approximation ◽  
Exponential Separation ◽  
Open Question

We study the communication complexity of incentive compatible auction-protocols between a monopolist seller and a single buyer with a combinatorial valuation function over n items [Rubinstein and Zhao 2021]. Motivated by the fact that revenue-optimal auctions are randomized [Thanassoulis 2004; Manelli and Vincent 2010; Briest et al. 2010; Pavlov 2011; Hart and Reny 2015] (as well as by an open problem of Babaioff, Gonczarowski, and Nisan [Babaioff et al. 2017]), we focus on the randomized communication complexity of this problem (in contrast to most prior work on deterministic communication). We design simple, incentive compatible, and revenue-optimal auction-protocols whose expected communication complexity is much (in fact infinitely) more efficient than their deterministic counterparts. We also give nearly matching lower bounds on the expected communication complexity of approximately-revenue-optimal auctions. These results follow from a simple characterization of incentive compatible auction-protocols that allows us to prove lower bounds against randomized auction-protocols. In particular, our lower bounds give the first approximation-resistant, exponential separation between communication complexity of incentivizing vs implementing a Bayesian incentive compatible social choice rule, settling an open question of Fadel and Segal [Fadel and Segal 2009].

Synthesis and characterization of Ni incorporated titanium dioxide thin films

2018 ◽  
Vol 33 (24) ◽  
pp. 4165-4172 ◽  
Author(s):  
Deepak Kumar ◽  
Prasanta Mandal ◽  
Anil Singh ◽  
Charu Pant ◽  
Sudesh Sharma
Keyword(s):  
Thin Films ◽  
Titanium Dioxide ◽  
Synthesis And Characterization ◽  
Titanium Dioxide Thin Films ◽  
Image Position

Abstract

Deposition and characterization of nanostructured Cu2O thin-film for potential photovoltaic applications

2013 ◽  
Vol 28 (13) ◽  
pp. 1740-1746 ◽  
Author(s):  
Nishant Gupta ◽  
Rajendra Singh ◽  
Fan Wu ◽  
Jagdish Narayan ◽  
Colin McMillen ◽  
...  
Keyword(s):  
Thin Film ◽  
Photovoltaic Applications ◽  
Cu2o Thin Film ◽  
Image Position

Abstract

scholarly journals Characterization of swift heavy ion irradiation damage in ceria

2015 ◽  
Vol 30 (9) ◽  
pp. 1473-1484 ◽  
Author(s):  
Clarissa A. Yablinsky ◽  
Ram Devanathan ◽  
Janne Pakarinen ◽  
Jian Gan ◽  
Daniel Severin ◽  
...  
Keyword(s):  
Ion Irradiation ◽  
Heavy Ion ◽  
Irradiation Damage ◽  
Swift Heavy Ion Irradiation ◽  
Heavy Ion Irradiation ◽  
Swift Heavy Ion ◽  
Image Position

Abstract

scholarly journals Orderability of topological spaces by continuous preferences

2001 ◽  
Vol 27 (8) ◽  
pp. 505-512 ◽  
Author(s):  
José Carlos Rodríguez Alcantud
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Properties ◽  
Linear Orders ◽  
Mathematical Economics

We extend van Dalen and Wattel's (1973) characterization of orderable spaces and their subspaces by obtaining analogous results for two larger classes of topological spaces. This type of spaces are defined by considering preferences instead of linear orders in the former definitions, and possess topological properties similar to those of (totally) orderable spaces (cf. Alcantud, 1999). Our study provides particular consequences of relevance in mathematical economics; in particular, a condition equivalent to the existence of a continuous preference on a topological space is obtained.

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