Kueker's conjecture for stable theories

1989 ◽  
Vol 54 (1) ◽  
pp. 207-220 ◽  
Author(s):  
Ehud Hrushovski
Keyword(s):  
Independent Interest ◽  
Linear Ordering ◽  
Stable Case ◽  
Skolem Functions

AbstractKueker's conjecture is proved for stable theories, for theories that interpret a linear ordering, and for theories with Skolem functions. The proof of the stable case involves certain results on coordinatization that are of independent interest.

scholarly journals ON THE COMPLEXITY OF THE SUCCESSIVITY RELATION IN COMPUTABLE LINEAR ORDERINGS

2010 ◽  
Vol 10 (01n02) ◽  
pp. 83-99 ◽  
Author(s):  
ROD DOWNEY ◽  
STEFFEN LEMPP ◽  
GUOHUA WU
Keyword(s):  
New Method ◽  
Independent Interest ◽  
Linear Ordering ◽  
Turing Degrees ◽  
Linear Orderings ◽  
Open Question ◽  
Computably Enumerable

In this paper, we solve a long-standing open question (see, e.g. Downey [6, Sec. 7] and Downey and Moses [11]), about the spectrum of the successivity relation on a computable linear ordering. We show that if a computable linear ordering [Formula: see text] has infinitely many successivities, then the spectrum of the successivity relation is closed upwards in the computably enumerable Turing degrees. To do this, we use a new method of constructing [Formula: see text]-isomorphisms, which has already found other applications such as Downey, Kastermans and Lempp [9] and is of independent interest. It would seem to promise many further applications.

Linear Ordering of the Chromatic Aggregate in Classical Symphonic Music

1996 ◽  
Vol 18 (1) ◽  
pp. 22-50 ◽  
Author(s):  
Henry Burnett ◽  
Shaugn O'Donnell
Keyword(s):  
Linear Ordering ◽  
Symphonic Music

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

Prognosticating the spread of covid-19 pandemic based on optimal arima estimators

2020 ◽  
Vol 20 ◽  
Author(s):  
Venuka Sandhir ◽  
Vinod Kumar ◽  
Vikash Kumar
Keyword(s):  
South Africa ◽  
Statistical Analysis ◽  
Moving Average ◽  
Arima Model ◽  
Information Criterion ◽  
Stable Case ◽  
Johns Hopkins University ◽  
Modelling Techniques ◽  
Auto Regressive ◽  
Global Threat

Background: COVID-19 cases have been reported as a global threat and several studies are being conducted using various modelling techniques to evaluate patterns of disease dispersion in the upcoming weeks. Here we propose a simple statistical model that could be used to predict the epidemiological extent of community spread of COVID-19from the explicit data based on optimal ARIMA model estimators. Methods: Raw data was retrieved on confirmed cases of COVID-19 from Johns Hopkins University (https://github.com/CSSEGISandData/COVID-19) and Auto-Regressive Integrated Moving Average (ARIMA) model was fitted based on cumulative daily figures of confirmed cases aggregated globally for ten major countries to predict their incidence trend. Statistical analysis was completed by using R 3.5.3 software. Results: The optimal ARIMA model having the lowest Akaike information criterion (AIC) value for US (0,2,0); Spain (1,2,0); France (0,2,1); Germany (3,2,2); Iran (1,2,1); China (0,2,1); Russia (3,2,1); India (2,2,2); Australia (1,2,0) and South Africa (0,2,2) imparted the nowcasting of trends for the upcoming weeks. These parameters are (p, d, q) where p refers to number of autoregressive terms, d refers to number of times the series has to be differenced before it becomes stationary, and q refers to number of moving average terms. Results obtained from ARIMA model showed significant decrease cases in Australia; stable case for China and rising cases has been observed in other countries. Conclusion: This study tried their best at predicting the possible proliferate of COVID-19, although spreading significantly depends upon the various control and measurement policy taken by each country.

Flat functors and classifying toposes

2018 ◽  
Author(s):  
Olivia Caramello
Keyword(s):  
General Theory ◽  
Geometric Theory ◽  
Small Category ◽  
Independent Interest ◽  
Yoneda Lemma ◽  
Geometric Morphisms ◽  
The Way

This chapter develops a general theory of extensions of flat functors along geometric morphisms of toposes; the attention is focused in particular on geometric morphisms between presheaf toposes induced by embeddings of categories and on geometric morphisms to the classifying topos of a geometric theory induced by a small category of set-based models of the latter. A number of general results of independent interest are established on the way, including developments on colimits of internal diagrams in toposes and a way of representing flat functors by using a suitable internalized version of the Yoneda lemma. These general results will be instrumental for establishing in Chapter 6 the main theorem characterizing the class of geometric theories classified by a presheaf topos and for applying it.

scholarly journals Jordan products of quantum channels and their compatibility

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Mark Girard ◽  
Martin Plávala ◽  
Jamie Sikora
Keyword(s):  
Quantum State ◽  
Sufficient Conditions ◽  
The Other ◽  
Independent Interest ◽  
Quantum Channels ◽  
Semidefinite Programs ◽  
Jordan Product ◽  
Marginal Problem ◽  
Jordan Products ◽  
Product Of Matrices

AbstractGiven two quantum channels, we examine the task of determining whether they are compatible—meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-and-prepare channels (i.e., entanglement-breaking channels) do not necessarily have a measure-and-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolarizing channels are compatible.

Time and Duration in Noninterleaving Concurrency

1993 ◽  
Vol 19 (3-4) ◽  
pp. 403-416
Author(s):  
David Murphy
Keyword(s):  
Partial Order ◽  
Independent Interest ◽  
Underlying Event ◽  
Strict Partial Order ◽  
Event Structures ◽  
Concurrency Theory ◽  
Finite Structures

The purpose of this paper is to present a real-timed concurrency theory in the noninterleaving tradition. The theory is based on the occurrences of actions; each occurrence or event has a start and a finish. Causality is modelled by assigning a strict partial order to these starts and finishes, while timing is modelled by giving them reals. The theory is presented in some detail. All of the traditional notions found in concurrency theories (such as conflict, confusion, liveness, and so on) are found to be expressible. Four notions of causality arise naturally from the model, leading to notions of securing. Three of the notions give rise to underlying event structures, demonstrating that our model generalises Winskel’s. Infinite structures are then analysed: a poset of finite structures is defined and suitably completed to give one containing infinite structures. These infinite structures are characterised as just those arising as limits of finite ones. Our technique here, which relies on the structure of time, is of independent interest.

scholarly journals A Decision-Making Approach Based on TOPSIS Method for Ranking Smart Cities in the Context of Urban Energy

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2691
Author(s):  
Sławomira Hajduk ◽  
Dorota Jelonek
Keyword(s):  
Decision Making ◽  
Smart Cities ◽  
Energy Performance ◽  
Linear Ordering ◽  
Topsis Method ◽  
Research Papers ◽  
The World ◽  
Urban Energy ◽  
World Council ◽  
Topsis Technique

This paper presents the use of multi-criteria decision-making (MCDM) for the evaluation of smart cities. During the development of the method, the importance of the decision-making approach in the linear ordering of cities was presented. The method of using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) was proposed for the preparation of ranking. The method was verified by the application in the measurement of energy performance in smart cities. The authors conducted a literature review of research papers related to urban energy and MCDM published in the period from 2010 to 2020. The paper uses data from the World Council on City Data (WCCD). The research conducted allowed for the identification of the most popular MCDM techniques in the field of urban energy such as TOPSIS, AHP and DEA. The TOPSIS technique was used to organize and group the analyzed cities. Porto took the top position, whereas Buenos Aries was the last.

scholarly journals Dispersive Estimates for Full Dispersion KP Equations

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Didier Pilod ◽  
Jean-Claude Saut ◽  
Sigmund Selberg ◽  
Achenef Tesfahun
Keyword(s):  
Stationary Phase ◽  
Initial Value Problem ◽  
Bessel Functions ◽  
Linear Part ◽  
Independent Interest ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Initial Value ◽  
Kp Equations ◽  
Well Posed

AbstractWe prove several dispersive estimates for the linear part of the Full Dispersion Kadomtsev–Petviashvili introduced by David Lannes to overcome some shortcomings of the classical Kadomtsev–Petviashvili equations. The proof of these estimates combines the stationary phase method with sharp asymptotics on asymmetric Bessel functions, which may be of independent interest. As a consequence, we prove that the initial value problem associated to the Full Dispersion Kadomtsev–Petviashvili is locally well-posed in $$H^s(\mathbb R^2)$$ H s ( R 2 ) , for $$s>\frac{7}{4}$$ s > 7 4 , in the capillary-gravity setting.

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