Partial orderings of fixed finite dimension: Model companions and density

1981 ◽  
Vol 46 (4) ◽  
pp. 789-802 ◽  
Author(s):  
Alfred B. Manaster ◽  
Jeffrey B. Remmel
Keyword(s):  
Finite Dimension ◽  
Partial Ordering ◽  
Common Language ◽  
Model Companion ◽  
Elementary Substructure ◽  
Undecidable Theory ◽  
Natural Notion ◽  
Partial Orderings ◽  
Definition Of ◽  
Model Completion

The model companions of the theories of n-dimensional partial orderings and n-dimensional distributive lattices are found for each finite n. Each model companion is given as the theory of a structure which is specified. The model companions are model completions only for n = 1. The structure of the model companion of the theory of n-dimensional partial orderings is a lattice only for n = 1. Each of the model companions is seen to be finitely axiomatizable, and a set of basic formulas, each of which is existential, is specified for each model companion. Finally a topolo-gically natural notion of dense n-dimensional partial ordering is introduced and shown to have a finitely axiomatizable undecidable theory.In this paragraph we shall define the notion of model companion (cf. [4]) and indicate the way in which we shall demonstrate that one theory is the model companion of another in this paper. For T and T* theories in a common language, T* is called a model companion of T if and only if the following two conditions are satisfied: first, Tand T* are mutually model consistent, which means that every model of either is embeddable in some model of the other; secondly, T* is model complete, which means that if and are both models of T* and is a substructure of , then is an elementary substructure of . A definition of model completion may be obtained by strengthening the notion of model companion to also require that T* admit elimination of quantifiers. In all of our examples the model companion will have only one countable model. Although the ℵ0-categoricity of the model companions follows from Saracino [8], we give specific proofs since these proofs fit so naturally in our analyses.

The model-companion of a class of structures

1972 ◽  
Vol 37 (3) ◽  
pp. 546-556 ◽  
Author(s):  
G. L. Cherlin
Keyword(s):  
Order Theory ◽  
Model Companion ◽  
Elementary Substructure ◽  
Closed Model ◽  
First Order ◽  
First Order Theory ◽  
Logical Equivalence ◽  
Closed Fields ◽  
Algebraically Closed Fields ◽  
Model Completion

If Σ is the class of all fields and Σ* is the class of all algebraically closed fields, then it is well known that Σ* is characterized by the following properties:(i) Σ* is the class of models of some first order theory K*.(ii) If m1m2 are in Σ* and m1 ⊆ m2 then m1 ≺ m2 (m1 is an elementary substructure of m2, i.e. any first order sentence true in m1 is true in m2).(iii) If m1 is in Σ then there is a structure m2 in Σ* such that m1 ⊆ m2.If Σ is some other class of models of a first order theory K and a subclass Σ* of Σ exists satisfying (i)–(iii) then Σ* is uniquely determined and K* (which is unique up to logical equivalence) is called the model-companion of K. This notion is a generalization of the fundamental notion of model-completion introduced and extensively studied by A. Robinson [6], When the model-companion exists it provides the basis for a satisfactory treatment of the notion of an algebraically closed model of K.Recently A. Robinson has developed a more general formulation of the notion of “algebraically closed” structures in Σ, which is applicable to any inductive elementary class Σ of structures (by elementary we always mean ECΔ). Condition (i) must be weakened to(i′) Σ* is closed under elementary substructure (i.e. if m1 is in Σ* and m2 ≺ m1 then m2 is in Σ*).

Natural Partial Orders

1968 ◽  
Vol 20 ◽  
pp. 535-554 ◽  
Author(s):  
R. A. Dean ◽  
Gordon Keller
Keyword(s):  
Partial Orders ◽  
Partial Ordering ◽  
Finite Set ◽  
Partial Orderings

Let n be an ordinal. A partial ordering P of the ordinals T = T(n) = {w: w < n} is called natural if x P y implies x ⩽ y.A natural partial ordering, hereafter abbreviated NPO, of T(n) is thus a coarsening of the natural total ordering of the ordinals. Every partial ordering of a finite set 5 is isomorphic to a natural partial ordering. This is a consequence of the theorem of Szpielrajn (5) which states that every partial ordering of a set may be refined to a total ordering. In this paper we consider only natural partial orderings. In the first section we obtain theorems about the lattice of all NPO's of T(n).

ROBUSTNESS OF THE MULTI‐OBJECTIVE MOORA METHOD WITH A TEST FOR THE FACILITIES SECTOR

2009 ◽  
Vol 15 (2) ◽  
pp. 325-375 ◽  
Author(s):  
Willem K. Brauers ◽  
Edmundas K. Zavadskas
Keyword(s):  
Linear Equation ◽  
Reference Point ◽  
Error Term ◽  
Cost Price ◽  
Common Language ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Definition Of ◽  
Moora Method

The definition of robustness in econometrics, the error term in a linear equation, was not only broadened, but in addition moved to the meaning of common language: from a cardinal to a qualitative one. These interpretations were tested by an application on the Facilities Sector in Lithuania. The application is multi‐objective: like costs, experience and effectiveness at the side of the contractors; quality, duration of the work and cost price at the side of the owners. These objectives having all different units the dimensionless ratios of the MOORA method avoids the difficulties of normalization. In a first part of MOORA these ratios were aggregated and in a second one they were used as distances to a reference point. The results of both parts control each other, a test on robustness. Additionally, MOORA shows a robust domination on all other methods of multi‐objective optimization. For the Facilities Sector in Lithuania, both parts of MOORA resulted in a comparable ranking. In this way a double check was made on the robustness of the results. Santrauka Patikimumo apibrėžimas ekonometrikoje, kaip neteisingas terminas tiesinėje lygtyje, buvo ne tik papildytas, bet ir išreikštas įprasta kalba: nuo kiekybinio prie kokybinio. Šios interpretacijos buvo patikrintos taikant jas Lietuvos paslaugų sektoriuje. Taikymas yra daugiatikslis: iš rangovo pusės kaip išlaidos, patirtis, efektyvumas; kokybė, darbo trukmė, kaina iš užsakovo pusės. Minėtieji tikslai turi skirtingus matavimo vienetus. O jų santykiniai dydžiai neturi mato vienetų, todėl taikant MOORA metodą yra išvengiama sunkumų juos normalizuojant. Pirmoje MOORA metodo taikymo dalyje šie santykiai yra sujungiami, o antroje dalyje ieškoma atstumo iki geriausio sprendinio. Abiejų metodo dalių rezultatai pagrindžia sprendinio teisingumą. Tai rodo aiškų MOORA metodo pranašumą, palyginti su kitais daugiatikslio optimizavimo metodais. Taikant abi MOORA metodo dalis Lietuvos paslaugų sektoriui buvo sudarytas lyginamasis rangavimas, buvo atliktas dvigubas rezultatų patikimumo patikrinimas.

scholarly journals MINORITY. THE MINOR-VICTIM AND THE MINOR-OFFENDER

2020 ◽  
Vol 15 (3-4) ◽  
pp. 17-30
Author(s):  
Diana GRUMEZA ◽  
Keyword(s):  
Sexual Behaviour ◽  
Research Literature ◽  
Chronological Age ◽  
Common Language ◽  
Limit Set ◽  
International Level ◽  
Rights Of The Child ◽  
Definition Of ◽  
Age Of Majority ◽  
Intention To Change

Research literature notes differently the time of the minority as compared to the time when the minor gives its assumed consent for sexual intercourse, in the latter case, the age in some jurisdictions being of 16 years old.( Taylor, Quayle,( 2003), : 3). At the international level, there was also the intention to change the biological age with the age that the minor seems to have, but the difficulties deriving from establishing an age that the minor has only apparently determined the maintenance of the chronological age as a criterion for establishing the minority, and implicitly, the existence of the crime. Particular attention is paid to adolescents, who are minors between the ages of 13 and 17. According to the UN Convention on the Rights of the Child (S.1), “child means any human being under the age of 18 (…).” However, the UN Convention leaves the states to determine alone the age of majority, which may be below or above the limit set by the Convention. That is why we find different ages worldwide for determining adulthood. In common language, the concepts of "pornography" and "obscenity" are substantially equal. However, pornography involving minors does not necessarily mean obscene behaviour, it can represent explicit, lewd or suggestive sexual behaviour Starting from the definition of the minor in the UN Convention on the Rights of the Child, we go beyond the multiple discussions in the research literature on the minority, the term "minor" being considered too imprecise, impliying both the criminal and civil minority. Criminologically speaking, the necessary distinction is made between child - adolescent - adult - elderly. So, both the child and adolescent are subsumed to the concept of minor. We also note that the minority can be a characteristic of the victim, but also of the offender.

CLASSIFICATION OF MULTIVARIATE LIFE DISTRIBUTIONS BASED ON PARTIAL ORDERING

2002 ◽  
Vol 16 (1) ◽  
pp. 129-137 ◽  
Author(s):  
Dilip Roy
Keyword(s):  
Present Article ◽  
Failure Rate ◽  
Partial Ordering ◽  
Increasing Failure Rate ◽  
Multivariate Generalization ◽  
Partial Orderings ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

Barlow and Proschan presented some interesting connections between univariate classifications of life distributions and partial orderings where equivalent definitions for increasing failure rate (IFR), increasing failure rate average (IFRA), and new better than used (NBU) classes were given in terms of convex, star-shaped, and superadditive orderings. Some related results are given by Ross and Shaked and Shanthikumar. The introduction of a multivariate generalization of partial orderings is the object of the present article. Based on that concept of multivariate partial orderings, we also propose multivariate classifications of life distributions and present a study on more IFR-ness.

On the comparison of waiting times in tandem queues

1981 ◽  
Vol 18 (03) ◽  
pp. 707-714 ◽  
Author(s):  
Shun-Chen Niu
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Waiting Times ◽  
Distribution Functions ◽  
Partial Ordering ◽  
Tandem Queues ◽  
Order Relations ◽  
Service Distribution ◽  
In Series ◽  
Definition Of

Using a definition of partial ordering of distribution functions, it is proven that for a tandem queueing system with many stations in series, where each station can have either one server with an arbitrary service distribution or a number of constant servers in parallel, the expected total waiting time in system of every customer decreases as the interarrival and service distributions becomes smaller with respect to that ordering. Some stronger conclusions are also given under stronger order relations. Using these results, bounds for the expected total waiting time in system are then readily obtained for wide classes of tandem queues.

Partial Orderings of Distributions Based on Right-Spread Functions

1998 ◽  
Vol 35 (1) ◽  
pp. 221-228 ◽  
Author(s):  
J. M. Fernandez-Ponce ◽  
S. C. Kochar ◽  
J. Muñoz-Perez
Keyword(s):  
Probability Distributions ◽  
Partial Ordering ◽  
Dispersion Measure ◽  
Dispersive Ordering ◽  
Partial Orderings

In this paper we introduce a quantile dispersion measure. We use it to characterize different classes of ageing distributions. Based on the quantile dispersion measure, we propose a new partial ordering for comparing the spread or dispersion in two probability distributions. This new partial ordering is weaker than the well known dispersive ordering and it retains most of its interesting properties.

Imaging techniques in endometriosis

2018 ◽  
Vol 10 (3) ◽  
pp. 136-150 ◽  
Author(s):  
Mercedes Espada ◽  
Elena Alvarez-Moreno ◽  
Mar Jimenez de la Pena ◽  
Veronica Munoz Capio ◽  
Shannon Reid ◽  
...  
Keyword(s):  
Systematic Review ◽  
Imaging Techniques ◽  
Verbal Description ◽  
Diagnostic Tools ◽  
Common Language ◽  
Female Population ◽  
Site Specific ◽  
Extensive Search ◽  
Preoperative Diagnostic ◽  
Definition Of

Endometriosis is a common gynecological condition affecting up to 15% of the general female population. Here, we present a systematic review of imaging techniques of endometriosis. The aim of this review is to determine the most accurate site-specific preoperative diagnostic tools in order to map, locate, evaluate the extension, and stage the disease. There are important reasons to stage endometriosis: to create a common language, to enable specificity of diagnosis, standardize comparisons, and to facilitate research applications. The requirements of an ideal endometriosis classification system are that it be empirically and scientifically based, be of general consensus, have unambiguous definition of terms, be comprehensive in all cases, have a simple translation from anatomic features to verbal description, reflect disease, predict fertility, predict pain relief, be useful to guide treatment, indicate risk of recurrence, identify clinical situations in which it does not apply, be simple to calculate, and be easy to communicate to women. An extensive search of papers regarding imaging techniques in endometriosis was performed in Pubmed from January 1992 to February 2018, including original peer-reviewed papers, reviews, and international guidelines.

Semantic web: golden era of information

2018 ◽  
Vol 7 (2.8) ◽  
pp. 436
Author(s):  
Prakhar Agarwal ◽  
Shivani Jain
Keyword(s):  
Semantic Web ◽  
Information Search ◽  
Review Paper ◽  
Development Project ◽  
Structured Data ◽  
Common Language ◽  
End User ◽  
Ontology Language ◽  
Shared Language ◽  
Definition Of

Semantic Web is the extension of existing web that allows well defined expressions for the meaning of information which can be understood by computers and people both. In this paper we are doing study on semantic and is our review paper. Semantic web is a recommended development project by W3C (World Wide Web Consortium) which focuses on the enhancing of information search by keeping the facts in structured form using eXtensible Mark-up Language (XML) and marked in such a way that it can be understand by the system. To make the development of semantic web promising, new international standard is developed for exchanging of ontologies called OWL Web Ontology language. In XML we just provide tag of the model and store data in the hierarchy without its meaning, that’s why the computer cannot be able to process the data but in Semantic Web user can provide with a definition so that the computer can better recognize its meaning and provide with the better displaying of information. A crux of semantic web is that it works on the definition of the ontologies. Ontologies are responsible for re-usability and sharing of information. Semantic Web provides with a shared language which has stored data in the non-ending linking of distinct databases which provides data related to the real world objects. RDF is a common language for semantic web and is responsible for the collection of data on web and assembles different database from diverse sources and SPARQL is there for linking of databases for unifying documents. Thus, semantic web is the well-structured data web that relates all the data that present on the web and understands them to provide the exact display requested by the end user.

A new ordering for stochastic majorization: theory and applications

1992 ◽  
Vol 24 (03) ◽  
pp. 604-634 ◽  
Author(s):  
Cheng-Shang Chang
Keyword(s):  
Sample Path ◽  
Stochastic Ordering ◽  
Partial Ordering ◽  
Scheduling Problems ◽  
Unified Approach ◽  
Finite Buffers ◽  
Routing And Scheduling ◽  
Partial Orderings ◽  
Stochastic Load ◽  
Stochastic Majorization

In this paper, we develop a unified approach for stochastic load balancing on various multiserver systems. We expand the four partial orderings defined in Marshall and Olkin, by defining a new ordering based on the set of functions that are symmetric, L-subadditive and convex in each variable. This new partial ordering is shown to be equivalent to the previous four orderings for comparing deterministic vectors but differs for random vectors. Sample-path criteria and a probability enumeration method for the new stochastic ordering are established and the ordering is applied to various fork-join queues, routing and scheduling problems. Our results generalize previous work and can be extended to multivariate stochastic majorization which includes tandem queues and queues with finite buffers.

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