On Finitely Generated Simple Complemented Lattices

Let L be a lattice, and let P and Q be partially ordered sets. We say that L is generated by P if there is an isotone mapping from P into L with its image generating L. P contains Q if there is a subset Q’ of P which, with the partial ordering inherited from P, gives an isomorphic copy of Q. For an integer n > 0, the lattice of partitions of an n-element set will be denoted by II(n); it is well-known that II(rc) is simple and complemented (cf. P. Crawley-R. P. Dilworth [1; p. 96]).

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Global solutions to nonlinear second order interval integrodifferential equations by fixed point in partially ordered sets

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v37i4.35867 ◽

2018 ◽

Vol 37 (4) ◽

pp. 153-172

Author(s):

Robab Alikhani ◽

Fariba Bahrani

Keyword(s):

Fixed Point ◽

Global Solution ◽

Existence And Uniqueness ◽

Initial Conditions ◽

Partially Ordered Sets ◽

Second Order ◽

Partial Ordering ◽

Order Interval ◽

Ordered Sets ◽

Partially Ordered

In this paper, we prove the existence and uniqueness of global solution for second order interval valued integrodifferential equation with initial conditions admitting only the existence of a lower solution or an upper solution. In this study, in order to make the global solution on entire $[0,b]$, we use a fixed point in partially ordered sets on the subintervals of $[0,b]$ and obtain local solutions. Also, under weak conditions we show being well-defined a special kind of H-difference involved in this work. Moreover, we compare the results of existence and uniqueness under consideration of two kind of partial ordering on fuzzy numbers.

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The 3-Irreducible Partially Ordered Sets

Canadian Journal of Mathematics ◽

10.4153/cjm-1977-040-3 ◽

1977 ◽

Vol 29 (2) ◽

pp. 367-383 ◽

Cited By ~ 44

Author(s):

David Kelly

Keyword(s):

Positive Integer ◽

Finite Dimension ◽

Ordered Set ◽

Partially Ordered Sets ◽

Partial Ordering ◽

Ordered Sets ◽

Linear Orders ◽

Compactness Property ◽

Partially Ordered ◽

Minimum Number

The dimension [4] of a partially ordered set (poset) is the minimum number of linear orders whose intersection is the partial ordering of the poset. For a positive integer m, a poset is m-irreducible[10] if it has dimension m and removal of any element lowers its dimension. By the compactness property of finite dimension, every m-irreducible poset is finite and every poset of dimension ≧ m contains an m-irreducible subposet.

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Galois Connections and Pair Algebras

Canadian Journal of Mathematics ◽

10.4153/cjm-1969-056-x ◽

1969 ◽

Vol 21 ◽

pp. 498-501 ◽

Cited By ~ 3

Author(s):

J. C. Derderian

Keyword(s):

Partially Ordered Set ◽

Ordered Set ◽

Partially Ordered Sets ◽

Order Relation ◽

Galois Connection ◽

Ordered Sets ◽

Residuated Mapping ◽

Partially Ordered ◽

Isotone Mapping ◽

Order Relations

Unless further restricted, P, Q, and R denote arbitrary partially ordered sets whose order relations are all written “≦” .An isotone mapping ϕ: P → Q is said to be residuated if there is an isotone mapping ψ: Q → P such that(RM 1) xϕψ ≧ x for all x i n P;(RM 2) yψϕ ≦ for all y in Q.Let Q* denote the partially ordered set with order relation dual to that of Q.(A) The following conditions are equivalent:(i) ϕ: P → Q* is a Galois connection;(ii) ϕ: P → Q is a residuated mapping;(iii) Max{z ∈ P: zy ≦ y} exists for all y in Q and is equal to yψ.Since ψ is uniquely determined by ϕ, it will be denoted by ϕ+.

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To the spectral theory of partially ordered sets

Sibirskii matematicheskii zhurnal ◽

10.33048/smzh.2019.60.308 ◽

2018 ◽

Vol 60 (3) ◽

pp. 578-598

Author(s):

Yu. L. Ershov ◽

M. V. Schwidefsky

Keyword(s):

Spectral Theory ◽

Partially Ordered Sets ◽

Ordered Sets ◽

Partially Ordered

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Modelling Nondeterministic Concurrent Processes with Event Structures

Fundamenta Informaticae ◽

10.3233/fi-1991-14103 ◽

1991 ◽

Vol 14 (1) ◽

pp. 39-73

Author(s):

Rita Loogen ◽

Ursula Goltz

Keyword(s):

Dynamic Behaviour ◽

Partially Ordered Sets ◽

Parallel Composition ◽

Ordered Sets ◽

Communicating Sequential Processes ◽

Partially Ordered ◽

Event Structures ◽

Transition Relation ◽

Concurrent Processes ◽

Sequential Processes

We present a non-interleaving model for non deterministic concurrent processes that is based on labelled event structures. We define operators on labelled event structures like parallel composition, nondeterministic combination, choice, prefixing and hiding. These operators correspond to the operations of the “Theory of Communicating Sequential Processes” (TCSP). Infinite processes are defined using the metric approach. The dynamic behaviour of event structures is defined by a transition relation which describes the execution of partially ordered sets of actions, abstracting from internal events.

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Estimating the area under a receiver operating characteristic curve using partially ordered sets

The International Journal of Biostatistics ◽

10.1515/ijb-2019-0127 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Ehsan Zamanzade ◽

Xinlei Wang

Keyword(s):

Roc Curve ◽

Characteristic Curve ◽

Partially Ordered Sets ◽

Sampling Technique ◽

Real Data ◽

Cost Effective ◽

Ordered Sets ◽

Operating Characteristics ◽

Partially Ordered ◽

Receiver Operating

AbstractRanked set sampling (RSS), known as a cost-effective sampling technique, requires that the ranker gives a complete ranking of the units in each set. Frey (2012) proposed a modification of RSS based on partially ordered sets, referred to as RSS-t in this paper, to allow the ranker to declare ties as much as he/she wishes. We consider the problem of estimating the area under a receiver operating characteristics (ROC) curve using RSS-t samples. The area under the ROC curve (AUC) is commonly used as a measure for the effectiveness of diagnostic markers. We develop six nonparametric estimators of the AUC with/without utilizing tie information based on different approaches. We then compare the estimators using a Monte Carlo simulation and an empirical study with real data from the National Health and Nutrition Examination Survey. The results show that utilizing tie information increases the efficiency of estimating the AUC. Suggestions about when to choose which estimator are also made available to practitioners.

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