scholarly journals Some Results on Characterizations of Matrix Partial Orderings

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hongxing Wang ◽  
Jin Xu
Keyword(s):  
Partial Ordering ◽  
Partial Orderings ◽  
Group Matrices

Some characterizations of the left-star, right-star, and star partial orderings between matrices of the same size are obtained. Based on those results, several characterizations of the star partial ordering between EP matrices are given. At last, one characterization of the sharp partial ordering between group matrices is obtained.

Families of life distributions characterized by two moments

1990 ◽  
Vol 27 (03) ◽  
pp. 720-725 ◽  
Author(s):  
Manish C. Bhattacharjee ◽  
Jayaram Sethuraman
Keyword(s):  
Exponential Distribution ◽  
Partial Ordering ◽  
Life Distribution ◽  
Partial Orderings ◽  
Life Distributions ◽  
The Moment

We consider several classical notions of partial orderings among life distributions which have been used to describe ageing properties and tail domination. We show that if a distribution G dominates another distribution F in one of these partial orderings introduced here, and if two moments of G agree with those of F, including the moment that describes this partial ordering, then G = F. This leads to a characterization of the exponential distribution among HNBUE and HNWUE life distribution classes, and thus extends the results of Basu and Bhattacharjee (1984) and rectifies an error in that paper.

Families of life distributions characterized by two moments

1990 ◽  
Vol 27 (3) ◽  
pp. 720-725 ◽  
Author(s):  
Manish C. Bhattacharjee ◽  
Jayaram Sethuraman
Keyword(s):  
Exponential Distribution ◽  
Partial Ordering ◽  
Life Distribution ◽  
Partial Orderings ◽  
Life Distributions ◽  
The Moment

We consider several classical notions of partial orderings among life distributions which have been used to describe ageing properties and tail domination. We show that if a distribution G dominates another distribution F in one of these partial orderings introduced here, and if two moments of G agree with those of F, including the moment that describes this partial ordering, then G = F. This leads to a characterization of the exponential distribution among HNBUE and HNWUE life distribution classes, and thus extends the results of Basu and Bhattacharjee (1984) and rectifies an error in that paper.

Minimal distributions in a stochastic partial ordering and bounds for Gaussian processes

1983 ◽  
Vol 20 (03) ◽  
pp. 529-536
Author(s):  
W. J. R. Eplett
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Partial Ordering ◽  
Boundary Crossing ◽  
Conditional Probabilities ◽  
Life Distribution ◽  
Life Distributions ◽  
Bounded Below ◽  
Crossing Probabilities

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.

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).

Characterization of protein primary sequences based on partial ordering

2008 ◽  
Vol 254 (4) ◽  
pp. 752-755 ◽  
Author(s):  
Jie Feng ◽  
Tian-ming Wang
Keyword(s):  
Partial Ordering

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.

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.

Minimal degrees and the jump operator

1973 ◽  
Vol 38 (2) ◽  
pp. 249-271 ◽  
Author(s):  
S. B. Cooper
Keyword(s):  
Minimal Degree ◽  
Partial Ordering ◽  
Jump Operator ◽  
Upper Semilattice ◽  
Recursively Enumerable ◽  
Original Number ◽  
Nonzero Degree ◽  
The Relationship ◽  
Degrees Of Unsolvability

The jump a′ of a degree a is defined to be the largest degree recursively enumerable in a in the upper semilattice of degrees of unsolvability. We examine below some of the ways in which the jump operation is related to the partial ordering of the degrees. Fried berg [3] showed that the equation a = x′ is solvable if and only if a ≥ 0′. Sacks [13] showed that we can find a solution of a = x′ which is ≤ 0′ (and in fact is r.e.) if and only if a ≥ 0′ and is r.e. in 0′. Spector [16] constructed a minimal degree and Sacks [13] constructed one ≤ 0′. So far the only result concerning the relationship between minimal degrees and the jump operator is one due to Yates [17] who showed that there is a minimal predecessor for each non-recursive r.e. degree, and hence that there is a minimal degree with jump 0′. In §1, we obtain an analogue of Friedberg's theorem by constructing a minimal degree solution for a = x′ whenever a ≥ 0′. We incorporate Friedberg5s original number-theoretic device with a complicated sequence of approximations to the nest of trees necessary for the construction of a minimal degree. The proof of Theorem 1 is a revision of an earlier, shorter presentation, and incorporates many additions and modifications suggested by R. Epstein. In §2, we show that any hope for a result analogous to that of Sacks on the jumps of r.e. degrees cannot be fulfilled since 0″ is not the jump of any minimal degree below 0′. We use a characterization of the degrees below 0′ with jump 0″ similar to that found for r.e. degrees with jump 0′ by R. W. Robinson [12]. Finally, in §3, we give a proof that every degree a ≤ 0′ with a′ = 0″ has a minimal predecessor. Yates [17] has already shown that every nonzero r.e. degree has a minimal predecessor, but that there is a nonzero degree ≤ 0′ with no minimal predecessor (see [18]; or for the original unrelativized result see [10] or [4]).

Characterization of DNA Primary Sequences by a New Similarity/Diversity Measure Based on the Partial Ordering.

ChemInform ◽  
2006 ◽  
Vol 37 (49) ◽  
Author(s):  
R. Todeschini ◽  
V. Consonni ◽  
A. Mauri ◽  
D. Ballabio
Keyword(s):  
Partial Ordering ◽  
Diversity Measure

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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