Performing Selection on a Monotonic Function in Lieu of Sorting Using Layer-Ordered Heaps

2021 ◽  
Vol 20 (4) ◽  
pp. 1849-1854
Author(s):  
Kyle Lucke ◽  
Jake Pennington ◽  
Patrick Kreitzberg ◽  
Lukas Käll ◽  
Oliver Serang
Keyword(s):  
Monotonic Function

A Decomposition of the Marginal Homogeneity Model for Square Contingency Tables with Ordered Categories

1993 ◽  
Vol 43 (1-2) ◽  
pp. 123-126 ◽  
Author(s):  
Sadao Tomizawa
Keyword(s):  
Contingency Tables ◽  
Short Note ◽  
Monotonic Function ◽  
Ordered Categories ◽  
Marginal Homogeneity ◽  
Statist Assoc

For square contingency tables, with ordered categories, this short note decomposes the marginal homogeneity (MH) model into an extended MH model and the model of equality of expectation of monotonic function of row and column variables. This decomposition is a generalization of the decomposition of the MH model which was earlier considered by Tomizawa (1991, Cal. Statist. Assoc. Bull., 41, 201-207).

scholarly journals A logarithmically completely monotonic function involving the gamma function and originating from the Catalan numbers and function

2015 ◽  
Vol 3 (4) ◽  
pp. 140 ◽  
Author(s):  
Fang-Fang Liu ◽  
Xiao-Ting Shi ◽  
Feng Qi
Keyword(s):  
Gamma Function ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Catalan Numbers ◽  
Monotonic Function ◽  
Completely Monotonic Function ◽  
Completely Monotonic ◽  
Logarithmically Completely Monotonic Function ◽  
And Function

<p><span>In the paper, the authors find necessary conditions and sufficient conditions for a function involving the gamma function and originating from investigation of properties of the Catalan numbers and function in combinatorics to be logarithmically completely monotonic.</span></p>

scholarly journals The Relativistic Boltzmann Equation and Two Times

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 804
Author(s):  
L. P. Horwitz
Keyword(s):  
Boltzmann Equation ◽  
Monotonic Function ◽  
Relativistic Boltzmann Equation ◽  
Pair Annihilation ◽  
System Of Particles ◽  
Normal Particle ◽  
Invariant Parameter ◽  
Relativistic Framework

We discuss a covariant relativistic Boltzmann equation which describes the evolution of a system of particles in spacetime evolving with a universal invariant parameter τ . The observed time t of Einstein and Maxwell, in the presence of interaction, is not necessarily a monotonic function of τ . If t ( τ ) increases with τ , the worldline may be associated with a normal particle, but if it is decreasing in τ , it is observed in the laboratory as an antiparticle. This paper discusses the implications for entropy evolution in this relativistic framework. It is shown that if an ensemble of particles and antiparticles, converge in a region of pair annihilation, the entropy of the antiparticle beam may decreaase in time.

Brake Lamp Photometrics and Automobile Rear Signaling

1987 ◽  
Vol 29 (5) ◽  
pp. 533-540
Author(s):  
Michael Sivak ◽  
Michael Flannagan ◽  
Paul L. Olson
Keyword(s):  
Reaction Time ◽  
Monotonic Function ◽  
Luminous Intensity ◽  
Relevant Parameter ◽  
Signal Identification ◽  
Relative Likelihood ◽  
Average Luminance ◽  
Current Minimum ◽  
Relationship Of ◽  
The Relationship

The objective of this study was to evaluate the relationship of lamp photometrics to differentiation between brake and presence signals. To assess this relationship, signal identification was evaluated as a function of lamp photometrics under simulated dusk/dawn conditions. The following were the main results: (1) Luminous intensity was a better predictor of signal identification than was average luminance. (2) The likelihood of identifying a signal as a brake signal was a monotonic function of lamp intensity. (3) Reaction time was positively related to the degree of subjects' uncertainty (as measured by the relative likelihood of “brake” responses): reaction time was slowest when the likelihood of “brake” or “presence” responses was close to 50%, and it decreased as the likelihood increased or decreased away from 50%. (4) Reaction time in a condition simulating typical U.S. rear-lighting configuration was significantly faster than in a condition simulating typical European configuration. The present results provide support for retaining luminous intensity as the relevant parameter of automobile brake-lighting specifications. Furthermore, these results argue against reducing the current minimum of 80 cd for the brake-lamp luminous intensity.

Variation of Inter-Item Associative Strength and Some Measures of Free Recall

1964 ◽  
Vol 15 (2) ◽  
pp. 527-534 ◽  
Author(s):  
Howard R. Pollio ◽  
Edward G. Christy
Keyword(s):  
Free Recall ◽  
Associative Strength ◽  
Stimulus Word ◽  
Monotonic Function ◽  
Interference Effects ◽  
The Third ◽  
Non Linear ◽  
The Relationship

Three groups of 20 Ss each were asked for the free recall of three different lists of 28 meaningful English words. Each list contained the associative responses evoked by a different Kent-Rosanoff stimulus word, and differed in the amount of its inter-item associative strength (IIAS). The words in a given list also differed in terms of the number of other words (Nc) in that list producing or cueing that word as an associate. Results showed that the number of items appearing in free recall was a non-monotonic function of IIAS. For two of the three word sets, Nc was positively correlated with the frequency of recall of individual items; while for the third set Nc value and frequency of recall were negatively correlated. The relationship between Nc and order of recall was non-linear, and some tendency toward alternating the recall of high and low Nc words appeared in the data. Thus, IIAS produced both facilitation and interference effects on free recall, the latter being the result of a factor similar to verbal satiation.

ORDERINGS FOR CLASSES OF AGGREGATION OPERATORS

1996 ◽  
Vol 04 (02) ◽  
pp. 145-156 ◽  
Author(s):  
L. BASILE ◽  
L. D’APUZZO
Keyword(s):  
Decision Making ◽  
Weighting Function ◽  
Multicriteria Decision Making ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Monotonic Function ◽  
Weighting Functions ◽  
Multicriteria Decision ◽  
Monotonic Functions

Some procedures for synthesizing values of judgements in multicriteria decision making have been provided by several authors. The functionals of synthesis they consider are frequently means. The most general form of these operators involves both a weighting function w and a continuous and strictly monotonic function φ. Our aim is to analyze the behaviour of the aggregation operator Fωφ depending on w and φ. To this purpose we introduce a pre-ordering relation on the set W of weighting functions and on the set Φ of continuous and strictly monotonic functions, which allows us to compare the synthesizing functionals.

UNIVERSAL CODOMAINS TO REPRESENT INTERVAL ORDERS

2009 ◽  
Vol 17 (02) ◽  
pp. 197-219 ◽  
Author(s):  
JUAN CARLOS CANDEAL ◽  
JAVIER GUTIÉRREZ GARCÍA ◽  
ESTEBAN INDURÁIN
Keyword(s):  
Binary Relation ◽  
Fuzzy Numbers ◽  
Monotonic Function ◽  
Interval Orders ◽  
Triangular Fuzzy Numbers

Given a binary relation defined on a set, we study its representability by means of a monotonic function that takes values on a suitable universal codomain (that depends on the kind of relation considered). We pay an special attention to the representability of interval orders, studying their alternative universal codomains, some of them equivalent to the set of symmetric triangular fuzzy numbers.

scholarly journals Completely monotonic function associated with the Gamma functions and proof of Wallis' inequality

2005 ◽  
Vol 36 (4) ◽  
pp. 303-307 ◽  
Author(s):  
Chao-Ping Chen ◽  
Feng Qi
Keyword(s):  
Monotonic Function ◽  
Completely Monotonic Function ◽  
Natural Numbers ◽  
Gamma Functions ◽  
Completely Monotonic ◽  
Logarithmically Completely Monotonic Function

We prove: (i) A logarithmically completely monotonic function is completely monotonic. (ii) For $ x>0 $ and $ n=0, 1, 2, \ldots $, then$$ (-1)^{n}\left(\ln \frac{x \Gamma(x)}{\sqrt{x+1/4}\,\Gamma(x+1/2)}\right)^{(n)}>0. $$(iii) For all natural numbers $ n $, then$$ \frac1{\sqrt{\pi(n+4/ \pi-1)}}\leq \frac{(2n-1)!!}{(2n)!!}

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