The Construction and Prediction of Psychophysical Power Functions for the Sweetness of Equiratio Sugar Mixtures

Perception ◽  
1983 ◽  
Vol 12 (6) ◽  
pp. 753-767 ◽  
Author(s):  
Jan E R Frijters ◽  
Peter A M Oude Ophuis
Keyword(s):  
Mixture Models ◽  
Power Function ◽  
Alternative Model ◽  
Power Functions ◽  
Great Precision ◽  
Sugar Mixtures ◽  
Simple Alternative ◽  
Single Compound ◽  
The Relationship ◽  
Interaction Phenomena

Psychophysical taste mixture models describe the relationship between the perceived intensities of the unmixed components and the intensity of the mixture. Three of these models are discussed. As all of these appear either to be internally inconsistent or lack sufficient generality, a simple alternative model has been developed especially for the prediction of the intensity of equiratio mixtures. This model was experimentally tested with glucose—fructose mixtures. On the basis of the data obtained it is shown that a psychophysical equiratio mixture function can be constructed in the same way as a power function for a single compound. The results show that the new mixture model can predict the functions for equiratio mixtures with great precision. Implications for mixture interaction phenomena are discussed.

scholarly journals On the Notion of Reproducibility and Its Full Implementation to Natural Exponential Families

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1568
Author(s):  
Shaul K. Bar-Lev
Keyword(s):  
Power Function ◽  
Exponential Family ◽  
Probability Distributions ◽  
Infinite Divisibility ◽  
Variance Function ◽  
Exponential Families ◽  
Natural Exponential Family ◽  
Natural Exponential Families ◽  
Convolution Properties ◽  
The Relationship

Let F=Fθ:θ∈Θ⊂R be a family of probability distributions indexed by a parameter θ and let X1,⋯,Xn be i.i.d. r.v.’s with L(X1)=Fθ∈F. Then, F is said to be reproducible if for all θ∈Θ and n∈N, there exists a sequence (αn)n≥1 and a mapping gn:Θ→Θ,θ⟼gn(θ) such that L(αn∑i=1nXi)=Fgn(θ)∈F. In this paper, we prove that a natural exponential family F is reproducible iff it possesses a variance function which is a power function of its mean. Such a result generalizes that of Bar-Lev and Enis (1986, The Annals of Statistics) who proved a similar but partial statement under the assumption that F is steep as and under rather restricted constraints on the forms of αn and gn(θ). We show that such restrictions are not required. In addition, we examine various aspects of reproducibility, both theoretically and practically, and discuss the relationship between reproducibility, convolution and infinite divisibility. We suggest new avenues for characterizing other classes of families of distributions with respect to their reproducibility and convolution properties .

scholarly journals Commutative semigroups whose endomorphisms are power functions

2021 ◽  
Author(s):  
Ryszard Mazurek
Keyword(s):  
Positive Integer ◽  
Power Function ◽  
Cyclic Group ◽  
Commutative Semigroup ◽  
Commutative Monoid ◽  
Power Functions ◽  
Commutative Semigroups ◽  
Finite Cyclic Group

AbstractFor any commutative semigroup S and positive integer m the power function $$f: S \rightarrow S$$ f : S → S defined by $$f(x) = x^m$$ f ( x ) = x m is an endomorphism of S. We partly solve the Lesokhin–Oman problem of characterizing the commutative semigroups whose all endomorphisms are power functions. Namely, we prove that every endomorphism of a commutative monoid S is a power function if and only if S is a finite cyclic group, and that every endomorphism of a commutative ACCP-semigroup S with an idempotent is a power function if and only if S is a finite cyclic semigroup. Furthermore, we prove that every endomorphism of a nontrivial commutative atomic monoid S with 0, preserving 0 and 1, is a power function if and only if either S is a finite cyclic group with zero adjoined or S is a cyclic nilsemigroup with identity adjoined. We also prove that every endomorphism of a 2-generated commutative semigroup S without idempotents is a power function if and only if S is a subsemigroup of the infinite cyclic semigroup.

scholarly journals Research on Damage Characteristics of Brick Masonry under Explosion Load

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jifeng Wei ◽  
Zhixin Du ◽  
Yonghui Zheng ◽  
Oundavong Ounhueane
Keyword(s):  
Power Function ◽  
Explosive Charge ◽  
Masonry Wall ◽  
Pressure Vessels ◽  
Brick Masonry ◽  
Ejection Velocity ◽  
Load Bearing ◽  
Damage Characteristics ◽  
Explosion Load ◽  
The Relationship

As the main structural component of partition wall or load-bearing wall, brick masonry has been widely used in construction engineering. However, brick and mortar are all brittle materials prone to crack. Nowadays, fireworks, gas stoves, high-pressure vessels, and other military explosives may explode to damage nearby structures. Many explosion casualties had shown that the load-bearing capacity of brick masonry decreased dramatically and cracks or fragments appeared. Previous studies mainly focused on noncontact explosion in which shock wave is the main damage element. In fact, the response and damage effect of brick masonry wall under contact explosion are more complex, which attracts more attention now. In order to explore the damage characteristics of brick masonry under explosion load, a series of simulations and verification experiments are conducted. RHT and MO granular material models are introduced to describe the behaviour of brick and masonry, respectively, in simulation. The combination effect of front compressive wave and back tensile wave are main factors influencing the breakage of masonry wall. The experimental results are well in accordance with the simulation results. The front cross section dimension of crater is closely related to the radius of spherical explosive charge. A power function predictive model is developed to express the relationship between the radius of hole and the radius of explosive. Furthermore, with increasing the quantity of explosive charge, the number and ejection velocity of fragments are all increased. The relationship between maximum ejection velocity and the quantity of explosive also can be expressed as a power function model.

scholarly journals CARACTERIZAÇÃO HIDRÁULICA DO MICROASPERSOR DAN SPRINKLERS GRUPO MODULAR

Irriga ◽  
2001 ◽  
Vol 6 (1) ◽  
pp. 13-18 ◽  
Author(s):  
Marcio Antonio Vilas Boas ◽  
Eurides Kuster Macedo Júnior ◽  
Silvio Cesar Sampaio ◽  
Melânia Inês Valiati
Keyword(s):  
Production Process ◽  
Power Function ◽  
Characteristic Equation ◽  
State University ◽  
The West ◽  
Potential Equation ◽  
Group 2 ◽  
The Relationship

CARACTERIZAÇÃO HIDRÁULICA DO MICROASPERSOR DAN SPRINKLERS GRUPO MODULAR                                     Márcio Antônio Vilas BoasEurides Kuster Macedo JuniorSilvio César SampaioMelânia Inês ValiatiUNIOESTE - Universidade Estadual do Oeste do ParanáCEP: 85814-110 - Cascavel – PR - Brasil - Cx. Postal   711Fone: (045) 225 -2100  (R-249) - Fax : (045) [email protected]  1 RESUMO  Este  trabalho  teve  como  objetivo  avaliar as características hidráulicas  do  microaspersor DAN SPRINKLERS do grupo modular de fabricação da DAN SPRINKLERS - ISRAEL, de uso recente no Oeste do Paraná. Os ensaios foram realizados no Laboratório de Hidráulica do Departamento de Engenharia da Universidade Estadual do Oeste do Paraná – UNIOESTE. Na  avaliação dos microaspersores  estudou-se, a variação decorrente do processo de fabricação e a determinação da equação característica da relação vazão–pressão. Os microaspersores do Grupo modular com diâmetros de bocais 0,94; 1,16;1,41;1,92 e 2,34 mm,  foram submetidos às pressões de 100, 150, 200, 250, 300 e 350 kPa. As equações características determinadas indicaram que o microaspersor testado não é auto-compensante , tolerante a sensibilidade de variações de pressões e que a equação potencial se ajusta bem aos dados. Os coeficientes de variação de fabricação obtidos foram menores que 5%, classificando-se, de acordo com a Norma ISO, como de categoria A. UNITERMOS: Microaspersão, coeficiente de variação, modelo potencial.  VILAS BÔAS, M. A., MACEDO JUNIOR, E. K. HYDRAULIC CHARACTERIZATION OF MICROSPRINKLER DAN SPRINKLER - MODULATE GROUP   2 ABSTRACT This work had as objective to evaluate the characteristics hydraulic of the microsprinklers of the group to modulate of production of DAN SPRINKLERS - ISRAEL, of recent use in the West of Paraná. The tests was accomplished in the Laboratory of Hydraulics of the Department of Engineering of the State University of the West of Paraná - UNIOESTE. In the evaluation of the microasprinklers it was studied such characteristics as, the variation due to the production process and the determination of the characteristic equation of the relationship vazão-pressure. The microsprinklers of the Group to modulate with diameters of nozzle 0,94; 1,16;1,41;1,92 and 2,34 mm, the pressures were submitted 100, 150, 200, 250, 300 and 350 kPa. The certain characteristic equations showed that the tested microsprinklers is not solemnity-compensante and that the potential equation was fit well to the data. The obtained coefficients of production variation were everybody below 5% being able to not this way to classify them in agreement with for ISO  category as A. KEYWORDS: Microsprinkler, coefficient variation, power function.

scholarly journals Flashover Performance and Process of Suspension Insulator Strings Artificially Covered with Snow

Energies ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 2916 ◽  
Author(s):  
Yuyao Hu ◽  
Sihua Guo ◽  
Richang Xian ◽  
Xingbo Han ◽  
Zhongyi Yang ◽  
...  
Keyword(s):  
Power Function ◽  
Electrical Performance ◽  
Salt Deposit ◽  
Influencing Mechanism ◽  
Suspension Insulator ◽  
Deposit Density ◽  
Ac Arc ◽  
Dc Arc ◽  
The Relationship ◽  
Snow Thickness

Snow accumulates on the surface of insulator string, causing a decrease in its electrical performance, seriously threatening the reliable operation of the power grid. Most previous studies have focused on iced insulators; however, there is a lack of research on snow-covered insulators. In this paper, to reveal the influencing mechanism that snow has on the electrical characteristics of insulator string, based on an artificial snowing test in a chamber, the effects of equivalent salt deposit density, applied voltage type, and snow thickness on the flashover performance of snow-covered insulators are analyzed, and the flashover process is investigated. The results show that the relationship between the arc flashover gradient and the equivalent salt deposit density is a power function with a negative exponent, which is similar to that of polluted and ice-covered insulator strings. For the insulator strings with the same snow accretion, the direct current (DC) arc flashover gradient is lower than the alternating current (AC) arc flashover gradient. The relationship between arc flashover gradient and snow thickness is also a power function. The formation of a dry band during the flashover of snow-covered insulator string is similar to the flashover of the polluted insulator, and the arc propagation along the surface of the snow-covered insulator is similar to the flashover of the iced insulator.

The Wind-Sand Flux Structure of Grassland on the Northern Foot of Yinshan Mountain

2014 ◽  
Vol 668-669 ◽  
pp. 1530-1537
Author(s):  
Hong Tao Jiang ◽  
Chun Rong Guo ◽  
Chun Xing Hai ◽  
Shan Shan Sun ◽  
Yun Hu Xie ◽  
...  
Keyword(s):  
Vertical Distribution ◽  
Power Function ◽  
Exponential Function ◽  
Vertical Direction ◽  
Power Functions ◽  
Height Range ◽  
Sand Flux ◽  
Soil Flux ◽  
The Vertical Distribution ◽  
Better Than

Sand samplers were layed out in the grassland located in the northern foot of Yinshan Mountain for collecting soil flux samples from 0 to 1.5m height above the surface from Mar., 1, 2008 to Feb., 29, 2009.Exponential and Power functions were both used for describing vertical distribution of sand flux in the grassland, the results indicated that determination coefficient of Power function varied from 0.898 to 0.992 while 0.432 to 0.661 for exponential function. Power function is better than exponential function in describing the vertical distribution of both annual and seasonal soil flux, summer excluded. Annual cumulative percentage of each height was determined indirectly according to the power function mentioned above, the result indicated that up to 2m height,15-25% of soil flux concentrated with in 10cm above the surface,25-35% of soil flux concentrated within 20cm above the surface,30-40% of soil flux concentrated within 30 cm above the surface, 43-54% of soil flux concentrated within 50 cm above the surface,85-90% of soil flux concentrated within 150 cm above the surface, respectively. No significant differences of soil flux structures in spring, autumn, winter and in the whole year were found. The research on wind erosion of grassland in the vertical direction more dispersed, in the height range of sediment accumulated percentage was lower than that of the previous research.

Using Logarithms to Explore Power and Exponential Functions

1994 ◽  
Vol 87 (3) ◽  
pp. 161-170
Author(s):  
James R. Rahn ◽  
Barry A. Berndes
Keyword(s):  
Experimental Data ◽  
Real Number ◽  
Positive Real Number ◽  
Power Functions ◽  
Exponential Functions ◽  
Positive Real ◽  
Nonzero Real Number ◽  
Physical Phenomena ◽  
The Relationship

Power functions and exponential functions often describe the relationship between variables in physical phenomena. Power functions are equations of the form y = kxn (see fig. 1), where k is a nonzero real number and n is a nonzero real number not equal to 1. Exponential functions are equations of the form y = kbx (see fig. 2), where k is a nonzero real number and b is a positive real number. Students should be able visually to recognize these functions so that they can easily identify their appearance when experimental data are graphed. When physical phenomena appear to describe exponential and power functions, logarithms can be used to locate approximate functions that represent the phenomena.

New Voices, New Visions: Toward A Lesbian/Gay Paradigm for Psychology

1989 ◽  
Vol 13 (4) ◽  
pp. 445-458 ◽  
Author(s):  
Laura S. Brown
Keyword(s):  
Gay Men ◽  
Alternative Model ◽  
Human Relationships ◽  
Lesbian And Gay ◽  
Men I ◽  
Psychological Inquiry ◽  
The Relationship ◽  
The Way

This article proposes an alternative model for psychological inquiry based in the experiences of lesbians and gay men. I propose that there are three elements that cross-situationally define a lesbian and gay reality: biculturalism, marginality, and normative creativity. Each of these elements is explored with examples of how these perspectives might alter the way that certain dominant notions about human relationships are understood. The article closes with questions regarding the application of this lesbian and gay paradigm to methodologies for inquiry. The relationship between a lesbian/gay paradigm for psychology and feminist questions regarding epistemology is also explored.

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