scholarly journals Modeling the Liberation of Comminuted Scheelite Using Mineralogical Properties

Minerals ◽  
2019 ◽  
Vol 9 (9) ◽  
pp. 536 ◽  
Author(s):  
Sarbast Ahmad Hamid ◽  
Pura Alfonso ◽  
Josep Oliva ◽  
Hernan Anticoi ◽  
Eduard Guasch ◽  
...  
Keyword(s):  
Beta Distribution ◽  
Test Performance ◽  
Distribution Density ◽  
Beta Function ◽  
Size Fraction ◽  
Distribution Functions ◽  
Plant Design ◽  
Mineral Liberation ◽  
Size Grade ◽  
Liberation Analysis

In this paper, the modeling of the liberation of scheelite is presented. A pattern of concentration experiments was performed to investigate the scheelite liberation and distribution density calculation procedure. In this work, one sample from a Mittersill tungsten ore was studied. This work describes a method for determining the downstream milling energy requirements for rod mill products based on a Bond mill test performance. The grade distribution of particles at a given size fraction was calculated using a predictive liberation model. The concentration behavior of these particles in size fractions was evaluated using batch concentrate tests. The recovery of particles in size/grade classes, image analysis using mineral liberation analysis (MLA), and function calculations were implemented for the modeling of the liberation. By describing the size, grade, and recovery data of particles in size/grade classes, a technique for the measurement of distribution functions was developed that relates beta distribution, a model for the function based on the incomplete beta function, and a solution to produce liberation modeling. It was shown that the predicted results agreed well with the observed results. With a procedure for measuring the liberation, it was possible to carry out the first experimental measurement of the beta distribution. This liberation/concentrate model has wide potential applications for metallurgy and plant design, where the liberation modeling is to be determined with the distribution density solution to the predictive mineral liberation function equation, which includes the liberation of ore samples and their liberation characteristics.

Characterisation of graphite by automated mineral liberation analysis

2014 ◽  
Vol 123 (3) ◽  
pp. 184-189 ◽  
Author(s):  
Dirk Sandmann ◽  
Sabine Haser ◽  
Jens Gutzmer
Keyword(s):  
Mineral Liberation ◽  
Liberation Analysis

Logarithmic concavity of the inverse incomplete beta function with respect to the first parameter

2021 ◽  
Vol 127 (1) ◽  
pp. 111-130
Author(s):  
Dimitris Askitis
Keyword(s):  
Distribution Function ◽  
Beta Distribution ◽  
Probability Distributions ◽  
Beta Function ◽  
Incomplete Beta Function ◽  
Univariate Function ◽  
Convexity Properties ◽  
Logarithmic Concavity ◽  
Two Parameter ◽  
Monotonicity Results

The beta distribution is a two-parameter family of probability distributions whose distribution function is the (regularised) incomplete beta function. In this paper, the inverse incomplete beta function is studied analytically as a univariate function of the first parameter. Monotonicity, limit results and convexity properties are provided. In particular, logarithmic concavity of the inverse incomplete beta function is established. In addition, we provide monotonicity results on inverses of a larger class of parametrised distributions that may be of independent interest.

scholarly journals Rare Earth Occurrences in Streams of Processing a Phosphate Ore

Minerals ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 262 ◽  
Author(s):  
Xiaosheng Yang ◽  
Hannu Tapani Makkonen ◽  
Lassi Pakkanen
Keyword(s):  
Rare Earth ◽  
Sulfuric Acid ◽  
Phosphoric Acid ◽  
Rare Earth Elements ◽  
Electron Probe Microanalysis ◽  
Electron Probe ◽  
Phosphate Ore ◽  
Mineral Liberation ◽  
Efficient Recovery ◽  
Liberation Analysis

Rare earth elements (REEs) are defined as lanthanides with Y and Sc. Rare earth occurrences including the REE-bearing phases and their distributions, measured by rare earth oxides (REOs), in the streams of processing a phosphate ore were determined by using MLA, the mineral liberation analysis and EPMA, the electron probe microanalysis. The process includes an apatite ore beneficiation by flotation and further processing of the beneficiation concentrate with sulfuric acid. Twenty-six, sixty-two and twelve percent of the total REOs (TREO) contents from the ore end up in the products of beneficiation tailings, phosphogypsum (PG) and phosphoric acid, respectively. Apatite, allanite, monazite and pyrochlore are identified as REE-bearing minerals in the beneficiation process. In the beneficiation tailings, the REEs are mainly distributed in monazite (10.3% TREO), apatite (5.9% TREO), allanite (5.4% TREO) and pyrochlore (4.3% TREO). Gypsum, monazite, apatite and other REE-bearing phases were found to host REEs in the PG and the REEs distributions are 44.9% TREO in gypsum, 15.8% TREO in monazite, 0.6% TREO in apatite and 0.6% TREO in other REE-bearing phases. Perspectives on the efficient recovery of REEs from the beneficiation tailings and the PG are discussed.

scholarly journals Evaluation of six leaf angle distribution functions in the Castillo® coffee variety

2017 ◽  
Vol 35 (1) ◽  
pp. 23-28 ◽  
Author(s):  
Carlos Andrés Unigarro M. ◽  
Álvaro Jaramillo R. ◽  
Claudia Patricia Flórez R.
Keyword(s):  
Coffea Arabica ◽  
Regression Coefficient ◽  
Statistical Tests ◽  
Beta Function ◽  
Distribution Functions ◽  
Leaf Angle ◽  
Angle Distribution ◽  
Leaf Angle Distribution ◽  
Two Parameters ◽  
Coffea Arabica L

The study was conducted at the "Estación Central Naranjal Ce-nicafé" (National Coffee Research Center, Chinchina, Caldas, Colombia) on Coffea arábica L. variety Castillo® to find the leaf angle distribution function that best described the tilt of the angles present in the canopy. Leaf angles were recorded for 1,559 leaves located in the upper, middle and lower profiles of the canopy. The observed leaf angle distribution was compared with the Beta, ellipsoidal and four de Wit distribution functions. The fit between comparisons was determined by the Pearson X2 test and its significance, the regression coefficient statistically equal to one and the RMSE. Likewise, the leaf angle distribution recorded in the field per profile and their combination was described based on three angle classes (1stclass: 0°-30°; 2nd class: 30°-60°; and 3rd class: 60°-90°) according to the Goudriaan criterion. Generally, the leaf angle distribution present in the canopy of Castillo® coffee variety is adequately described by the Beta function with two parameters and the ellipsoidal function based on the adjustment provided by the statistical tests.

A Statistical Index for Monitoring Tooth Cracks in a Gearbox

1995 ◽  
Author(s):  
Fathy Ismail ◽  
Hugh R. Martin ◽  
Farag Omar
Keyword(s):  
Beta Distribution ◽  
General Equation ◽  
Beta Function ◽  
Statistical Moments ◽  
Tooth Root ◽  
Statistical Index ◽  
Damage Indicator ◽  
Small Cracks ◽  
Root Crack

Abstract This paper is concerned with detecting and monitoring the growth of a tooth root crack in a gearbox. It uses the reciprocal of the Kurtosis of the beta distribution 1/k for each tooth period, as the damage indicator. A general equation to generate the statistical moments strictly in terms of the α and β parameters of the beta function is developed. To monitor the growth of the crack, a new index, called the “Kurtosis Index”, is formulated from 1/k’s of all the teeth. This index correlates well with the size of the crack, and it shows that small cracks can be detected.

Comparison of Cardinal Temperatures of Lettuce Using Bilinear, Parabolic, and Beta Distribution Functions

2014 ◽  
Vol 23 (1) ◽  
pp. 39-42
Author(s):  
Mi-Kyung Cha ◽  
경 차미 ◽  
Chun-Sik Kim ◽  
Jirapa Austin ◽  
Young-Yeol Cho ◽  
...  
Keyword(s):  
Beta Distribution ◽  
Distribution Functions ◽  
Cardinal Temperatures

Comparison of the lognormal and beta distribution functions to describe the uncertainty in permeability

2005 ◽  
Vol 313 (3-4) ◽  
pp. 248-256 ◽  
Author(s):  
Karen L. Ricciardi ◽  
George F. Pinder ◽  
Kenneth Belitz
Keyword(s):  
Beta Distribution ◽  
Distribution Functions
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