Class of Skewed Generalized Distributions Based on a Two-Piece Generalized Framework

2021 ◽  
Author(s):  
Panayiotis Theodossiou
Keyword(s):  
Generalized Distributions ◽  
Generalized Framework

scholarly journals KR20 and KR21 for Some Nondichotomous Data (It’s Not Just Cronbach’s Alpha)

2021 ◽  
pp. 001316442199253
Author(s):  
Robert C. Foster
Keyword(s):  
Exponential Family ◽  
Exponential Families ◽  
Natural Exponential Family ◽  
Cronbach’S Alpha ◽  
Natural Exponential Families ◽  
Cronbach's Alpha ◽  
Generalized Framework ◽  
The Common ◽  
Poisson Data ◽  
Poisson Count

This article presents some equivalent forms of the common Kuder–Richardson Formula 21 and 20 estimators for nondichotomous data belonging to certain other exponential families, such as Poisson count data, exponential data, or geometric counts of trials until failure. Using the generalized framework of Foster (2020), an equation for the reliability for a subset of the natural exponential family have quadratic variance function is derived for known population parameters, and both formulas are shown to be different plug-in estimators of this quantity. The equivalent Kuder–Richardson Formulas 20 and 21 are given for six different natural exponential families, and these match earlier derivations in the case of binomial and Poisson data. Simulations show performance exceeding that of Cronbach’s alpha in terms of root mean square error when the formula matching the correct exponential family is used, and a discussion of Jensen’s inequality suggests explanations for peculiarities of the bias and standard error of the simulations across the different exponential families.

scholarly journals Detailed Derivations of Formulas for Heat Release Rate Calculations Revisited: A Pedagogical and Systematic Approach

2019 ◽  
Vol 124 ◽  
Author(s):  
Jiann C. Yang
Keyword(s):  
Oxygen Consumption ◽  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Chemical Engineering ◽  
Chemical Species ◽  
Flow Process ◽  
Generalized Framework ◽  
Oxygen Consumption Calorimetry ◽  
Engineering Practices

The derivations of the formulas for heat release rate calculations are revisited based on the oxygen consumption principle. A systematic, structured, and pedagogical approach to formulate the problem and derive the generalized formulas with fewer assumptions is used. The operation of oxygen consumption calorimetry is treated as a chemical flow process, the problem is formulated in matrix notation, and the associated material balances using the tie component concept commonly used in chemical engineering practices are solved. The derivation procedure described is intuitive and easy to follow. Inclusion of other chemical species in the measurements and calculations can be easily implemented using the generalized framework developed here.

Anion packing density: a universal quantity for both dense and porous crystalline inorganic phases

2002 ◽  
Vol 58 (3) ◽  
pp. 457-462 ◽  
Author(s):  
F. Liebau ◽  
H. Küppers
Keyword(s):  
High Pressure ◽  
Packing Density ◽  
Three Dimensional ◽  
Ionic Radii ◽  
Generalized Framework ◽  
Molal Volumes ◽  
Definition Of ◽  
Anion Packing ◽  
Very High ◽  
Framework Density

To compare densities of inorganic high-pressure phases their molal volumes or specific gravities are usually employed, whereas for zeolites and other microporous materials the so-called framework density, FD, is applied. The definition of FD, which refers only to phases with three-dimensional tetrahedron frameworks, is extended to a `generalized framework density' d f, which is independent of the dimensionality of the framework and the coordination number(s) of the framework cations. In this paper the anion packing density, d ap, is introduced as a new quantity which is not only applicable to any inorganic phase but, in contrast to FD and d f, also allows quantitative comparisons to be made for crystalline inorganic phases of any kind. The anion packing density can readily be calculated if the volume and content of the unit cell and the radii of the anions of a phase are known. From d ap values calculated for high-pressure silica polymorphs studied under very high pressure, it is concluded that Shannon–Prewitt effective ionic radii do not sufficiently take into account the compressibility of the anions.

A New Weak Galerkin Finite Element Scheme for the Brinkman Model

2016 ◽  
Vol 19 (5) ◽  
pp. 1409-1434 ◽  
Author(s):  
Qilong Zhai ◽  
Ran Zhang ◽  
Lin Mu
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Optimal Order ◽  
Brinkman Model ◽  
Weak Galerkin ◽  
Order Error ◽  
Brinkman Equations ◽  
Generalized Distributions ◽  
Variational Form ◽  
Weak Derivatives

AbstractThe Brinkman model describes flow of fluid in complex porous media with a high-contrast permeability coefficient such that the flow is dominated by Darcy in some regions and by Stokes in others. A weak Galerkin (WG) finite element method for solving the Brinkman equations in two or three dimensional spaces by using polynomials is developed and analyzed. The WG method is designed by using the generalized functions and their weak derivatives which are defined as generalized distributions. The variational form we considered in this paper is based on two gradient operators which is different from the usual gradient-divergence operators for Brinkman equations. The WG method is highly flexible by allowing the use of discontinuous functions on arbitrary polygons or polyhedra with certain shape regularity. Optimal-order error estimates are established for the corresponding WG finite element solutions in various norms. Some computational results are presented to demonstrate the robustness, reliability, accuracy, and flexibility of the WG method for the Brinkman equations.

Generalized Framework to Simulate Gravel Packing in Wellbore Completions

2018 ◽  
Author(s):  
A. Mimouna ◽  
A. Verma ◽  
M. N. Guddati
Keyword(s):  
Generalized Framework ◽  
Gravel Packing

scholarly journals Traversal Caches: A Framework for FPGA Acceleration of Pointer Data Structures

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
James Coole ◽  
Greg Stitt
Keyword(s):  
Data Structures ◽  
Reconfigurable Computing ◽  
Application Development ◽  
Sequential Memory ◽  
Generalized Framework ◽  
Field Programmable ◽  
Order Of Magnitude ◽  
Programmable Gate Arrays ◽  
Irregular Data ◽  
Access Patterns

Field-programmable gate arrays (FPGAs) and other reconfigurable computing (RC) devices have been widely shown to have numerous advantages including order of magnitude performance and power improvements compared to microprocessors for some applications. Unfortunately, FPGA usage has largely been limited to applications exhibiting sequential memory access patterns, thereby prohibiting acceleration of important applications with irregular patterns (e.g., pointer-based data structures). In this paper, we present a design pattern for RC application development that serializes irregular data structure traversals online into a traversal cache, which allows the corresponding data to be efficiently streamed to the FPGA. The paper presents a generalized framework that benefits applications with repeated traversals, which we show can achieve between 7x and 29x speedup over pointer-based software. For applications without strictly repeated traversals, we present application-specialized extensions that benefit applications with highly similar traversals by exploiting similarity to improve memory bandwidth and execute multiple traversals in parallel. We show that these extensions can achieve a speedup between 11x and 70x on a Virtex4 LX100 for Barnes-Hut n-body simulation.

Full-wavefield Marchenko using a generalized framework for focusing functions

2021 ◽  
Author(s):  
Leon Diekmann ◽  
Ivan Vasconcelos
Keyword(s):  
Generalized Framework
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