IDENTIFICATION OF THE DISTRIBUTION FUNCTION AND CHARACTERIZATION OF THE NANO– AND MICROPOWDERS SIZES

В работе предлагаются два новых эффективных алгоритма, реализованных коротким программным кодом в MS Excel, предназначенных для идентификации и характеризации размеров нано– и микропорошков частиц в виде обобщенного гамма или логнормального распределений по данным опытных гистограмм. Предлагаемый метод представляет собой новый и достаточно общий подход к решению обратных задач идентификации параметров дифференциальных функций распределения по экспериментальным данным на основе на минимизации функционала, представляющего собой коэффициент детерминации.Алгоритм реализован формулами (менее 10) наиболее распространенного инструментария (электронных таблиц MS Excel без использования макросов), позволяющего исследователям, не обладающими навыками профессиональных программистов, простоту проверки и воспроизведения представленного материала, а также возможность модификации кода для решения более широкого круга задач. Текст статьи и комментарии на рабочих листах скриншотов представляют собой готовые инструкции по решению задач идентификация функций распределения и характеризации размеров нано– и микропорошков. The paper proposes two new efficient algorithms, implemented by a short program code in MS Excel, designed to identify and characterize the sizes of nano- and micropowders of particles in the form of generalized gamma or lognormal distributions according to experimental histograms. The proposed method is a new general approach to solving inverse problems of identifying the parameters of differential distribution functions from experimental data based on minimizing the functional that is the coefficient of determination.The algorithm is implemented with formulas (less than 10) of the most common tools (MS Excel spreadsheets without the use of macros), which allow researchers without the skills of professional programmers to easily check and reproduce the presented material, as well as the ability to modify the code to solve a wider range of problems. The text of the article and comments on the worksheets of screenshots represent ready-made instructions for solving problems of identification of distribution functions and characterization of the sizes of nano- and micropowders.

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Inverse Problems of Single Mode about Some Indeterminate Beams

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.432.139 ◽

2013 ◽

Vol 432 ◽

pp. 139-143

Author(s):

Qi Shen Wang ◽

Ming Hui Liu ◽

Li Hua Zhang ◽

Min He

Keyword(s):

Distribution Function ◽

Inverse Problems ◽

Fundamental Mode ◽

Single Mode ◽

Distribution Functions ◽

Positive Functions ◽

Stiffness Distribution

In this paper, the conditions and method of constructing the stiffness distribution function of various parameters indeterminate beams by the fundamental mode and specified polynomial density distributing function were made up. It is discussed that the constructed stiffness distribution functions are positive functions in case with different density distributing.

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Cluster Origin of Solvation Features of C-Nanostructures in Organic Solvents

Advances in Medical Technologies and Clinical Practice - Advancing Pharmaceutical Processes and Tools for Improved Health Outcomes ◽

10.4018/978-1-5225-0248-7.ch008 ◽

2016 ◽

pp. 189-293

Author(s):

Francisco Torrens ◽

Gloria Castellano

Keyword(s):

Experimental Data ◽

Free Energy ◽

Distribution Function ◽

Diffusion Coefficient ◽

Organic Solvents ◽

Distribution Functions ◽

Heat Of Solution ◽

Carbon Nanocones ◽

Single Wall Carbon ◽

Sharp Concentration

The existence of fullerenes, Single-Wall Carbon Nanocones (SWNCs), especially Nanohorns (SWNHs), Single-Wall Carbon Nanotube (SWNT) (CNT) (NT), NT-Fullerene Bud (NT-BUD), Nanographene (GR) and GR-Fullerene Bud (GR-BUD) in cluster form is discussed in organic solvents. Theories are developed based on columnlet, bundlet and droplet models describing size-distribution functions. The phenomena present a unified explanation in the columnlet model in which free energy of cluster-involved GR comes from its volume, proportional to number of molecules n in cluster. Columnlet model enables describing distribution function of GR stacks by size. From geometrical considerations, columnlet (GR/GR-BUD), bundlet (SWNT/NT-BUD) and droplet (fullerene) models predict dissimilar behaviours. Interaction-energy parameters are derived from C60. An NT-BUD behaviour or further is expected. Solubility decays with temperature result smaller for GR/GR-BUD than SWNT/NT-BUD than C60 in agreement with lesser numbers of units in clusters. Discrepancy between experimental data of the heat of solution of fullerenes, CNT/NT-BUDs and GR/GR-BUDs is ascribed to the sharp concentration dependence of the heat of solution. Diffusion coefficient drops with temperature result greater for GR/GR-BUD than SWNT/NT-BUD than C60 corresponding to lesser number of units in clusters. Aggregates (C60)13, SWNT/NT-BUD7 and GR/GR-BUD3 are representative of droplet, bundlet and columnlet models.

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Extreme Value Theory: a New Characterization of the Distribution Function for the Mixed Method

International Journal of Statistics and Probability ◽

10.5539/ijsp.v6n1p71 ◽

2016 ◽

Vol 6 (1) ◽

pp. 71

Author(s):

Kane Ladji ◽

Diawara Daouda ◽

Diallo Moumouni

Keyword(s):

Distribution Function ◽

Mixed Method ◽

Conditional Distribution ◽

Convex Combination ◽

Value Theory ◽

Distribution Functions ◽

Cumulative Distribution ◽

Underlying Distribution ◽

Generalized Pareto

Consider the sample X1, X2, ..., XN of N independent and identically distributed (iid) random variables with common cumulative distribution function (cdf)F, and let Fu be their conditional excess distribution function F. We define the ordered sample by . Pickands (1975), Balkema and de Haan (1974) posed that for a large class of underlying distribution functions F , and large u ,Fu is well approximated by the Generalized Pareto Distribution.The mixed method is a method for determining thresholds. This method consists in minimizing the variance of a convex combination of other thresholds.The objective of the mixed method is to determine by which probability distribution one can approach this conditional distribution. In this article, we propose a theorem which specifies the conditional distribution of excesses when the deterministic threshold tends to the end point.

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The Determination of Affinity Distributions: A Numerical Algorithm and its Application for Estimating the Energetic Heterogeneity of Complexing Silicas and Humic Substances

Adsorption Science & Technology ◽

10.1260/0263617001493431 ◽

2000 ◽

Vol 18 (3) ◽

pp. 267-294 ◽

Cited By ~ 4

Author(s):

Yu. Kholin ◽

S. Myerniy ◽

G. Varshal

Keyword(s):

Electrostatic Interactions ◽

Distribution Functions ◽

Differential Distribution ◽

Chemically Modified ◽

Energetic Heterogeneity ◽

Ill Posed ◽

Integral Distribution ◽

Methodological Difficulties

The characterization of energetic heterogeneity has been discussed in the investigation of ion-binding and chemisorption processes. Both the calculation and the interpretation of the distribution of affinity constants are ambiguous. Methodological difficulties arise connected to the fact that electrostatic effects are difficult to separate from energetic heterogeneity because of the chemical biography of a given material. Only a close similarity between the distribution functions calculated for different ionic strengths allows the electrostatic interactions to be neglected. The numerical estimation of the distribution functions is complicated by the ill-posed nature of the problem. Some computational methods are briefly compared and methods for providing robust and unbiased estimations outlined. In contrast to differential distribution functions, the computation of integral ones may be transformed into the conventionally correct problem. On this basis, a fast and robust method for calculating integral distribution functions is proposed. In addition, this ensures numerically stable estimations of differential distribution functions. The method has been applied to a study of the energetic heterogeneity of 20 silicas chemically modified with aliphatic amines. When H+ ions are chemisorbed, the energetic heterogeneity observed is dependent on the surface topography and its hydration state. In addition, the binding properties of ashless fulvic and humic acids relative to H+, Hg2+ and Pb2+ ions have been examined. The existence of functional groups with different acidities and complexing abilities has been established.

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Analysis of the pore structure of adsorbents and its characterization by a numerical method

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19842721 ◽

1984 ◽

Vol 49 (12) ◽

pp. 2721-2738 ◽

Cited By ~ 4

Author(s):

Ondřej Kadlec ◽

Jerzy Choma ◽

Helena Jankowska ◽

Andrzej Swiatkowski

Keyword(s):

Distribution Function ◽

Pore Structure ◽

Numerical Method ◽

Active Carbon ◽

Numerical Evaluation ◽

Suggested Algorithm

This paper describes the algorithm of numerical evaluation of the parameters of the pore structure of adsorbents ( the micro, mezo and macropores). The structure of individual types of pores is described with the equation proposed by one of the present authors and giving the total distribution function of the pores with respect to their radii. The reliability of the suggested algorithm was verified in a number of calculations using a specially developed program. The results of the analysis and characterization of three different specimens of active carbon are shown as an example.

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Scaling

10.1093/oso/9780198821939.003.0003 ◽

2018 ◽

Author(s):

Stefan Thurner ◽

Rudolf Hanel ◽

Peter Klimekl

Keyword(s):

Distribution Function ◽

Dynamical Systems ◽

Complex Systems ◽

Power Law ◽

Scaling Laws ◽

Power Laws ◽

Distribution Functions ◽

Temporal Process ◽

Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

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Inverse problems for finite Jacobi matrices and Krein–Stieltjes strings

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2020-0112 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Alexander Mikhaylov ◽

Victor Mikhaylov

Keyword(s):

Dynamical System ◽

Inverse Problems ◽

Jacobi Matrix ◽

Jacobi Matrices ◽

Unknown Parameters ◽

Stieltjes String ◽

Propagation Of Waves ◽

Dynamic Inverse

Abstract We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein–Stieltjes string. We offer three methods of recovering unknown parameters: entries of a Jacobi matrix in the first problem and point masses and distances between them in the second, from dynamic Dirichlet-to-Neumann operators. We also answer a question on a characterization of dynamic inverse data for these two problems.

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Development and Evaluation of a Fluctuating Plume Model for Odor Impact Assessment

Applied Sciences ◽

10.3390/app11083310 ◽

2021 ◽

Vol 11 (8) ◽

pp. 3310

Author(s):

Marzio Invernizzi ◽

Federica Capra ◽

Roberto Sozzi ◽

Laura Capelli ◽

Selena Sironi

Keyword(s):

Experimental Data ◽

Distribution Functions ◽

Plume Model ◽

Probability Distribution Functions ◽

Weibull Pdf ◽

Fluctuating Plume ◽

Concentration Statistics ◽

Modified Weibull ◽

Instantaneous Concentration ◽

Mean Concentration

For environmental odor nuisance, it is extremely important to identify the instantaneous concentration statistics. In this work, a Fluctuating Plume Model for different statistical moments is proposed. It provides data in terms of mean concentrations, variance, and intensity of concentration. The 90th percentile peak-to-mean factor, R90, was tested here by comparing it with the experimental results (Uttenweiler field experiment), considering different Probability Distribution Functions (PDFs): Gamma and the Modified Weibull. Seventy-two percent of the simulated mean concentration values fell within a factor 2 compared to the experimental ones: the model was judged acceptable. Both the modelled results for standard deviation, σC, and concentration intensity, Ic, overestimate the experimental data. This evidence can be due to the non-ideality of the measurement system. The propagation of those errors to the estimation of R90 is complex, but the ranges covered are quite repeatable: the obtained values are 1–3 for the Gamma, 1.5–4 for Modified Weibull PDF, and experimental ones from 1.4 to 3.6.

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