Simple equations method (SEsM) and its particular cases: Hirota method

2021 ◽  
Author(s):  
Nikolay K. Vitanov ◽  
Zlatinka I. Dimitrova
Keyword(s):  
Hirota Method ◽  
Simple Equations

Optimal Experimental Design With Nesting of Persons in Organizations

2013 ◽  
Vol 221 (3) ◽  
pp. 145-159 ◽  
Author(s):  
Gerard J. P. van Breukelen
Keyword(s):  
Repeated Measures ◽  
Optimal Number ◽  
Health Centers ◽  
Randomized Experiments ◽  
Optimal Sample ◽  
Treatment Conditions ◽  
Sampling Cost ◽  
Nested Designs ◽  
Simple Equations ◽  
Number Of Individuals

This paper introduces optimal design of randomized experiments where individuals are nested within organizations, such as schools, health centers, or companies. The focus is on nested designs with two levels (organization, individual) and two treatment conditions (treated, control), with treatment assignment to organizations, or to individuals within organizations. For each type of assignment, a multilevel model is first presented for the analysis of a quantitative dependent variable or outcome. Simple equations are then given for the optimal sample size per level (number of organizations, number of individuals) as a function of the sampling cost and outcome variance at each level, with realistic examples. Next, it is explained how the equations can be applied if the dependent variable is dichotomous, or if there are covariates in the model, or if the effects of two treatment factors are studied in a factorial nested design, or if the dependent variable is repeatedly measured. Designs with three levels of nesting and the optimal number of repeated measures are briefly discussed, and the paper ends with a short discussion of robust design.

scholarly journals Simple Equations Pertaining to the Particle Number and Surface Area of Metallic, Polymeric, Lipidic and Vesicular Nanocarriers

2021 ◽  
Vol 89 (2) ◽  
pp. 15
Author(s):  
M. R. Mozafari ◽  
E. Mazaheri ◽  
K. Dormiani
Keyword(s):  
Drug Delivery ◽  
Surface Area ◽  
Particle Number ◽  
Analytical Techniques ◽  
Metallic Particles ◽  
Nutraceutical Compounds ◽  
Mathematical Formulas ◽  
Simple Equations

Introduction: Bioactive encapsulation and drug delivery systems have already found their way to the market as efficient therapeutics to combat infections, viral diseases and different types of cancer. The fields of food fortification, nutraceutical supplementation and cosmeceuticals have also been getting the benefit of encapsulation technologies. Aim: Successful formulation of such therapeutic and nutraceutical compounds requires thorough analysis and assessment of certain characteristics including particle number and surface area without the need to employ sophisticated analytical techniques. Solution: Here we present simple mathematical formulas and equations used in the research and development of drug delivery and controlled release systems employed for bioactive encapsulation and targeting the sites of infection and cancer in vitro and in vivo. Systems covered in this entry include lipidic vesicles, polymeric capsules, metallic particles as well as surfactant- and tocopherol-based micro- and nanocarriers.

Circumferential Creep Strain of Cylinders Subjected to Internal Pressure: A Comparison of the Theories of Johnson and Bailey

1966 ◽  
Vol 8 (1) ◽  
pp. 22-26 ◽  
Author(s):  
E. C. Larke ◽  
R. J. Parker
Keyword(s):  
Internal Pressure ◽  
Creep Strain ◽  
Wall Thickness ◽  
Circumferential Strain ◽  
Axial Stress ◽  
Integration Procedure ◽  
Graphical Integration ◽  
Simple Equations

When considering the creep of cylinders subjected to internal pressure, the theory of Johnson et al. takes into account progressive changes of radial, circumferential and axial stress at any point in the wall thickness. This approach differs from that put forward by Bailey, who assumed that these stresses remained constant with time. The present paper summarizes an examination of both theories, with particular reference to outside and bore diameters, and presents simple equations which enable circumferential strain to be calculated without using the complex graphical integration procedure suggested by Johnson. Furthermore, it is demonstrated that these equations are mathematically identical with those derived by Bailey.

Using float–sink data in simple equations to predict sulfur contents

2002 ◽  
Vol 76 (3) ◽  
pp. 231-239 ◽  
Author(s):  
Yakup Cebeci ◽  
Nevzat Aslan
Keyword(s):  
Simple Equations

scholarly journals Global Tree Taper Modelling: A Review of Applications, Methods, Functions, and Their Parameters

Forests ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 913
Author(s):  
Serajis Salekin ◽  
Cristian Higuera Catalán ◽  
Daniel Boczniewicz ◽  
Darius Phiri ◽  
Justin Morgenroth ◽  
...  
Keyword(s):  
Measurement Techniques ◽  
Principal Component ◽  
Climatic Conditions ◽  
Modern Times ◽  
Taper Function ◽  
Complex Functions ◽  
Artificial Neural Network Ann ◽  
Species Specific ◽  
Simple Equations ◽  
Taper Equations

Taper functions are important tools for forest description, modelling, assessment, and management. A large number of studies have been conducted to develop and improve taper functions; however, few review studies have been dedicated to addressing their development and parameters. This review summarises the development of taper functions by considering their parameterisation, geographic and species-specific limitations, and applications. This study showed that there has been an increase in the number of studies of taper function and contemporary methods have been developed for the establishment of these functions. The reviewed studies also show that taper functions have been developed from simple equations in the early 1900s to complex functions in modern times. Early taper functions included polynomial, sigmoid, principal component analysis (PCA), and linear mixed functions, while contemporary machine learning (ML) approaches include artificial neural network (ANN) and random forest (RF). Further analysis of the published literature also shows that most of the studies of taper functions have been carried out in Europe and the Americas, meaning most taper equations are not specifically applicable to tropical tree species. Developing well-conditioned taper functions requires reducing the variation due to species, measurement techniques, and climatic conditions, among other factors. The information presented in this study is important for understanding and developing taper functions. Future studies can focus on developing better taper functions by incorporating emerging remote sensing and geospatial datasets, and using contemporary statistical approaches such as ANN and RF.

A general model for growth trajectories of linear carbonate platforms

2020 ◽  
Vol 90 (9) ◽  
pp. 1139-1155
Author(s):  
Nicolas Goudemand ◽  
Pulkit Singh ◽  
Jonathan L. Payne
Keyword(s):  
Growth Trajectories ◽  
Carbonate Platforms ◽  
Seawater Chemistry ◽  
Forward Models ◽  
Sedimentary Deposits ◽  
Sediment Production ◽  
Carbonate Sedimentation ◽  
Platform Margin ◽  
Simple Equations ◽  
Analytical Expressions

ABSTRACT A key challenge regarding development of carbonate platforms is predicting the temporal pattern of platform-margin progradation, aggradation, retrogradation, and drowning. Numerical forward models of carbonate sedimentation have been widely applied to this problem, shedding substantial light on the roles of sediment production, transport, tectonic subsidence, and eustasy on the evolution of carbonate platforms. However, forward models are typically complex and computationally expensive, preventing comprehensive exploration of parameter space. In addition, the interactions among parameters are often nonlinear, preventing the development of simple expressions relating the position of the platform margin to the governing parameters of the model. To complement the considerable insights derived from numerical forward models, this study presents analytical expressions for the temporal evolution of the position of platform margins using the simplest possible assumptions regarding sediment production and transport. These expressions provide useful null models, deviations from which can be used to identify the particular effects of biology or seawater chemistry on carbonate factories in influencing the development of these important sedimentary deposits. Application of the model to synthetic and outcrop examples demonstrates that these simple equations are useful for parameter estimation that can then be used to guide more detailed, process-based numerical forward models.

scholarly journals The Values of Versatility: Pharmacists, Plants, and Place in the French (Post)Colonial World

2016 ◽  
Vol 58 (2) ◽  
pp. 432-462 ◽  
Author(s):  
Laurence Monnais ◽  
Noémi Tousignant
Keyword(s):  
Medicinal Plant ◽  
Scientific Activity ◽  
Public Health Care ◽  
French West Africa ◽  
Post Colonial ◽  
Plant Medicine ◽  
History Of ◽  
French Colonial ◽  
Simple Equations ◽  
The Relationship

AbstractColonial pharmacists bio-prospected, acclimatized, chemically screened, and tinkered with plants and their parts, hoping to create products to supply colonial public health care, metropolitan industries, and imperial markets. This article's approach is to examine the trajectories of expertise of two French colonial pharmacists, Franck Guichard and Joseph Kerharo, to illuminate the history of modern medicinal plant research. Both men studied medicinal plants as part of their colonial duties, yet their interests in indigenous therapies exceeded and outlived colonial projects. We take this “overflow” as our point of departure to explore how science transformed medicinal plant values in French colonial and postcolonial contexts. Our focus is on the relationship between value and space—on the processes of conceptual and material (de-/re-)localization through which plant value is calculated, intensified, and distributed. We study and compare these processes in French Indochina and French West Africa where Guichard and Kerharo, respectively, engaged in them most intensively. We show that their engagements with matter, value, knowledge, and mobility defy easy categorizations of medicinal plant science as either extractive or neo-traditionalist. By eschewing simple equations of scientists' motivations with political projects and knowledge-production, we argue that approaching plant medicine through trajectories of expertise opens up grounds for finer analyses of how colonial power and projects, and their legacies, shaped scientific activity.

scholarly journals Effects of cosmic ray decreases on cloud microphysics

2012 ◽  
Vol 12 (2) ◽  
pp. 3595-3617 ◽  
Author(s):  
J. Svensmark ◽  
M. B. Enghoff ◽  
H. Svensmark
Keyword(s):  
Cloud Condensation Nuclei ◽  
Cosmic Ray ◽  
Liquid Water Content ◽  
Total Solar Irradiance ◽  
Cloud Microphysics ◽  
Forbush Decreases ◽  
Cloud Data ◽  
Sigma Level ◽  
Cloud Properties ◽  
Simple Equations

Abstract. Using cloud data from MODIS we investigate the response of cloud microphysics to sudden decreases in galactic cosmic radiation – Forbush decreases – and find responses in effective emissivity, cloud fraction, liquid water content, and optical thickness above the 2–3 sigma level 6–9 days after the minimum in atmospheric ionization and less significant responses for effective radius and cloud condensation nuclei (<2 sigma). The magnitude of the signals agree with derived values, based on simple equations for atmospheric parameters. Furthermore principal components analysis gives a total significance of the signal of 3.1 sigma. We also see a correlation between total solar irradiance and strong Forbush decreases but a clear mechanism connecting this to cloud properties is lacking. There is no signal in the UV radiation. The responses of the parameters correlate linearly with the reduction in the cosmic ray ionization. These results support the suggestion that ions play a significant role in the life-cycle of clouds.

scholarly journals Analyses of Accumulation of Silica in the Growth of Two Tropical Forages using Simple Equations

10.5109/24285 ◽  
1999 ◽  
Vol 43 (3/4) ◽  
pp. 395-401
Author(s):  
Masataka Shimojo ◽  
Takashi Bungo ◽  
Manabu Tobisa ◽  
Yoshimi Imura ◽  
Naoki Koga ◽  
...  
Keyword(s):  
Tropical Forages ◽  
Simple Equations
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