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The kaolinite crystallization by homogeneous precipitation with previous hydrolysis of the feldspars added has been followed by pH and potassium concentration measurements. The synthesized products were studied by X-ray powder diffraction and electron microscopy and consist of kaolinite and mica, accompanied occasionally by traces of smectite. The relative quantities of the synthesized minerals depend fundamentally on the supply rate of the alkaline ions.
The equilibrium diagrams developed for Al-hydroxide and for kaolinite by Garrels and Christ (1965) have been modified by taking into account the existence of gels. From the stability zones obtained, the “appropriate” concentrations can be deduced and utilized for synthesizing these species, provided the requirements to insure good crystal growth are observed. Among procedures to promote these crystallizations, homogeneous precipitation processes (La Iglesia et al., 1974, 1976) appear to be particularly adequate.
The theoretical considerations provide an explanation for most of the processes observed until now, both successful and unsuccessful syntheses, and also give an explanation for many field observations. The crystallizations, however, remain poorly reproducible, indicating that many factors are still poorly known. Some points requiring further investigation include (i) better values for ΔGr0, (ii) the influence of organic complexes, (iii) the effect of preexisting crystalline phases, (iv) those involving dehydration processes in these systems.
Halloysite (metahalloysite) of various particle sizes has been altered with oxalic and EDTA acids, at room temperature and during different periods of time (5–90 days). The oxalic acid attack at first achieved only a recrystallization of halloysite. The recrystallization is much more significant the smaller the size of the treated halloysite particles. Later the material is destroyed. The EDTA treatment also has provoked during the first days a recrystallization of the halloysitic material which is destroyed again after about 20–25 days. Later kaolinite is formed. The kinetic curve of kaolinite formation is symmetrical with respect to that corresponding to the diminution of amorphous material in the sample. The influence of the halloysite particle size and the complexing effect of the acids in relation to the resulting products are discussed.
Kaolinite is synthesized in approximately the same time in three temperature ranges: (1) from 200–250° to 350–400° (hydrothermal processes); (2) from 120 to 175° (semihydrothermal ones); (3) at ordinary temperature. It is thus evident that the rate process cannot be explained by the Arrhenius equation only, but is explained well by considering that kaolinite formation obeys the laws of crystal growth. It occurs only in slightly supersaturated solutions in which the nucleation process is possible and in which a slow and regular rate of growth has been insured. Concentrations calculated from the thermodynamical equilibria correspond to those of the experimental conditions for the low temperature processes. For the higher temperature ones, a similar relationship is delineated, at least as far as the thermodynamical treatment can be carried out.
Well ordered kaolinite was isostatically and uniaxially pressurized up to 13,200 kg/cm2 for 10 min in dry conditions and the effects of pressure on kaolinite order were determined by analyzing the shapes of two-dimensional diffraction bands on X-ray powder diffraction patterns. Increased pressure decreased the percentage of low-defect kaolinite phase, and isostatic pressure proved to be more effective than uniaxial pressure in increasing disorder, e.g. the degree of disorder resulting from 2000 kg/cm2 isostatic pressure was equivalent to that caused by a 3200 kg/cm2 uniaxial pressure. Also, the effect of high pressure was similar to that obtained with lower pressures applied several times (e.g. the effect of applying 8500 kg/cm2 pressure for 10 min was comparable to using 3200 kg/cm2 pressure five times).
In addition, six kaolinites of different structural order were isostatically pressurized up to 4000 kg/cm2 for 10 min, both in dry and wet (water) conditions. Under dry conditions, changes in structurally ordered kaolinite were comparable to those cited above whereas kaolinite pressurized in wet conditions showed a moderate improvement in structural order.
These results may contribute to our understanding of kaolinite behavior during burial diagenesis and low-grade metamorphism. In addition, these results can also be used in industry to improve kaolin technological properties that depend on kaolinite structural order by application of appropriate industrial pressure processes.
Mental health is inextricably linked to both poverty and future life chances such as education, skills, labour market attachment and social function. Poverty can lead to poorer mental health, which reduces opportunities and increases the risk of lifetime poverty. Cash transfer programmes are one of the most common strategies to reduce poverty and now reach substantial proportions of populations living in low- and middle-income countries. Because of their rapid expansion in response to the COVID-19 pandemic, they have recently gained even more importance. Recently, there have been suggestions that these cash transfers might improve youth mental health, disrupting the cycle of disadvantage at a critical period of life. Here, we present a conceptual framework describing potential mechanisms by which cash transfer programmes could improve the mental health and life chances of young people. Furthermore, we explore how theories from behavioural economics and cognitive psychology could be used to more specifically target these mechanisms and optimise the impact of cash transfers on youth mental health and life chances. Based on this, we identify several lines of enquiry and action for future research and policy.
We consider the spectral analysis of several examples of bilateral birth–death processes and compute explicitly the spectral matrix and the corresponding orthogonal polynomials. We also use the spectral representation to study some probabilistic properties of the processes, such as recurrence, the invariant distribution (if it exists), and the probability current.
This chapter gives an introduction to orthogonal polynomials. It also includes the concept of the Stieltjes transform and some of its properties, which will play a very important role in the spectral analysis of discrete-time birth–death chains and birth–death processes. A section on the spectral theorem for orthogonal polynomials (or Favard’s theorem) will give insights into the relationship between tridiagonal Jacobi matrices and spectral probability measures. The chapter then focuses then on the classical families of orthogonal polynomials, of both continuous and discrete variables. These families are characterized as eigenfunctions of second-order differentials or difference operators of hypergeometric type solving certain Sturm–Liouville problems. These classical families are part of the so-called Askey scheme.
This chapter is devoted to the spectral analysis of discrete-time birth–death chains on nonnegative integers, which are the most basic and important discrete-time Markov chains. These chains are characterized by a tridiagonal one-step transition probability matrix. The so-called Karlin–McGregor integral representation formula of the n-step transition probability matrix is obtained in terms of orthogonal polynomials with respect to a probability measure with support inside the interval [–1, 1]. An extensive collection of examples related to orthogonal polynomials is provided, including gambler’s ruin, the Ehrenfest model, the Bernoulli–Laplace model and the Jacobi urn model. The chapter concludes with applications of the Karlin–McGregor formula to probabilistic aspects of discrete-time birth–death chains, such as recurrence, absorption, the strong ratio limit property and the limiting conditional distribution. Finally, spectral methods are applied to discrete-time birth–death chains on the integers, which are not so much studied in the literature.
This chapter is devoted to the spectral analysis of one-dimensional diffusion processes, which are the most basic and important continuous-time Markov processes where now the state space is a continuous interval contained in the real line. Diffusion processes are characterized by an infinitesimal operator which is a second-order differential operator with drift and diffusion coefficients. A spectral representation of the transition probability density of the process is obtained in terms of the orthogonal eigenfunctions of the corresponding infinitesimal operator, for which a Sturm–Liouville problem with certain boundary conditions will be solved. An analysis of the behavior of these boundary points will also be made. An extensive collection of examples related to special functions and orthogonal polynomials is provided, including the Brownian motion with drift and scaling, the Orstein–Uhlenbeck process, a population growth model, the Wright–Fisher model, the Jacobi diffusion model and the Bessel process, among others. Finally, the concept of quasi-stationary distributions is studied, for which the spectral representation plays an important role.
This chapter is devoted to the spectral analysis of birth–death processes on nonnegative integers, which are the most basic and important continuous-time Markov chains. These processes will be characterized by an infinitesimal operator which is a tridiagonal matrix whose spectrum is always contained in the negative real line (including 0). The Karlin–McGregor integral representation formula of the transition probability functions of the process is obtained in terms of orthogonal polynomials with respect to a probability measure with support inside a positive real interval. Although many of the results are similar or equivalent to those of discrete-time birth–death chains, the methods and techniques are quite different. The chapter gives an extensive collection of examples related to orthogonal polynomials, including the M/M/k queue for any k servers, the continuous-time Ehrenfest and Bernoulli–Laplace urn models, a genetics model of Moran and linear birth–death processes. As in the case of discrete-time birth–death chains, the Karlin–McGregor formula is applied to the probabilistic aspects of birth–death processes, such as processes with killing, recurrence, absorption, the strong ratio limit property, the limiting conditional distribution, the decay parameter, quasi-stationary distributions and bilateral birth–death processes on the integers.
In pioneering work in the 1950s, S. Karlin and J. McGregor showed that probabilistic aspects of certain Markov processes can be studied by analyzing orthogonal eigenfunctions of associated operators. In the decades since, many authors have extended and deepened this surprising connection between orthogonal polynomials and stochastic processes. This book gives a comprehensive analysis of the spectral representation of the most important one-dimensional Markov processes, namely discrete-time birth-death chains, birth-death processes and diffusion processes. It brings together the main results from the extensive literature on the topic with detailed examples and applications. Also featuring an introduction to the basic theory of orthogonal polynomials and a selection of exercises at the end of each chapter, it is suitable for graduate students with a solid background in stochastic processes as well as researchers in orthogonal polynomials and special functions who want to learn about applications of their work to probability.
Cannabis use in pregnancy is related to developmental and mental disorders. The acknowledgement of prenatal exposure frequently depends on the mother’s report, which can often be omitted. There exists little bibliography of the different methods to detect the use of cannabis during pregnancy, with no standardized screening available.
Objectives
The objective of this study is to review the available bibliography about screening of cannabis use during pregnancy and neonates and to analyze the different methods of prenatal screening being used in clinical practice.
Methods
A systematic review of the methods of screening of cannabis use during pregnancy and neonates was carried out in PubMed (July 2020) in English, French and Spanish(10 years) with the keywords: screening, test, detection, analysis, urine, blood, hair, meconium.107 studies were analyzed: 52 included and 55 excluded (Figure 1.).
Results
The studies analyzed stand out for its large heterogeneity. Self-report of pregnant women, meconium and maternal urine analysis are used the most. The type of analysis technique is not reported or chromatography mass spectrometry (GC/MS) and enzyme-linked inmunoabsorbent assay (ELISA) is used(Figure 2.). Urine seems to be the most accurate method for maternal testing. Neonatal meconium and umbilical cord tissue indicates fetal exposure during second and third trimester, neonatal hair third trimester exposure and maternal serum and hair can also be used (Figure 3.).
Conclusions
Nowadays, the available bibliography is heterogeneous and lacks information. Consequentially, further investigation needs to be carried out in order as to establish standardized prenatal screening of cannabis during pregnancy to draw more comparable and precise conclusions.