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Cordia sinensis, locally known as ‘Goondi’ in India, is an underexploited multipurpose fruit species found in hot arid regions that is well adapted to drought, salt and hot conditions. The present study was undertaken to collect fruit samples from different locations in the Kachchh region of Gujarat, India, and to determine their field establishment for characterization, conservation and utilization. The maximum distribution of the species was observed in Bhuj (45%) and Mandvi (25%). Field boundaries (35%) and scrub forests (30%) had greater frequencies, whereas backyards had rarer frequencies (10%). The species most commonly occurred on levelled topography (60%) with a soil pH in the range of 8–8.5 (63%). Morphological data of three-year-old plants in the field gene bank showed a maximum coefficient of variation in the number of leaves per plant (66.6), followed by the number of branches per plant (45.62) and collar diameter (27.69). Wide variations were recorded in plant height (121.67–212 cm), spread (118–223 cm2) and the number of branches per plant (6–24.33). Specific accessions were identified for fodder (CBCG-12, CBCG-13 and CBCG-16), early flowering and fruiting (CBCG-12, CBCG-13 and CBCG-14), easier propagation by seeds (CBCG-12 and CBCG-13) and salt tolerance (CBCG-15 and CBCG-16). Preliminary findings and information provided about this species' utilization and other aspects might be useful for future research on its domestication, sole plantation and conservation aspects, improving the exploitation of this species by present and future generations.
The onset of magnetic reconnection in space, astrophysical and laboratory plasmas is reviewed discussing results from theory, numerical simulations and observations. After a brief introduction on magnetic reconnection and approach to the question of onset, we first discuss recent theoretical models and numerical simulations, followed by observations of reconnection and its effects in space and astrophysical plasmas from satellites and ground-based detectors, as well as measurements of reconnection in laboratory plasma experiments. Mechanisms allowing reconnection spanning from collisional resistivity to kinetic effects as well as partial ionization are described, providing a description valid over a wide range of plasma parameters, and therefore applicable in principle to many different astrophysical and laboratory environments. Finally, we summarize the implications of reconnection onset physics for plasma dynamics throughout the Universe and illustrate how capturing the dynamics correctly is important to understanding particle acceleration. The goal of this review is to give a view on the present status of this topic and future interesting investigations, offering a unified approach.
By formulating a hypothesis for the elasticity of the cumulative distribution function, Dagum derived a set of eleven frequency distributions some of which are commonly employed in water engineering. This system is called as the Dagum system or family. This chapter revisits this system, discusses its properties, and derives its individual frequency distributions.
The Pearson system of frequency distributions is based on a differential equation which satisfies certain mathematical conditions but its physical basis remains obscure. This chapter discusses this system and the distributions that are derived therefrom. Some of these distributions, such as gamma, Pearson type III and its logarithmic version, exponential, and normal and its logarithmic version, are frequently used in water engineering. This chapter presents the Pearson system and its underlying hypothesis and derives different member distributions of this system.
A wide spectrum of frequency distributions that are commonly used in hydrologic, hydraulic, environmental and water resources engineering can be derived by employing the principle of maximum entropy. Entropy maximization provides a general framework for deriving any probability distribution subject to appropriate constraints. This chapter discusses this framework and derives a number of distributions which satisfy different constraints.
The D’Addario system contains a number of distributions that are commonly used in environmental and water engineering. These distributions result from the integration of a probability generating function and a transformation function. This chapter discusses the D’Addario system and discusses the hypotheses that are used for deriving this system and the distribution members of the system.
Using a slightly different definition of distribution elasticity, Esteban proposed a system of distributions some of which are used in hydrologic, hydraulic, environmental, and water resources engineering. This chapter visits the Esteban system of distributions and discusses the hypotheses that are used for deriving distributions of this system.
A wide range of random variables occur in hydrometeorology, hydrology, geohydrology, hydraulics, and water quality engineering. These random variables are described by frequency distributions. The usual practice is to plot the data of the variable and then fit an appropriate distribution. Often more than one distribution can be adequately fitted. These distributions originate from one or the other type of system of distributions. This chapter outlines these systems and discusses the need for describing these distribution systems. The chapter is concluded with the organization of the book.
Previously we have revisited the different distribution systems. In this chapter, we will discuss one more system based on the genetic theory, i.e., Charlier type A and B curves, which are based on the fundamental hypothesis of elementary errors.
Employing the elasticity of the cumulative distribution function (CDF) F(x), Stoppa (1993) proposed a differential equation which can be used to derive a set of distributions which constitute the Stoppa system or family. Some of these distributions are quite general. This chapter revisits this system and derives its individual frequency distributions.
Systems of frequency distributions are derived by the use of Bessel functions and the method of expansions in terms of cumulants or moments. The resulting distributions may be useful in hydrologic, hydraulic, environmental, and water resources engineering. These methods are discussed in this chapter.
A wide variety of frequency distributions are used in hydrologic, hydraulic, environmental, and water resources engineering. Using a hypothesis that relates the probability density function to the cumulative distribution function and its complement, Burr derived a set of twelve distributions that exhibit different characteristics and some of these distributions are commonly used in water engineering. This paper revisits the Burr system of distributions and discusses the hypothesis that is used for deriving these distributions. Using this hypothesis, it then derives these distributions and discusses the theory of cumulative moments for deriving parameters of these distributions.
There are many frequency distributions whose cumulative distribution functions (CDFs) cannot be expressed in closed form. Examples of such distributions are normal, lognormal, gamma, Pearson type III, among others. If a distribution has a closed form CDF then its probability density function (PDF) can be easily obtained by differentiation but vice versa is not tractable. Using certain hypotheses on the relation between PDF and CDF based on empirical data, the CDFs of a large number of distributions can be derived. This chapter discusses the derivation of CDFs of such distributions many of which are frequently used in hydrologic, hydraulic, environmental, and water resources engineering.