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Analysis over and over again
Analysis over and over again
Announcement of a book on qualitative analysis

In this thoroughly updated third edition, the authors have provided a series of carefully designed and tested field and laboratory exercises that represent the full scope of limnology. In using this text, students will gain a solid foundation in this complex, multidisciplinary field of ecology as they explore the physical, chemical, and biological characteristics of standing and running waters. Limnological Analyses, Third Edition illustrates accepted standard methods as well as modern metabolic and experimental approaches and their research applications. Each exercise is preceded by an introductory section and concludes with questions for students as well as suggestions for further reading. As a textbook, Limnological Analyses, Third Edition is a highly structured, concise presentation with a research-oriented approach that openly invites active participation by students

During the last several years Greece has been under consistent and severe economic pressure; high national debt, trade deficit, and an undefined future has led to a persistent climate of uncertainty and presents a threat to economic recovery. As a result of the near-bankruptcy of Greece in 2010, the Greek government now receives financial relief from members of the European Monetary Union (EMU) and International Monetary Fund (IMF), both of the afore-mentioned parties monitoring, with the European Central Bank (ECB) and European Commission, the economic transformation process and guiding the Greek economy towards international competitiveness. Yet available data proves that Greece's economy is still shrinking-- while unemployment rates still rise, debt to GDP ratio worsens, and private investment sinks. Furthermore, there is still controversy whether Greece will remain within the monetary union or not. Is Greece's economy better of outside the European Monetary Union?

SummaryAnalysis of variance.Introduction: Some theory of I inear vector spaces can be applied at not too hard a mathematical level to some problems of analysis of variance. It is then possible to define some much used notions (main effect, interaction, confounding, orthogonality) and many experimental designs and their analysis get rather transparent, partly as a consequence of simple notations.§ 1. A function (y1, …yN) defined over N points (= e.g. experimental units in agricultural field trials) assigns a real number to any of these points. Such functions can be added and they can be multiplied with a real number: they can be considered as vectors and then form an N‐dimensional vector space E. Subspaces are: the I‐dimensional space of constant functions (of general means); the space of functions that are constant within the classes of a classification of the N points (fig. 2). If the classification corresponds with some influence A (amount cf phosphor added to the field; variety; fertility) then this space denoted by A is called the space of impure main‐effects of influence A. An independent basis, and hence the dimension of A are determined. The number of degrees of freedom of a sub‐space of E is defined to be its dimension. Also a space of impure interactions of two (or more) influences A and B is defined.§2. The stochastic variables y1, …yn have a normal distribution with expectation values y̌1…, y̌N and all with the same variance a. They are combined to a stochastic N‐dimensional vector y with expectation vector y̌.It has sense to define a metric in the vector space, determined by a scalar product:(a, b) = a1 b2+ a2 b2+…+ aN bN. The length of a vector is √(a,a) The angle between a and b isϕ :cosϕ= (a, b)/√(a,a).(b,b) The orthogonal projection of a vector yon a linear space A is denoted by yA. It follows that§ 3. The space A* of pure main effects of the influence A is the linear subspace of A perpendicular to the space of general means.§4. The space of pure interactions of A and B is defined to be the subspace of the space A X B of impure interactions, perpendicular to the spaces A and B.§5. Two influences or interactions are confounded, if their (pure) spaces meet in a space of dimension > o. Confounding may be complete or partial.§6. All orthogonal two‐way classifications are determined.§7‐ Statistical considerations are given. In particular the F‐test is mentioned.§8. Two examples of orthogonal two‐way‐classifications.§9. How to deal with non‐orthogonal classifications. An iteration technique to approximate likelihood estimates for two main effects, given by Stevens and Ha mm in g, is proved and understood in terms of vectors.§10. An example with two effects, one of which is linear fertility, is given in detail.§11. Latin squares.§12. Factorial designs.