Tableau

Figure 15.1 Tableau of the experimental 2 analysis for the interaction between the variables A and B by the 2 test...

Peron, F., and Lesueur, C. A. (1809). Tableau des caracteres generiques et specifiques de toutes les especes de Meduses connues jusqu a ce jour. Ann. Mus. Hist. Nat. Paris 14 325-366. 

Voici un premier tableau qui indiquera bien I accroissement enorme de Taction toxique (ou anaphylaxie) par Teffet d injections antecedents. 

From a given Young diagram we can, in n different ways, form a "Young tableau t by filling the boxes, in any order, with the site numbers 1,2,.., n. Fig. 2 shows examples of tableaux formed from the diagrams of Fig. 1. 

A tableau may be used to define certain subgroups of which are themselves direct products of smaller permutation groups the symmetrizing and antisymmetrizing operators for these subgroups lead, as we shall see, to projection operators on irreducible representations of... 

Given a tableau t, we first define the subgroup 1, consisting of all permutations q among sites in the same column of t. Evidently, 1 is just the direct product of the permutation groups for the sites in the... 

Combining the operators P, Q, we obtain the Young operator" associated with the tableau t ... 

A standard tableau is defined as one in which the numbers increase when one reads from left to right in each row and from top to bottom in each column. It can be shown Mi) that the dimension of a representation is equal to the number of standard tableaux associated with the corresponding diagram. The reader is also referred to the literature Mi) for methods of calculating characters of the representations from the diagrams. 

The Young operator Y in (1) antisymmetrizes with respect to permutations of sites in the same column in its tableau. The monomial yi, therefore, cannot be symmetrical with respect to any two sites in the same column, i.e., it cannot contain the same power of A for any two such sites. The powers of A for the sites in a given column, therefore, must all be different. The lowest possible choice consistent with this is that they be 0, 1, 2,. .., p, for a column of length /t. Thus, y can be chosen to be independent of A for sites in the first row of the tableau, and to contain A for sites in the second row, A2 for those in the third, etc. The total order is therefore... 

Commenting on the unfinished state of the second (and third) volumes of Capital, Joan Robinson warned, The waters are dark and it may be that whoever peers in them sees his own face (Robinson 1968 111). From these murky waters, a host of different models and perspectives have emerged. In the absence of any clear statement of the purpose of the reproduction tables, there is no agreement as to what they are for, how they relate to the rest of Capital, volume 2, and how they relate to Capital as a whole. For Tsuru (1994 191), Participants in the discussion...concretized the original simple tableau of Marx in whatever way most suited for their respective conclusions. ... 

Now economists are very fond of diagrams, and one of the few diagrams Marx ever used was to summarize Quesnay s Tableau Economique (Marx 1969a). Quesnay was the doyen of the physiocrats, who thought that land was the source of all value hence the tableau shows the circulation of commodities between farmers and landlords. As shown by Pressman (1994), Marx shaped this model into his reproduction schema a model of how commodities circulate between capitalists and workers. For Marx (1969a 344), the tableau was an extremely brilliant conception, incontestably the most brilliant for which political economy had up to then been responsible . 

The role of inventories in the reproduction schema can be illustrated using Marx s numerical example (Table 4.3a). The elements of this schema can be recast in a tableau representing three periods of production, as shown in Table 4.4. Outputs of the production process are represented for this year and last year. First, the outputs of last year are shown as inputs of production in the current period. For example, the 4,000 units of constant capital used up by Department 1 this year were produced by Department 1 in the previous year. Similarly, the 1,000 units of variable capital (consumption goods) used up by Department 1 this year were produced by Department 2 in the previous year. 

Pressman, S. (1994) Quesnay s Tableau Economique A Critique and Reassessment, Fairfield, NJ Kelley. 

Chemists working on the same problems could only know they were studying the same substances if they spoke the same language. The chemical language, like chemical instruments, defined the discipline.46 The instruments and the nomenclature were illustrated in elaborate diagrams and "tableaus." Lavoisier s "Tableau des substances simples" is one of the most famous. (See fig. 1.) Here he organizes thirty-three simple substances into four categories ... 

Lavoisier s "Tableau des Substances Simples" from his Traite elementaire de chimie (Paris Cuchet, 1789), p. 192. Courtesy of History of Science Collections, University of Oklahoma. 

The explanatory system which dramatically combined the classification methods of natural history with the quantitative methods of physical laws was the periodic system worked out by Dmitri Mendeleev (and independently, although less successfully, by Meyer). What is the great tableau that is the periodic table Is it icon, index, or symbol It is not metaphor. Is it a model There is no chemical laboratory in the world where Mendeleev s table does not hang on the wall, despite the fact that the original version is well over one hundred years old. Its center remains untouched. Give a chemist a choice between the periodic table (fig. 4) and Schrodinger s equation. Which would she take ... 

The representations of U(2) are, in general, labeled by two quantum numbers. However, since we are considering only boson realizations, these representations must be totally symmetric and can thus be characterized by only one quantum number, that is, the first entry in the Young tableau... 

The integers As are often arranged into a diagram, called a Young diagram (or tableau). The first row in the diagram is A1 the second is A2,... 

Carey McWilliams, an architect of the nation of nations tradition in American social thought, stands out for his refusal to ldse sight of the overall complexity of the American mosaic and for his refusal to make race identical with the Negro in American political life. Unlike Gun-nar Myrdal and other social scientists, who would effectively expel from consideration those pegged neither as white nor as black, McWilliams demonstrated a keen sensitivity to the complex racial tableau in... 

For fermions, the projection operators are simply Young operators, derived from the appropriate Young tableau, as will be shown below. 

Projection operators for irreducible representations of the symmetric group are obtained easily from their corresponding Young tableaux. A Young tableau is created from a Young frame. A Young frame is a series of connected boxes such as... 

For example, for the four-electron case mentioned above, we take the first Young tableau... 

Another method that may be used to generate the projection operator involves the use a matrix representation of the operator. In particular, we will use the orthogonal representation. First we must assign a Yamanouchi symbol to each tableau we have created. This is done by going through the numbers from 1 to n in each tableau and writing down in which row the number occurs. Thus if we assign names to the above tableaux ... 

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