RA plot

Abstract: Introduces the structure and function of PP (Stablized Probability Plot) and QQ (Quantile-Quantile Plot), and uses MATLAB to produce two sets of exponential distribution and normal distribution. The sample number is 20 and 45 respectively. The fitting of QQ plot and PP plot are respectively used to obtain the superiority of PP in the exponential distribution. In normal distribution, the QQ plot is more advantageous.

Abstract: An attempt was made to explain the physical sense of the special r o /r a vs. r t /r a plot being a phase diagram for the variety of chromium compounds, especially spinels, Krok-Kowalski et al., J. Alloys Compd. 315, 62 (2001). Here r t is the ionic radius of cations in the tetrahedral positions, r o the ionic radius of cations in the octahedral positions, r a the ionic radius of anions. Therefore, a model was proposed in which only the direct and RKKY exchanges were taken into account. The predictions of the presented model are adequate to the experimental data contained in this plot.

Abstract: which the descendents of AND nodes are processed in a sequential machine. The alternating nature is obviously itself irrelevant since an arbitrary AND/OR graph can be made alternating by the suitable addition of nodes. Only finiteness is critical. Thus there is a correspondence between finite AND/OR graphs and context-free grammars. This equivalence is of more than intellectual interest, for it shows that computational problems of AND/OR graphs may be well known and solved within the framework of context-free grammars. The standard problem of AND/OR graphs is that of \"finding a solution\" (see [4]): that is, find a subtree of the graph involving only one edge out of the OR nodes, all edges out of the AND nodes, with leaves being nodes in the original graph with no edges leaving them. A solution of an AND/OR graph is precisely a derivation tree of some sentence in the associated context-free grammar. Finding a solution is then synonymous to finding a sentence in the associated language together with its derivation tree. This problem has been solved in language theory in the form of the \"emptiness problem\" (see for example [2]). Simon and Lee [4] state, \"Although the general methods are still at large, we have found an efficient way to obtain optimal solutions to AND/OR series-parallel graphs.\" Clearly, through the equivalence with context-free grammars, we obtain general methods for the solution of AND/OR graphs, though \"optimality\" needs a little clarification. The algorithm for the emptiness problem would (normally) deliver the string whose derivation tree has fewest levels, thus finding the solution to the AND/OR graph whose longest path from start to terminal problem is minimal: as a measure of solution cost this is appealing though not the same as the cost measures of Nilsson [3]. Elaborations on the algorithm will optimize other measures. This application of language theory to AND/OR graphs, while the most significant, is not the only one possible. The equivalence of AND/OR graphs (we must of course define equivalence carefully) is unsolvable. And so on. It is also worth remarking that language theory also gains in that the graphs usually associated with regular languages are degenerate cases of context-free AND/OR graphs, while at the informal level this communication emphasizes that syntax is a problem solving tool: in programming languages syntax between program and statement allows problem decomposition. Submittal of an algorithm for consideration for publication in Communications of the ACM …

Abstract: We propose a quantification of the p-p plot that assigns equal weight to all distances between the respective distributions: the surface between the p-p plot and the diagonal. This surface is labeled the Harmonic Weighted Mass (HWM) index. We introduce the diagonal-deviation (d-d) plot that allows the index to be computed exactly under all circumstances. This two-dimensional d-d plot accommodates a straightforward extension to the k-sample HWM index, with k > 2. A Monte Carlo simulation based on an example involving long-term sovereign credit ratings illustrates the power of the HWM test.