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I color-coded the left and right axes labels to help guide readers who might be less familiar with this type of chart, and will try to do the same in the future. Having the different sets of data in one chart makes it easier to get into more complex comparisons. Questions? If there’...
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The analytic continuation of a function is unique, so nailing down ζ(s) for s>1 is all you need to continue it out into the complex plane.Complex numbers take the form “A+Bi” (where ). The only thing about complex numbers you’ll need to know here is that complex numbers are ...
Step 1. The online version of Mathematica can be accessed on the Wolfram website after a simple sign-up process. Step 2. Once you gain access to the platform, you can upload one or more PDF files for conversion to CDF. Step 3. An imported PDF file will have all its pages converted ...
Anarithmetic functionis any function from the set of natural numbers (whole, non-negative numbers that we use to count) to the set ofcomplex numbers. In other words, it’s acomplex-valued functionthat is defined on the set of natural numbers. In notation, that’s: ...
Of course, there are many ways to generalize the concept of adjacency matrix by replacing the zero entries with p-adic numbers carrying graph theoretical information. After some computer experiments, we suggest the following replacements: Given a graph G with vertex set {1, 2, . . . , n} ...
Two of the most popular rules to characterize the aromaticity of molecules are those due to Hückel and Baird, which govern the aromaticity of singlet and triplet states. In this work, we study how these rules fade away as the ring structure increases and an optimal overlap between p orbital...
In pattern recognition applications, the goal can be merely to model the distribution of the data, and the clustering result is used as a part in a more complex system. In [16], the quality of the clustering was shown not to be critical for the speaker recognition performance when any ...