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Mat 2675 Calculus Iii, Spring 2019, Oer Syllabus, Caner Koca
Mat 2675 Calculus Iii, Spring 2019, Oer Syllabus, Caner Koca
Open Educational Resources
No abstract provided.
Special Values Of Ibukiyama-Saito L-Functions, Brad Isaacson
Special Values Of Ibukiyama-Saito L-Functions, Brad Isaacson
Publications and Research
Following the method of Arakawa, we express the special values of an L-function originally introduced by Arakawa and Hashimoto and later generalized by Ibukiyama and Saito at non-positive integers by finite sums of products of Bernoulli polynomials. As a corollary, we prove an infinite family of identities expressing finite sums of products of Bernoulli polynomials by generalized Bernoulli numbers.
Validation Of A Lottery, Xiaona Zhou
Validation Of A Lottery, Xiaona Zhou
Publications and Research
The NY Pick 4 lottery consists of four "randomly" chosen digits from 0 to 9. For this to be fair, each digit should be equally likely to occur. To determine whether this is the case, a Chi-squared goodness of fit test will be applied to historical data. This provides a quantitative way of measuring how well the observed frequency of digits matches our expectations of a fair lottery. The Chi-squared distribution gives us a number beyond which we reject fairness. However, there is another possibility. If the difference between the fair model and the observed frequency is too small, that …
Higher Cluster Categories And Qft Dualities, Sebastián Franco, Gregg Musiker
Higher Cluster Categories And Qft Dualities, Sebastián Franco, Gregg Musiker
Publications and Research
We introduce a unified mathematical framework that elegantly describes minimally supersymmetry gauge theories in even dimensions, ranging from six dimensions to zero dimensions, and their dualities. This approach combines and extends recent developments on graded quivers with potentials, higher Ginzburg algebras, and higher cluster categories (also known as m-cluster categories). Quiver mutations studied in the context of mathematics precisely correspond to the order-(m + 1) dualities of the gauge theories. Our work indicates that these equivalences of quiver gauge theories sit inside an infinite family of such generalized dualities.