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Articles 1 - 7 of 7
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Evidence For Maxwell's Equations, Fields, Force Laws And Alternative Theories Of Classical Electrodynamics, Max Tran
Publications and Research
The set of equations known today as Maxwell's equations along with a few constitutive equations lie at the heart of classical electromagnetism. A common misconception held by many is that Maxwell's equations are essential, and that classical electromagnetic theory is settled science and is no longer an active field of investigations. We will review the four Maxwell's equations and related equations, their supporting experimental evidence, the field concept, and the Lorentz and Ritz force laws. We will give a brief outline of two approaches to classical electromagnetism which bypass Maxwell's equations, the propagated potential approach and the direct action approach …
Character Sums Of Lee And Weintraub, Brad Isaacson
Character Sums Of Lee And Weintraub, Brad Isaacson
Publications and Research
We prove two conjectures of Lee and Weintraub and one conjecture of Ibukiyama and Kaneko about character sums arising as fixed point contributions in the Atiyah–Singer holomorphic Lefshetz formula applied to finite group actions on the space of certain Siegel cusp forms.
R Program For Estimation Of Group Efficiency And Finding Its Gradient. Stochastic Data Envelopment Analysis With A Perfect Object Approach, Alexander Vaninsky
R Program For Estimation Of Group Efficiency And Finding Its Gradient. Stochastic Data Envelopment Analysis With A Perfect Object Approach, Alexander Vaninsky
Publications and Research
The data presented here are related to the research article “Energy-environmental efficiency and optimal restructuring of the global economy” (Vaninsky, 2018) [1]. This article describes how the world economy can be restructured to become more energy-environmental efficient, while still increasing its growth potential. It demonstrates how available energy-environmental and economic information may support policy-making decisions on the atmosphere preservation and climate change prevention. This Data article presents a computer program in R language together with examples of input and output files that serve as a means of implementation of the novel approach suggested in publication[1]. The computer program utilizes stochastic …
Recent Trends In The Frequency And Duration Of Global Floods, Nasser Najibi, Naresh Devineni
Recent Trends In The Frequency And Duration Of Global Floods, Nasser Najibi, Naresh Devineni
Publications and Research
Frequency and duration of floods are analyzed using the global flood database of the Dartmouth Flood Observatory (DFO) to explore evidence of trends during 1985–2015 at global and latitudinal scales. Three classes of flood duration (i.e., short: 1–7, moderate: 8–20, and long: 21 days and above) are also considered for this analysis. The nonparametric Mann–Kendall trend analysis is used to evaluate three hypotheses addressing potential monotonic trends in the frequency of flood, moments of duration, and frequency of specific flood duration types. We also evaluated if trends could be related to large-scale atmospheric teleconnections using a generalized linear model framework. …
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.