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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Determinism Of Stochastic Processes Through The Relationship Between The Heat Equation And Random Walks, Gurmehar Singh Makker
Determinism Of Stochastic Processes Through The Relationship Between The Heat Equation And Random Walks, Gurmehar Singh Makker
Publications and Research
We study the deterministic characteristics of stochastic processes through investigation of random walks and the heat equation. The relationship is confirmed by discretizing the heat equation in time and space and determining the probability distribution function for random walks in dimension d = 1, 2. The existence of the relationship is presented both through theoretical analysis and numerical computation.
Planck's And Callendar's Blackbody Radiation Formulas And Their Fitness To Experimental Data, Max Tran
Planck's And Callendar's Blackbody Radiation Formulas And Their Fitness To Experimental Data, Max Tran
Publications and Research
In this paper, we compare the blackbody radiation density formula obtained with classical physics by Hugh L Callendar and the formula obtained by Max Planck using quantization of energy. We use R and Maxima to analyze their fitness on coordinating experimental data and indicate some limitations with experiments in this area.
On Properties Of Distance-Based Entropies On Fullerene Graphs, Modjtaba Ghorbani, Matthias Dehmer, Mina Rajabi-Parsa, Abbe Mowshowitz, Frank Emmert-Streib
On Properties Of Distance-Based Entropies On Fullerene Graphs, Modjtaba Ghorbani, Matthias Dehmer, Mina Rajabi-Parsa, Abbe Mowshowitz, Frank Emmert-Streib
Publications and Research
In this paper, we study several distance-based entropy measures on fullerene graphs. These include the topological information content of a graph Ia(G), a degree-based entropy measure, the eccentric-entropy Ifs(G), the Hosoya entropy H(G) and, finally, the radial centric information entropy Hecc. We compare these measures on two infinite classes of fullerene graphs denoted by A12n+4 and B12n+6. We have chosen these measures as they are easily computable and capture meaningful graph properties. To demonstrate the utility of these measures, we investigate the Pearson correlation between them on the fullerene graphs.
Understanding Water Consumption And Energy Trends In New York City, Wen Yong Huang, Johann Thiel
Understanding Water Consumption And Energy Trends In New York City, Wen Yong Huang, Johann Thiel
Publications and Research
In this study, we will be using the NYC Open Data website to examine publicly available data sets on water and energy consumption in New York City. In particular, we will use various scientific programming and machine learning modules in Python to analyze and visualize trends in water and energy usage within the five boroughs.
On The Complexity Of Computing Galois Groups Of Differential Equations, Mengxiao Sun
On The Complexity Of Computing Galois Groups Of Differential Equations, Mengxiao Sun
Dissertations, Theses, and Capstone Projects
The differential Galois group is an analogue for a linear differential equation of the classical Galois group for a polynomial equation. An important application of the differential Galois group is that a linear differential equation can be solved by integrals, exponentials and algebraic functions if and only if the connected component of its differential Galois group is solvable. Computing the differential Galois groups would help us determine the existence of the solutions expressed in terms of elementary functions (integrals, exponentials and algebraic functions) and understand the algebraic relations among the solutions.
Hrushovski first proposed an algorithm for computing the differential …