Three related topics on the periodic tables of elements [PDF]
A large variety of periodic tables of the chemical elements have been proposed. It was Mendeleev who proposed a periodic table based on the extensive periodic law and predicted a number of unknown elements at that time. The periodic table currently used worldwide is of a long form pioneered by Werner in 1905. As the first topic, we describe the work of
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C^1-generic billiard tables have a dense set of periodic points [PDF]
We prove that the set of periodic points of a generic C^1-billiard table is dense in the phase space.
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A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networks [PDF]
We present a simple and effective method for representing periodic functions and enforcing exactly the periodic boundary conditions for solving differential equations with deep neural networks (DNN). The method stems from some simple properties about function compositions involving periodic functions. It essentially composes a DNN-represented arbitrary
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From the Mendeleev periodic table to particle physics and back to the periodic table [PDF]
We briefly describe in this paper the passage from Mendeleev's chemistry (1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and particle physics (from 1953 to 2006). We show how the consideration of symmetries, largely used in physics since the end of the 1920's, gave rise to a new format of the periodic table in the 1970's. More
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Period Error Estimation for the Kepler Eclipsing Binary Catalog [PDF]
The Kepler Eclipsing Binary Catalog (KEBC)describes 2165 eclipsing binaries identified in the 115 deg^2 Kepler Field based on observations from Kepler quarters Q0, Q1, and Q2. The periods in the KEBC are given in units of days out to six decimal places but no period errors are provided.
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Periodic Table of Geometric Numbers [PDF]
Perhaps the most significant, if not the most important, achievements in chemistry and physics are the Periodic Table of the Elements in Chemistry and the Standard Model of Elementary Particles in Physics. A comparable achievement in mathematics is the Periodic Table of Geometric Numbers discussed here.
arxiv
Deep-Learning Estimation of Band Gap with the Reading-Periodic-Table Method and Periodic Convolution Layer [PDF]
We verified that the deep learning method named reading periodic table introduced by ref. Deep Learning Model for Finding New Superconductors, which utilizes deep learning to read the periodic table and the laws of the elements, is applicable not only for superconductors, for which the method was originally applied but also for other problems of ...
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Period changes in the RR Lyrae stars of NGC 6171 (M107) [PDF]
Based on photometric data obtained between 1935 and 2017, $O-C$ diagrams were built for 22 RR Lyrae stars in the globular cluster NGC 6171, leading to the discovery of secular period changes in 4 variables for which we have calculated their period change rates $\beta$.
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Long and Short Periodic Billiard Trajectories in the Regular Pentagon [PDF]
In any periodic direction on the regular pentagon billiard table, there exists two combinatorially different billiard paths, with one longer than the other. For each periodic direction, McMullen asked if one could determine whether the periodic trajectory through a given point is long, short, or a saddle connection.
arxiv
An Alternate Graphical Representation of Periodic table of Chemical Elements [PDF]
Periodic table of chemical elements symbolizes an elegant graphical representation of symmetry at atomic level and provides an overview on arrangement of electrons. It started merely as tabular representation of chemical elements, later got strengthened with quantum mechanical description of atomic structure and recent studies have revealed that ...
arxiv