inSTEMM Journal https://journal.stemm.global/index.php/instemm <p><em><strong>inSTEMM Journal </strong></em>is a multidisciplinary, peer-reviewed, open access journal showcasing cutting edge research across all major scientific, technological, and engineering disciplines. The journal is both free to publish and free to read (gold open access compliant).</p> <p><em>inSTEMM Journal </em>is the flagship journal of the <a href="https://stemm.global/">STEMM Global Scientific Society</a> – the only truly international scientific society across all STEMM disciplines. Central to the <em>inSTEMM</em> mission is the promotion of interdisciplinary exchange of ideas, knowledge, and discovery to maximise the benefits and impact of scientific endeavour.</p> <p><em>inSTEMM journal</em> publishes articles of any length that make a scientifically valid and valuable contribution to any field within the broad remit of science, technology, engineering, mathematics, and medicine.</p> <p><strong>Current Special Issues open for submission:</strong><br /><a href="https://journal.stemm.global/index.php/instemm/issue/view/expinmat">Experiments in Mathematics</a></p> <p><a href="https://journal.stemm.global/index.php/instemm/issue/view/smartnano">Smart Nanomaterials</a></p> STEMM Global Scientific Society en-US inSTEMM Journal 2753-6939 Eigenvalue Density, Li's Positivity, and the Critical Strip https://journal.stemm.global/index.php/instemm/article/view/23 <p class="p1">We rewrite the zero-counting formula within the critical strip of the Riemann zeta function as a cumulative density distribution;this subsequently allows us to formally derive an integral expression for the Li coefficients associated with the Riemann Xi-function which, in particular, indicate that their positivity criterion is obeyed, whereby entailing the criticality of the non-trivial zeros. We conjecture the validity of this and related expressions without the need for the Riemann Hypothesis and also offer a physical interpretation of the result and discuss the Hilbert-Polya approach.</p> Yang-Hui He Vishnu Jejjala Djordje Minic Copyright (c) 2022 inSTEMM Journal https://creativecommons.org/licenses/by-sa/4.0 2022-07-15 2022-07-15 1 S1 1 14 10.56725/instemm.v1iS1.23 On Fields over Fields https://journal.stemm.global/index.php/instemm/article/view/9 <p>We investigate certain arithmetic properties of field theories. In particular, we study the vacuum structure of supersymmetric gauge theories as algebraic varieties over number fields of finite characteristic. Parallel to the Plethystic Programme of counting the spectrum of operators from the syzygies of the complex geometry, we construct, based on the zeros of the vacuum moduli space over finite fields, the local and global Hasse-Weil zeta functions, as well as develop the associated Dirichlet expansions. We find curious dualities wherein the geometrical properties and asymptotic behaviour of one gauge theory is governed by the number theoretic nature of another.</p> Yang-Hui He Copyright (c) 2022 inSTEMM Journal https://creativecommons.org/licenses/by-sa/4.0 2022-07-15 2022-07-15 1 S1 15 46 10.56725/instemm.v1iS1.9 An Elementary End of the Periodic Table https://journal.stemm.global/index.php/instemm/article/view/6 <p>Using the Planck scale as an absolute bound of half-life, we give a quick estimate, in the manner of Feynman's fine-structure method, of the highest possible atomic number. We find, upon simple extrapolation, that element 168 would constitute the end of the Periodic Table and its isotope with atomic weight 411, being the most stable. These are remarkably close to current best estimates obtained from sophisticated and much more involved Hartree-Fock calculations.</p> Yang-Hui He Stavros Garoufalidis Copyright (c) 2022 inSTEMM Journal https://creativecommons.org/licenses/by-sa/4.0 2022-07-15 2022-07-15 1 S1 47 49 10.56725/instemm.v1iS1.6 Erland Samuel Bring's "Transformation of Algebraic Equations" https://journal.stemm.global/index.php/instemm/article/view/7 <p>We translate Erland Samuel Bring's treatise Meletemata quaedam Mathematica circa Transformationem Aequationum Alebraicarum (Some selected mathematics on the Transformation of Algebraic Equations) written as his Promotionschrift at the University of Lund in 1786, from its Latin into English, with modern mathematical notation.<br>Bring (1736 - 98) made important contributions to algebraic equations and obtained the canonical form x^5+px+q = 0 for quintics before Jerrard, Ruffini and Abel. In due course, he realized the significance of the projective curve which now bears his name: the complete intersection of the homogeneous Fermat polynomials of degrees 1,2,3 in CP^4.</p> Yang-Hui He John McKay Alexander Chen Copyright (c) 2022 inSTEMM Journal https://creativecommons.org/licenses/by-sa/4.0 2022-07-15 2022-07-15 1 S1 50 60 10.56725/instemm.v1iS1.7