We introduce two new packages, Nemo and Hecke, written in the Julia programming language for computer algebra and number theory. We demonstrate that high performance generic algorithms can be implemented in Julia, without the need to resort to a low-...
The Brunn-Minkowski theory in convex geometry concerns, among other things, the volumes, mixed volumes, and surface area measures of convex bodies. We study generalizations of these concepts to Borel measures with density in $\mathbb{R}^n$-- in parti...
Laplace formulated the mathematical theory of interparticulate forces which could be applied to mechanical, thermal, and optical phenomena. This theory was replaced in the 1820s, but its …
Within the class of ontological interpretations of quantum theory where a physical system comprises a particle and a field (wavefunction) guiding it, an empty wave is a segment of the wavefunction not containing the particle. We examine the impact of...
In this paper, graph theory is used to explore the musical notion of tonal modulation, in theory and application. We define (pivot) modulation graphs based on the common scales used in popular music. Properties and parameters of these graphs are disc...
We summarize some of the main ideas and results around symplectic field theory, from its early inception up to recent and ongoing developments....
https://dissentfromdarwin.org/ Sign Today to show the Scientific Community contests the Theory of Evolution. https://dissentfromdarwin.org/scientists/ https://dissentfromdarwin.org/resources-for-s...
We use bordered Floer theory to study properties of twisted Mazur pattern satellite knots $Q_{n}(K)$. We prove that $Q_n(K)$ is not Floer homologically thin, with two exceptions. We calculate the 3-genus of $Q_{n}(K)$ in terms of the twisting paramet...
Using bordered Floer theory, we construct an invariant $\widehat{\mathit{HFO}}(Y^{\text{orb}})$ for $3$-orbifolds $Y^{\text{orb}}$ with singular set a knot that generalizes the hat flavor $\widehat{\mathit{HF}}(Y)$ of Heegaard Floer homology for clos...
Following his observation the author has described in the papers [1] to [4] the formation of a Lightning Ball (LB)with the help of a new theory of symmetry breaking of the vortex ring. In the frame of this theory he emphasizes the primordial rule of...
We formulate and prove a Conner-Floyd isomorphism for the algebraic K-theory of arbitrary qcqs derived schemes. To that end, we study a stable $\infty$-category of non-$\mathbb A^1$-invariant motivic spectra, which turns out to be equivalent to the $...
The masses and vertex functions of heavy and heavy-light mesons, described as quark-antiquark bound states, are calculated with the Covariant Spectator Theory (CST). We use a kernel with an adjustable mixture of Lorentz scalar, pseudoscalar, and vect...
Since in coupled-cluster (CC) theory ground-state and excitation energies are eigenvalues of a non-Hermitian matrix, these energies can in principle take on complex values. In this paper we discuss the appearance of complex energy values in CC calcul...
This paper presents the general theory of canonical transformations of coordinates in quantum mechanics. First, the theory is developed in the formalism of phase space quantum mechanics. It is shown that by transforming a star-product, when passing t...
To appear in Theory and Practice of Logic Programming (TPLP) Bound Founded Answer Set Programming (BFASP) is an extension of Answer Set Programming (ASP) that extends stable model semantics to numeric variables. While the theory of BFASP is defined...
The naive calculation of black hole evaporation makes the thermal emission depend on the arbitrary high frequency behaviour of the theory where the theory is certainly wrong. Using the sonic analog to black holes-- dumb holes-- I show numerically t...
The Sleeping Beauty Problem remains a paradoxical problem that penetrates multiple disciplines that include probability theory, self-locating belief, decision theory, cognitive science, the philosophy of mathematics and science. It asks the credence...
We study the time-periodic version of Evans approach to weak KAM theory. Evans minimization problem is equivalent to a first oder mean field game system. For the mechanical Hamiltonian we prove the existence of smooth solutions. We introduce the corr...
We prove a formula expressing the $K$-theoretic log Gromov-Witten invariants of a product of log smooth varieties $V \times W$ in terms of the invariants of $V$ and $W$. The proof requires introducing log virtual fundamental classes in $K$-theory and...
In numerical computations of response properties of electronic systems, the standard model is Kohn-Sham density functional theory (KS-DFT). Here we investigate the mathematical status of the simplest class of excitations in KS-DFT, HOMO-LUMO excitati...