We introduce and consider a certain probability question involving elementary number theory and the likelihood that a fixed prime will appear in a certain recursively defined factorization of an integer. We derive several convergent infinite products...
We investigate the vacuum properties of a massless scalar field theory in constrained spatial geometry, namely, the instantaneous appearance of a thick Dirichlet boundary inside a one-dimensional (1D) Dirichlet cavity and divides it into two parts. O...
We study the universal PGL_n$character variety over M_g whose fiber over a point [C] is the space of PGL_n-local systems on the curve C. We use nonabelian Hodge theory and properties of Saito's mixed Hodge modules to show that the Leray-Serre spectra...
The purpose of these notes is to give a categorical presentation/analysis of homotopy type theory. The notes are incomplete as they stand (October 2017). The chapter on univalent tribes is missing. The references are not always connected to the text....
This is the first of the proposed sets of notes to be published in the website Gonit Sora (http://gonitsora.com). The notes will hopefully be able to help the students to learn their subject in an easy and comprehensible way. These notes are aimed at...
The collective behavior of the SL(2,R) covariant brane states of non-critical c=1 string theory found in a previous work, is studied in the Fermi liquid approximation. It is found that such states mimick the coset WZW model, whereas only by further...
Recent microscopic calculation based on the density functional theory predicts long-lived superheavy elements in a variety of shapes, including spherical, axial and triaxial configurations. Only when N=184 is approached one expects superheavy nucle...
The claim that at the so-called Planck scale our current physics breaks down and a new theory of quantum gravity is required is ubiquitous, but the evidence is shakier than the confidence of those assertions warrants. In this paper, I survey five arg...
We introduce Multiplicative Modular Nim (MuM), a variant of Nim in which the traditional nim-sum is replaced by heap-size multiplication modulo m. We establish a complete theory for this game, beginning with a direct, Bouton-style analysis for prime...
Sep 1, 2020 · For example, if $X \neq \emptyset$ and $W \neq \emptyset$ and $X \cap W = \emptyset$, and $f$ is any constant function, then the left part is empty, but the right part is not.
Proof \begin {align*} f (E\cup F)&=\ {f (x):x\in E \cup F\}\\ &=\ {f (x):x\in E \text { or } F\}\\ &=\ {f (x):x\in E \text { or } f (x):x\in F\}\\ &=f (E)\cup f (F) \end {align*} I feel there is something wrong with the …
We consider eventually positive operator semigroups and study the question whether their eventual positivity is preserved by bounded perturbations of the generator or not. We demonstrate that eventual positivity is not stable with respect to large po...
The eventual paracanonical map was introduced by Barja, Pardini, and Stoppino in order to prove refined Severi-type inequalities. We study the general structures of the eventual paracanonical maps by generic vanishing theory. In particular, we obtain...
The one loop 3-point vertex functions of QCD in the maximal abelian gauge (MAG) are evaluated at the fully symmetric point at one loop. As a consequence the theory is renormalized in the various momentum (MOM) schemes which are defined by the trivale...
In classical physics, calculating the slack of a hanging chain is a problem that has attracted interest. This study aims to solve this problem through experiment and theory. When the length and distance of both the ends of a hanging chain are given,...
We consider minimal immersions in MxR. We study existence and uniqueness of associate and conjugate isometric immersions to a given minimal surface. We use the theory of univalent harmonic map between surfaces. Then we study the geometry of associa...
Gravitational wave science is on the verge of direct observation of the waves predicted by Einstein's General Theory of Relativity and opening the exciting new field of gravitational wave astronomy. In the coming decades, ultra-sensitive arrays of gr...
We develop and study the hydrodynamic theory of flocking with autochemotaxis. This describes large collections of self-propelled entities all spontaneously moving in the same direction, each emitting a substance which attracts the others (e.g., ants)...
We develop the hydrodynamic theory of dry, polar ordered, active matter (``flocking") with autochemotaxis; i.e., self-propelled entities moving in the same direction, each emitting a substance which attracts the others (e.g., ants). We find that suff...
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