Related papers: Upside Down Numerical Equation, Bimagic Squares, a…
We present a lattice QCD determination of the average up-down, strange and charm quark masses based on simulations performed by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$ dynamical fermions. We simulated at three…
This paper deals with those positive integers N such that, for given integers g and k with 1< k<g, the base-g digits of N and kN appear in reverse order. Such N are called (g, k) reverse multiples. Anne Ludington Young, in 1992, developed a…
In this paper we give solutions of certain diophantine equations related to triangular and tetrahedral numbers and propose several problems connected with these numbers. The material of this paper was presented in part at the 11th…
Using computational techniques we derive six new upper bounds on the classical two-color Ramsey numbers: R(3,10) <= 42, R(3,11) <= 50, R(3,13) <= 68, R(3,14) <= 77, R(3,15) <= 87, and R(3,16) <= 98. All of them are improvements by one over…
In this paper, we prove that for $d=3,\dots,8$, every natural number can be written as $t_x+t_y+3t_z+dt_w$, where $x$, $y$, $z$, and $w$ are nonnegative integers and $t_k=k(k+1)/2$ $(k=0,1,2,\ldots)$ is a triangular number. Furthermore, we…
The purpose of this paper is to introduce the idea of triangular Ramsey numbers and provide values as well as upper and lower bounds for them. To do this, the combinatorial game Mines is introduced; after some necessary theorems about…
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
We study the so-called magic mixing angles for doubly heavy baryons. Defining that a magic mixing angle rotates states with definite $^{2S+1}(l_\lambda)_J$ to make them heavy-quark symmetric states, we derive the magic mixing angle only in…
A random jigsaw puzzle is constructed by arranging $n^2$ square pieces into an $n \times n$ grid and assigning to each edge of a piece one of $q$ available colours uniformly at random, with the restriction that touching edges receive the…
Binary black holes with spins that are aligned with the orbital angular momentum do not precess. However, post-Newtonian calculations predict that "up-down" binaries, in which the spin of the heavier (lighter) black hole is aligned…
In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic…
As an extension of Polya's classical result on random walks on the square grids ($\Z^d$), we consider a random walk where the steps, while still have unit length, point to different directions. We show that in dimensions at least 4, the…
For a set of distances $D$, a graph $G$ of order $n$ is said to be $D-$magic if there exists a bijection $f:V\rightarrow \{1,2, \ldots, n\}$ and a constant $k$ such that for any vertex $x$, $\sum_{y\in N_D(x)} f(y) =k$, where…
This note investigates the combinatorics of permutations underlying the NYT daily word game Waffle. It helps to solve Waffle games and helps to understand why some games are easy to solve while others are very hard. It shows that a perfect…
The geometry of rotations in dimensions 3, 4, and 5 is discussed using the matrix exponential map. Explicit closed formulas for the exponential of an antisymmetric matrix, as well as the logarithm of a rotation, are given for these…
Magic squares have always been and are still fascinating for many people, be it only because of their mathematical properties. Their origin is still but certain : we find no magic squares in Greece, and only a 3x3 one in China at the…
The effects of the finite charm quark mass on bottom quark mass determinations from $\Upsilon$ sum rules are examined in detail. The charm quark mass effects are calculated at next-to-next-to-leading order in the non-relativistic power…
We give a one dimensional octonionic representation of the different Clifford algebra Cliff(5,5)\sim Cliff(9,1), Cliff(6,6)\sim Cliff(10,2) and lastly Cliff(7,6)\sim Cliff(10,3) which can be given by (8x8) real matrices taking into account…
The present work looks at semiautomatic rings with automatic addition and comparisons which are dense subrings of the real numbers and asks how these can be used to represent geometric objects such that certain operations and…
A number system coding for the permutations generated by cyclic shift is described. The system allows to find the rank of a permutation given how it has been generated, and to determine a permutation given its rank. It defines a code…