Related papers: Sums of Cubes in Quaternion Rings
The concept of QCD sum rules is extended to bound states composed of particles with finite mass such as scalar quarks or strange quarks. It turns out that mass corrections become important in this context. The number of relevant corrections…
The Gauss Circle Problem concerns finding asymptotics for the number of lattice point lying inside a circle in terms of the radius of the circle. The heuristic that the number of points is very nearly the area of the circle is surprisingly…
We compute the limit of tangents of an arbitrary surface. We obtain as a byproduct an embedded version of Jung's desingularization theorem for surface singularities with finite limits of tangents.
On the Waring's problems for matrices over a commutative ring, there are some trace conditions provided for matrices eligibly expressed as a sum of $k$-th powers with $k=2,3,4,5,6,7,8$ in several literatures. In this paper, we provide the…
We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is A_5+A_1.
We compute the dynamical degrees of certain compositions of reflections in points on a smooth cubic fourfold. Our interest in these computations stems from the irrationality problem for cubic fourfolds. Namely, we hope that they will…
In the current paper we are seeking P1(y),P2(y),P3(y) with the highest possible degree polynomials with integer coefficients, and Q(y) via the lowest possible degree polynomial, such that P1(y)^3+P2(y)^3+P3(y)^3=Q(y). Actually, the solution…
In the space of marked group, we determine the structure of groups which are limit points of the set of all generalized quaternion groups.
The diameter of the Cayley graph of the Rubik's Cube group is the fewest number of turns needed to solve the Cube from the hardest initial configuration. For the 2$\times$2$\times$2 Cube, the diameter is 11 in the half-turn metric, 14 in…
It has been recently suggested that the dynamics of a quantum spin system may provide a natural mechanism for transporting quantum information. We show that one dimensional rings of qubits with fixed (time-independent) interactions,…
We show the 3 by 3 magic square of squares problem equivalent to solving quartic polynomials with certain factorization constraints over an abelian extension of the rationals. We analyze a particular case in which said extension is assumed…
In this paper, cyclic codes are established over some finite quaternion integer rings with respect to the quaternion Mannheim distance, and de- coding algorithm for these codes is given.
In this paper, we present a new method for solving standard quaternion equations. Using this method we reobtain the known formulas for the solution of a quadratic quaternion equation, and provide an explicit solution for the cubic…
We propose one and a half criteria for determining how many measurements are needed to quantify entanglement reliably. We base these criteria on Bayesian analysis of measurement results, and apply our methods to four-qubit entanglement, but…
The new necessary and sufficient affine invariant conditions for the existence and for determining the number of centers for general quadratic system are pointed out. These conditions correspond to the partition of 12-dimensional…
In this paper, the composition of Bhargava's cubes is generalized to the ring of integers of a number field of narrow class number one, excluding the case of totally imaginary number fields.
In this paper, we will present a new iterative construction for the auxiliary equation of Waring's problem, which seems a little simpler than the one of so called "smooth numbers" in papers [4] and [8], and give same upper bounds of G(k) as…
In this paper, we give a uniform upper bound on the rational points of bounded height provided by conics in a cubic surface. For this target, we give a generalized version of the global determinant method of Salberger by Arakelov geometry.
We summarize previous work on $\bar b \bar bud$ four-quark systems in the Born-Oppenheimer approximation and discuss first steps towards an extension to the theoretically more challenging $b\bar b u\bar d$ system. Strategies to identify a…
Functions of several quaternion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the $\tilde \partial $-equations are studied. Moreover, quaternion Stein manifolds are…