Aeran Kim · Asian Journal of Research and Reviews in Physics · 2019
In this article we consider the two end-points of the string to be attached to D-brane with the different Born-Infeld field strength F and calculate the total momenta for the special case.
Aeran Kim · Asian Research Journal of Mathematics · 2019
In this paper we investigate the properties of the general linear recursive sequences started from the Lucas sequence and give an application to matrices.
Aeran Kim · Asian Research Journal of Mathematics · 2018
For a1, a2, , a6 we dene and mainly we obtain some convolution sums and etc.
Aeran Kim · Asian Research Journal of Mathematics · 2018
In this paper we evaluate the number of representations of n(∈ N) as a sum of four triangular numbers by simple method based on Jacobi's theta functions dened by
Aeran Kim · Asian Research Journal of Mathematics · 2018
We transform a zeta function to the alternative sum as and represent it as some series, for example etc., where (s)n = s(s + 1) ... (s + n-1), Re(s) > 1, and we obtain their formulas.
Aeran Kim · Physical Science International Journal · 2017
In this paper we consider the coherent states which play an important role in quantum optics, especially in laser physics and much work in this field. Here we connect the coherent states with the Lucas numbers and Fibonacci numbers.
Aeran Kim · Asian Research Journal of Mathematics · 2017
We focus on the summation of and express it as simple polynomials and find a relation between them.
Aeran Kim · Physical Science International Journal · 2017
In this paper we calculate the Bloch vector length with respect to the eigenvalues of the density matrix and the mixed states.
Aeran Kim · Asian Research Journal of Mathematics · 2017
In this paper we deduce the integer n satisfying Ln respectively after obtaining the Legendre-Jacobi symbol for (mod 4) with
Aeran Kim · Physical Science International Journal · 2016
In this paper we obtain some identities related to the Hamiltonian operator composed with momentum and position operators and Euler polynomials and confirm these properties through examples.
Aeran Kim · Asian Research Journal of Mathematics · 2016
For all natural number n we deduce binomial convolution sums formulae composed with Fibonacci numbers and Lucas numbers. Moreover we obtain those of similar convolution sums without a binomial symbol.
Aeran Kim · Asian Research Journal of Mathematics · 2016
In this article we construct some convolutions sums related to Fibonacci and Lucas numbers and obtain their generalized formulae.
Aeran Kim · Asian Research Journal of Mathematics · 2016
A formula expressing an in nite product as an infinite sum is called a product-to-sum identity. In this paper we try to consider a special product-to-sum as and so for integers r, u, a, b, c, x, y and z we deduce all solutions of (r, u, a, b, c, x, y, z) with r ≥ 0.
Aeran Kim · Journal of Advances in Mathematics and Computer Science · 2014
Originating from the convolution sum for n 2 N by Kim’s result, we try to induce the convolution sum formulae as therefore we obtain the desired results. Moreover we construct some various convolution sums and obtain their formulae
Aeran Kim · Journal of Advances in Mathematics and Computer Science · 2014
In this paper, we obtain the convolution sum formulae of Moreover we obtain some identities induced from the above convolution sums and we find a coefficients relation.
Aeran Kim · Journal of Advances in Mathematics and Computer Science · 2014
In this paper we obtain the convolution sum formulae of for n(∈ ) and an odd positive integer e and f. Moreover we obtain some identities induced from
Aeran Kim · Journal of Advances in Mathematics and Computer Science · 2014
In this paper we obtain some various convolution sum formulae especially, focusing on the form for and an odd positive integer e and f. Furthermore, we obtain some identities related to the convolution sums.
Aeran Kim · Journal of Advances in Mathematics and Computer Science · 2014
Aeran Kim, Keum Yeon Lee & Hwasin Park · Journal of Advances in Mathematics and Computer Science · 2014
In this paper, we are based on the Huard, Ou, Spearman and Williams’s generalization of Liouville’s Identity so we obtain and etc. Also, independently we attempt to consider the Liouville’s Identity, therefore as the application of his identity, we have the restricted combinato...
Aeran Kim · Journal of Advances in Mathematics and Computer Science · 2014
In [1] we can find some formulas of binomial combinatorial convolution sums. Starting from these formulas, we obtain various binomial combinatorial convolution sums.
Aeran Kim · Journal of Advances in Mathematics and Computer Science · 2014
We calculate some special convolution sums related to the odd divisors multiplied by the even divisors. Also according to the Ramanujan’s functions implying σ1(n), σ3(n), and σ5(n), we obtain various convolution formulas.
Aeran Kim · Journal of Advances in Mathematics and Computer Science · 2013
The convolution sum m<n=8 _3(m)_3(n - 8m) is evaluated for all n 2 N. This evaluation is used to determine the formulae of the convolution sums etc., and the number of representations of n through the sum of eight triangular numbers.
Aeran Kim · Journal of Advances in Mathematics and Computer Science · 2013
In [1] and [3] we can find some formulas of binomial combinatorial convolution sums involving divisor functions. Starting from these formulas, we obtain a multinomial combinatorial convolution sum.
Aeran Kim · Journal of Advances in Mathematics and Computer Science · 2013
In this paper, we study the summations P (a,b,c)EN3 (f(a + b) + f(b + c) + f(c + a)) and P(a;b;c;d)2N4 (f(a + b + c) + f(b + c + d) + f(c + d + a)). Especially, for the first summation we obtain some relations related to Bernoulli and Euler polynomials.