• Journal of applied mathematics & informatics
• /
• v.32 no.5_6
• /
• pp.675-685
• /
• 2014

Suppose G is a simple graph. The irregularity of G, irr(G), is the summation of imb(e) over all edges $uv=e{\in}G$, where imb(e) = |deg(u)-deg(v)|. In this paper, we investigate the behavior of this graph parameter under some old and new graph operations.

• Kyungpook Mathematical Journal
• /
• v.50 no.4
• /
• pp.473-482
• /
• 2010

In the present paper we define a q-extension of the Leibniz rule for q-derivatives via Weyl type q-derivative operator. Expansions and summation formulae for the generalized basic hypergeometric functions of one and more variables are deduced as the applications of the main result.

• Honam Mathematical Journal
• /
• v.32 no.1
• /
• pp.61-71
• /
• 2010

The aim of this paper is to extend a number of transformation formulas for the four $X_4$, $X_5$, $X_7$, and $X_8$ among twenty triple hypergeometric series $X_1$ to $X_{20}$ introduced earlier by Exton. The results are derived from the generalized Kummer's theorem and Dixon's theorem obtained earlier by Lavoie et al..

• Journal of Advanced Marine Engineering and Technology
• /
• v.29 no.8
• /
• pp.877-882
• /
• 2005

This paper discusses the lateral vibration of a bar which has its tip free. The uniform bar has a solution by summation of some simple exponential functions But if its shape is not uniform, its solution could be by Bessel's function, or mathematical solution could not be existed. Enen if the solution of Bessel's function exists. as Bessel function is a series function. we must got the solution by numerical method Hereby the author Proposes the ununiform beam solution of the matrix method by Ritz's method. and Proposes a new deflection shape function.

• Bulletin of the Korean Mathematical Society
• /
• v.32 no.2
• /
• pp.329-336
• /
• 1995

Let $A_1, A_2, \ldots, A_n$ be a sequence of events on a given probability space and let $m_n$ be the number of those A's which occur. Put $S_{0,n} = 1$ and $$ S_{k,n} = \Sigma P(A_i_1 \cap A_i_2 \cap \cdots \cap A_i_k), (a \leq k)$$ where the summation is over all subscripts satisfying $1 \let i_1 < i_2 < \cdots < i_k \leq n$.

• Communications of the Korean Mathematical Society
• /
• v.31 no.2
• /
• pp.329-342
• /
• 2016

Motivated essentially by Brychkov's work [1], we evaluate some new integrals involving hypergeometric function and the logarithmic function (including those obtained by Brychkov[1], Choi and Rathie [3]), which are expressed explicitly in terms of Gamma, Psi and Hurwitz zeta functions suitable for numerical computations.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.345-354
• /
• 2020

In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of ₂𝜓₂ series $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a,c;q)_n}{(b,d;q)_n}}z^n$$ and Ramanujan's sum $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a;q)_n}{(b;q)_n}}z^n$$.

• 전기의세계
• /
• v.24 no.6
• /
• pp.97-101
• /
• 1975

The electrical neuronal model described in this paper simulates the most important functional properties of nerve cells. An model circuit incorporating many of the digital and analog properties of neurons is described. Having such properties as variable threshold level, action potential, summation, all-or-none output, absolute and relative refract oriness, and ingibition, it exhibits a considerable amount of functional equivalence to biological structures. This electrical neuronal model has utility not only for studying single unit properties but also for investigating group interactions. Such studies may be relevent to elucidation of neuronal network behavior.

• Korean Journal of Mathematics
• /
• v.12 no.2
• /
• pp.193-200
• /
• 2004

We shall introduce the notion of the windowed Fourier transform in $\mathbb{Q}_p$ and show that, for any given function $g{\in}L^2(\mathbb{Q}_p)$ of norm, the windowed Fourier transform of $f$ with respect to $g$ be a function of norms, and moreover be expressible to a summation form. The results obtained in this paper will be usable to the field of research in data compression for signal processing according to the following scheme.

• Honam Mathematical Journal
• /
• v.31 no.2
• /
• pp.167-176
• /
• 2009

The aim of this paper is to obtain three interesting results for reducibility of Kamp$\'{e}$ de $\'{e}$riet function. The results are derived with the help of contiguous Gauss's second summation formulas obtained earlier by Lavoie et al. The results obtained by Bailey, Rathie and Nagar follow special cases of our main findings.