Joohee Jeong

A note on the Analogue of Lebesgue-Radon-Nikodym theorem with respect to weighted p-adic q-measure on Z p

We give the analogue of the Lebesgue-Radon-Nikodym theorem with respect to a weighted p-adic q-measure on Zp. In a special case, when the weight qx is 1, we can derive the same result as Kim et al. (Abstr. Appl. Anal. 2011:637634, 2011). And if q=1, we have the same result as Kim (Russ. J. Math. Phys. 19:193-196, 2012).MSC:11B68, 11S80.

Some Identities Involving Euler Polynomials Arising from a Non-linear Differential Equation

We derive a family of non-linear differential equations from the generating functions of the Euler polynomials and study the solutions of these differential equations. Then we give some new and interesting identities and formulas for the Euler polynomials of higher order by using our non-linear differential equations.

A note on the Analogue of Lebesgue-Radon-Nikodym theorem with respect to weighted pZpp

We give the analogue of the Lebesgue-Radon-Nikodym theorem with respect to a weighted p-adic q-measure on Zp. In a special case, when the weight qx is 1, we can derive the same result as Kim et al. (Abstr. Appl. Anal. 2011:637634, 2011). And if q=1, we have the same result as Kim (Russ. J. Math. Phys. 19:193-196, 2012).MSC:11B68, 11S80.

A Note on the Lebesgue-Radon-Nikodym Theorem with respect to Weighted -adic Invariant Integral on ℤ

We will give the Lebesgue-Radon-Nikodym theorem with respect to weighted 𝑝-adic 𝑞-measure on ℤ𝑝. In special case, 𝑞=1, we can derive the same result as Kim, 2012; Kim et al., 2011.

Reduction of Hilbert-type proof systems to the if-then-else equational logic

We present a construction of the linear reduction of Hilbert type proof systems for propositional logic to if-then-else equational logic. This construction is an improvement over the same result found in [4] in the sense that the technique used in the construction can be extended to the linear reduction of first-order logic to if-then-else equational logic.

A note on the Analogue of Lebesgue-Radon-Nikodym theorem with respect to weighted p-adic q-measure on Z p Open image in new window

We give the analogue of the Lebesgue-Radon-Nikodym theorem with respect to a weighted p-adic q-measure on Zp. In a special case, when the weight qx is 1, we can derive the same result as Kim et al. (Abstr. Appl. Anal. 2011:637634, 2011). And if q=1, we have the same result as Kim (Russ. J. Math. Phys. 19:193-196, 2012).MSC:11B68, 11S80.

A New Approach to the Lebesgue-Radon-Nikodym Theorem. with respect to Weighted p-adic Invariant Integral on ℤ p

We will give a new proof of the Lebesgue-Radon-Nikodym theorem with respect to weighted p-adic q-measure on , using Mahler expansion of continuous functions, studied by the authors in 2012. In the special case, q = 1, we can derive the same result as in Kim, 2012, Kim et al, 2011.

Identities on the Bernoulli and Genocchi Numbers and Polynomials

We give some interesting identities on the Bernoulli numbers and polynomials, on the Genocchi numbers and polynomials by using symmetric properties of the Bernoulli and Genocchi polynomials.

Integral Formulae of Bernoulli and Genocchi Polynomials

Recently, some interesting and new identities are introduced in the work of Kim et al. (2012). From these identities, we derive some new and interesting integral formulae for Bernoulli and Genocchi polynomials.

A Note on the Lebesgue-Radon-Nikodym Theorem with respect to Weighted

We will give the Lebesgue-Radon-Nikodym theorem with respect to weighted 𝑝-adic 𝑞-measure on ℤ𝑝. In special case, 𝑞=1, we can derive the same result as Kim, 2012; Kim et al., 2011.