• Journal of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.537-547
• /
• 2012

In this paper, we define a $p$, $q$-difference operator and obtain an explicit formula which is used to express the $p$, $q$-analogue of the unified generalization of Stirling numbers and its exponential generating function in terms of the $p$, $q$-difference operator. Explicit formulas for the non-central $q$-Stirling numbers of the second kind and non-central $q$-Lah numbers are derived using the new $q$-analogue of Newton's interpolation formula. Moreover, a $p$, $q$-analogue of Newton's interpolation formula is established.

• Proceedings of the IEEK Conference
• /
• 2002.07a
• /
• pp.26-29
• /
• 2002

Radial Basis Function (RBF) networks is known as efficient method in classification problems and function approximation. The basis function of RBF networks is usual adopted normal distribution like the Gaussian function. The output of the Gaussian function has the maximum at the center and decrease as increase the distance from the center. For learning of neural network, the method treating the limited area of input space is sometimes more useful than the method treating the whole of input space. The q-normal distribution is the set of probability density function include the Gaussian function. In this paper, we introduce the RBF networks with the basis function of q-normal distribution and actually approximate a function using the RBF networks.

• Journal of applied mathematics & informatics
• /
• v.36 no.1_2
• /
• pp.29-38
• /
• 2018

In this paper, we introduce a degenerate q-poly-Bernoulli numbers and polynomials include q-logarithm function. We derive some relations with this polynomials and the Stirling numbers of second kind and investigate some symmetric identities using special functions that are involving this polynomials.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.133-138
• /
• 2020

It is shown that each sequence lying sufficiently close in the hyperbolic sense to a Q^#_p-sequence for a meromorphic function f in the unit disc is also a Q^#_p-sequence for f.

• Journal of applied mathematics & informatics
• /
• v.38 no.5_6
• /
• pp.611-623
• /
• 2020

In this paper, we define a q-analogue of the poly-Euler numbers and polynomials which is generalization of the poly Euler numbers and polynomials including q-analogue of polylogarithm function. We also give the relations between generalized poly-Euler polynomials. Furthermore, we introduce zeta fuctions of Arakawa-Kaneko type and talk their properties and the relation with q-analogue of poly-Euler polynomials.

• Honam Mathematical Journal
• /
• v.45 no.3
• /
• pp.542-554
• /
• 2023

Given a real number α, the Lagrange number of α is the supremum of all real numbers L > 0 for which the inequality |α - p/q| < (Lq²)^-1 holds for infinitely many rational numbers p/q. All Lagrange numbers less than 3 can be arranged as a set {l_p/q : p/q ∈ ℚ ∩ [0, 1]} using the Farey index. The present paper considers a function C(α) devised from Sturmian words. We demonstrate that the function C(α) contains all information on Lagrange numbers less than 3. More precisely, we prove that for any real number α ∈ (0, 1], the value C(α) - C(0) is equal to the sum of all numbers 3 - l_p/q where the Farey index p/q is less than α.

• Communications of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.1175-1199
• /
• 2019

We construct a general bi-basic inverse series relation which provides extension to several q-polynomials including the Askey-Wilson polynomials and the q-Racah polynomials. We introduce a general class of polynomials suggested by this general inverse pair which would unify certain polynomials such as the q-extended Jacobi polynomials and q-Konhauser polynomials. We then emphasize on applications of the general inverse pair and obtain the generating function relations, summation formulas involving the associated polynomials and derive the p-deformation of some of the q-analogues of Riordan's classes of inverse series relations. We also illustrate the companion matrix corresponding to the general class of polynomials; this is followed by a chart showing the reducibility of the extended p-deformed Askey-Wilson polynomials as well as the extended p-deformed q-Racah polynomials.

• Korean Journal of Mathematics
• /
• v.31 no.2
• /
• pp.229-242
• /
• 2023

In this paper, we investigate the [p, q] - φ order and [p, q] - φ type of f₁ + f₁, ${\frac{f_1}{f_2}}$ and f₁ f₁, where f₁ and f₁ are analytic or meromorphic functions with the same [p, q]-φ order and different [p, q]-φ type in the unit disc. Also, we study the [p, q]-φ order and [p, q]-φ type of different f and its derivative. At the end, we investigate the relationship between two different [p, q] - φ convergence exponents of f. We extend some earlier precedent well known results.

• The KIPS Transactions:PartB
• /
• v.10B no.6
• /
• pp.587-592
• /
• 2003

Many real world control problems have continuous states and actions. When the state space is continuous, the reinforcement learning problems involve very large state space and suffer from memory and time for learning all individual state-action values. These problems need function approximators that reason action about new state from previously experienced states. We introduce Fuzzy Q-Map that is a function approximators for 1 - step Q-learning and is based on fuzzy clustering. Fuzzy Q-Map groups similar states and chooses an action and refers Q value according to membership degree. The centroid and Q value of winner cluster is updated using membership degree and TD(Temporal Difference) error. We applied Fuzzy Q-Map to the mountain car problem and acquired accelerated learning speed.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.14 no.2
• /
• pp.93-111
• /
• 2010

The purpose of this paper is to obtain new complexity results for a second-order cone optimization (SOCO) problem. We define a proximity function for the SOCO by a kernel function. Furthermore we formulate an algorithm for a large-update primal-dual interior-point method (IPM) for the SOCO by using the proximity function and give its complexity analysis, and then we show that the new worst-case iteration bound for the IPM is $O(q\sqrt{N}(logN)^{\frac{q+1}{q}}log{\frac{N}{\epsilon})$, where $q{\geqq}1$.