• Kyungpook Mathematical Journal
• /
• v.58 no.1
• /
• pp.67-79
• /
• 2018

In this paper, we present new generalized incomplete Pochhammer symbols and using this we introduce the extended generalized incomplete hypergeometric functions. We derive certain properties, generating functions and reduction formulas of these extended generalized incomplete hypergeometric functions. Special cases of this extended generalized incomplete hypergeometric functions are also discussed.

• Communications of the Korean Mathematical Society
• /
• v.32 no.2
• /
• pp.287-304
• /
• 2017

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] by means of the incomplete Pochhammer symbols $({\lambda};{\kappa})_{\nu}$ and $[{\lambda};{\kappa}]_{\nu}$, we first introduce incomplete Fox-Wright function. We then define the families of incomplete extended Hurwitz-Lerch Zeta function. We then systematically investigate several interesting properties of these incomplete extended Hurwitz-Lerch Zeta function which include various integral representations, summation formula, fractional derivative formula. We also consider an application to probability distributions and some special cases of our main results.

• Honam Mathematical Journal
• /
• v.36 no.3
• /
• pp.531-542
• /
• 2014

Recently, Srivastava et al. [18] introduced the incomplete Pochhammer symbol and studied some fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions. Here we introduce the incomplete Lauricella function ${\gamma}_D^{(n)}$ and ${\Gamma}_D^{(n)}$ of n variables, and investigate certain properties of the incomplete Lauricella functions, for example, their various integral representations, differential formula and recurrence relation, in a rather systematic manner. Some interesting special cases of our main results are also considered.

• Kyungpook Mathematical Journal
• /
• v.58 no.1
• /
• pp.19-35
• /
• 2018

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [30] and the second Appell function [6], we introduce here the incomplete Lauricella functions ${\gamma}^{(n)}_A$ and ${\Gamma}^{(n)}_A$ of n variables. We then systematically investigate several properties of each of these incomplete Lauricella functions including, for example, their various integral representations, finite summation formulas, transformation and derivative formulas, and so on. We provide relevant connections of some of the special cases of the main results presented here with known identities. Several potential areas of application of the incomplete hypergeometric functions in one and more variables are also pointed out.

• Journal of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.363-379
• /
• 2016

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] and the second Appell function [Appl. Math. Comput. 219 (2013), 8332-8337] by means of the incomplete Pochhammer symbols $({\lambda};{\kappa})_{\nu}$ and $[{\lambda};{\kappa}]_{\nu}$, we introduce here the family of the incomplete generalized ${\tau}$-hypergeometric functions $2{\gamma}_1^{\tau}(z)$ and $2{\Gamma}_1^{\tau}(z)$. The main object of this paper is to study these extensions and investigate their several properties including, for example, their integral representations, derivative formulas, Euler-Beta transform and associated with certain fractional calculus operators. Further, we introduce and investigate the family of incomplete second ${\tau}$-Appell hypergeometric functions ${\Gamma}_2^{{\tau}_1,{\tau}_2}$ and ${\gamma}_2^{{\tau}_1,{\tau}_2}$ of two variables. Relevant connections of certain special cases of the main results presented here with some known identities are also pointed out.

• The Korean Journal of Applied Statistics
• /
• v.24 no.4
• /
• pp.647-656
• /
• 2011

Incidence matrix is a useful tool for presenting incomplete block designs; however, it is inadequate to use only an incidence matrix in examining whether a certain incomplete block design becomes a balanced incomplete block design or not. We can use a structural matrix as a useful tool to show whether a certain incomplete block design becomes a balanced incomplete block design or not. We propose an augmented incidence matrix and ${\lambda}$ matrix as another tools for evaluating incomplete block designs. Through the augmented incidenc matrix and ${\lambda}$ matrix, we can ascertain whether a certain incomplete block design becomes a balance incomplete block design or not.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.551-568
• /
• 2000

We propose new parallelizable block incomplete factorization preconditioners for a symmetric block-tridiagonal H-matrix. Theoretical properties of these block preconditioners are compared with those of block incomplete factorization preconditioners for the corresponding comparison matrix. Numerical results of the preconditioned CG(PCG) method using these block preconditioners are compared with those of PCG method using a standard incomplete factorization preconditioner to see the effectiveness of the block incomplete factorization preconditioners.

• Journal of applied mathematics & informatics
• /
• v.8 no.3
• /
• pp.705-720
• /
• 2001

We propose a variant of parallel block incomplete factorization preconditioners for a symmetric block-tridiagonal H-matrix. Theoretical properties of these block preconditioners are compared with those of block incomplete factoriztion preconditioners for the corresponding somparison matrix. Numerical results of the preconditioned CG(PCG) method using these block preconditioners are compared with those of PCG using other types of block incomplete factorization preconditioners. Lastly, parallel computations of the block incomplete factorization preconditioners are carried out on the Cray C90.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.11 no.5
• /
• pp.441-447
• /
• 2001

In general, Rough Set theory is used for classification, inference, and decision analysis of incomplete data by using approximation space concepts in information system. Information system can include quantitative attribute values which have interval characteristics, or incomplete data such as multiple or unknown(missing) data. These incomplete data cause tole inconsistency in information system and decrease the classification ability in system using Rough Sets. In this paper, we present various types of incomplete data which may occur in information system and propose INcomplete information Processing System(INiPS) which converts incomplete information system into complete information system in using Rough Sets.

• Korean Journal of Cleft Lip And Palate
• /
• v.4 no.2
• /
• pp.51-68
• /
• 2001

Midfacial hypoplasia in patients with clefts of the lip and palate is considered to be the result of congenital dysmorphogenesis. And cleft lip and palate developes facial deformity, jaw abnormality, speech problem, which is most frequent hereditary deformity in maxillofacial region. So cleft lip and palate is characterized by midface deformity which shaws maxillary anterior nasal septal deviation and deformity. Our study describes congenital correlates of midfacial hypoplasia by examining the displacement of a normal complement of parts, a triangular tissue deficiency low on the lip border on the columellar side, and a linear deficiency and displacement in the line of the bilateral cleft lip. 15 patients with bilateral cleft lip and palate were taken impression before operation, but the patient who had other abnormalities and complications were excluded. Average age is 3.4 months and they were classified into both complete, both incomplete and complete & incomplete group. The obtained results were as follows 1. There were no differences on intercanthal width and canthal width between each of the groups. 2. Both complete group had longer lateral ala length than both incomplete group, but there were no differences between both complete group and complete side of com. & incom. group and both incomplete group and incomplete side of com. & incom. group. 3. Columella length was greater in both incomplete group than in both complete group, but there was no difference between both complete group and complete side of com. & incom. group and both incomplete group and incomplete side of com. & incom. group. 4. Both complete group had longer ala width & ala base width than both incomplete group had. But there were no differences between both complete group and complete side of com. & incom. group and both incomplete group and incomplete side of com. & incom. group. 5. There were no differences between each of the groups on upper lip length, but nose/mouth width ratio was greater in both complete group than in both incomplete group. 6. Pronasale(pm), subnasle(sn), la~rale superioris(ls), stomion(sto) points were located around the central vertical line of face but deviated to incomplete side in com. & incom. group. 7. Nasal tip protrusion was greater in both incomplete group and com. & incom. group than both complete group, but there was no difference between both incomplete group and com. & incom. group.