• Honam Mathematical Journal
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• v.34 no.1
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• pp.113-124
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• 2012

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_A$.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.137-145
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• 2012

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_B$.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.863-870
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• 2019

In this paper, we obtain the enumeration results on the number of linear extensions of diamond posets. We find the recurrence relations and exponential generating functions for the number of linear extensions of diamond posets. We also get some results for the volume of graph polytope associated with bipartite graphs which are underlying graphs of diamond posets.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.99-110
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• 2022

The main object of this paper is to provide necessary and sufficient conditions for the generalized Struve functions of first kind to be in the classes 𝒮(k, λ) and 𝒞(k, λ). Furthermore, we give conditions for the integral operator 𝓛(m, c, z) = ∫^z₀(2 - u_p(t))dt to be in the class 𝒞^*(k, λ). Several corollaries and consequences of the main results are also considered.

• The Pure and Applied Mathematics
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• v.19 no.1
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• pp.43-57
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• 2012

By simply splitting the hypergeometric Saran function $F_E$ into eight parts, we show how some useful and generalized relations between $F_E$ and Srivas- tava's hypergeometric function $F^{(3)}$ can be obtained. These main results are shown to be specialized to yield certain relations between functions $_0F_1$, $_1F_1$, $_0F_3$, ${\Psi}_2$, and their products including different combinations with different values of parameters and signs of variables.

• Korean Journal of Mathematics
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• v.8 no.1
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• pp.73-86
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• 2000

We study the Sobolev spaces to the generalized Sobolev spaces $H^s_{\mathcal{G}}$ of exponential type based on the Silva space $\mathcal{G}$ and investigate its properties such as imbedding theorem and structure theorem. In fact, the imbedding theorem says that for $s$ > 0 $u{\in}H^s_{\mathcal{G}}$ can be analytically continued to the set {$z{\in}\mathbb{C}^n{\mid}{\mid}Im\;z{\mid}$ < $s$}. Also, the structure theorem means that for $s$ > 0 $u{\in}H^{-s}_{\mathcal{G}}$ is of the form $$u={\sum_{\alpha}\frac{s^{{|\alpha|}}}{{\alpha}!}D^{\alpha}g{\alpha}$$ where $g{\alpha}$'s are square integrable functions for ${\alpha}{\in}\mathbb{N}^n_0$. Moreover, we introduce a classes of symbols of exponential type and its associated pseudo-differential operators of exponential type, which naturally act on the generalized Sobolev spaces of exponential type. Finally, a generalized Bessel potential is defined and its properties are investigated.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.586-592
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• 1999

We investigate the characteristic of 소데 responses of the Manabe standard form which is used recently for design of the controller. We obtain some theorems and these theorems have the properties of the relationship between the roots of the polynomial and the stability indices which are used for the Manabe standard form. The Manabe standard form has the following properties: The sum of the squal to zero, the sum of the reciprocal of the squared roots is greater than zero and the parameter $\tau$ is the negative value of the sum of the reciprocal of the roots. We compare the step responses of the Manabe standard form with those of the ITAE form, the dead beat response and Bessel forms. We choose the 6th order closed loop polynomial and keep the same settling time for the four forms. Under these conditions we find that the Manabe standard form have faster 90% rising time than the Bessel and dead beat response. We see that the ITAE, bessel and dead beat responses have some overshoot, whereas the Manabe standard form has none. We also compare the Manabe form with the other three forms for the controller design using the pole assignment technique. If the open loop transfer function is a type-1 system (transfer functions having one integrator), then, for the closed loop system associated with the open loop transfer function, the steady state error of the unit ramp input is obtained in terms of the parameter $\tau$ of the Manabe standard form.

• Communications for Statistical Applications and Methods
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• v.21 no.1
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• pp.81-91
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• 2014

This study derives the characteristic functions of (multivariate/generalized) t distributions without contour integration. We extended Hursts method (1995) to (multivariate/generalized) t distributions based on the principle of randomization and mixtures. The derivation methods are relatively straightforward and are appropriate for graduate level statistics theory courses.

• Structural Engineering and Mechanics
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• v.20 no.2
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• pp.209-223
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• 2005

A new method for deriving analytical solution of the annular elastic plate on elastic foundation under axisymmetric loading is presented. The formulation is based on application of Hankel integral transforms and Bessel functions' properties in the corresponding boundary-value problem. A representative example is studied and the obtained solution is compared with published numerical results indicating excellent agreement.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.3
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• pp.141-149
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• 2010

The aim of this work is to determine the quasi-static thermal stresses of an infinitely long circular cylinder having constant initial temperature under steady-state field. The arbitrary heat flux is applied on the lower surface and the upper surface of the cylinder is at initial temperature. The fixed circular edge is thermally insulated. The results are obtained in series form in terms of Bessel's functions. These have been computed numerically and illustrated graphically.