• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.807-819
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• 2023

In 2019, Mathur and Solanki [7, 8] obtained a few transformation formulas for Appell, Horn and the Kampé de Fériet functions. Unfortunately, some of the results are well-known and very old results in literature while others are erroneous. Thus the aim of this note is to provide the results in corrected forms and some of the results have been written in more compact form.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.745-758
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• 2011

Generalizing the Burchnall-Chaundy operator method, the authors are aiming at presenting certain decomposition formulas for the chosen six Exton functions expressed in terms of Appell's functions $F_3$ and $F_4$, Horn's functions $H_3$ and $H_4$, and Gauss's hypergeometric function F. We also give some integral representations for the Exton functions $X_i$ (i = 6, 8, 14) each of whose kernels contains the Horn's function $H_4$.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.257-264
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• 2012

Exton introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ${\ldots}$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function ${\Psi}_1$, and a Humbert function ${\Phi}_2$. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function $X_8$, whose kernels include the Exton functions ($X_2$, $X_8$) itself, the Horn's function $H_4$, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.21 no.9
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• pp.1-11
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• 2022

Recently, there has been continuous technological development in the semiconductor industry, and semiconductor manufacturing technologies are being advanced and highly integrated. For this reason, ceramic material having excellent heat resistance, wear resistance, and conductivity are used as components in semiconductor manufacturing. Among them, the probe card's space transformer is used as ceramic material to prevent electronic signal noise during the electrical die sorting of semiconductor function testing. However, implementing a bulk-type space transformer with a thickness of 5.6 mm or more is challenging, and thus it is produced in a structure with a stacked ceramic film. The stacked space transformer has low productivity because it is difficult to ensure hole clogging and a precise shape. In this research, an ultrasonic horn is designed to manufacture a bulk-type ceramic space transformer through ultrasonic drilling. Vibration characteristics were analyzed according to the ultrasonic horn, and the natural frequency was measured.

• Communications of the Korean Mathematical Society
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• v.24 no.4
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• pp.517-521
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• 2009

The object of this note is to derive Padmanabham's transformation formula for Exton's triple hypergeometric series $X_8$ by using a different method from that of Padmanabham's. An interesting special case is also pointed out.

• Honam Mathematical Journal
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• v.27 no.4
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• pp.603-608
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• 2005

In 1999 and 2003, Padmanabham established two results (one each) for Exton's triple hypergeometric series $X_8$. We aim at showing that Exton's later result can be derived from his former one.

• Honam Mathematical Journal
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• v.32 no.3
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• pp.389-397
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• 2010

Exton introduced 20 distinct triple hypergeometric functions whose names are Xi (i = 1,$\ldots$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function $\Psi_2$, a Humbert function $\Phi_2$. The object of this paper is to present 25 (presumably new) integral representations of Euler types for the Exton hypergeometric function $X_5$ among his twenty $X_i$ (i = 1,$\ldots$, 20), whose kernels include the Exton function X5 itself, the Exton function $X_6$, the Horn's functions $H_3$ and $H_4$, and the hypergeometric function F = $_2F_1$.

• Journal of Korea Multimedia Society
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• v.3 no.4
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• pp.380-388
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• 2000

In computing the optical flow, Horn and Schunck's method which is a representative algorithm is based on differentiation. Therefore it is difficult to estimate the velocity for a large displacement by this algorithm. In this paper, we propose a method for estimating nonuniform motion from sequential images which is based on integral brightness constancy constraints. The equations which transform a source image to a target image are expressed as a function of the displacement field. If marginal effects can be neglected, the form of the transformation integral transform or orthogonal expansion can be determined from the expansion coefficients of the two images. The apparent displacement field is then computed iteratively by a projection method which utilities the functional derivatives of the linearized moment equations. We demonstrate that the performance of the orthogonal function transform on the data set of large motion.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.4
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• pp.490-498
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• 1993

A variety of methods for measuring the velocity from an image sequence use the relationship between the spatial and temporal gradients of image brightness function. In most situations, an additional constraint is required because the velocity is not determined uniquely by a above relationship. Horn and Schunch proposed a constraint that the velocity field should vary smoothly over the image. This requirement, however, forces the velocity field to vary smoothly even across motion boundaries. To complement this probe, Nagel introduced and 'oriented smoothness' constraint which restricts variations of velocity field only in directions with small or no variation of image brightness function. On the other hand, Paquin and Dubois proposed a different type of constraint that the velocity is constant in a small area of image. But, this constraint also creates difficulties at motion boundaries which large variations in velocity field often occur. We propose the method to overcome these difficulties by utilizing the information of discontinuities in image brightness function, and present the experimental results.

• International Journal of Oral Biology
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• v.37 no.3
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• pp.121-129
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• 2012

Previous clinical studies have demonstrated that gabapentin, a drug that binds to the voltage-gated calcium channel ${\alpha}2{\delta}1$ subunit proteins, is effective in the management of neuropathic pain, but there is limited evidence that addresses the participation of glial cells in the antiallodynic effects of this drug. The present study investigated the participation of glial cells in the anti-nociceptive effects of gabapentin in rats with trigeminal neuropathic pain produced by mal-positioned dental implants. Under anesthesia, the left mandibular second molar was extracted and replaced by a miniature dental implant to induce injury to the inferior alveolar nerve. Mal-positioned dental implants significantly decreased the air-puff thresholds both ipsilateral and contralateral to the injury site. Gabapentin was administered intracisternally beginning on postoperative day (POD) 1 or on POD 7 for three days. Early or late treatment with 0.3, 3, or 30 ${\mu}g$ of gabapentin produced significant anti-allodynic effect in the rats with mal-positioned dental implants. On POD 9, in the mal-positioned dental implants group, OX-42, a microglia marker, and GFAP, an astrocyte marker, were found to be up-regulated in the medullary dorsal horn, compared with the naive group. However, the intracisternal administration of gabapentin (30 ${\mu}g$) failed to reduce the number of activated microglia or astrocytes in the medullary dorsal horn. These findings suggest that gabapentin produces significant antinociceptive effects, which are not mediated by the inhibition of glial cell function in the medullary dorsal horn, in a rat model of trigeminal neuropathic pain.