• The Pure and Applied Mathematics
• /
• v.8 no.2
• /
• pp.127-135
• /
• 2001

The main object of this paper is to present a transformation formula for a finite series involving $_3F_2$ and some identities associated with the binomial coefficients by making use of the theory of Legendre polynomials $P_{n}$(x) and some summation theorems for hypergeometric functions $_pF_q$. Some integral formulas are also considered.

• Communications of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.619-630
• /
• 2018

In this paper, we obtain a (p, q)-extension of the Whittaker function $M_{k,{\mu}}(z)$ together with its integral representations, by using the extended confluent hypergeometric function of the first kind ${\Phi}_{p,q}(b;c;z)$ [recently extended by J. Choi]. Also, we give some of its main properties, namely the summation formula, a transformation formula, a Mellin transform, a differential formula and inequalities. In addition, our extension on Whittaker function finds interesting connection with the Laguerre polynomials.

• Geophysics and Geophysical Exploration
• /
• v.21 no.2
• /
• pp.112-124
• /
• 2018

Ocean-bottom seismic survey is a seismic acquisition technique which measures data by installing 4-component receiver on the sea floor. It can produce more improved data in quality than any other acquisition techniques. In the ocean-bottom seismic survey, however, the number of receivers is limited due to high cost. Since only a small number of receivers are used for acquisition, ocean-bottom seismic data may suffer from discontinuities of events over traces, which can result in spatial aliasing. In this paper, we implemented Kirchhoff migration using mirror-imaging algorithm to improve the quality of ocean-bottom seismic image. In order to implement the mirror imaging algorithm, the seismograms should be separated into up-going and down-going wavefields and the down-going wavefield should be used for migration. In this paper, we use the P-Z summation method to separate the wavefield. Numerical examples show that the migration results using mirror imaging algorithm have wider illumination than the conventional migration, especially in the shallow layers.

• Structural Engineering and Mechanics
• /
• v.2 no.1
• /
• pp.95-112
• /
• 1994

This paper describes the formulation and application of a dynamic model for a conventional rail track subjected to arbitary loading functions that simulate wheel/rail impact forces. The rail track is idealized as a periodic elastically coupled beam system resting on a Winkler foundation. Modal parameters of the track structure are first obtained from the natural vibration characteristics of the beam system, which is discretized into a periodic assembly of a specially-constructed track element and a single beam element characterized by their exact dynamic stiffness matrices. An equivalent frequency-dependent spring coefficient representing the resilient, flexural and inertial characteristics of the rail support components is introduced to reduce the degrees of freedom of the track element. The forced vibration equations of motion of the track subjected to a series of loading functions are then formulated by using beam bending theories and are reduced to second order ordinary differential equations through the use of mode summation with non-proportional modal damping. Numerical examples for the dynamic responses of a typical track are presented, and the solutions resulting from different rail/tie beam theories are compared.

• The Journal of Korean Academy of Prosthodontics
• /
• v.25 no.1
• /
• pp.17-40
• /
• 1987

The purpose of this study was to clarify the effect of clasp design on abutment tooth adjacent to a distal extension base under the influence by the location of functional loading. The RPI clasp, the Akers clasp and the combination clasp were selected for evaluation. Tests were performed at 10Kg, 20Kg, 30Kg loads on the buccal, central, lingual, mesial and distal positions of loading platform of each mandibular distal extension partial denture. The laser reflexion method was used for three dimensional measurement of abutment movement, which is possible to measure precisely without contact. The movement in the mesiodistal(X), buccolingual(Y), and occlusoapical(Z) directions and the rotational movement(R) were measured, and in addition, the total movement (SV) as expressed by the three dimensional summation vector independent of direction was calculated. The data were analyzed using Student t-test, p<.05. The following results were obtained from this study; 1. Clasp design did not generally affect the direction of abutment tooth movement except the movement in an undesirable occlusal direction in case of the Akers clasp and the combination clasp. 2. The greater the load on the prosthesis, the greater was the abutment tooth movement, and the direction of abutment tooth movement was affected by positional loading. 3. Each prosthesis was dislodged from the test base under the small amount of load in the distal load position, and the buccal loading showed the greatest abutment tooth movement under the maximum load. 4. RPI clasp was evaluated as the most favorable design.