• Honam Mathematical Journal
• /
• v.46 no.2
• /
• pp.168-180
• /
• 2024

The main object of this article is to propose a unified extension of Bernoulli, Euler and Genocchi polynomials by means of a new family of mixed polynomials whose generating function is given in terms of generalized Bessel function. We also discuss here some fundamental properties of our introduced mixed polynomials by making use of the series arrangement technique. Furthermore, some conclusions of our present study are also pointed out in the last section.

• Journal of the Korean Mathematical Society
• /
• v.37 no.6
• /
• pp.915-927
• /
• 2000

This paper is concerned with degenerate Volterra equations Mu(t) + ∫(sub)0(sup)t k(t-s) Lu(s)ds = f(t) in Banach spaces both in the hyperbolic case, and the parabolic one. The key assumption is played by the representation of the underlying space X as a direct sum X = N(T) + R(T), where T is the bounded linear operator T = ML(sup)-1. Hyperbolicity means that the part T of T in R(T) is an abstract potential operator, i.e., -T(sup)-1 generates a C(sub)0-semigroup, and parabolicity means that -T(sup)-1 generates an analytic semigroup. A maximal regularity result is obtained for parabolic equations. We will also investigate the cases where the kernel k($.$) is degenerated or singular at t=0 using the results of Pruss[8] on analytic resolvents. Finally, we consider the case where $\lambda$ is a pole for ($\lambda$L + M)(sup)-1.

• Journal of Oral Medicine and Pain
• /
• v.21 no.1
• /
• pp.67-78
• /
• 1996

This study was performed to compare the TMJ sounds by means of vibration-related items by Sonopak such as integral, high integral, above 300/(0-300) ratio, peak amplitude, peak frequency and median frequency before and after occlusa1 splint therapy as well as counselling, physical modalities. For this study 22 patients with craniomandibular disorders (CMDs) were selected and examined by routine diagnostic procedure for CMDs including Transcranial and Panoramic radiographs and were classified into 3 CMDs subgroups : disc displacement with reduction, disc displacement without reduction, and degenerative joint disease. Visual analogue scale (VAS) about joint sound was recorded during treatment period and VAS treatment index (VAS Ti) was calculated from the VAS data and treatment duration. The author evaluated and compared treatment results by several parmeters such as symptom duration, timing of joint sound, parafunctional habits, trauma, and diagnostic classification. The obtained results were as follows : 1. Before the treatment, the highest value of peak amplitude was observed in disc displacement with reduction group and value of median frequency was highest in degenerative joint disease group. In addition the highest values of peak frequency and ratio ware observed in degenerative joint disease group, though they were not significant. Furthermore the lowest value of high integral was observed in disc displacement without reduction group and though it was not significant, value of integral was lowest in that group. 2. Among 3CMDs subgroups disc displacement with reduction group showed the significantly decreased value of high integral and degenerative joint disease group had the significantly decreased value of integral after conservative treatment including occlusal splint therapy. Conclusively conservative treatment including occlusal splint therapy vay be effective in the treatment of CMDs including TMJ sound. 3. Fair prognosis for conservative treatment was observed in acute group under 6 months than chronic group, 6 months over in symptom duration but there was no statistical difference. The result for conservative treatment was observed slightly poor in subjects with bruxism, clenching, unilateral chewing habit and trauma history but there were no statistical differences.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.11 no.6
• /
• pp.33-37
• /
• 1974

In this paper, the radiation characteristics for the array of a circular loop antenna is studied in moving media. The medium is assumed to be homogeneous, isotropic, and to move with a constant velocity much less than the speed of light. The integral equation for the current distribution is derived and the current functions is found by means of courier Series as a solution of the integral equation. The electric field is derived from the current on circular loop antenna and the Dyadic Green's Function in moving media. The numerical calculation of the electric field concerning to the two element antenna array,, in which one element is parasitic, is carried out. The field patterns are plotted from the computed values. As a result, the field patterns in moving media, compared with the patterns in stationary media, are found to decrease in the direction of media velocity and increase in the opposite direction, and the maximum directivity is shifted.

• 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 Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.7 no.2
• /
• pp.105-116
• /
• 1996

The design and analysis of the transversely fed EMC(electromagnetically coupled) microstrip dipole have been accomplished by using the integral equation and MOM(method of moment)in frequency domain in order to find the current distribution of the dipole. In this study, we proposed the possibilities for design and analysis of EMC micro-strip dipole array antenna by means of calculating the current distribution of each dipole directly using the FDTD(finite difference time domain) method. In this case, we applied the formulation which is the finite difference expression of the Maxwell's integral equation. From the current distribution of each dipole, we calculated the far field electric component and showed that the calculation process and running time was reduced with respect to the method which calculates the radiation field with surface electric and magnetic current density.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.9
• /
• pp.2423-2430
• /
• 1994

Several factors of the efficient combustion process are shape of combustion chamber, position of spark plug, turbulence flow and so on. the shape of combustion chamber and position of spark plug are constrained to geometrically, and then it could not make a change the shape easily. But the turlence flow in combustion chamber have a great influence on combustion phenomena, and which is much easier to control relatively. And since characteristics of turbulence flow would be very important to the stability of combustion and performances, This study is also essential to future engine-low emission and lean burn engine. This paper shows that the visualization of the turbulence flow of single cylinder engine by using 2way, $45^{\circ}$ inclined and 2 channel hot wire probe through the park plug hole. We also study the characteristics of turbulence flow by means of ensemble averaged mean velocity, turvulence intensity and integral length scale.

• Economic and Environmental Geology
• /
• v.18 no.1
• /
• pp.41-47
• /
• 1985

The filtering ability of $J_0$ and $J_1$ digital linear filters is compared by means of an adaptive linear filter. Any $J_0$ domain Hankel transform integral can be transformed mathematically into its corresponding $J_1$ domain integral. The apparent resistivities for any electrode configuration employed in resistivity soundings can be evaluated with a single $J_1$ filter. The $J_1$ filter usually has similar accuracy to, but shorter length than, the corresponding $J_0$ filter. The domain transformation from $J_0$ to $J_1$ enables us to use effective expressions of apparent resistivity, involving $J_1$ alone, not only for Schlumberger but also for dipole-dipole array.

• Structural Engineering and Mechanics
• /
• v.23 no.1
• /
• pp.63-74
• /
• 2006

In this paper, the scattering of harmonic elastic anti-plane shear waves by two collinear cracks in functionally graded materials is investigated by means of nonlocal theory. The traditional concepts of the non-local theory are extended to solve the fracture problem of functionally graded materials. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress field near the crack tips. To make the analysis tractable, it is assumed that the shear modulus and the material density vary exponentially with coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips.

• Structural Engineering and Mechanics
• /
• v.54 no.4
• /
• pp.607-622
• /
• 2015

This paper presents a comparative study of analytical method and finite element method (FEM) for analysis of a continuous contact problem. The problem consists of two elastic layers loaded by means of a rigid circular punch and resting on semi-infinite plane. It is assumed that all surfaces are frictionless and only compressive normal tractions can be transmitted through the contact areas. Firstly, analytical solution of the problem is obtained by using theory of elasticity and integral transform techniques. Then, finite element model of the problem is constituted using ANSYS software and the two dimensional analysis of the problem is carried out. The contact stresses under rigid circular punch, the contact areas, normal stresses along the axis of symmetry are obtained for both solutions. The results show that contact stresses and the normal stresses obtained from finite element method (FEM) provide boundary conditions of the problem as well as analytical results. Also, the contact areas obtained from finite element method are very close to results obtained from analytical method; disagree by 0.03-1.61%. Finally, it can be said that there is a good agreement between two methods.