• Korean Journal of Mathematics
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• 제26권1호
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• pp.87-101
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• 2018

The purpose of this paper is to define a new class of hyperholomorphic functions spaces, which will be called $F^{\alpha}_{{\omega},G}$(p, q, s) type spaces. For this class, we characterize hyperholomorphic weighted ${\alpha}$-Bloch functions by functions belonging to $F^{\alpha}_{{\omega},G}$(p, q, s) spaces under some mild conditions. Moreover, we give some essential properties for the extended weighted little ${\alpha}$-Bloch spaces. Also, we give the characterization for the hyperholomorphic weighted Bloch space by the integral norms of $F^{\alpha}_{{\omega},G}$(p, q, s) spaces of hyperholomorphic functions. Finally, we will give the relation between the hyperholomorphic ${\mathcal{B}}^{\alpha}_{{\omega},0}$ type spaces and the hyperholomorphic valued-functions space $F^{\alpha}_{{\omega},G}$(p, q, s).

• 호남수학학술지
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• 제36권3호
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• pp.531-542
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• 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.

• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.245-256
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• 2018

In the paper, we introduce some new classes of generalized logh-convex functions in the first sense and in the second sense. We establish Hermite-Hadamard type inequality for different classes of generalized convex functions. It is shown that the classes of generalized log h-convex functions in both senses include several new and known classes of log h convex functions. Several special cases are also discussed. Results proved in this paper can be viewed as a new contributions in this area of research.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.435-446
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• 2018

Using the theory of combinatoric convolution sums, we establish some arithmetic identities involving Liouville functions and restricted divisor functions. We also prove some relations involving restricted divisor functions and Stirling numbers of the first kind for divisor functions.

• 대한수학회논문집
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• 제32권4호
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• pp.835-850
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• 2017

A remarkably large number of special functions (such as the Gamma and Beta functions, the Gauss hypergeometric function, and so on) have been investigated by many authors. Motivated the works of both works of both Burchnall and Chaundy and Chaundy and very recently, Brychkov and Saad gave interesting generalizations of Appell type functions. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present some new differential formulas for the generalized Appell's type functions ${\kappa}_i$, $i=1,2,{\ldots},18$ by considering the product of two $_4F_3$ functions.

• 대한수학회논문집
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• 제33권4호
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• pp.1285-1301
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• 2018

This paper is devoted to the study of $Tur{\acute{a}}n$-type inequalities for some well-known special functions such as Gauss hypergeometric functions, generalized complete elliptic integrals and confluent hypergeometric functions which are derived by using a new form of the Cauchy-Bunyakovsky-Schwarz inequality. We also apply these inequalities for some sample of interest such as incomplete beta function, incomplete gamma function, elliptic integrals and modified Bessel functions to obtain their corresponding $Tur{\acute{a}}n$-type inequalities.

• Kyungpook Mathematical Journal
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• 제52권2호
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• pp.109-136
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• 2012

We aim at presenting certain unexpected functional relations among various hypergeometric functions of one or several variables (for example, see the identities in Corollary 5) by making use of Carlson's method employed in his work (Some extensions of Lardner's relations between $_0F_3$ and Bessel functions, SIAM J. Math. Anal. 1(2)(1970), 232-242).

• Structural Engineering and Mechanics
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• 제4권5호
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• pp.469-484
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• 1996

Green's functions are obtained in exact closed-forms for the elastic fields in bi-material elastic solids with slipping interface and differing transversely isotropic properties induced by concentrated point and ring force vectors. For the concentrated point force vector, the Green functions are expressed in terms of elementary harmonic functions. For the concentrated ring force vector, the Green functions are expressed in terms of the complete elliptic integral. Numerical results are presented to illustrate the effect of anisotropic bi-material properties on the transmission of normal contact stress and the discontinuity of lateral displacements at the slipping interface. The closed-form Green's functions are systematically presented in matrix forms which can be easily implemented in numerical schemes such as boundary element methods to solve elastic problems in computational mechanics.

• Journal of the Optical Society of Korea
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• 제18권2호
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• pp.101-109
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• 2014

In this paper, four apodization functions are proposed for silicon-on-insulator (SOI) strip waveguides with sidewall-corrugated gratings. The effects of apodization functions on the full width at half maximum (FWHM), the side-lobe level, and the reflectivity of the reflection spectrum are studied using the coupled-mode theory (CMT) and the transfer-matrix method (TMM). The results show that applying proposed apodization functions creates very good filtering characteristics. Among investigated apodized waveguides, the apodization functions of Polynomial and z-power have the best performance in reducing side-lobes, where the side-lobe oscillations are entirely removed. Four functions are also used for precise adjustment of the bandwidth. Simulation results show that the minimum and maximum values of the FWHM are 0.74 nm and 8.48 nm respectively. In some investigated functions, changing the apodization parameters decreases the reflectivity which is compensated by increasing the grating length.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제5권4호
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• pp.339-346
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• 2005

Artificial potential field (APF) is a widely used method for local path planning of autonomous mobile robot. So far, many different types of APF have been implemented. Once the artificial potential functions are selected, how to choose appropriate parameters of the functions is also an important work. In this paper, a detailed analysis is given on how to choose proper parameters of artificial functions to eliminate free path local minima and avoid collision between robots and obstacles. Two kinds of potential functions: Gaussian type and Quadratic type of potential functions are used to solve the above local minima problem respectively. To avoid local minima occurred in realistic situations such as 1) a case that the potential of the goal is affected excessively by potential of the obstacle, 2) a case that the potential of the obstacle is affected excessively by potential of the goal, the design guidelines for selecting appropriate parameters of potential functions are proposed.