• Journal of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1207-1220
• /
• 2018

The generalized hyperharmonic numbers $h^{(m)}_n(k)$ are defined by means of the multiple harmonic numbers. We show that the hyperharmonic numbers $h^{(m)}_n(k)$ satisfy certain recurrence relation which allow us to write them in terms of classical harmonic numbers. Moreover, we prove that the Euler-type sums with hyperharmonic numbers: $$S(k,m;p):=\sum\limits_{n=1}^{{\infty}}\frac{h^{(m)}_n(k)}{n^p}(p{\geq}m+1,\;k=1,2,3)$$ can be expressed as a rational linear combination of products of Riemann zeta values and harmonic numbers. This is an extension of the results of Dil [10] and $Mez{\ddot{o}}$ [19]. Some interesting new consequences and illustrative examples are considered.

• Proceedings of the KIEE Conference
• /
• 2005.05a
• /
• pp.27-29
• /
• 2005

Using a generalized regression neural network, etch microtrenching was modeled. All neurons in the pattern layer were equipped with multi-factored spreads and their complex effects on the prediction performance were optimized by means of a genetic algorithm. For comparison, GRNN model was constructed in a conventional way. Comparison result revealed that GA-GRNN model was more accurate than GRNN model by about 30%. The microtrenching data were collected during the etching of silicon oxynitride film and the etch process was characterized by a statistical experimental design.

• Proceeding of KASS Symposium
• /
• 2008.05a
• /
• pp.89-94
• /
• 2008

This paper deals with the method of self-equilibrium stress mode analysis of cable dome structures. From the point of view of analysis, cable dome structure is a kind of unstable truss structure which is stabilized by means of introduction of prestressing. The prestress must be introduced according to a specific proportion among different structural member and it is determined by an analysis called self-equilibrium stress mode analysis. The mathematical equation involved in the self-equilibrium stress mode analysis is a system of linear equations which can be solved numerically by adopting the concept of Moore-Penrose generalized inverse. The calculation of the generalized inverse is carried out by rank factorization method. This method involves a parameter called epsilon which plays a critical role in self-equilibrium stress mode analysis. It is thus of interest to investigate the range of epsilon which produces consistent solution during the analysis of self-equilibrium stress mode.

• Structural Engineering and Mechanics
• /
• v.19 no.4
• /
• pp.459-475
• /
• 2005

This paper deals with a novel application of the Generalized Differential Quadrature (G.D.Q.) method to the linear elastic static analysis of isotropic rotational shells. The governing equations of equilibrium, in terms of stress resultants and couples, are those from Reissner-Mindlin shear deformation shell theory. These equations, written in terms of internal-resultants circular harmonic amplitudes, are first put into generalized displacements form, by use of the strain-displacements relationships and the constitutive equations. The resulting systems are solved by means of the G.D.Q. technique with favourable precision, leading to accurate stress patterns.

• Structural Engineering and Mechanics
• /
• v.40 no.2
• /
• pp.279-295
• /
• 2011

A solution of space curved bars with generalized Winkler soil found by means of Transfer Matrix Method is presented. Distributed, concentrated loads and imposed strains are applied to the beam as well as rigid or elastic boundaries are considered at the ends. The proposed approach gives the analytical and numerical exact solution for circular beams and rings, loaded in the plane or perpendicular to it. A well-approximated solution can be found for general space curved bars with complex geometry. Elastic foundation is characterized by six parameters of stiffness in different directions: three for rectilinear springs and three for rotational springs. The beam has axial, shear, bending and torsional stiffness. Numerical examples are given in order to solve practical cases of straight and curved foundations. The presented method can be applied to a wide range of problems, including the study of tanks, shells and complex foundation systems. The particular case of box girder distortion can also be studied through the beam on elastic foundation (BEF) analogy.

• East Asian mathematical journal
• /
• v.17 no.1
• /
• pp.135-146
• /
• 2001

Several families of infinite series were summed recently by means of certain operators of fractional calculus(that is, calculus of derivatives and integrals of any real or complex order). In the present sequel to this recent work, it is shown that much more general classes of infinite sums can be evaluated without using fractional calculus. Some other related results are also considered.

• Journal of the Korean Professional Engineers Association
• /
• v.29 no.2
• /
• pp.71-79
• /
• 1996

This paper evaluates the clustering performance of a neural network and a statistical method. Algorithms which are used in this paper are the GLVQ(Generalized Loaming vector Quantization) for a neural method and the k -means algorithm for a statistical clustering method. For comparison of two methods, we calculate the Rand's c statistics. As a result, the mean of c value obtained with the GLVQ is higher than that obtained with the k -means algorithm, while standard deviation of c value is lower. Experimental data sets were the Fisher's IRIS data and patterns extracted from handwritten numerals.

• Journal of Mechanical Science and Technology
• /
• v.16 no.8
• /
• pp.1072-1078
• /
• 2002

The constrained motion requires the determination of constraint force acting on unconstrained systems for satisfying given constraints. Most of the methods to decide the force depend on numerical approaches such that the Lagrange multiplier method, and the other methods need vector analysis or complicated intermediate process. In 1992, Udwadia and Kalaba presented the generalized inverse method to describe the constrained motion as well as to calculate the constraint force. The generalized inverse method has the advantages which do not require any linearization process for the control of nonlinear systems and can explicitly describe the motion of holonomically and/or nongolonomically constrained systems. In this paper, an explicit equation to describe the constrained motion is derived by minimizing the performance index, which is a function of constraint force vector, with respect to the constraint force. At this time, it is shown that the positive-definite weighting matrix in the performance index must be the inverse of mass matrix on the basis of the Gauss's principle and the derived differential equation coincides with the generalized inverse method. The effectiveness of this method is illustrated by means of two numerical applications.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.35 no.5C
• /
• pp.415-422
• /
• 2010

In this paper, we derive exact closed-form formulas, in terms of Meijer's G-function, for the ergodic capacity of space-time block codes (STBCs) from generalized linear complex orthogonal designs (GLCODs) and generalized coordinate interleaved orthogonal designs (GCIODs) in quasi-static frequency-nonselective i.i.d. Nakagami-m fading channels. The derived analytical results show an excellent agreement with Monte-Carlo simulation results. Thus, a useful means for analyzing and predicting the ergodic capacity performance of STBCs from GLCODs or GCIODs can be provided in various antenna configurations and different channel conditions without extensive Monte-Carlo simulations. We present some numerical results to verify the accuracy of the derived formulas.

• Journal of the Chungcheong Mathematical Society
• /
• v.5 no.1
• /
• pp.103-110
• /
• 1992

In this paper, T. Kawata's result[2] is generalized, by means of Beurling's norm, in the case of periodic stochastic processes of the second order which belong to Lipschitz class.