• Kyungpook Mathematical Journal
• /
• v.48 no.1
• /
• pp.155-163
• /
• 2008

This is an extended version of the paper [K] of the author. The average formulas on the circles and disks around arbitrary points of Nevanlinna counting functions of holomorphic self-maps of the unit disk, given in terms of the boundary values of the selfmaps, are shown to give another characterization of the whole class or a special subclass of inner functions in terms of Nevanlinna counting function in addition to the previous applications to Rudin's orthogonal functions.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.135-145
• /
• 2024

We consider a function-field analogue of Dirichlet series associated with the Goldbach counting function, and prove that it can, or cannot, be continued meromorphically to the whole plane. When it cannot, we further prove the existence of the natural boundary of it.

• Journal of the Korean Society for Precision Engineering
• /
• v.15 no.12
• /
• pp.97-105
• /
• 1998

The fiber oriented condition inside fiber reinforced composite material is a basic factor of mechanical properties of composite materials. It is very important to meausure the fiber orientation angle for the determination of molding conditions, mechanical characteristics, and the design of composite materials. In the work, the fiber orientation distribution of simulation figure plotted by PC is measured using image processing in order to examine the accuracy of intersection counting method. The fiber orientation function measured by intersection counting method using image processing is compared with the calculated fiber orientation function. The results show that the measured value of fiber orientation function using intersection counting method is lower than the calculated value, because the number of intersection between the scanning line and the fiber with smaller fiber aspect ratio is counted less than with larger fiber aspect ratio.

• Journal of the Korean Data and Information Science Society
• /
• v.25 no.1
• /
• pp.169-176
• /
• 2014

Counting processes are widely used in many fields, whose properties are determined by the intensity function. For estimation of the parameters of the intensity functions when the process is observed continuously over a fixed interval, the likelihood function is of interest. However in the literature there are only heuristic derivations and some results are not coincident. We thus in this note derive the likelihood function of the counting process in a rigorous way. So this note fill up a hole in derivation of the likelihood function.

• Communications for Statistical Applications and Methods
• /
• v.4 no.1
• /
• pp.281-292
• /
• 1997

In this paper we are concered with the counting processes with intersity function $g_n(t)$, where $g_n(t)$ not only depends on t but n. It is shown that under certain conditions the number of events in [0, t] follows a generalizes Poisson distribution. A counting process is also provided such that $g_i(t)$$\neq$$g_i(t)$ for i$\neq$j and the number of events in [0, t] has a transformed geometric distribution.

• The KIPS Transactions:PartB
• /
• v.12B no.2 s.98
• /
• pp.209-214
• /
• 2005

The use of protein interaction data is highly reliable for predicting functions to proteins without function in proteomics study. The computational studies on protein function prediction are mostly based on the concept of guilt-by-association and utilize large-scale interaction map from revealed protein-protein interaction data. This study compares graph-based approaches such as neighbor-counting and $\chi^2-statistics$ methods using protein-protein interaction data and proposes an approach that is effective in analyzing large-scale protein interaction data. The proposed approach is also based protein interaction map but sequence similarity and heuristic knowledge to make prediction results more reliable. The test result of the proposed approach is given for KDD Cup 2001 competition data along with those of neighbor-counting and $\chi^2-statistics$ methods.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.42 no.1
• /
• pp.19-28
• /
• 2017

Moments of stationary intervals and those of the counting process can be used for moment fittings of the point processes. As for the Markovian arrival processes, the moments of stationary intervals are given as a polynomial function of parameters whereas the moments of the counting process involve exponential terms. Therefore, moment fittings are more complicated with the counting process than with stationary intervals. However, in queueing network analysis, cross-correlation between point processes can be modeled more conveniently with counting processes than with stationary intervals. A Laplace-Stieltjies transform of the stationary intervals of MAP (3)s is recently proposed in minimal number of parameters. We extend the results and present the Laplace transform of the counting process of MAP (3)s. We also show how moments of the counting process such as index of dispersions for counts, IDC, and limiting IDC can be used for moment fittings. Examples of exact MAP (3) moment fittings are also presented on the basis of moments of stationary intervals and those of the counting process.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1996.04a
• /
• pp.556-560
• /
• 1996

In order to examine thd accuracy of intersection counting method, the fiber orientation distribution of simulation figure platted by PC is measured using image processing. The fiber orientation distribution obtained by an image processing method is compared with those by the intersection counting method. The result shows that the errors of the intersection counting method are large because its measurement is made by the cross point of the scanning line and the fiber.

• Ocean and Polar Research
• /
• v.35 no.3
• /
• pp.239-247
• /
• 2013

Digital image processing is a process to analyze a large volume of information on digital images. In this study, Artemia hatching rate was measured by automatically classifying and counting cysts and larvae based on color imaging data from cyst hatching experiments using an image processing technique. The Artemia hatching rate estimation consists of a series of processes; a step to convert the scanned image data to a binary image data, a process to detect objects and to extract their shape information in the converted image data, an analysis step to choose an optimal discriminant function, and a step to recognize and classify the objects using the function. The function to classify Artemia cysts and larvae is optimally estimated based on the classification performance using the areas and the plan-form factors of the detected objects. The hatching rate using the image data obtained under the different experimental conditions was estimated in the range of 34-48%. It was shown that the maximum difference is about 19.7% and the average root-mean squared difference is about 10.9% as the difference between the results using an automatic counting (this study) and a manual counting were compared. This technique can be applied to biological specimen analysis using similar imaging information.

• Korean Journal of Optics and Photonics
• /
• v.8 no.4
• /
• pp.353-355
• /
• 1997

A single molecule detection system, which consists of confocal fluorescence microscope and single photon counter, has been used to observe the dye concentration dependence of photon counting rate. With increasing concentration, a saturation effect of counting is observed and demonstrated on the basis of the dead time of photon detector. The equations presented here show the relations between the counting rate and some parameters such as probe volume, quantum efficiency of detector, and fluorescence photon number entered onto detector. The signal-to-noise ratio is also discussed briefly.