• Journal of Applied and Pure Mathematics
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• v.5 no.5_6
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• pp.407-414
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• 2023

In this article we continue the study of smooth Picard singular integral operators that started in [2], see there chapters 10-14. This time the foundation of our research is a trigonometric Taylor's formula. We establish the convergence of our operators to the unit operator with rates via Jackson type inequalities engaging the first modulus of continuity. Of interest here is a residual appearing term. Note that our operators are not positive. Our results are pointwise and uniform.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.377-381
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• 2005

We present a convenient recursive formula for the sums of alternating harmonic series of odd order. The recursion is obtained by expanding in Fourier series certain elementary functions.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.10a
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• pp.387-394
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• 1999

Artificial Neural Network (ANN) is a computational model inspired by the structure and operations of the brain. It is massively parallel system consisting of a large number of highly interconnected and simple processing units. The purpose of this paper is to verify the applicability of ANN to predict experimental results through the use of measured experimental data. Although there have been accumulated data based on hysteretic characteristics of structural element with cyclic loading tests, it is difficult to directly apply them for the analysis of elastic and plastic response. Thus, simple models with mathematical formula such as Bi-Linear Model, Ramberg-Osgood Model, Degrading Tri Model, Takeda Model, Slip type Model, and etc, have been used. To verify the practicality and capability of this study, ANN is adapted to several models with mathematical formula using numerical data To show the efficiency of ANN in nonlinear analysis, it is important to determine the adequate input and output variables of hysteretic models and to minimize an error in ANN process. The application example is Beam-Column joint test using the ANN in modeling of the linear and nonlinear hysteretic behavior of structure.

• Communications for Statistical Applications and Methods
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• v.25 no.3
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• pp.321-328
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• 2018

In clinical trials with repeated measurements, the time-averaged difference (TAD) may provide a more powerful evaluation of treatment efficacy than the rate of changes over time when the treatment effect has rapid onset and repeated measurements continue across an extended period after a maximum effect is achieved (Overall and Doyle, Controlled Clinical Trials, 15, 100-123, 1994). The sample size formula has been investigated by many researchers for the evaluation of TAD in two treatment groups. For the evaluation of TAD in multi-arm trials, Zhang and Ahn (Computational Statistics & Data Analysis, 58, 283-291, 2013) and Lou et al. (Communications in Statistics-Theory and Methods, 46, 11204-11213, 2017b) developed the sample size formulas for continuous outcomes and count outcomes, respectively. In this paper, we derive a sample size formula to evaluate the TAD of the repeated binary outcomes in multi-arm trials using the generalized estimating equation approach. This proposed sample size formula accounts for various correlation structures and missing patterns (including a mixture of independent missing and monotone missing patterns) that are frequently encountered by practitioners in clinical trials. We conduct simulation studies to assess the performance of the proposed sample size formula under a wide range of design parameters. The results show that the empirical powers and the empirical Type I errors are close to nominal levels. We illustrate our proposed method using a clinical trial example.

• Nuclear Engineering and Technology
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• v.46 no.4
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• pp.481-488
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• 2014

An analysis of the uncertainty quantification related to LBLOCA using the Monte-Carlo calculation has been performed and compared with the tolerance level determined by the Wilks' formula. The uncertainty range and distribution of each input parameter associated with the LOCA phenomena were determined based on previous PIRT results and documentation during the BEMUSE project. Calulations were conducted on 3,500 cases within a 2-week CPU time on a 14-PC cluster system. The Monte-Carlo exercise shows that the 95% upper limit PCT value can be obtained well, with a 95% confidence level using the Wilks' formula, although we have to endure a 5% risk of PCT under-prediction. The results also show that the statistical fluctuation of the limit value using Wilks' first-order is as large as the uncertainty value itself. It is therefore desirable to increase the order of the Wilks' formula to be higher than the second-order to estimate the reliable safety margin of the design features. It is also shown that, with its ever increasing computational capability, the Monte-Carlo method is accessible for a nuclear power plant safety analysis within a realistic time frame.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.3
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• pp.245-258
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• 2012

ILM(incremental launching method) is a way of construction, installing a girder producing spot behind the abutment, making the bridge girder infilled with concrete continuously and launching with using by jack. The superstructure of the bridge constructed by this method is temporarily located on the center of the span and the supporting points under construction. Therefore, the sections are structurally undergone maximum positive moment, maximum negative moment, and maximum shear force arising from self weight. On the other hand, launching nose is attached to the front of the girder to decrease the cantilever effect. The magnitude of this temporary stress creating on the upper section is dependent upon the launching nose's characteristics. This study has proposed an analysis formula simplified on the assumption that the launching nose section is a quasi-equivalent section(rigid; equivalent section, weight; tapered section) in order to ensure the accuracy of the analysis formula and improve its usage with reference to the interaction between the launching nose and the upper section; and a prismatic analysis formula modified by displacing a diaphragm's weight by a concentrated load in order to improve the accuracy of the existing analysis formula that assumes the launching nose section as the equivalent section. To judge the accuracy and usage of two analysis formulas proposed, we have compared and analyzed computational structural analysis programs and existing analysis formulas based on actual ILM bridge data. As a result, all of two reveal the superior accuracy and also their usage has been improved by the simplification of analysis formulas.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.123-130
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• 2002

A general formulation for shape design sensitivity analysis over three dimensional beam structure is developed based on a variational formulation of the beam in linear elasticity. Sensitivity formula is derived based on variational equations in cartesian coordinates using the material derivative concept and adjoint variable method for the displacement and Von-Mises stress functionals. Shape variation is considered for the beam shape in general 3-dimensional direction as well as for the orientation angle of the beam cross section. In the sensitivity expression, the end points evaluation at each beam segment is added to the integral formula, which are summed over the entire structure. The sensitivity formula can be evaluated with generality and ease even by employing piecewise linear design velocity field despite the bending model is fourth order differential equation. For the numerical implementation, commercial software ANSYS is used as analysis tool for the primal and adjoint analysis. Once the design variable set is defined using ANSYS language, shape and orientation variation vector at each node is generated by making finite difference to the shape with respect to each design parameter, and is used for the computation of sensitivity formula. Several numerical examples are taken to show the advantage of the method, in which the accuracy of the sensitivity is evaluated. The results are found excellent even by employing a simple linear function for the design velocity evaluation. Shape optimization is carried out for the geometric design of an archgrid and tilted bridge, which is to minimize maximum stress over the structure while maintaining constant weight. In conclusion, the proposed formulation is a useful and easy tool in finding optimum shape in a variety of the spatial frame structures.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.183-192
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• 1996

The least squares cross validated bandwidth is the mini-mizer of the corss validation function for choosing the smooth parame-ter of a kernel density estimator. It is a completely automatic method but it requires inordinate amounts of computational time. We present a convenient formula for calculation of the cross validation function when the kernel function is a symmetric polynomial with finite sup-port. Also we suggest an algorithm for finding global minima of the crass validation function.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.10a
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• pp.11-18
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• 1996

Inelastic buckling stress of Welded Thin-Walled Steel Sections was investigated by - using Spline Finite Strip Method. Several types of membrane residual stress and nonlinear stress-strain relationship were considered to produce reasonable fits to test results. A simple formula for the inelastic local buckling stress of welded sections was also proposed and compared with Korean Standard Specifications for Highway Bridges.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1405-1417
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• 2018

The aim of this work is to introduce several different volume computational methods of graph polytopes associated with various types of finite simple graphs. Among them, we obtained the recursive volume formula (RVF) that is fundamental and most useful to compute the volume of the graph polytope for an arbitrary finite simple graph.