• Honam Mathematical Journal
• /
• v.30 no.4
• /
• pp.733-741
• /
• 2008

Let T be Gauss transformation on the unit interval defined by T (x) = ${\frac{1}{x}}$ where {x} is the fractional part of x. Gauss transformation is closely related to the continued fraction expansions of real numbers. We show that almost every x is mod M normal number of Gauss transformation with respect to intervals whose endpoints are rational or quadratic irrational. Its connection to Central Limit Theorem is also shown.

• Kyungpook Mathematical Journal
• /
• v.28 no.2
• /
• pp.185-196
• /
• 1988

We study existence of polynomial integrating factors and solutions F(x, y)=c of first order nonlinear differential equations. We characterize the homogeneous case, and give algorithms for finding existence of and a basis for polynomial solutions of linear difference and differential equations and rational solutions or linear differential equations with polynomial coefficients. We relate singularities to nature of the solution. Solution of differential equations in closed form to some degree might be called more an art than a science: The investigator can try a number of methods and for a number of classes of equations these methods always work. In particular integrating factors are tricky to find. An analogous but simpler situation exists for integrating inclosed form, where for instance there exists a criterion for when an exponential integral can be found in closed form. In this paper we make a beginning in several directions on these problems, for 2 variable ordinary differential equations. The case of exact differentials reduces immediately to quadrature. The next step is perhaps that of a polynomial integrating factor, our main study. Here we are able to provide necessary conditions based on related homogeneous equations which probably suffice to decide existence in most cases. As part of our investigations we provide complete algorithms for existence of and finding a basis for polynomial solutions of linear differential and difference equations with polynomial coefficients, also rational solutions for such differential equations. Our goal would be a method for decidability of whether any differential equation Mdx+Mdy=0 with polynomial M, N has algebraic solutions(or an undecidability proof). We reduce the question of all solutions algebraic to singularities but have not yet found a definite procedure to find their type. We begin with general results on the set of all polynomial solutions and integrating factors. Consider a differential equation Mdx+Ndy where M, N are nonreal polynomials in x, y with no common factor. When does there exist an integrating factor u which is (i) polynomial (ii) rational? In case (i) the solution F(x, y)=c will be a polynomial. We assume all functions here are complex analytic polynomial in some open set.

• Earthquakes and Structures
• /
• v.2 no.2
• /
• pp.171-187
• /
• 2011

Rational scaling of design earthquake ground motions for tall buildings is essential for safer, risk-based design of tall buildings. This paper provides the structural designers with an insight for more rational scaling based on drift and input energy demands. Since a resonant sinusoidal motion can be an approximate critical excitation to elastic and inelastic structures under the constraint of acceleration or velocity power, a resonant sinusoidal motion with variable period and duration is used as an input wave of the near-field and far-field ground motions. This enables one to understand clearly the relation of the intensity normalization index of ground motion (maximum acceleration, maximum velocity, acceleration power, velocity power) with the response performance (peak interstory drift, total input energy). It is proved that, when the maximum ground velocity is adopted as the normalization index, the maximum interstory drift exhibits a stable property irrespective of the number of stories. It is further shown that, when the velocity power is adopted as the normalization index, the total input energy exhibits a stable property irrespective of the number of stories. It is finally concluded that the former property on peak drift can hold for the practical design response spectrum-compatible ground motions.

• Journal of Educational Research in Mathematics
• /
• v.25 no.3
• /
• pp.263-279
• /
• 2015

The introduction of real numbers is one of the most difficult steps in the teaching of school mathematics since the mathematical justification of the extension from rational to real numbers requires the completeness property. The author elucidated what questions about real numbers can be unanswered as the "institutional didactic void" in school mathematics defining real numbers as the union of the rational and irrational numbers. The pre-service teachers' explanations on the extension from rational to real numbers and the raison d'$\hat{e}$tre of arbitrary non-recurring decimals showed the superficial and fragmentary understanding of real numbers. Connecting school mathematics to university mathematics via the didactic void, the author discussed how pre-service teachers could break the illusion of transparency about the real number.

• Korean Journal of Remote Sensing
• /
• v.21 no.2
• /
• pp.135-143
• /
• 2005

RPC(Rational Polynomial Camera) models have become the replacement model of choice for a number of high resolution satellite imagery providers. RPCs(Rational Polynomial Coefficients) provide a compact accurate representation of the ground to image geometry, allowing users to perform full photogrammetric processing of satellite imagery including block adjustment, 3D feature extraction and orthorectification. This paper presents an algorithm for 3D feature extraction using downhill simpler method which requires only function evaluations, not derivatives. The algorithm was implemented as an executable software program and tested using stereo IKONOS images of Seoul city. The results showed that the proposed algorithm was fast and accurate enough to be used as a practical method for the 3D feature extraction from stereo images with RPCs.

• Journal of the Korean Institute of Rural Architecture
• /
• v.11 no.1
• /
• pp.47-56
• /
• 2009

According to the user recognizing, the propose of this study is to establish the systematic church-design and the plan of rational process. When the plan of church design is rational come out, the local community will be risen and there is the possibility which will raise the essential function of church construction and design. The results from the study are as follow. Firstly, the area of the front-window and the number of the external entrance are correlated with the accessibility of the building. Secondly, the height of a bell-tower is related with the feelings of a tediously and a intimate degree. Thirdly, the ground clearance of the whole surface is correlated with the church-character and the community formation of a local society.

• Proceedings of the KSR Conference
• /
• 2004.10a
• /
• pp.1566-1574
• /
• 2004

This study tried to find out alternatives adjusting basic fare using customer survey. But it merely verified that train fare decision is made by government's role and market status. Also, it has a limitation deciding resonable fare of KTX that average cost and marginal cost calculation is impossible because Korean National Railroad does not follow 'Activity Based Costing'. It is rational fare decision that performing survey to railroad experts and general customers, and compare two results. Summarizing results of this study, 1. The hypothesis 'Experts' perceived fare level of KTX is higher than that of general customer. 'is carried. It suggests that following experts' opinion with general customer's is very rational method to decide fare level. 2. The hypothesis 'Experts expect lower level of fare discount rate than general customer.' is carried. 3. It is hard to decide priority among many kinds of discount for difference of two group's preference. However, following recent research project is maximized by discounting fare 30$\%$ on 40$\%$ of total passenger and expand number of discount kinds step by step are desirable.

• Proceedings of the Korean Geotechical Society Conference
• /
• 2008.10a
• /
• pp.85-110
• /
• 2008

Ground investigation data to be used as a basis for geotechnical analysis and foundation design are usually troubled with large uncertainty, due to natural variability and limited number of data. Statistical methods can be a rational tool for handling such uncertain ground data, in particular with a view to the selection of characteristic values for estimating ground design parameters used in design. The characteristic values of soil properties for use in geotechnical design have oftenly based on not only a subjective judgment but also engineer's past acumulated experience. This paper discussed some statistical methods which can handle such intrinsic ground uncertainty data with a case design in a rational manner.

• Honam Mathematical Journal
• /
• v.45 no.3
• /
• pp.542-554
• /
• 2023

Given a real number α, the Lagrange number of α is the supremum of all real numbers L > 0 for which the inequality |α - p/q| < (Lq²)^-1 holds for infinitely many rational numbers p/q. All Lagrange numbers less than 3 can be arranged as a set {l_p/q : p/q ∈ ℚ ∩ [0, 1]} using the Farey index. The present paper considers a function C(α) devised from Sturmian words. We demonstrate that the function C(α) contains all information on Lagrange numbers less than 3. More precisely, we prove that for any real number α ∈ (0, 1], the value C(α) - C(0) is equal to the sum of all numbers 3 - l_p/q where the Farey index p/q is less than α.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.1 no.1
• /
• pp.151-170
• /
• 1976

There are many cases of production processes which intermittently produce several different kinds of products for stock through one set of physical facility. In this case, an important question is what size of production run should be prduced once we do set-up for a product in order to minimize the total cost, that is, the sum of the set-up, carrying, and stock-out costs. This problem is used to be called scheduling of multiple products through a single facility in the production management field. Despite the very common occurrence of this type of production process, no one has yet devised a method for determining the optimal production schedule. The purpose of this study is to develop quantitative analytical models which can be used practically and give us rational production schedules. The study is to show improved models with application to a can-manufacturing plant. In this thesis the economic production quantity (EPQ) model was used as a basic model to develop quantitative analytical models for this scheduling problem and two cases, one with stock-out cost, the other without stock-out cost, were taken into consideration. The first analytical model was developed for the scheduling of products through a single facility. In this model we calculate No, the optimal number of production runs per year, minimizing the total annual cost above all. Next we calculate No$_{i}$ is significantly different from No, some manipulation of the schedule can be made by trial and error in order to try to fit the product into the basic (No schedule either more or less frequently as dictated by) No$_{i}$, But this trial and error schedule is thought of inefficient. The second analytical model was developed by reinterpretation by reinterpretation of the calculating process of the economic production quantity model. In this model we obtained two relationships, one of which is the relationship between optimal number of set-ups for the ith item and optimal total number of set-ups, the other is the relationship between optimal average inventory investment for the ith item and optimal total average inventory investment. From these relationships we can determine how much average inventory investment per year would be required if a rational policy based on m No set-ups per year for m products were followed and, alternatively, how many set-ups per year would be required if a rational policy were followed which required an established total average inventory inventory investment. We also learned the relationship between the number of set-ups and the average inventory investment takes the form of a hyperbola. But, there is no reason to say that the first analytical model is superior to the second analytical model. It can be said that the first model is useful for a basic production schedule. On the other hand, the second model is efficient to get an improved production schedule, in a sense of reducing the total cost. Another merit of the second model is that, unlike the first model where we have to know all the inventory costs for each product, we can obtain an improved production schedule with unknown inventory costs. The application of these quantitative analytical models to PoHang can-manufacturing plants shows this point.int.