• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.345-352
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• 2024

We introduce a new class of bi-partition function c_k(n), which counts the number of bi-color partitions of n in which the second color only appears at the parts that are multiples of k. We consider two partitions to be the same if they can be obtained by switching the color of parts that are congruent to zero modulo k. We show that the generating function for c_k(n) involves the partial theta function and obtain the following congruences: c₂(27n + 26) ≡ 0 (mod 3) and c₃(4n + 2) ≡ 0 (mod 2).

• The Journal of Information Technology
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• v.8 no.3
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• pp.1-10
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• 2005

Cosine and Sine function is widely used for the arithmetic, translation, object drawing, Simulation and etc. of Computer Graphics in Natural Science and Engineering. In general, Cordic Algorithm is effective method since it has relatively small size and simple architecture on trigonometric function generation. However profitably it has those merits, the problem of operation speed is occurred. In graphic display system, the operation result of object drawing is quantized and has the condition that is satisfied with rms error less than 1. So in this paper, the proposed generator is composed of partition operation at each ${\pi}/4$ and basic Cosine, Sine function generator in the range of $0{\sim}{\pi}/4$ using the lower order of Tayler's series in an acceptable error range, that enlarge the range of $0{\sim}2{\pi}$ according to a definition of the trigonometric function for the purpose of having a high speed Cosine, Sine function generation. And, division operator using code partition for divisor three is proposed, the proposed function generator has high speed operation, but it has the problems in the other application parts with accurate results, is need to increase the speed of the multiplication.

• Korean Journal of Heritage: History & Science
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• v.55 no.4
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• pp.196-209
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• 2022

This study compared and analyzed the spatial division function and role of partitions by comparing the entire space and the spatial changes before and after the installation of partitions in <Donggwoldo>, which was manufactured in the late Joseon Dynasty. As a research method, a set standard was prepared to decompose the space of <Donggwoldo> into a unit space, and the standard was set according to the role and height of the space by classifying it into a main space, sub space, and transition space. Two convex maps were prepared according to before and after the installation of the Panjang, and the values of connectivity, control, and integration, which are spatial syntax variables, were calculated and analyzed. The results of the study are as follows. First, the partition in <Donggwoldo(東闕圖)> did not affect the overall spatial arrangement and control or connection of Donggwol, but the movement and access of space is limited to specific areas. Second, the partition was a facility intensively distributed in Naejeon(內殿) and Donggung(東宮) to be used actively in the way of space utilization. It shows that the unit space increased rapidly due to the installation of the partition. Since the partition was installed in the spaces that were open and under high control in the case of Naejeon(內殿), it helped to secure private spaces as closed ones under low control. On the other hand, for Donggung(東宮), the spaces were compartmented and divided with the partition to guide the movement path through narrow gates of the partition and increase the depth of the space. This helped to create spaces that are free and can be hidden as it increased the number of spaces coming through. Third, In addition to the functions of "eye blocking, space division, and movement path control" revealed in prior research, the partition has created a "space that is easy to control" within a specific area. The installation of the partition reduced the scale through the separation of spaces, but it occurred the expansion of the movement path and space. Also, the partition functioned to strengthen hiding and closure or increase openness as well through space division. This study is significant in that it revealed the value of the spatial control function of panjang through the analysis of spatial control and depth by analyzing the function of the partition with a mathematical model in addition to the analysis and study of the function and role of panjang. In addition, it is valuable in that it has prepared a framework for analysis tools that can be applied to traditional residential complexes similar to palaces by applying space syntax to <Donggungdo> to create convex spaces according to unit space division and connection types of palace architecture and landscape elements.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.471-487
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• 2020

We find congruences modulo 32, 64 and 128 for the partition function ${\overline{PP}_o}(n)$, the number of overpartition pairs of n into odd parts, with the aid of Ramamnujan's theta function identities and some known identities of t_k(n), for k = 6, 7, where t_k(n) denotes the number of representations of n as a sum of k triangular numbers. We also find two Ramanujan-like congruences for ${\overline{PP}_o}(n)$ modulo 128.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2019.05a
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• pp.398-399
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• 2019

This paper presents a method of the circuit design of the multiple-valued digital logic switching functions based on the modular techniques. Fisr of all, we introduce the necessity, background and concepts of the modular design techniques for the digital logic systems. Next, we discuss the definitions that are used in this paper. For the purpose of the circuit design for the multiple-valued digital logic switching functions, we discuss the extraction of the partition functions. Also we describe the construction method of the building block, that is called the modules, based on each partition functions. And we apply the proposed method to the example, we compare the results with the results of the earlier methods. In result, we decrease the control functions, it means that we obtain the effective cost in the digital logic design for any other earlier methods. In the future research, we require the universal module that traet more partition functions and more compact module.

• The Journal of the Convergence on Culture Technology
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• v.7 no.3
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• pp.481-486
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• 2021

Machine learning algorithms adopt criterion function as a key component to measure the quality of their model derived from data. Cluster analysis also uses this function to rate the clustering result. All the criterion functions have in general certain types of favoritism in producing high quality clusters. These clusters are then described by attributes and their values. Category utility and partition utility play an important role in cluster analysis. These are fully analyzed in this research particularly in terms of how they are related to the favoritism in the final results. In this research, several data sets are selected and analyzed to show how different results are induced from these criterion functions.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.607-613
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• 2009

In this paper, we define the C-integral and prove the integration by parts formula for the C-integral.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.1
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• pp.130-134
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• 2012

In this paper, we propose a space partitioning technique for swarm robots by using the Centroidal Voronoi Tessellation. The proposed method consists of two parts such as space partition and collision avoidance. The space partition for searching a given space is carried out by a density function which is generated by some accidents. The collision avoidance is implemented by the potential field method. Finally, the numerical experiments show the effectiveness and feasibility of the proposed method.

• Proceedings of the Korean Society of Applied Pharmacology
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• 1996.04a
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• pp.286-286
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• 1996

In order to elucidate the mechanism of action of transdermal absorption-enhancing compounds, i.e., pyrrolidone derivatives (2-pyrrolidone, 1-methyl-2-pyrrolidone, 1-ethyl-2-pyrrolidone, 1,5-dimethyl-pyrrolidone and 5-methyl-2-pyrrolidone), multilamellar liposome was prepared from the simulated stratum corneum lipid and employed as a model system for the barrier function of the stratum corneum. The liposomal membrane of the stratum corneum lipid liposome (SCLL) behaves as an osmometer and has an excellent barrier function. In addition, its phase transition temperatures are similar to those of human stratum corneum intercellular lipid region. Therefore, SCLL seems to be a useful skin model. To estimate the barrier function of SCLL, the osmotic behavior of SCLL was measured in the presence of pyrrolidone derivatives and the effect on the phase transition temperature of SCLL was also investigated using differential calorimetry. Above a certain concentration (MLAC), enhances perturb the barrier function of the liposome. The relationship between MLACs and the partition coefficient of the pyrrolidone derivatives was observed; the greater the partition coefficients, the smaller the MLAC. This suggests that the more hydrophobic enhancers penetrate into the lipid layer more easily and reduce the barrier function of membrane more effectively. The results of differential scanning thermograms of the SCLL suggest that the pyrrolidone derivatives had incorporated into the lipid layer in the liposome and increased the fluidity of the lipid layer in the liposome. Such activity might have some correlation with the transdermal absorption-enhancing activity these compounds.

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.557-560
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• 1988

In this paper, we present a new k-way partitioning algorithm for a graph of an electrical circuit wherein nodes and edges are regarded as cells (modules) and nets, respectively. In contrast to the previous work, our method is based upon a linearly ordered partition paradigm. We also claim that the maximum number of netcuts mostly governs the performance of k-way partitioning, thus having influence on the construction of a new cost function. In addition, our approach elaborates upon balancing the partition size. Our experiments show excellent results in comparison with previous k-way partitioning algorithms.