• Coupled systems mechanics
• /
• v.2 no.3
• /
• pp.255-269
• /
• 2013

This paper targets to investigate the solution of fuzzy quadratic Riccati differential equations with various types of fuzzy environment using Homotopy Perturbation Method (HPM). Fuzzy convex normalized sets are used for the fuzzy parameter and variables. Obtained results are depicted in term of plots to show the efficiency of the proposed method.

• Journal of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.67-80
• /
• 2019

For positive integers a, b, c, and an integer n, the number of integer solutions $(x,y,z){\in}{\mathbb{Z}}^3$ of $a{\frac{x(x-1)}{2}}+b{\frac{y(y-1)}{2}}+c{\frac{z(z-1)}{2}}=n$ is denoted by t(a, b, c; n). In this article, we prove some relations between t(a, b, c; n) and the numbers of representations of integers by some ternary quadratic forms. In particular, we prove various conjectures given by Z. H. Sun in [6].

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.21 no.11
• /
• pp.1496-1508
• /
• 1997

The effects of porous wind fence on the pressure characteristics around a 2-dimensional prism model of triangular cross-section were investigated experimentally. The fence and prism model were embedded in a neutral atmospheric surface boundary layer over the city suburb. In this study, various fences of different porosity, back fence, inclination angle of prism and location of additional back prisms were tested to investigate their effects on the pressure and wall shear stress of the prism surface. The fence and prism had the same height of 40 mm and Reynolds number based on the model height was Re=3.9*10$^{4}$. The porous fence with porosity 40% was found to be the best wind fence for decreasing the mean and pressure fluctuations on the prism surface. By installing the fence of porosity 40%, the wall shear stress on the windward surface of prism was largely decreased up to 1/3 of that without the fence. This indicates that the porous fence is most effective to abate the wind erosion. Pressure fluctuations on the model surface were decreased more than half when a back fence was located behind the prism in addition to the front fence. With locating several back prisms and decreasing the inclination angle of triangular prism, the pressure fluctuations on the model surface were increased on the contrary.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.19 no.2
• /
• pp.4377-4384
• /
• 1977

The curvilinear hydrograph can be replaced by an equivalent triangular hydrograph which is more easily constructed and, for routing through reservoirs or stream channels, gives results about as accurate as those obtained using the curvilinear hydrograph. A synthetic hydrograph is prepared using the data from a number of watersheds to develop a dimensionless unit hydrograph applicable to ungauged watersheds. The dimensionless unit hydrograph for the NakDong River Basin was prepared from the unit hydrographs of a variety of nine subwatersheds. The equation for the peak rate of flow (unit volume of runoff in 1.0mm) was derived as {{{{ { q}_{p } = { 0.21AR} over { {T }_{p } } }}}} The results summarized in this study are as follows: 1) It found that the watershed lag time (Lg, hrs) could be expressed by Lg=0.253(L.Lca)0.4171 The product L.Lca is a measure of the size and shape of the watershed. Correlation coefficient for Lg was 0.97 which defined with high significance. 2) The base length of the unitgraph, in hours, was adopted as Tb=17.51+2.073Lg with high significant correlation coefficient, 0.92. 3) Time in hour from start of rise to peak rate (TP) generally occured at the position of 0.289 Tb with some indication of higher values for larger watershed. 4) Triangular hydrograph is a dimensionless unitgraph prepared from the 40 unitgraphs. The equation is shown as {{{{ { q}_{p } = { K.A.R} over { { T}_{p } } }}}}. The constant K=0.21 is defined to NakDong River basin. 5) In the light of the results analyzed in this study, average errors in the peak discharge of the Trjangular unitgraph was estimated as 5.34 percent to the peak of observed average unitgraph. Each ordinate of the Triangular unitgraph was approached closely to the observed one.

• Journal of Electrical Engineering and Technology
• /
• v.12 no.2
• /
• pp.621-631
• /
• 2017

In this paper, we study the various impacts of connecting distributed generation (DG) to the distribution network. The comprehensive evaluation index system (CEIS) of four hierarchies is established, considering economy, reliability and voltage quality, and the calculation methods of different indexes are presented. This paper puts forward an improved triangular fuzzy number analytic hierarchy process (ITFNAHP) to weight the second level indexes (SLI) and the third level indexes (TLI), and calculates the variation coefficient to weight the fourth level indexes (FLI). We calculate the comprehensive weight coefficients based on the weight coefficients of the SLI, TLI and FLI, and then calculate the comprehensive evaluation of satisfaction (CES) of different access schemes. On the basis of the IEEE 33-bus example system, simulations of the calculation methods and the comprehensive evaluation method are carried out under different DG access schemes according to the same total investment cost and the same permeability, respectively, and the simulation results are analyzed and discussed.

• Journal of Industrial Technology
• /
• v.13
• /
• pp.81-87
• /
• 1993

Two dimensional analysis on the triangular fin for both the insulated fin tip and non-insulated fin tip and one dimensional analysis on that when the temperature of the fin tip is finite are made. The effect of the fin tip is shown by comparing the heat loss from the fin and the temperature along the fin length varing the non-dimensional fin length and Biot number for each three cases. The results are following. When the non-dimensional fin length is very short, the relative error of the heat loss from the fin with insulated fin tip to that from the fin with non-insulated fin tip is very high. The value of the temperature variation along the non-dimensional fin length is minimum for the finite fin tip temperature using one dimensional analysis and is maximum for the insulated fin tip using two dimensional anaysis.

• 유체기계공업학회:학술대회논문집
• /
• 2005.12a
• /
• pp.459-466
• /
• 2005

The present study investigates the heat transfer characteristics of a triangular channel. Three different rib configurations are tested. The ribs are installed on two sides of the channel. The rib height (e) to channel hydraulic diameter is 0.079 and the rib-to-rib pitch (p) is 8 times of the rib height. The rotation number ranges from 0.0 to 0.1 while the Reynolds number is fixed at 10,000. The copper blocks with heaters are installed on the channel walls to measure the regionally averaged heat transfer coefficients. For the stationary $45^{\circ}$ and $135^{\circ}$ ribbed channels, a pair of counter rotating vortices is induced by the angled rib arrangements, and high heat transfer coefficients are obtained on the regions near the inner wall for the $45^{\circ}$ ribbed channel and near the leading edge for the $90^{\circ}$ ribbed channel. The heat transfer coefficients of angled ribbed channels are changed little with rotation, whereas those of the transverse ribbed channel are changed significantly with rotation.

• Journal of the Korea Management Engineers Society
• /
• v.23 no.4
• /
• pp.87-103
• /
• 2018

This paper introduces the method to develop two main types of the fuzzy OEE (Overall Equipment Effectiveness) models via triangular membership function for measuring uncertainty. The fuzzy OEE includes model type 1 and model type 2. The model type 1 is used when the theoretical machine speed only reflects the time loss whereas model type 2 is used when the actual machine speed reflects both time and speed loss. Model type 2 has shown to perform a lower availability rate and a higher performance rate compared to model type 1. In addition, the fuzzy UPH (Unit Per Hour) which is derived from using the fuzzy OEE is presented to satisfy demand uncertainty. The fuzzy UPH can easily measure the fuzzy tact time and cycle time by reciprocating itself. Finally, this study demonstrates the fuzzy OEE models using IVIFS (Interval-Valued Intuitionistic Fuzzy Set) based on the characterization via membership function, non-membership function and hesitant function. For the purpose of analyzing the fuzzy system OEE, the OEE for each machine of plant structure is considered triangular interval-valued intuitionistic fuzzy number. Regardless of plant structure, the validity degree of fuzzy membership function of system OEE decreases when the number of machine with worst value of the validity degree increases. Corresponding examples are presented in this paper for practitioner to understand the applicability and practicability of the proposed fuzzy OEE methods.

• Journal of applied mathematics & informatics
• /
• v.42 no.1
• /
• pp.1-14
• /
• 2024

Let G = (V, E) be a (p, q) graph. Define $$\begin{cases}\frac{p}{2},\:if\:p\:is\:even\\\frac{p-1}{2},\:if\:p\:is\:odd\end{cases}$$ and L = {±1, ±2, ±3, ···, ±ρ} called the set of labels. Consider a mapping f : V → L by assigning different labels in L to the different elements of V when p is even and different labels in L to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f(u) - f(v)| such that |Δ_f1 - Δ_f^c1| ≤ 1, where Δ_f1 and Δ_f^c1 respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of subdivision of some graphs.

• Journal of the Optical Society of Korea
• /
• v.6 no.4
• /
• pp.172-179
• /
• 2002

Like the conventional digital storage systems, volume holographic memory can be deteriorated by burst errors due to its high-density storage characteristics. These burst errors are used byoptical defects such as scratches, dust particles, etc. and are two-dimensional in a data page. To deal with these errors, we introduce some concepts for describing them and propose efficient two- dimensional interleaving schemes. The schemes are two-dimensional lattices of an error-correction code word and have equilateral triangular and square structures. Using these structures, we can minimize the number of code words that are interleaved and improve the efficiency of the system. For large size burst errors, the efficient interleaving structure is an equilateral triangular lattice. However, for some small size burst errors, it is reduced to a square lattice.