• Honam Mathematical Journal
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• v.31 no.4
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• pp.611-632
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• 2009

The orders in a quaternion algebra play a central role of the theory of Hecke operators. In this paper, we study the arithmetic properties of optimal embeddings of orders in a quaternion algebra over a dyadic local field.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.977-988
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• 2022

The Padovan sequence is the third-order linear recurrence (𝓟_n)_n≥0 defined by 𝓟_n = 𝓟_n-2 + 𝓟_n-3 for all n ≥ 3 with initial conditions 𝓟₀ = 0 and 𝓟₁ = 𝓟₂ = 1. In this paper, we investigate a generalization of the Padovan sequence called the k-generalized Padovan sequence which is generated by a linear recurrence sequence of order k ≥ 3. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences.

• Journal of information and communication convergence engineering
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• v.8 no.3
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• pp.317-322
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• 2010

This paper presents an algorithm generating inverse element over finite fields GF($3^m$), and constructing method of inverse element generator based on inverse element generating algorithm. An inverse computing method of an element over GF($3^m$) which corresponds to a polynomial over GF($3^m$) with order less than equal to m-1. Here, the computation is based on multiplication, square and cube method derived from the mathematics properties over finite fields.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.331-351
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• 2007

Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k$, $q=e^{{\pi}i\tau}$. We find a lot of algebraic properties derived from theta functions, and by using this we explore some new algebraic numbers from Rogers-Ramanujan continued fractions.

• Journal of Periodontal and Implant Science
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• v.49 no.5
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• pp.310-318
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• 2019

Purpose: Surface alterations of titanium discs following instrumentation with either a nylon brush or a metal brush were evaluated. Methods: A total of 27 titanium discs with 3 surface types (9 discs for each type), including machined (M) surfaces, sandblasted and acid-etched (SA) surfaces, and surfaces treated by resorbable blast media (RBM), were used. Three discs were instrumented with a nylon brush, another 3 discs were instrumented with a metal brush, and the remaining 3 discs were used as controls for each surface type. Surface properties including the arithmetic mean value of a linear profile (Ra), maximum height of a linear profile (Rz), skewness of the assessed linear profile (Rsk), arithmetic mean height of a surface (Sa), maximum height of a surface (Sz), developed interfacial area ratio (Sdr), skewness of a surface profile (Ssk), and kurtosis of a surface profile (Sku) were measured using confocal microscopy. Results: Instrumentation with the nylon brush increased the Ra, Sa, and Sdr of the M surfaces. On the SA surfaces, Ra, Sa and Sdr decreased after nylon brush use. Meanwhile, the roughness of the RBM surface was not affected by the nylon brush. The use of the metal brush also increased the Ra, Sa, and Sdr of the M surface; however, the increase in Sdr was not statistically significant (P=0.119). The decreases in the Rz, Sz, Ra, Sa, and Sdr of the SA surfaces were remarkable. On the RBM surfaces, the use of the metal brush did not cause changes in Ra and Sa, whereas Rz, Sz, and Sdr were reduced. Conclusions: Titanium surfaces were altered when instrumented either with a nylon brush or a metal brush. Hence, it is recommended that nylon or metal brushes be used with caution in order to avoid damaging the implant fixture/abutment surface.

• Journal of Biosystems Engineering
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• v.40 no.3
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• pp.212-223
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• 2015

Purpose: Physical properties of Detarium microcarpum seeds were investigated as a function of moisture content to explore the possibility of developing bulk handling and processing equipment. Methods: Seed size, surface area, and 1,000-seed weight were determined by measuring the three principal axes, measuring area on a graph paper, and counting and weighing seeds. Particle and bulk densities were determined using liquid displacement and weight in a measuring cylinder, respectively. Porosity was computed from particle and bulk densities. Roundness and sphericity were measured using shadowgraphs. Angle of repose and static and kinetic coefficients of friction were determined using the vertical cylindrical pipe method, an inclined plane, and a kinetic coefficient of friction apparatus. Results: In the moisture range of 8.2%-28.5% (db), the major, intermediate, and the minor axes increased from 2.95 to 3.21 cm, 1.85 to 2.61 cm, and 0.40 to 1.21 cm, respectively. Surface area, 1,000-seed weight, particle density, porosity, and angle of repose increased from 354.62 to $433.19cm^2$, 3.184 to 3.737 kg, 1060 to $1316kg/m^3$, and 30.0% to 53.1%, respectively, whereas bulk density decreased from 647.6 to $617.2kg/m^3$. Angle of repose increased from $13.9^{\circ}$ to $28.4^{\circ}$. Static and kinetic coefficients of friction varied between 0.096 and 0.638 on different structural surfaces. Conclusions: Arithmetic mean, geometric mean, and equivalent sphere effective diameters determined at the same moisture level were significantly different from each other, with the arithmetic mean diameter being greatest. Surface area, 1,000-seed weight, particle density, porosity, and angle of repose all increased linearly with moisture content. Bulk density decreased linearly with moisture content. The coefficients of friction had linear relationships with moisture content. The highest values of static and kinetic coefficients of friction were observed on galvanized steel and hessian fabric, respectively, whereas the lowest values were observed on fiberglass.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.541-553
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• 2012

In this paper, we study some limit properties of the harmonic mean of random transition probability for a second-order nonhomogeneous Markov chain on the generalized gambling system indexed by a tree by constructing a nonnegative martingale. As corollary, we obtain the property of the harmonic mean and the arithmetic mean of random transition probability for a second-order nonhomogeneous Markov chain indexed by a double root tree.

• 한국전산유체공학회:학술대회논문집
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• 2009.04a
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• pp.283-289
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• 2009

In level set method, material properties are made to change smoothly across an interface of two materials with different properties by introducing an interpolation or smoothing scheme. So far, the weighted arithmetic mean (WAM) method has been exclusively adopted in level set method, without complete assessment for its validity. We showed here that the weighted harmonic mean (WHM) method for rate constants of various rate processes, including viscosity, thermal conductivity, electrical conductivity, and permittivity, gives much more accurate results than the WAM method. The selection of interpolation scheme is particularly important in multi-phase electrohydrodynamic problems in which driving force for fluid flow is electrical force exerted on the phase interface. Our analysis also showed that WHM method for both electrical conductivity and permittivity gives not only more accurate, but also more physically realistic distribution of electrical force at the interface. Our arguments are confirmed by numerical simulations of drop deformation under DC electric field.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.8 no.2
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• pp.15-21
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• 2008

This paper discuss the sequential digital logic systems and arithmetic operation algorithms which is the important material in computer architecture using analysis and synthesis which is based on extension logic for binary logic over galois fields. In sequential digital logic systems, we construct the moore model without feedback sequential logic systems after we obtain the next state function and output function using building block T-gate. Also, we obtain each algorithms of the addition, subtraction, multiplication, division based on the finite fields mathematical properties. Especially, in case of P=2 over GF($P^m$), the proposed algorithm have a advantage which will be able to apply traditional binary logic directly.The proposed method can construct more efficiency digital logic systems because it can be extended traditional binary logic to extension logic.

• Journal of Ocean Engineering and Technology
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• v.23 no.6
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• pp.105-110
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• 2009

The objective of this paper is to investigate the statistical properties of Vickers hardness (HV) for friction welded parts in a Ni-based super alloy (Alloy718). In the case of post weld heat treatment (PWHT) parts, hardness tests were repeated for three different applied loads, 100, 200, and 300 g, with a duration time of 10 seconds. The arithmetic means of the Vickers hardness in heat affected zone (HAZ) materials were smaller than those of the base metal (BM) in all of the applied loads. The coefficient of variation (COV) for the BM and HAZ decreased by increasing the applied load. The probability distribution of the Vickers hardness followed the Weibull distribution well. The distribution of the Vickers hardness was not found to be symmetric. The shape parameter and scale parameter increased by increasing the applied load at both the BM and HAZ.