• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.285-298
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• 2015

In [41], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed positive integer l holds for all x₁, ⋯ , x_2l ∈ V . For the above equality, we can define the following functional equation Using the fixed point method, we prove the Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.535-542
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• 2017

Let R be an associative ring and ${\alpha},{\beta}:R{\rightarrow}R$ ring homomorphisms. An additive mapping $d:R{\rightarrow}R$ is called an (${\alpha},{\beta}$)-derivation of R if $d(xy)=d(x){\alpha}(y)+{\beta}(x)d(y)$ is fulfilled for any $x,y{\in}R$, and an additive mapping $D:R{\rightarrow}R$ is called a generalized (${\alpha},{\beta}$)-derivation of R associated with an (${\alpha},{\beta}$)-derivation d if $D(xy)=D(x){\alpha}(y)+{\beta}(x)d(y)$ is fulfilled for all $x,y{\in}R$. In this note, we intend to generalize a theorem of Vukman [5], and a theorem of Daif and El-Sayiad [2].

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.539-548
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• 2024

Let R be a ring and P be a prime ideal of R. A mapping d : R → R is called a multiplicative derivation if d(xy) = d(x)y + xd(y) for all x, y ∈ R. In this paper, our main motive is to obtain the well-known theorem due to Posner in the ring R/P for generalized derivations associated with a multiplicative derivation defined by an additive mapping F : R → R such that F(xy) = F(x)y + xd(y), where d : R → R is a multiplicative derivation not necessarily additive. This article discusses the use of generalized derivations associated with a multiplicative derivation to investigate the commutativity of the quotient ring R/P.

• Journal of Powder Materials
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• v.29 no.4
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• pp.303-308
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• 2022

The plastic deformation behavior of additively manufactured anisotropic structures are analyzed using the finite element method (FEM). Hill's quadratic anisotropic yield function is used, and a modified return-mapping method based on dual potential is presented. The plane stress biaxial loading condition is considered to investigate the number of iterations required for the convergence of the Newton-Raphson method during plastic deformation analysis. In this study, incompressible plastic deformation is considered, and the associated flow rule is assumed. The modified return-mapping method is implemented using the ABAQUS UMAT subroutine and effective in reducing the number of iterations in the Newton-Raphson method. The anisotropic tensile behavior is computed using the 3-dimensional FEM for two tensile specimens manufactured along orthogonal additive directions.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.52 no.6
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• pp.241-248
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• 2003

$Bi_{1.84}Pb_{0.34}Sr_{1.91}Ca_{2.03}Cu_{3.06}O_{10+\delta}$ high $T_{c}$ superconductors containing Ag as an additive were fabricated by a solid-state reaction method. The superconducting properties, such as the structural characteristics, the critical temperatures, the grain size and the image of mapping on the surface were investigated. Samples with Ag and Au of 50 wt% each were sintered at various temperature(820~$850^{\circ}C$). The structural characteristics, the microstructure of surface and the critical temperature with respect to the each samples were analyzed by XRD and SEM, EDS and four-prove methode respectively. The critical temperature showed the result which the Ag additive samples are higher than Au additive samples. The microstructure of the surface showed the tendency which the Ag additive samples become more minuteness than Au additive samples.

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.363-372
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• 2023

In this paper, we consider two functional equations: (1) h(𝓕(x, y, z) + 2x + y + z) + h(xy + z) + yh(x) + yh(z) = h(𝓕(x, y, z) + 2x + y) + h(xy) + yh(x + z) + 2h(z), (2) h(𝓕(x, y, z) - y + z + 2e) + 2h(x + y) + h(xy + z) + yh(x) + yh(z) = h(𝓕(x, y, z) - y + 2e) + 2h(x + y + z) + h(xy) + yh(x + z), without any regularity assumption for all x, y, z in a unital algebra A, where 𝓕 : A³ → A is defined by 𝓕(x, y, z) := h(x + y + z) - h(x + y) - h(z) for all x, y, z ∈ A. Also, we find general solutions of these equations in unital algebras. Finally, we prove the Hyers-Ulam stability of (1) and (2) in unital Banach algebras.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.16 no.6
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• pp.522-531
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• 2003

Samples with the nominal composition, B $i_{1.84}$P $b_{0.34}$S $r_{1.91}$C $a_{2.03}$C $u_{3.06}$ $O_{10+{\delta}}$ high- $T_{c}$ superconductors containing MgO as an additive were fabricated by a solid-state reaction method. Samples with MgO of 5~30 wt% each were sintered at 820~86$0^{\circ}C$ for 24 hours. The structural characteristics, critical temperature, grain size and image of mapping with respect to MgO contents were analyzed by XRD(X-Ray Diffraction), SEM(Scanning Electron Microscope) and EDS(Energy dispersive X-ray spectrometer) respectively. As MgO contents increased, intensity of MgO Peaks and ratio of Bi-2212 phase in superconductors intensified and the proportion of the phase transition from Bi-2223 to Bi-2212 was increased.

• The Pure and Applied Mathematics
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• v.29 no.2
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• pp.179-188
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• 2022

In this paper we investigate the Hyers-Ulam stability of the s-variable additive and l-variable quadratic functional equations of the form $$f\(\sum\limits_{i=1}^{s}x_i\)+\sum\limits_{j=1}^{s}f\(-sx_j+\sum\limits_{i=1,i{\neq}j}^{s}x_i\)=0$$ and $$f\(\sum\limits_{i=1}^{l}x_i\)+\sum\limits_{j=1}^{l}f\(-lx_j+\sum\limits_{i=1,i{\neq}j}^{l}x_i\)=(l+1)$$$\sum\limits_{i=1,i{\neq}j}^{l}f(x_i-x_j)+(l+1)\sum\limits_{i=1}^{l}f(x_i)$ (s, l ∈ N, s, l ≥ 3) in quasi-Banach spaces.

• Asian-Australasian Journal of Animal Sciences
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• v.28 no.7
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• pp.926-935
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• 2015

The efficiency of genome-wide association analysis (GWAS) depends on power of detection for quantitative trait loci (QTL) and precision for QTL mapping. In this study, three different strategies for GWAS were applied to detect QTL for carcass quality traits in the Korean cattle, Hanwoo; a linkage disequilibrium single locus regression method (LDRM), a combined linkage and linkage disequilibrium analysis (LDLA) and a $BayesC{\pi}$ approach. The phenotypes of 486 steers were collected for weaning weight (WWT), yearling weight (YWT), carcass weight (CWT), backfat thickness (BFT), longissimus dorsi muscle area, and marbling score (Marb). Also the genotype data for the steers and their sires were scored with the Illumina bovine 50K single nucleotide polymorphism (SNP) chips. For the two former GWAS methods, threshold values were set at false discovery rate <0.01 on a chromosome-wide level, while a cut-off threshold value was set in the latter model, such that the top five windows, each of which comprised 10 adjacent SNPs, were chosen with significant variation for the phenotype. Four major additive QTL from these three methods had high concordance found in 64.1 to 64.9Mb for Bos taurus autosome (BTA) 7 for WWT, 24.3 to 25.4Mb for BTA14 for CWT, 0.5 to 1.5Mb for BTA6 for BFT and 26.3 to 33.4Mb for BTA29 for BFT. Several candidate genes (i.e. glutamate receptor, ionotropic, ampa 1 [GRIA1], family with sequence similarity 110, member B [FAM110B], and thymocyte selection-associated high mobility group box [TOX]) may be identified close to these QTL. Our result suggests that the use of different linkage disequilibrium mapping approaches can provide more reliable chromosome regions to further pinpoint DNA makers or causative genes in these regions.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.147-162
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• 2011

In this paper, we investigate the Ulam-Hyers stability of $C^{\star}$-ternary algebra 3-homomorphisms for the functional equation $$f(x_1+x_2,y_1+y_2,z_1+z_2)=\;\displaystyle\sum_{1{\leq}i,j,k{\leq}2}\;f(x_i,y_j,z_k)$$ in $C^{\star}$-ternary algebras.