• Journal of applied mathematics & informatics
• /
• v.34 no.3_4
• /
• pp.227-237
• /
• 2016

In this paper we introduce a new graph labeling called k-prime cordial labeling. Let G be a (p, q) graph and 2 ≤ p ≤ k. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called a k-prime cordial labeling of G if |v_f (i) − v_f (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |e_f (0) − e_f (1)| ≤ 1 where v_f (x) denotes the number of vertices labeled with x, e_f (1) and e_f (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate the k-prime cordial labeling behavior of a star and we have proved that every graph is a subgraph of a k-prime cordial graph. Also we investigate the 3-prime cordial labeling behavior of path, cycle, complete graph, wheel, comb and some more standard graphs.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2000.07a
• /
• pp.548-551
• /
• 2000

Spinel phase LiF $e_{y}$M $n_{2-y}$ $O_4$samples are synthesized by calcining a LiOH.$H_2O$, Mn $O_2$and F $e_2$ $O_3$mixture at 80$0^{\circ}C$ for 36h in air. Preparing LiF $e_{y}$M $n_{2-y}$ $O_4$showed spinel phase with cubic phase. The ununiform distortion of the crystallite of the spinel LiF $e_{y}$M $n_{2-y}$ $O_4$was more stable than that of the pure. The discharge capacity of the cathode for the Li/LiF $e_{0.1}$M $n_{1.9}$ $O_4$cell at the first than that of the pure. The discharge capacity of the cathode for the Li/LiF $e_{0.1}$M $n_{1.9}$ $O_4$cell at the first cycle and at the 70th cycle was about 113 and 90mAh/g, respectively. This cell capacity was retained about 82% of the first cycle after 70th cycle. Impedance profile of this cell was more stable than that pure. The resistance, the capacitance and chemical diffusion coefficients of lithium ion showed approximately 80$\Omega$, 36133.87$\mu$F ; 1.4$\times$10$^{-8}$ c $m^2$ $s^{-1}$ , respectively. , respectively.ely.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.9 no.1
• /
• pp.188-198
• /
• 2005

The Goldschmidt iterative algorithm for finding a floating point square root calculated it by performing a fixed number of multiplications. In this paper, a variable latency Goldschmidt's square root algorithm is proposed, that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the square root of a floating point number F, the algorithm repeats the following operations: $R_i=\frac{3-e_r-X_i}{2},\;X_{i+1}=X_i{\times}R^2_i,\;Y_{i+1}=Y_i{\times}R_i,\;i{\in}\{{0,1,2,{\ldots},n-1} }}'$with the initial value is $'\;X_0=Y_0=T^2{\times}F,\;T=\frac{1}{\sqrt {F}}+e_t\;'$. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than $'e_r=2^{-p}'$. The value of p is 28 for the single precision floating point, and 58 for the doubel precision floating point. Let $'X_i=1{\pm}e_i'$, there is $'\;X_{i+1}=1-e_{i+1},\;where\;'\;e_{i+1}<\frac{3e^2_i}{4}{\mp}\frac{e^3_i}{4}+4e_{r}'$. If '|X_i-1|<2^{\frac{-p+2}{2}}\;'$ is true, $'\;e_{i+1}<8e_r\;'$ is less than the smallest number which is representable by floating point number. So, $\sqrt{F}$ is approximate to $'\;\frac{Y_{i+1}}{T}\;'$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal square root tables ($T=\frac{1}{\sqrt{F}}+e_i$) with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a square root unit. Also, it can be used to construct optimized approximate reciprocal square root tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

• Journal of the Korean Magnetics Society
• /
• v.11 no.2
• /
• pp.58-62
• /
• 2001

The L $i_{0.5}$F $e_{2.5-x}$A $l_{x}$ $O_4$ systems (x=0, 0.3, 0.6, 0.9, 1.2, 1.5) were investigated by X-ray diffraction and Mossbauer spectroscopy. The structure of all the samples is cubic spinel type and lattice constant decrease with increasing Al content x. The Moissbauer spectra reveal two sextet for 0$\leq$x$\leq$0.6, two sextet and a doublet for 0.9$\leq$x$\leq$1.2, and a doublet for x=1.5. The cation distribution of the samples is (L $i_{1-a}$$^{+}$F $e_{a}$ $^{3+}$)$^{A}$[L $i_{a-0.5}$$^{+}$A $l_{2.5-a-x}$$^{+}$F $e_{2.5-a-x}$$^{3+}$]$^{B}$ $O_4$$^{2-}$ and substituted $Al^{3+}$ ions decrease the covalency of F $e^{3+}$- $O^{2-}$ bond in B-sites and A-B super-exchange interactions.tions.s.tions.ons.s.

• Molecules and Cells
• /
• v.27 no.3
• /
• pp.329-336
• /
• 2009

To evaluate the involvement of translation initiation factors eIF4E and eIFiso4E in Chilli veinal mottle virus (ChiVMV) infection in pepper, we conducted a genetic analysis using a segregating population derived from a cross between Capsicum annuum 'Dempsey' containing an elF4E mutation ($pvr1^2$) and C. annuum 'Perennial' containing an elFiso4E mutation (pvr6). C. annuum 'Dempsey' was susceptible and C. annuum 'Perennial' was resistant to ChiVMV. All $F_1$ plants showed resistance, and $F_2$ individuals segregated in a resistant-susceptible ratio of 166:21, indicating that many resistance loci were involved. Seventy-five $F_2$ and 329 $F_3$ plants of 17 families were genotyped with $pvr1^2$ and pvr6 allele-specific markers, and the genotype data were compared with observed resistance to viral infection. All plants containing homozygous genotypes of both $pvr1^2$ and pvr6 were resistant to ChiVMV, demonstrating that simultaneous mutations in elF4E and eIFiso4E confer resistance to ChiVMV in pepper. Genotype analysis of $F_2$ plants revealed that all plants containing homozygous genotypes of both $pvr1^2$ and pvr6 showed resistance to ChiVMV. In protein-protein interaction experiments, ChiVMV viral genome-linked protein (VPg) interacted with both eIF4E and eIFiso4E. Silencing of elF4E and eIFiso4E in the VIGS experiment showed reduction in ChiVMV accumulation. These results demonstrated that ChiVMV can use both eIF4E and eIFiso4E for replication, making simultaneous mutations in eIF4E and eIFiso4E necessary to prevent ChiVMV infection in pepper.

• Journal of the Korean Mathematical Society
• /
• v.45 no.6
• /
• pp.1613-1622
• /
• 2008

Let G be a graph with vertex set V(G) and edge set E(G), and let g, f be two nonnegative integer-valued functions defined on V(G) such that $g(x)\;{\leq}\;f(x)$ for every vertex x of V(G). We use $d_G(x)$ to denote the degree of a vertex x of G. A (g, f)-factor of G is a spanning subgraph F of G such that $g(x)\;{\leq}\;d_F(x)\;{\leq}\;f(x)$ for every vertex x of V(F). In particular, G is called a (g, f)-graph if G itself is a (g, f)-factor. A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {$F_1$, $F_2$, ..., $F_m$} be a factorization of G and H be a subgraph of G with mr edges. If $F_i$, $1\;{\leq}\;i\;{\leq}\;m$, has exactly r edges in common with H, we say that F is r-orthogonal to H. If for any partition {$A_1$, $A_2$, ..., $A_m$} of E(H) with $|A_i|=r$ there is a (g, f)-factorization F = {$F_1$, $F_2$, ..., $F_m$} of G such that $A_i\;{\subseteq}E(F_i)$, $1\;{\leq}\;i\;{\leq}\;m$, then we say that G has (g, f)-factorizations randomly r-orthogonal to H. In this paper it is proved that every (0, mf - (m - 1)r)-graph has (0, f)-factorizations randomly r-orthogonal to any given subgraph with mr edges if $f(x)\;{\geq}\;3r\;-\;1$ for any $x\;{\in}\;V(G)$.

• Journal of the Korean Electrochemical Society
• /
• v.3 no.2
• /
• pp.109-114
• /
• 2000

The relation between the phase-shift profile fur the intermediate frequencies and the Langmuir adsorption isotherm at the poly-Ir/0.1 M $H_2SO_4$ aqueous electrolyte interface has been studied using ac impedance measurements, i.e., the phase-shift methods. The simplified interfacial equivalent circuit consists of the serial connection of the electrolyte resistance $(R_s)$, the faradaic resistance $(R_F)$, and the equivalent circuit element $(C_P)$ of the adsorption pseudoca-pacitance $(C_\phi)$. The comparison of the change rates of the $\Delta(-\phi)/{\Delta}E\;and\;\Delta{\theta}/{\Delta}E$ are represented. The delayed phase shift $(\phi)$ depends on both the cathode potential (E) and frequency (f), and is given by $\phi=tan^{-1}[1/2{\pi}f(R_s+R_F)C_P]$. The phase-shift profile $(-\phi\;vs.\;E)$ for the intermediate frequency (ca. 1 Hz) can be used as an experimental method to determine the Langmuir adsorption isotherm $(\theta\;vs.\;E)$. The equilibrium constant (K) for H adsorption and the standard free energy $({\Delta}G_{ads})$ of H adsorption at the poly-Ir/0.1 M $H_2SO_4$ electrolyte interface are $2.0\times10^{-4}$ and 21.1kJ/mol, respectively. The H adsorption is attributed to the over-potentially deposited hydrogen (OPD H).

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.745-762
• /
• 2024

In this paper, we study the existence of finite order meromorphic solutions of the following non-linear difference equation fⁿ(z) + P_d(z, f) = p₁e^α1z + p₂e^α2z + p₃e^α3z, where n ≥ 2 is an integer, P_d(z, f) is a difference polynomial in f of degree d ≤ n - 2 with small functions of f as its coefficients, p_j (j = 1, 2, 3) are small meromorphic functions of f and α_j (j = 1, 2, 3) are three distinct non-zero constants. We give the expressions of finite order meromorphic solutions of the above equation under some restrictions on α_j (j = 1, 2, 3). Some examples are given to illustrate the accuracy of the conditions.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.4
• /
• pp.991-1002
• /
• 2020

We show that when n > m, the following delay differential equation fⁿ(z)f'(z) + p(z)(f(z + c) - f(z))^m = r(z)e^q(z) of rational coefficients p, r doesn't admit any transcendental entire solutions f(z) of finite order. Furthermore, we study the conditions of α₁, α₂ that ensure existence of transcendental meromorphic solutions of the equation fⁿ(z) + f^n-2(z)f'(z) + P_d(z, f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z). These results have improved some known theorems obtained most recently by other authors.

• Communications of the Korean Mathematical Society
• /
• v.21 no.1
• /
• pp.37-43
• /
• 2006

We prove that $M_1\longrightarrow^f\;M_2$ is an injective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ if and only if $M_1\;and\;M_2$ are injective left R-modules, $M_1\longrightarrow^f\;M_2$ is isomorphic to a direct sum of representation of the types $E_l{\rightarrow}0$ and $M_1\longrightarrow^{id}\;M_2$ where $E_l\;and\;E_2$ are injective left R-modules. Then, we generalize the result so that a representation$M_1\longrightarrow^{f_1}\;M_2\; \longrightarrow^{f_2}\;\cdots\;\longrightarrow^{f_{n-1}}\;M_n$ of a quiver $Q={\bullet}{\rightarrow}{\bullet}{\rightarrow}{\cdots}{\rightarrow}{\bullet}$ is an injective representation if and only if each $M_i$ is an injective left R-module and the representation is a direct sum of injective representations.