• Journal of the Chungcheong Mathematical Society
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• v.32 no.3
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• pp.337-347
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• 2019

In this paper, we investigate the generalized Hyers-Ulam stability of the quadratic and quartic type functional equations $$f(kx+y)+f(kx-y)-k^2f(x+y)-k^2f(x-y)-2f(kx)\\{\hfill{67}}+2k^2f(x)+2(k^2-1)f(y)=0,\\f(x+5y)-5f(x+4y)+10f(x+3y)-10f(x+2y)+5f(x+y)\\{\hfill{67}}-f(-x)=0,\\f(kx+y)+f(kx-y)-k^2f(x+y)-k^2f(x-y)\\{\hfill{67}}-{\frac{k^2(k^2-1)}{6}}[f(2x)-4f(x)]+2(k^2-1)f(y)=0$$ by using the fixed point theory in the sense of L. $C{\breve{a}}dariu$ and V. Radu.

• Bulletin of the Korean Chemical Society
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• v.16 no.6
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• pp.539-542
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• 1995

The crystal structure of K92-X (K92Al92Si100O384), a=25.128(1) Å, dehydrated at 360 ℃ and 2X 10-6 Torr, has been determined by single-crystal X-ray diffraction techniques in the cubic space group Fd&bar{3} at 21(1) ℃. The structure was refined to the final error indices R1=0.044 and Rw=0.039 with 242 reflections for which I<3σ(I). In this structure, ninety-two K+ ions are located at the five different crystallographic sites. Sixteen K+ ions are located at the centers of the double six rings (site I; K(1)-O(3)=2.65(2) Å and O(3)-K(1)-O(3)=92.0(6)°). About twelve K+ ions lie at site I' in the sodalite cavity opposite double six rings (D6R's) and these K+ ions are recessed ca. 1.62 Å into the sodalite cavity from their O(3) plane (K(2)-O(3)=2.74(2) Å, O(3)-K(2)-O(3)=88.5(8)°). About thirty-two K+ ions are located at the site II in the supercage and these K+ ions are recessed ca. 1.20 Å into the supercage from their O(2) plane (K(3)-O(2)=2.64(2) Å, and O(2)-K(3)-O(2)=101(1)°). About twenty-two K+ ions lie at the site III in the supercage opposite 4-ring ladder and the remaining ten K+ ions lie at the site III' near the 4-ring ladder in the supercage (K(4)-O(4)=2.88(3) Å, O(4)-K(4)-O(4)=79.8(9)°, K(5)-O(4)=2.8(2) Å, and O(4)-K(5)-O(4)=68(5)°).

• Journal of the Korean Institute of Telematics and Electronics T
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• v.36T no.4
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• pp.115-122
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• 1999

The Y2K bug, what is called "millennium bug" or "2000 year bug", take place because the year after 2000 year is not recognize as the year marking method of the computer designed for take up two-digit number. This takes place because the RTC chip architecture of PC can not change the century information to the operating together with date. In this paper, we make an analysis about Y2K hardware bug of RTC in the IBM compatible PC, and make a Y2K compensation board in order to solve Y2K hardware bug. And the test results by various Y2K diagnosis program is bug before put in Y2K compensation board, but is not bug after put in Y2K compensation board. Therefore, we suggest a solution method for Y2K hardware bug of RTC in the IBM compatible PC.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.159-168
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• 2020

In this paper, we investigate Hyers-Ulam-Rassias stability of a functional equation f(x + ky) + f(x - ky) - k²f(x + y) - k²f(x - y) + 2(k² - 1)f(x) + (k² + k³)f(y) + (k² - k³)f(-y) - 2f(ky) = 0.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.521-534
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• 2022

In this paper, we introduce a new class 𝓡^k_λ(λ ≥ 1, k is any positive real number) of univalent complex functions, which consists of functions f of the form f(z) = z + Σ^∞_n=2 a_nzⁿ (|z| < 1) satisfying the subordination condition $$(1-{\lambda}){\frac{f(z)}{z}}+{\lambda}f^{\prime}(z){\prec}{\frac{1+r^2_kz^2}{1-k{\tau}_kz-{\tau}^2_kz^2}},\;{\tau}_k={\frac{k-{\sqrt{k^2+4}}}{2}$$, and investigate the Fekete-Szegö problem for the coefficients of f ∈ 𝓡^k_λ which are connected with k-Fibonacci numbers $F_{k,n}={\frac{(k-{\tau}_k)^n-{\tau}^n_k}{\sqrt{k^2+4}}}$ (n ∈ ℕ ∪ {0}). We obtain sharp upper bound for the Fekete-Szegö functional |a₃-𝜇a²₂| when 𝜇 ∈ ℝ. We also generalize our result for 𝜇 ∈ ℂ.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.983-991
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• 2013

For each real number $n$ > 6, we prove that there is a sequence $\{pk(n,z)\}^{\infty}_{k=1}$ of fourth degree self-reciprocal polynomials such that the zeros of $p_k(n,z)$ are all simple and real, and every $p_{k+1}(n,z)$ has the largest (in modulus) zero ${\alpha}{\beta}$ where ${\alpha}$ and ${\beta}$ are the first and the second largest (in modulus) zeros of $p_k(n,z)$, respectively. One such sequence is given by $p_k(n,z)$ so that $$p_k(n,z)=z^4-q_{k-1}(n)z^3+(q_k(n)+2)z^2-q_{k-1}(n)z+1$$, where $q_0(n)=1$ and other $q_k(n)^{\prime}s$ are polynomials in n defined by the severely nonlinear recurrence $$4q_{2m-1}(n)=q^2_{2m-2}(n)-(4n+1)\prod_{j=0}^{m-2}\;q^2_{2j}(n),\\4q_{2m}(n)=q^2_{2m-1}(n)-(n-2)(n-6)\prod_{j=0}^{m-2}\;q^2_{2j+1}(n)$$ for $m{\geq}1$, with the usual empty product conventions, i.e., ${\prod}_{j=0}^{-1}\;b_j=1$.

• Applied Chemistry for Engineering
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• v.21 no.3
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• pp.284-290
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• 2010

In this study, as one of the carbon dioxide ($CO_2$) adsorbents the aqueous potassium carbonate ($K_2CO_3$)/promoter mixtures were investigated. Equilibrium partial pressure ($P_{CO_2}^*$) and pressure change were measured by using VLE (Vapor-liquid equilibrium) equipment in the mixture solution at 60 and $80^{\circ}C$, respectively. Absorption capacity was estimated in the semi-batch absorption apparatus at 40, 60 and $80^{\circ}C$. We proposed to use homopiperazine (homoPZ), cyclic diamine compound as a promoter of $K_2CO_3$ solution, to prevent crystalline formation and increase absorption capacity of aqueous $K_2CO_3$ solution. The absorption capacity of $K_2CO_3$/homoPZ was compared with MEA, $K_2CO_3$ and $K_2CO_3$/piperazine (PZ). Based on the results, we found that the mixture solution containing homoPZ had lower equilibrium partial pressure than that of $K_2CO_3$ solution and the absorption rate was approximately 0.375-times faster at $60^{\circ}C$, 0.343-times faster at $80^{\circ}C$ than that of aqueous $K_2CO_3$ solution without homoPZ. $K_2CO_3$/homoPZ solution showed excellent CO2 loading capacity compared with MEA solution at $60^{\circ}C$.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.257-267
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• 2016

We find examples of Ideals in a tridiagonal algebra ALGL_∞ and study some properties of Ideals in ALGL_∞. We prove the following theorems: Let k and j be fixed natural numbers. Let A be a subalgebra of ALGL_∞ and let A_2,{k} ⊂ A ⊂ {T ∈ ALGL_∞ | T_(2k-1,2k) = 0}. Then A is an ideal of ALGL_∞ if and only if A = A_2,{k} where A_2,{k} = {T ∈ ALGL_∞ | T_(2k-1,2k) = 0, T_(2k-1,2k-1) = T_(2k,2k) = 0}. Let B be a subalgebra of ALGL_∞ such that B_2,{j} ⊂ B ⊂ {T ∈ ALGL_∞ | T_(2j+1,2j) = 0}. Then B is an ideal of ALGL_∞ if and only if B = B_2,{j}, where B_2,{j} = {T ∈ ALGL_∞ | T_(2j+1,2j) = 0, T_(2j,2j) = T_(2j+1,2j+1) = 0}.

• Applied Chemistry for Engineering
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• v.7 no.3
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• pp.580-587
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• 1996

Synthesis of long fibrous $K_2Ti_4O_9$ was attempted to find a method to produce long fibrous $K_2Ti_6O_{13}$ and other derivatives and also phase transformation of $K_2Ti_4O_9$ synthesized was investigated. Long fibrous $K_2Ti_4O_9$ was succesively synthesized by the calcination reaction under the following reaction conditions ; reaction temperature of $1050^{\circ}C$, $TiO_2$ mole ratio to $K_2CO_3$ of 2.8 and reaction time of 3hrs, and scattering of calcined products for 10hrs with hot boiling water. $K_2Ti_4O_9$ showed lower structural stability under heat treatment and the structure of $K_2Ti_4O_9$ was converted to $K_2Ti_6O_{13}$ under heating temperature of over $250^{\circ}C$.

• Korean Journal of Microbiology
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• v.35 no.4
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• pp.270-276
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• 1999

Production of stress shock proteins in Burkholderia cepacia YK-2 in response to the phenoxyherbicide 2,4-dichlorophenoxyacetic acid(2,4-D) as an environmental contaminant was investrigated. The stress schock proteins were synthesized at different 2,4-D concentrations in exponentially growing cultures of B. capacia YK-2. This response involved the production of 43kDa and 41kDa GroEL proteins. The proteins were characterized by SDS-PAGE and Western blot using the anti-DnaK nad anti-GroEL monoclonal antibodies. Total stress shock proteins were analyzed by 2-D PAGE. Survival of B. cepacia YK-2 with time in the presence of different concentrations of 2,4-D was monitored, and viable counts paralleled the production of the stress shock proteins in this bacterium.