• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.3
• /
• pp.275-281
• /
• 2006

In this article, we establish the stability of the orthogonally cubic type functional equation 2f(x + 2y) + 2f(x - 2y) + 2f(2x)+7[f(x)+f(-x)] = 4f(x)+8[f(x+y)+f(x-y)], $x{\bot}y$ in which ${\bot}$ is the orthogonality in the sense in the R$\ddot{a}$tz.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2000.10a
• /
• pp.355-360
• /
• 2000

This paper presents properties of piecewise cubic B-spline function and Rayleigh-Ritz method to compute the smallest eigenvales. In order to compute the smallest eigenvalues, Rayleigh quotient approach is used and four different types of finite element approximating functions corresponding to the statical deflection curve, spanned by the linearly independent set of piecewise cubic B-spline functions with equally spaced 5 knots from a partion of [0, 1], each satisfying homogeneous boundary conditions with constraining effects are used to compute the smallest eigenvalues for a Sturm-Lionville boundary equations of u"＋ λ²u＝0, u(0.0)＝u(0.0)＝0, 0≤x≤1.0.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.1
• /
• pp.9-18
• /
• 2020

In this paper, we investigate the stability of a quadratic-cubic-quartic functional equation $$f(x+ky)+f(x-ky)-k^2f(x+y)-k^2f(x-y)-2(1-k^2)f(x)-{\frac{k^2(k^2-1)}{6}}(f(2y)+2f(-y)-6f(y))=0$$ by applying the direct method in the sense of Gǎvruta.

• The Pure and Applied Mathematics
• /
• v.29 no.2
• /
• pp.189-199
• /
• 2022

In this paper, we introduce a new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation and obtain its general solution. Furthermore, we prove the Hyers-Ulam stability of the new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation in orthogonality normed spaces.

• Biomolecules & Therapeutics
• /
• v.16 no.3
• /
• pp.226-230
• /
• 2008

Monoolein-based cubic liquid crystalline systems were formulated for the local delivery of oregonin and hirsutanonol for the treatment of atopic dermatitis. The liquid crystalline phase and its nanodispersion containing drugs were prepared. The skin permeation and deposition properties of the drugs were examined in normal and delipidized rat skin. The proportion of oregonin (%) deposited in normal skin after topical administration of the drugs in the form of aqueous solution, cubic phase or cubic nanodispersions were $1.53\;{\pm}\;0.46$, $3.62\;{\pm}\;0.17$ and $5.13\;{\pm}\;0.73$, and those of hirsutanonol were $2.46\;{\pm}\;0.02$, $5.44\;{\pm}\;0.27$ and $17.28\;{\pm}\;2.19$, respectively. The greater lipophilicity and thus greater skin affinity of hirsutanonol than oregonin contributed the greater amount of skin deposition. The monoolein-based liquid crystalline phases significantly increased the amount of both drugs permeated and deposited. Approximately 3.2, 2.1 and 3.0 times greater amount of oregonin, and 3.4, 2.1 and 2.2 times greater amount of hirsutanonol were deposited in delipidized skin after administration of each drug in the form of aqueous solution, cubic phase and cubic nanodispersions system, respectively, because of lowered barrier function of the delipidized skin. In this study, the effects of drug property, vehicles type and skin condition on skin deposition and permeation properties of drug were examined and concluded that monoolein-based liquid crystalline systems would be a promising formulation for the local delivery of drugs.

• Journal of Digital Convergence
• /
• v.12 no.12
• /
• pp.553-560
• /
• 2014

In this paper, we propose a method to convert 2D image to 3D anaglyph using quadratic & cubic B$\acute{e}$zier Curves in HTML5. In order to convert 2D image to 3D anaglyph image, we filter the original image to extract the RGB color values and create two images for the left and right eyes. Users are to set up the depth values of the image through the control point using the quadratic and cubic B$\acute{e}$zier curves. We have processed the depth values of 2D image based on this control point to create the 3D image conversion reflecting the value of the control point which the users select. All of this work has been designed and implemented in Web environment in HTML5. So we have made it for anyone who wants to create their 3D images and it is very easy and convenient to use.

• Korean Journal of Materials Research
• /
• v.11 no.5
• /
• pp.393-397
• /
• 2001

Fer the purpose of improving ductility of $Al_3$Ti intermetallic compound has potential to industrial application, we investigated formation behavior of cubic Ll$_2$ structure and effect of Mn addition. Nanocrystalline cubic Ll$_2$Al$_3$Ti intermetallic compound, has 10nm size of grain, was fabricated by mechanical alloying for 20hr at the composition of Al-8Mn-25Ti. Ternary cubic Ll$_2$Al$_3$Ti, added Mn, did not showed phase transformation from Ll$_2$ to D0$_{23}$ or D0$_{22}$ unlike binary cubic Ll$_2$Al$_3$Ti and maintained Ll$_2$ structure.

• Honam Mathematical Journal
• /
• v.34 no.4
• /
• pp.597-601
• /
• 2012

In this paper we study the density of imaginary cubic function fields having the infinite Hilbert 3-class field tower.

• The Pure and Applied Mathematics
• /
• v.17 no.2
• /
• pp.185-188
• /
• 2010

In this note the distribution of roots of cubic equations in contrast to 0 is given, which is useful to discuss eigenvalues for qualitative properties of differential equations.

• Korean Journal of Mathematics
• /
• v.22 no.3
• /
• pp.419-427
• /
• 2014

Let $k=\mathbb{F}_q(T)$ be the rational function field over a finite field $\mathbb{F}_q$, where $q{\equiv}1$ mod 3. In this paper, we determine asymptotic values of average of ideal class numbers of some family of cubic Kummer extensions of k.