• Kyungpook Mathematical Journal
• /
• 제49권4호
• /
• pp.691-700
• /
• 2009

We use the fixed alternative theorem to establish Hyers-Ulam-Rassias stability of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approximately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the mapping. We also give a few applications of our results in some special cases.

• 한국진공학회:학술대회논문집
• /
• 한국진공학회 2011년도 제40회 동계학술대회 초록집
• /
• pp.12-12
• /
• 2011

Interfacing functional materials with electrical or biological systems is of prime importance in terms of expanding applicative fields and obtaining high performances of devices. Herein, I report the functionalization of graphenes through supramolecular assembly and their electrochemical applications into fuel cells, supercapacitors, and biosensor devices. The solution processable nanohybridization of graphenes by functional materials such as ionic liquids, polyelectrolytes, block copolymers, and biomaterials, described herein would pave the way to obtain high performances of flexible energy and biosensor devices as well as to overcome the existing technology barriers.

• Bulletin of the Korean Chemical Society
• /
• 제34권2호
• /
• pp.661-664
• /
• 2013

• Nonlinear Functional Analysis and Applications
• /
• 제26권1호
• /
• pp.35-64
• /
• 2021

In this paper, we investigate an initial boundary value problem for a nonlinear pseudoparabolic equation. At first, by applying the Faedo-Galerkin, we prove local existence and uniqueness results. Next, by constructing Lyapunov functional, we establish a sufficient condition to obtain the global existence and exponential decay of weak solutions.

• Nonlinear Functional Analysis and Applications
• /
• 제26권5호
• /
• pp.1105-1114
• /
• 2021

In this paper, we prove a fixed point theorem for G-contractive type non-self mapping in cone metric space endowed with a graph. Our result generalizes many results in the literature and provide a new pavement for solving nonlinear functional equations.

• Nonlinear Functional Analysis and Applications
• /
• 제28권1호
• /
• pp.237-249
• /
• 2023

In this paper, by means of the Schauder fixed point theorem and Arzela-Ascoli theorem, the existence and uniqueness of solutions for a class of not instantaneous impulsive problems of nonlinear fractional functional Volterra-Fredholm integro-differential equations are investigated. An example is given to illustrate the main results.

• Kyungpook Mathematical Journal
• /
• 제64권2호
• /
• pp.245-260
• /
• 2024

In this study, we establish some new characterizations for a class of anisotropic Herz spaces in which all exponents are considered as variables. We also provide a description of these spaces based on bloc decomposition. As an application, we investigate the boundedness of certain sublinear operators within these function spaces.

• Nonlinear Functional Analysis and Applications
• /
• 제28권4호
• /
• pp.887-902
• /
• 2023

In this article, we investigate an approximate quadratic Lie *-derivation of a quadratic functional equation f(ax + by) + abf(x - y) = (a + b)(af(x) + bf(y)), where ab ≠ 0, a, b ∈ ℕ, associated with the identity f([x, y]) = [f(x), y²] + [x², f(y)] on a 𝜌-complete convex modular *-algebra χ_𝜌 by using ∆₂-condition via convex modular 𝜌.

• Journal of Electrochemical Science and Technology
• /
• 제12권2호
• /
• pp.204-211
• /
• 2021

We report, synthesis of high surface area composite carbon aerogel using additive based polymerization technique by incorporating graphitic porous carbon as additive. This additive was separately prepared using sol-gel polymerization of resorcinol-furfuraldehyde in iso-propyl alcohol medium at much above the routine gelation temperature to yield porous carbon (CA-IPA) having graphitic layered morphology. CA-IPA exhibited a unique combination of meso-pore dominated surface area (~ 700 m²/g) and good conductivity of ~ 300 S/m. The composite carbon aerogel (CCA) was synthesized by traditional aqueous medium based resorcinol-formaldehyde gelation with CA-IPA as additive. The presence of CA-IPA favored enhanced meso-porosity as well as contributed to improvement in bulk conductivity. Based on the surface area characteristics, CCA-8 composition having 8% additive was found to be optimum. It showed specific surface area of ~ 2056 m²/g, mesopore area of 827 m²/g and electrical conductivity of 180 S/m. The electrode formed with CCA-8 showed improved electrochemical behavior, with specific capacitance of 148 F/g & ESR < 1 Ω, making it a better choice as super capacitor for energy storage applications.

• Communications for Statistical Applications and Methods
• /
• 제20권4호
• /
• pp.271-281
• /
• 2013

This paper considers a problem of classification of variable stars based on functional data analysis. For a better understanding of galaxy structure and stellar evolution, various approaches for classification of variable stars have been studied. Several features that explain the characteristics of variable stars (such as color index, amplitude, period, and Fourier coefficients) were usually used to classify variable stars. Excluding other factors but focusing only on the curve shapes of variable stars, Deb and Singh (2009) proposed a classification procedure using multivariate principal component analysis. However, this approach is limited to accommodate some features of the light curve data that are unequally spaced in the phase domain and have some functional properties. In this paper, we propose a light curve estimation method that is suitable for functional data analysis, and provide a classification procedure for variable stars that combined the features of a light curve with existing functional data analysis methods. To evaluate its practical applicability, we apply the proposed classification procedure to the data sets of variable stars from the project STellar Astrophysics and Research on Exoplanets (STARE).