• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.409-421
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• 2012

In this paper, using an efficient change of variables we refine the Hyers-Ulam stability of the alternative Jensen functional equations of J. M. Rassias and M. J. Rassias and obtain much better bounds and remove some unnecessary conditions imposed in the previous result. Also, viewing the fundamentals of what our method works, we establish an abstract version of the result and consider the functional equations defined in restricted domains of a group and prove their stabilities.

• Korean Journal of Mathematics
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• v.19 no.1
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• pp.33-52
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• 2011

We prove the Hyers-Ulam stability of partitioned functional equations in Banach modules over a unital $C^*$-algebra. It is applied to show the stability of algebra homomorphisms in Banach algebras associated with partitioned functional equations in Banach algebras.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.343-361
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• 2004

We prove the generalized Hyers-Ulam-Rassias stability of cyclic functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with cyclic functional equations in Banach algebras.

• Journal for History of Mathematics
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• v.31 no.5
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• pp.211-222
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• 2018

This paper surveys the theory of symmetry group of differential equations. A proof of the simplest version of the Noether's theorem on conservation laws has been presented with examples in the classical mechanics. As a new approach to the conservation laws the theory of characteristic cohomology due to S. H. Wang and others has been presented.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.29-45
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• 2004

We prove the Cauchy-Rassias stability of cyclic functional equations in Banach modules over a unital $C^*$-algebra.

• Tribology and Lubricants
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• v.11 no.5
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• pp.10-14
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• 1995

Over 300 equations and models were found in the leterature on friction and wear. No single equation on limited group of equations could be found for general on practical use. Recommandations are offered for improving the future yield of useful equatio

• International Journal of Aeronautical and Space Sciences
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• v.4 no.2
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• pp.1-8
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• 2003

Satellite formation flying is the placing micro-satellites with the same mission into nearby orbits to form a cluster. Clohessy-Wiltshire equations are used to describe the relative motion and control strategies between satellites within a cluster, which are known as Hill's equations. Even though Hill's equations are powerful in determining initial conditions for the satellite formation flying, they can not accurately express the relative motion under J2 perturbation. Some methods have been developed for the determination of initial conditions to avoid limits of Hill's equation. This paper gives a new method of determining initial conditions using mean elements. For this research mean elements were transformed to osculating elements using Brouwer's theory and the orbit was propaeated with the consideration of J2-J8 to get a relative position. The results show that satellites within a cluster are maintained in the desired boundary for long period and the method is effective on a fuel saving for satellite formation flying.

• Journal of the Korea Concrete Institute
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• v.11 no.3
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• pp.113-122
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• 1999

The present study is to investigate the possibility of overestimation or underestimation when the ACI Code equations are used to evaluate the unbonded tendon stress. An experimental program was planned with 6 beams which divided into two groups. Each group consisted of 3 beams to check the possibility of overestimation or underestimation of unbonded tendon stress. The experimental results were also compared with various design equations including the one proposed by Moon and Lim. It was proven that the ACI Code equations may overestimate or underestimate the unbonded tendon stress in certain cases.

• Journal of electromagnetic engineering and science
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• v.18 no.3
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• pp.160-168
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• 2018

A wide spectrum of potential applications using substrate integrated waveguide (SIW) technologies in conjunction with air hole regions is introduced, and an efficient optimization methodology to cope with the multiple air hole effect in SIW applications is proposed. The methodology adopts a genetic algorithm to obtain optimum air hole dimensions for the specific propagation constant that can be accurately calculated using the recursive and closed form equations presented. The optimization results are evaluated by designing an SIW bandpass filter, and they show excellent performance. The optimization methodology using the proposed equations is effective in performance enhancement for the purposes of low loss and broadband SIW applications.

• Korean Journal of Materials Research
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• v.11 no.9
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• pp.727-732
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• 2001

The cure kinetics of diglycidyl ether of bisphenol A (DGEBA)/4,4'- methylene dianiline (MDA) system with synthesized phenyl glycidyl ether-dimethylurea (PGE-DMU) was studied by Kissinger and Ozawa equations with DSC analysis in the temperature range of $20~300^{\circ}C$ To investigate the reaction mechanism between epoxy group of PGE and urea group of DMU, FT-lR spectroscopy analysis was used. The epoxide group of PGE reacted with the urea group of DMU and formed a hydroxyl group which acted as a catalyst on the cure reaction of other epoxide and amine groups. The activation energy of DGEBA/MDA system without PGE-DMU was 46.5 kJ/mol and those of the system with 5 and 10 phr of PGE- DMU were 43.4 and 37.0 kJ/mol, respectively. Ozawa method also showed the same tendency.