• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.777-785
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• 2010

Let X be a linear space and Y be a complete quasi p-norm space. We will show that for each function f : X $\rightarrow$ Y, which satisfies the inequality ${\parallel}{\Delta}_x^nf(y)\;-\;n!f(x){\parallel}\;{\leq}\;\varphi(x,y)$ for suitable control function $\varphi$, there is a unique monomial function M of degree n which is a good approximation for f in such a way that the continuity of $t\;{\mapsto}\;f(tx)$ and $t\;{\mapsto}\;\varphi(tx,\;ty)$ imply the continuity of $t\;{\mapsto}\;M(tx)$.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.387-397
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• 2017

In order to react the dynamic behavior of the system more actually, it is necessary to solve the first problem of synchronization for Markovian jump complex network system in practical engineering problem. In this paper, the problem of local stochastic synchronization for Markovian nonlinear coupled neural network system is investigated, including nonlinear coupling terms and mode-dependent delays, that is less restriction to other system. By designing the Lyapunov-Krasovskii functional and applying less conservative inequality, we get a new criterion to ensure local synchronization in mean square for Markovian nonlinear coupled neural network system. The criterion introduced some free matrix variables, which are less conservative. The simulation confirmed the validity of the conclusion.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.429-438
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• 2015

The objective of this paper is to obtain sharp upper bound for the second Hankel functional associated with the $k^{th}$ root transform $[f(z^k)]^{\frac{1}{k}}$ of normalized analytic function f(z) when it belongs to the class of starlike and convex functions with respect to symmetric points, defined on the open unit disc in the complex plane, using Toeplitz determinants.

• The Pure and Applied Mathematics
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• v.16 no.2
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• pp.199-212
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• 2009

We investigate the multiplicity of the nontrivial periodic solutions for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition. We show that the system has at least two nontrivial periodic solutions by the abstract version of the critical point theory on the manifold with boundary. We investigate the geometry of the sublevel sets of the corresponding functional of the system and the topology of the sublevel sets. Since the functional is strongly indefinite, we use the notion of the suitable version of the Palais-Smale condition.

• The Pure and Applied Mathematics
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• v.24 no.2
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• pp.109-127
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• 2017

In this paper, we solve the following quadratic ${\rho}-functional$ inequalities ${\parallel}f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z){\parallel}$ (0.1) ${\leq}{\parallel}{\rho}(f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z)){\parallel}$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < ${\frac{1}{{\mid}4{\mid}}}$, and ${\parallel}f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z){\parallel}$ (0.2) ${\leq}{\parallel}{\rho}(f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z)){\parallel}$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < ${\mid}8{\mid}$. Using the direct method, we prove the Hyers-Ulam stability of the quadratic ${\rho}-functional$ inequalities (0.1) and (0.2) in non-Archimedean Banach spaces and prove the Hyers-Ulam stability of quadratic ${\rho}-functional$ equations associated with the quadratic ${\rho}-functional$ inequalities (0.1) and (0.2) in non-Archimedean Banach spaces.

• Journal of The Korean Society of Integrative Medicine
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• v.1 no.2
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• pp.37-46
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• 2013

Purpose : The purpose of the research was to analyze foot pressure, foot temperature, and correlation between foot pressure and foot temperature to grasp impact on foot pressure and body temperature distribution chart depending on functional difference of leg length. Method : After measuring leg length, put 15 students whose functional difference of leg length was over 10mm to difference group and 15 students whose functional difference of leg length was under 5mm to normal group and categorize soles of foot into 6 sections of hallux head, 1st metatarsal head, 2-4 metatarsal head, 5 metatarsal head, lateral heel, and then measure by foot pressure analyzer to analyze characteristic of pressure distribution and classify into front of the lower leg, back of the lower leg, soles of foot and measure by body temperature analyzer to analyze by checking body temperature. Result : Weight difference depending on foot pressure and body temperature was bigger when functional difference of leg length was bigger, and it could be confirmed that foot pressure and body temperature of short leg side were higher than those of short leg side. Thus, if difference exists in leg length, weight load on short leg side increases which results in higher foot pressure and body temperature, therefore enabling an assumption that mechanical problem will occur in short leg. Conclusion : When functional leg length inequality, weight bearing and pressure was getting high as a result, temperature was getting high in short leg.

• Journal of the Korean Society of Physical Medicine
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• v.2 no.2
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• pp.101-112
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• 2007

Purpose : The purpose of this study was to evaluate influence of sacroiliac joint mobilization on lower extremity muscle strength. Methods : The subjects were consisted of thirty patients who had Leg length inequality(LLI) of more than 10mm(16 females. 14 males) from 21 to 41 years of age(mean aged 24.87). All subjects randomly assigned to sacroiliac joint mobilization group(n=15), control group(n=15). sacroiliac joint mobilization group received sacroiliac joint mobilization about 10 minutes for 3 times per week during 4 weeks period. Control group not received intervention during 4 weeks period. The tape measure method(TMM) was used to measure functional Leg length inequality. Biodex System 3 Pro was used to measure strength of Knee extension & flexion. All measurements of each subjects were measured at pre-test, 2weeks post-test and 4weeks post-test. Results : 1. The LLI of sacroiliac joint mobilization group was significantly reduced according to within treatment period(p<.05), most significantly reduced between pre-test and post-test(p<.05). sacroiliac joint mobilization group significantly more reduced than control group(p<.05). 2. The knee extension strength of sacroiliac joint mobilization group was significantly increased according to within treatment period(p<.05), most significantly increased between pre-test and post-test(p<.05). sacroiliac joint mobilization group significantly more increased than control group(p<.05). 3. The knee flexion strength of sacroiliac joint mobilization group was significantly increased according to within treatment period(p<.05), most significantly increased between pre-test and post-test(p<.05). sacroiliac joint mobilization group significantly more increased than control group(p<.05). Conclusion : sacroiliac joint mobilization can reduce LLI and increased lower extremity muscle strength.

• Korean Journal of Health Education and Promotion
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• v.32 no.2
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• pp.27-37
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• 2015

Objectives: As the increasing of the length of the lifespan, more recent policy interest are concerned with how many years of life are lived without functional disability or activity limitation. We investigated the relationship between deprivation and activity limitation at the 251 local authority level. Methods: The data were derived from the 2010 Census 10% sample data. Crude and age-standardized activity limitation rates by gender at the ages of 50 or over and deprivation index were calculated. Mapping and multiple linear regression analysis were applied to explore relationship between area activity limitation and area deprivation. Results: There were considerable differences in activity limitation rate across the 251 local authorities. Age-standardized activity limitation rate in both male and female were strongly associated with the level of area deprivation. Especially, low social class, male unemployment, or non-apartment residents at the local level were strong positive association with local authorities' age-standardized activity limitation. Conclusion: More policy attention is needed for tackling regional inequality in activity limitation among older adults.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.249-259
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• 2022

Let 𝓐 be a unital C^*-algebra. Then it follows that $\sum\limits_{i=1}^{n}(a_ia^*_i)^{\frac{1}{2}}{\leq}\sqrt{n}\(\sum\limits_{i=1}^{n}a_ia^*_i\)^{\frac{1}{2}}$, ∀n ∈ ℕ, ∀a₁, …, a_n ∈ 𝓐. By modifications of arguments of Botelho-Andrade, Casazza, Cheng, and Tran given in 2019, for certain n-tuple x = (a₁, …, a_n) ∈ 𝓐ⁿ, we give a method to compute a positive element c_x in the C^*-algebra 𝓐 such that the equality $$\sum\limits_{i=1}^{n}(a_ia^*_i)^{\frac{1}{2}}=c_x\sqrt{n}\(\sum\limits_{i=1}^{n}a_ia^*_i\)^{\frac{1}{2}}$$ holds. We give an application for the integral of Kasparov. We also derive a formula for the exact constant for the continuous ℓ₁ - ℓ₂ inequality.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.963-972
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• 2023

In this paper, geometrically convex and s-convex functions in third and fourth sense are merged to form (g, s)-convex function. Characterizations of (g, s)-convex function, algebraic and functional properties are presented. In addition, novel functions based on the integral of (g, s)-convex functions in the third sense are created, and inequality relations for these functions are explored and examined under particular conditions. Further, there are also some relationships between (g, s)-convex function and previously defined functions. The (g, s)-convex function and its derivatives will then be used to extend the well-known H-H and Fejer's type inequalities. In order to obtain the previously mentioned conclusions, several special cases from previous literature for extended H-H and Fejer's inequalities are also investigated. The relation between the average (mean) values and newly created H-H and Fejer's inequalities are also examined.