• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.331-345
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• 2021

Let p(z)be a polynomial of degree n. Then Bernstein's inequality [12,18] is $${\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;n\;{\max_{{\mid}z{\mid}=1}{\mid}(z){\mid}}$$. For q > 0, we denote $${\parallel}p{\parallel}_q=\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}$$, and a well-known fact from analysis [17] gives $${{\lim_{q{\rightarrow}{{\infty}}}}\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}={\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p(z){\mid}$$. Above Bernstein's inequality was extended by Zygmund [19] into L^q norm by proving ║p'║_q ≤ n║p║_q, q ≥ 1. Let p(z) = a₀ + ∑ⁿ_𝜈=𝜇 a_𝜈z^𝜈, 1 ≤ 𝜇 ≤ n, be a polynomial of degree n having no zero in |z| < k, k ≥ 1. Then for 0 < r ≤ R ≤ k, Aziz and Zargar [4] proved $${\max\limits_{{\mid}z{\mid}=R}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;{\frac{nR^{{\mu}-1}(R^{\mu}+k^{\mu})^{{\frac{n}{\mu}}-1}}{(r^{\mu}+k^{\mu})^{\frac{n}{\mu}}}\;{\max\limits_{{\mid}z{\mid}=r}}\;{\mid}p(z){\mid}}$$. In this paper, we obtain the L^q version of the above inequality for q > 0. Further, we extend a result of Aziz and Shah [3] into L^q analogue for q > 0. Our results not only extend some known polynomial inequalities, but also reduce to some interesting results as particular cases.

• The Korean Journal of Food And Nutrition
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• v.22 no.4
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• pp.577-586
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• 2009

Aging is associated with decreased energy expenditure, thermogenesis and energy requirements. Maintenance of physical fitness of the elderly has been reported to reduce the rate at which the basal metabolic rate, muscle strength, skeletal muscle mass and bone density deteriorate. Skeletal muscle disease is known to increase the risk of physical disability and psychological problems. This study was conducted to investigate changes in disability, emotional problems, body compositions, obesity indices and nutrient intake levels according to physical fitness with the elderly in rural areas. According to the results, physical fitness was negatively related with Activities of Daily Living(ADL, p<0.05), Instrumental Activities of Daily Living(IADL, p<0.001), Body Mass Index(BMI, p<0.001) and abdominal obesity(p<0.05), while it showed a positive correlation with the General Self Efficacy Scale(GSES)(p<0.001) and nutrient intake(p<0.05). When changes in these factors were compared according to the range of quartile of the Fullerton Advanced Balance Scale(FAB Scale), GSES(Q1=35.3, Q2=43.5, Q3=53.2, Q4=51.9, p<0.001), BMI(Q1=36.1%, Q2=34.7%, Q3=33.2%, Q4=28.6%, p<0.01), abdominal obesity(Q1=1.02, Q2=0.99, Q3=0.97, Q4=0.94, p<0.001) and nutrient intake(Q1=71.1%, Q2=75.4%, Q3=80.6%, Q4=80.2%, p<0.05) differed significantly. Taken together, these results suggested that better physical fitness would lead to a reduction in negative factors including physical disability and obesity indices, but to an increase in positive factors such as GSES and nutrient intake. The results of this study are expected to be used as basic data for the development of programs to promote the health of the elderly in a local society.

• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.1-11
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• 1995

Let $p, q \in R^2 and H : R^{2n} \to R^n$ be differentiable. An autonomous Hamiltonian system has the form $$ (0.1) \dot{p} = -\frac{\partial q}{\partial H}(p, q), \dot{q} = \frac{\partial p}{\partial H}(p, q) $$.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.69-74
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• 1999

In [2], the author discusses derivations of A(p,q) when A(p,q) is prime and p,q $\in$ A satisfy the condition A=Ap+Aq+R where R is a subspace of Z(A). In this paper, we consider a general-ization of Theorem 1 in [2] for the semiprime case of A(p,q).

• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.221-231
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• 2022

In this paper, we study differential equations arising from the generating functions of (p, q)-Hermite polynomials. We use this differential equation to give explicit identities for (p, q)-Hermite polynomials.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.671-694
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• 2018

In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\;{\mathbb{R}}^n,\;w_1){\times}{\cdots}{\times}L^{p_m}(l^{q_m};\;{\mathbb{R}}^n,\;w_m)$ to $L^p(l^q;\;{\mathbb{R}}^n,\;{\nu}_{\vec{w}})$, with $p_1,{\cdots},p_m$, $q_1,{\cdots},q_m{\in}(1,\;{\infty})$, $1/p=1/p_1+{\cdots}+1/p_m$, $1/q=1/q_1+{\cdots}+1/q_m$ and ${\vec{w}}=(w_1,{\cdots},w_m)$ a multiple $A_{\vec{P}}$ weights. Our argument also leads to the weighted weak type endpoint estimates for the commutators. As applications, we obtain some new weighted estimates for the $Calder{\acute{o}}n$ commutator.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.207-213
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• 2010

In this paper, we define the q-extension of the Hardy-Littlewood-type maximal operator related to q-Volkenborn integral. By the meaning of the extension of q-Volkenborn integral, we obtain the boundedness of the q-extension of the Hardy-Littlewood-type maximal operator in the p-adic integer ring.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.235-250
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• 2023

Let 1 ≤ p, q < ∞ be fixed, and let R = [r_jk] be an infinite scalar matrix such that 1 ≤ r_jk < ∞ and sup_j,k r_jk < ∞. Let 𝓑(𝑙_p, 𝑙_q) be the set of all bounded linear operator from 𝑙_p into 𝑙_q. For a fixed Banach algebra 𝐁 with identity, we define a new vector space S^R_p,q(𝐁) of infinite matrices over 𝐁 and a paranorm G on S^R_p,q(𝐁) as follows: let $$S^R_{p,q}({\mathbf{B}})=\{A:A^{[R]}{\in}{\mathcal{B}}(l_p,l_q)\}$$ and $G(A)={\parallel}A^{[R]}{\parallel}^{\frac{1}{M}}_{p,q}$, where $A^{[R]}=[{\parallel}a_{jk}{\parallel}^{r_{jk}}]$ and M = max{1, sup_j,k r_jk}. The existance of S^R_p,q(𝐁) equipped with the paranorm G(·) including its completeness are studied. We also provide characterizations of β -dual of the paranormed space.

• Korean Journal of Soil Science and Fertilizer
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• v.37 no.4
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• pp.220-227
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• 2004

Phosphorus desorption study is essential to understanding P behavior in agricultural and environmental soils because phosphorus is considered as two different aspects, a plant nutrient versus an environmental contaminant. This study was conducted to determine soil P buffering power related to P desorption quantity intensity (Q/I) parameters, $Q_{max}$(an index of P release capacity) and $l_0$(an index of the intensity factor), and to investigate the characteristics of relationship between the P desorption Q/I parameters and the soil properties. Soil samples were prepared with treatments of 0 and $100mg\;P\;kg^{-1}$ applied as $KH_2PO_4$ solution. The P desorption Q/I curves were obtained by a procedure using anion exchange resin beads and described by an empirical equation ($Q=aI^{-1}+bln(I+1)+c$). The P desorption Q/I curves for the high available P (${\g}20mg\;kg^{-1}$ of Olsen P) soils were characteristic concave trends with or without soil P enrichment, whereas for the low available P (${\lt}20mg\;kg^{-1}$ of Olsen P) soils, the anticipated Q/I concave curves could not be obtained without a proper amount of P addition. When the soils were enriched in phosphates, the values of desorbed solid phase labile P and solution P, such as $Q_{max}$ and $I_0$ respectively, were increased, but the ratio of $Q_{max}$ versus $I_0$ was decreased. Thus, the slope of desorption Q/I curve represented as phosphorus buffering power, $|BP_0|$, is decreased. The $|BP_0|$ values of the high available P soils ranged between 48 and $61L\;kg^{-1}$ in the P untreated samples and between 18 and $44L\;kg^{-1}$ in the P enriched samples. Overall $|BP_0|$ values of both low and high available P soils treated with $l00mg\;P\;kg^{-1}$ ranged between 14 and $79L\;kg^{-1}$. The $Q_{max}$, values ranged between 71.4 and $173.1mg\;P\;kg^{-1}$, and the lo values ranged between 0.98 and $3.82mg\;P\;L^{-1}$ in the P enriched soils. The $Q_{max}$ and $I_0$ values that control the P buffering power may be not specifically related to a specific soil property, but those values were complicatedly related to soil pH, clay content, soil organic matter content, and lime. Also, phosphorus release activity, however, markedly depended on the desorbability of the applied P as well as the native labile P.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.899-927
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• 2019

In this paper we establish some results depending on the comparative growth properties of composite entire and meromorphic functions using relative (p, q)-th order and relative (p, q)-th lower order where p, q are any two positive integers and that of a special type of differential polynomial generated by one of the factors.