• Nonlinear Functional Analysis and Applications
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• 제26권2호
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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.

• 한국식품영양학회지
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• 제22권4호
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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.

• 대한수학회보
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• 제32권1호
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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 $$ (0.1) \dot{p} = -\frac{\partial q}{\partial H}(p, q), \dot{q} = \frac{\partial p}{\partial H}(p, q) $$.

• 대한수학회논문집
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• 제14권1호
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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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• 제4권5_6호
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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.

• 대한수학회지
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• 제55권3호
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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.

• 충청수학회지
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• 제23권2호
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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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• 제63권2호
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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.

• 한국토양비료학회지
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• 제37권4호
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• pp.220-227
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• 2004

인산은 식물 영양 물질과 환경 오염원으로 대비되는 불질이의로, 인산의 탈착 반응에 대한 연구는 농업과 환경에 관련된 토양 중에서 인산의 작용기작을 이해하기 위하여 필수적이다. 본 연구는 인산 탈착 유효량(Q)과 가용량(I)의 매개 변수($Q_{max}$ 및 $I_0$)와 관련된 인산 완충력을 측정하고, 그 매개 변수와 토양 특성간의 상관관계에 대한 특징을 조사하였다. 토양은 인산 무처리 표본과 $KH_2PO_4$ 용액을 사용하여 $100mg\;P\;kg^{-1}$의 농토를 처리한 표본을 이용하였다. 인산 탈착 Q/I 곡선은 음이온교환수지비즈법을 사용하여 얻었고, 실험 방정식 ($Q=aI^{-1}+bIn(I+1)+c$)을 이용하여 탈착 곡선을 설명하였다. 유효 인산 함량이 높은 토양 (${\g}20mg\;kg^{-1}$ of Olsen P)에서는 인산 처리 유무와 관계 없이 인산 탈착 Q/I 곡선은 특징적인 오목형 곡선 형태를 보였으나, 유효 인산 함량이 낮은 토양 (${\lt}20mg\;kg^{-1}$ of Olsen P)에서는 인산의 추가 처리 없이는 오목형 인산 탈착 Q/I 곡선을 얻을 수 없었다. 인산 추가 처리 시, 고형의 불안정 결합형 인산량$Q_{max}$)과 용액 내 인산량($I_0$)은 증가하였으나, $Q_{max}$ 와 $I_0$의 비율은 감소하였다. 그로 인하여, 인산의 완충력($|BP_0|$)을 나타내는 인산 탈차 Q/I 곡선의 경사가 감소하였다. 유효 인산 함량이 높은 토양 중 인산 무처러 표본의 인산 완충력($|BP_0|$)은 $48\;61L\;kg^{-1}$ 인산 추가 처리 표본의 인산 완충력은 $18\;44L\;kg^{-1}$ 사이에서 나타났으며, 실험에 사용된 모든 토양에 인산을 추가 처리한 후 나타난 인산 완충력은 $14\;79L\;kg^{-1}$ 사이에서 나타났으며, 또한 $Q_{max}$ 계수는 $71.4\;173.1mg\;P\;kg^{-1}$, $I_0$ 계수는 $0.98\;3.72mg\;P\;L^{-1}$ 사이에서 다양하게 나타났다. 인산 완충력을 지배하는 $Q_{max}$ 및 $I_0$, 계수는 토양 특성 중 하나의 특정 인자와 관련된 것으로는 볼 수 없었다. 그러나, 이들 계수는 토양 pH, 점토함량, 유기물함량 빛 석회함유 여부와 복잡하게 관련되어 있다. 또한, 토양으로부터 인산의 방출 활성은 처리된 인산의 천연 불안정 인산의 탈착성에 현저히 의존하였다.

• Korean Journal of Mathematics
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• 제27권4호
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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.