• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.687-689
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• 2012

We find an upper bound on the least positive exponent of a nonzero Fourier coefficient for a modular form with a nonzero constant term for ${\Gamma}_0(N)$ under certain conditions where N is a prime number $p$ or $2p$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.983-991
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• 2013

For each real number $n$ > 6, we prove that there is a sequence $\{pk(n,z)\}^{\infty}_{k=1}$ of fourth degree self-reciprocal polynomials such that the zeros of $p_k(n,z)$ are all simple and real, and every $p_{k+1}(n,z)$ has the largest (in modulus) zero ${\alpha}{\beta}$ where ${\alpha}$ and ${\beta}$ are the first and the second largest (in modulus) zeros of $p_k(n,z)$, respectively. One such sequence is given by $p_k(n,z)$ so that $$p_k(n,z)=z^4-q_{k-1}(n)z^3+(q_k(n)+2)z^2-q_{k-1}(n)z+1$$, where $q_0(n)=1$ and other $q_k(n)^{\prime}s$ are polynomials in n defined by the severely nonlinear recurrence $$4q_{2m-1}(n)=q^2_{2m-2}(n)-(4n+1)\prod_{j=0}^{m-2}\;q^2_{2j}(n),\\4q_{2m}(n)=q^2_{2m-1}(n)-(n-2)(n-6)\prod_{j=0}^{m-2}\;q^2_{2j+1}(n)$$ for $m{\geq}1$, with the usual empty product conventions, i.e., ${\prod}_{j=0}^{-1}\;b_j=1$.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.28 no.2
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• pp.267-271
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• 1983

The southern parts varieties have shown higher content of Oleic acid, Linoleic acid, Vitamin A, Alcaloid, Ca, P and Fe than northern parts Varieties. The $N.\;P_2O_5\;and\;K_2O content of narrow leaf were higher than wide leaf, on the other hand the Ca, Mg, Fe and $SiO_2$ content of wide leaf were higher than narrow leaf. The content of $N, \;P_2O_5, \;K_2O$ have shown higher in first yellow leaf date, the content of Ca has shown higher in first falling leaf date and the content of Mn and Cu content have shown higher in second new leaf date.

• Journal of Magnetics
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• v.18 no.2
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• pp.81-85
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• 2013

We investigate the electronic and magnetic properties in Cu-doped InN with the N vacancy ($V_N$) from first principles calculations. There is the long-range ferromagnetic order between two Cu atoms, attributed to the hole-mediated double exchange through the strong p-d interaction between the Cu atom and neighboring N atom. The system of $V_N$ defect in Cu-doped InN has the lowest formation energy. Due to the hybridization between the Cu-3d and $V_N$ states, the spin-polarization on the Cu atoms in the InN lattice is reduced by $V_N$ defect. So, it shows a weak ferromagnetic behavior.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.243-257
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• 2022

In this paper, we present and prove an new theorem on symmetric functions. By using this theorem, we derive some new generating functions of the products of (p, q)-Fibonacci numbers, (p, q)-Lucas numbers, (p, q)-Pell numbers, (p, q)-Pell Lucas numbers, (p, q)-Jacobsthal numbers and (p, q)-Jacobsthal Lucas numbers with Chebyshev polynomials of the first kind.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.341-352
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• 2019

Let M be an n-dimensional closed Riemannian manifold with metric g, $d{\mu}=e^{-{\phi}(x)}d{\nu}$ be the weighted measure and ${\Delta}_{p,{\phi}}$ be the weighted p-Laplacian. In this article we will study the evolution and monotonicity for the first nonzero eigenvalue problem of the weighted p-Laplace operator acting on the space of functions along the Yamabe flow on closed Riemannian manifolds. We find the first variation formula of it along the Yamabe flow. We obtain various monotonic quantities and give an example.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1429-1440
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• 2007

Let ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ be a multiple Kravchuk polynomial with respect to r discrete Kravchuk weights. We first find a lowering operator for multiple Kravchuk polynomials ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ in which the orthogonalizing weights are not involved. Combining the lowering operator and the raising operator by Rodrigues# formula, we find a (r+1)-th order difference equation which has the multiple Kravchuk polynomials ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ as solutions. Lastly we give an explicit difference equation for ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ for the case of r=2.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.931-940
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• 2009

Given a system of smooth 1-forms $\theta$ = ($\theta^1$,...,$\theta^s$) on a smooth manifold $M^m$, we give a necessary and sufficient condition for M to be foliated by integral manifolds of dimension n, n $\leq$ p := m - s, and construct an integrable supersystem ($\theta,\eta$) by finding additional 1-forms $\eta$ = ($\eta^1$,...,$\eta^{p-n}$). We also give a necessary and sufficient condition for M to be foliated by reduced submanifolds of dimension n, n $\geq$ p, and construct an integrable subsystem ($d\rho^1$,...,$d\rho^{m-n}$) by finding a system of first integrals $\rho=(\rho^1$,...,$\rho^{m-n})$. The special case n = p is the Frobenius theorem on involutivity.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.521-534
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• 2009

In this paper we present new large-update primal-dual interior point algorithms for $P_*$ linear complementarity problems(LAPS) based on a class of kernel functions, ${\psi}(t)={\frac{t^{p+1}-1}{p+1}}+{\frac{1}{\sigma}}(e^{{\sigma}(1-t)}-1)$, p $\in$ [0, 1], ${\sigma}{\geq}1$. It is the first to use this class of kernel functions in the complexity analysis of interior point method(IPM) for $P_*$ LAPS. We showed that if a strictly feasible starting point is available, then new large-update primal-dual interior point algorithms for $P_*$ LAPS have $O((1+2+\kappa)n^{{\frac{1}{p+1}}}lognlog{\frac{n}{\varepsilon}})$ complexity bound. When p = 1, we have $O((1+2\kappa)\sqrt{n}lognlog\frac{n}{\varepsilon})$ complexity which is so far the best known complexity for large-update methods.

• Nutrition Research and Practice
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• v.15 no.3
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• pp.367-381
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• 2021

BACKGROUND/OBJECTIVES: This study aimed to establish a mother and child cohort in the Chinese population, and investigate human breastmilk (HBM) composition and its relationship with maternal body mass index (BMI) and infant growth during the first 3 mon of life. SUBJECTS/METHODS: A total of 101 Chinese mother and infant pairs were included in this prospective cohort. Alterations in the milk macronutrients of Chinese mothers at 1 mon (T1), 2 mon (T2), and 3 mon (T3) lactation were analyzed. HBM fatty acid (FA) profiles were measured by gas chromatography (GC), and HBM proteomic profiling was achieved by matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometry (MS). RESULTS: During the first 3 mon of lactation (P < 0.05), significant decreases were determined in the levels of total energy, fat, protein, and osteopontin (OPN), as well as ratios of long-chain saturated FA (including C16:0, C22:0 and C24:0), monounsaturated FA (including C16:1), and n-6 poly unsaturated FA (PUFA) (including C20:3n-6 and C20:4n-6, and n-6/n-3). Conversely, butyrate, C6:0 and n-3 PUFA C18:3n-3 (α-linolenic acid, ALA) were significantly increased during the first 3 mon (P < 0.05). HBM proteomic analyses distinguished compositional protein differences over time (P = 0.001). Personalized motherinfant analyses demonstrated that HBM from high BMI mothers presented increased total energy, fat, protein and OPN, and increased content of n-6 PUFA (including C18:3n-6, C20:3n-6 and n-6/n-3 ratio) as compared with low BMI mothers (P < 0.05). Furthermore, BMI of the mothers positively correlated with the head circumference (HC) of infants as well as the specific n-6 PUFA C20:3n-6 over the 3 time points examined. Infant HC was negatively associated with C18:0. CONCLUSION: This study provides additional evidence to the Chinese HBM database, and further knowledge of FA function. It also helps to establish future maternal strategies that support the healthy growth and development of Chinese infants.