• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.429-460
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• 2018

Let us consider that ${\mathbb{K}}$ be a complete ultrametric algebraically closed field and ${\mathcal{A}}({\mathbb{K}})$ be the ${\mathbb{K}}-algebra$ of entire functions on ${\mathbb{K}}$. In this paper we introduce the notions of (p, q)-th relative order and (p, q)-th relative type of p adic entire functions where p and q are any two positive integers and then study some growth properties of composite p adic entire functions in the light of their (p, q)-th relative order and (p, q)-th relative type. After that we show that (p, q) th relative order and (p, q)-th relative type are remain unchanged for derivatives under some certain conditions.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.411-421
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• 2016

In this paper, we investigate the problem of transcendental entire functions that share two values with one of their derivative. Let f be a transcendental entire function, n and k be two positive integers. If $f^n-Q_1$ and $(f^n)^{(k)}-Q_2$ share 0 CM, and $n{\geq}k+1$, then $(f^n)^{(k)}{\equiv}{\frac{Q_2}{Q_1}}f^n$. Furthermore, if $Q_1=Q_2$, then $f=ce^{\frac{\lambda}{n}z}$, where $Q_1$, $Q_2$ are polynomials with $Q_1Q_2{\not\equiv}0$, and c, ${\lambda}$ are non-zero constants such that ${\lambda}^k=1$. This result shows that the Conjecture given by W. $L{\ddot{u}}$, Q. Li and C. Yang [On the transcendental entire solutions of a class of differential equations, Bull. Korean Math. Soc. 51 (2014), no. 5, 1281-1289.] is true. Also we exhibit some examples to show that the conditions of our result are the best possible.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.179-196
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• 2018

In this paper we extend the two q-additions with powers in the umbrae, define a q-multinomial-coefficient, which implies a vector version of the q-binomial theorem, and an arbitrary complex power of a JHC power series is shown to be equivalent to a special case of the first q-Lauricella function. We then present several q-analogues of hypergeometric integral formulas from the two books by Exton and the paper by Choi and Rathie. We also find multiple q-analogues of hypergeometric integral formulas from the recent paper by Kim. Finally, we prove several multiple q-hypergeometric integral formulas emanating from a paper by Koschmieder, which are special cases of more general formulas by Exton.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.133-147
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• 2021

Our aim in this paper is to derive several new monotonicity properties and functional inequalities of some functions involving the q-gamma, q-digamma and q-polygamma functions. More precisely, some classes of functions involving the q-gamma function are proved to be logarithmically completely monotonic and a class of functions involving the q-digamma function is showed to be completely monotonic. As applications of these, we offer upper and lower bounds for this special functions and new sharp upper and lower bounds for the q-analogue harmonic number harmonic are derived. Moreover, a number of two-sided exponential bounding inequalities are given for the q-digamma function and two-sided exponential bounding inequalities are then obtained for the q-tetragamma function.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.443-458
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• 2022

In this paper, we apply the concept of intuitionistic Q-fuzzy set to PMS-algebras. We study the concept of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras and investigate some related properties of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras. We provide the relationship between an intuitionistic Q-fuzzy PMS-subalgebra and an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra. We establish a condition for an intuitionistic Q-fuzzy set in a PMS-algebra to be an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra. Characterizations of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras in terms of their level sets are given.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.475-490
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• 2019

Let C^(q) be the q-commuting arithmetic table of (x + y)ⁿ with noncommuting variables. We study sequential properties of diagonal sums of C^(q) with various q > 0. One of our results shows that each diagonal sum plays like Fibonacci number with some minor conditions.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.233-242
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• 2022

The purpose of this paper is to find some properties and identities for (p, q)-cosine Genocchi polynomials. This polynomials which is one of Appell polynomials, have multifarious relations of (p, q)-other polynomials.

• Applied Chemistry for Engineering
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• v.7 no.2
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• pp.379-386
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• 1996

Photosensitive compound, 1-methyl-4-[2-(4-diethylacetylphenyl)ethenyl] pridinium methosulfate(SbQ-A salt), was synthesized from dimethyl sulfate, terephthalaldehyde mono-(diethylacetal) and 4-picoline. SbQ-A salts were reacted with poly(vinyl alcohol)s, (PVA) in aqueous solution with phosphoric acid as catalyst to give photosensitive PVA-SbQ with different SbQ content and molecular weight. Relative photosensitivity of PVA-SbQ was determined by gray scale(GS) method. The rotative sensitivity of PVA-SbQ increased with increasing amount of bound SbQ in the case of high molecular weight(MW=77,000-79,000g/mol) as substrate and decreased with decreasing molecular weight of PVA with about constant(1.3mol%) amount of bound SbQ. The most sensitive polymer was obtained when SbQ group content in PVA-SbQ reached about 2.63mol% in the case of high molecular weight(77,000-79,000g/mol) PVA. This sample showed 90 times greater sensitivity than dichromated PVA as reference photosensitive system. PVA-SbQ photosensitive polymer synthesized was applied to the photolithographic screening process of phosphor on the panel of cathode ray tube(CRT). Phosphor slurry was made with PVA-SbQ, phosphor, a small amount of surfactant and other additives using water as medium. The slurry was coated onto panel, dried by heater, exposed to UV light and then developed by distilled water. When a small amount of cationic surfactant such as cetyltrimethylammonium chloride was used in the slurry formulation, the sharpness of phosphor pattern was equal to or better than that of dichromated PVA photosensitive polymer system used currently.

• Korean Journal of Environmental Biology
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• v.27 no.2
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• pp.191-197
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• 2009

In order to characterize the ecological traits of Q. mongolica, we treated the seedlings of this species with three environmental factors, light, moisture and nutrient gradients from March to October 2007, and measured morphological and ecological 17 characters. Lastly calculated ecological niche breadth and niche overlap between Q. mongolica-Q. acutissima and Q. mongolica-Q. variabilis, and analysed them with a special reference to ecological distribution pattern and their competition relationship in Korea. The ecological niche breadth of Q. mongolica showed the lowest in nutrient treatment, but the highest in soil moisture treatment. The ecological niche value under light was intermediate. On comparison of the ecological niche breadth of three oak species, Q. mongolica showed the highest in light environment, which might be a reason for the dominant distribution in the forest plant community, Korea. The ecological niche overlap of Q. mongolica-Q. acutissima and Q. mongolica-Q. varabilis was the widest in moisture treatment, but the narrowest in nutrient treatment and the intermediate in light one. These results means that these three oak species be most competitive in moisture environment than light or nutrient one, and that there are least differentiated among oak species for soil moisture condition. Cluster and PCA ordination showed that Q. mongolica and Q. acutissima were more closely arranged than Q. mongolica and Q. variabilis. From these results, it can be explained that Q. mongolica have more similar ecological niche with Q. acutissima than with Q. variabilis, consequently competition between Q. mongolica and Q. acutissima is intensive than Q. mongolica and Q. variabilis for environment condition, especially in soil moisture.

• Korean Journal of Plant Resources
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• v.22 no.3
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• pp.266-272
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• 2009

Morphological characteristics of leaves, trichomes and acorns were investigated in 6-year-old artificial hybrids of Q. aliena ${\times}$ Q. mongolica var. crispula and Q. serrata ${\times}$ Q. mongolica var. crispula. Leaf shapes of Q. aliena ${\times}$ Q. mongolica var. crispula $F_{1}$ were obovate and resembled to that of Q. aliena. But several characters including the size of leaf and petiole and the shape of leaf base resembled to those of Q. mongolica var. crispula. In F1 hybrids, small stellate hairs distributed sparsely on the abaxial surface and their lay length was intermediate between both parents. There were no big differences on characters of nuts and cupules between both parents and $F_{1}$ hybrids. Leaf shapes of Q. serrata ${\times}$ Q. mongolica var. crispula $F_{1}$ were obovate-elliptic, and the leaf shape and leaf base and the length of petiole resembled to those of Q. mongolica var. crispula, but leaf size and serration resembled to those of Q. serrata. The number of serration in a leaf was intermediate between both parents. Small stellate hairs distributed sparsely and large single hairs were mixed on the reverse side of leaves. there were no big differences on the number and size of stellate hairs between $F_{1}$ hybrid and Q. serrata. It is able to distinguish $F_{1}$ hybrids from both parents by the size leaf size and shapes, leaf base and serration, petiole length and trichome type in the leaf.