• Honam Mathematical Journal
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• v.45 no.1
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• pp.42-53
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• 2023

The main aim of this paper is to introduce the definition of 𝜑-proximate order of a meromorphic function on the complex plane. By considering the concept of 𝜑-proximate order, we will extend some previous results of Lahiri [11]. Furthermore, as an application of 𝜑-proximate order, a result concerning the growth of composite entire and meromorphic function will be given.

• Korean Journal of Organic Agriculture
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• v.5 no.1
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• pp.87-99
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• 1996

Cultural conditions for mass production of the antagonistic bacteria, Bacillus subtills CAP134 against pathogens causing major airborne diseases to apple tree, effect of temperature, pH, carbon and nitrogen source in the culture broth were investigated. The bacterial growth was most vigorous when the temperature and pH of the culture broth was 30~$35^{\circ}$C, and 7, respectively. As for carbon source, dextrose was best followed in order by dextrose(monosaccharides)>sucrose(disaccharides)$\geq$saccharose(di-saccharides)>starch (polysaccharides). Among different sugars, bacterial growth was favored by in the order of brown, black and white sugars, indicating that the bacterial growth might be promoted by the minor elements presented as impurities in the less purified sugars. As for nitrogen source, organic forms were better to bacterial growth than inorganic forms, that is polypeptone was best followed in order by soy sauce, soybeen milk and inoganic nitrogens. Differences in bacterial growth among different forms of inorganic nitrogen were negligible.

• Korean Journal of Organic Agriculture
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• v.6 no.1
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• pp.85-98
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• 1997

Cultural conditions for mass production of the antagonistic bacteria, Bacillus subtills CAP141 against pathogens causing major airborne diseases to apple trees, effects of temperature, pH, carbon and nitrogen source in the culture broth were investigated. The bacterial growth was most vigorous when the temperature and pH of the culture broth was 30~35$^{\circ}$C and 7, respectively. As for carbon source, dextrose was best followed in order by dextrose(monosaccharide) > sucrose(disaccharide) $\geq$ saccharose (market disaccharides) > starch (polysaccharieds). Among different sugars, bacterial growth was favored by in the order of brown, black and white supars, indicating that the bacterial growth might be promoted by the minor elements presented as impurities in the less purified sugars. As for nitrogen source, organic forms were better to bacterial growth than inorganic forms, that is polypeptone was best followed in order by soy sauce, soybeen milk and inorganic nitrogens. Differences in bacterial growth among different forms of inorganic nitrogen were negligible.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.485-494
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• 2018

In this paper some newly developed results based on the growth properties of relative order (relative lower order), relative type (relative lower type) and relative weak type of entire and meromorphic functions on the basis of integer translation applied upon them are investigated.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.229-241
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• 2020

For a second order linear differential equation f" + A(z)f' + B(z)f = 0, with A(z) and B(z) being transcendental entire functions under some restrictions, we have established that all non-trivial solutions are of infinite order. In addition, we have proved that these solutions, with a condition, have exponent of convergence of zeros equal to infinity. Also, we have extended these results to higher order linear differential equations.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.123-132
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• 2008

In this paper, we investigate higher-order linear differential equations with entire coefficients of iterated order. We improve and extend the result of L. Z. Yang by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen and the extended Wiman-Valiron theory by Wang and Yi. We also consider the nonhomogeneous linear differential equations.

• The Pure and Applied Mathematics
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• v.29 no.2
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• pp.125-139
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• 2022

In this paper we wish to establish some results relating to the growths of composition of two entire functions with their corresponding left and right factors on the basis of their generalized relative order (α, β) and generalized relative lower order (α, β) where α and β are continuous non-negative functions defined on (-∞, +∞).

• Journal of Plant Biology
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• v.13 no.1
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• pp.56-64
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• 1970

The present experiments differning from that conducted by agriculturists with the first consideration of food or seed production were performed in order to investigate the density effect on dry matter production in the artified population of maize. Three experimental plots were established and one seed was sown in the first plot, 2 seeds in the second plot and 3 seeds in the third plot, respectively. The space of each ridge was designed with 30cm in width and 50cm in length. The space of each seed was 4cm and the growth amount by density was measured through three times. The results obtained are as follows: 1) The total growth amount per unit area was in the order of the third, second and first plots until the second sampling. At the third sampling the whole plots showed almost the same growth amount except the first plot which showed a slightly smaller amount. 2) The growth amount per individual plant was in the order of the third, second and first plots until the second sampling, while the first plot showed drastic growth compared with the other two plots at the third sampling. 3) The growth amount by each organ(leaf, stem and root) of the plant body was markedly abundant in the stem of the non-productive part compared with that in the leaf of the productive part. Especially the root was affected remarkably by density and the first plot showed an abundant growth in comparison with the other plots which were too poor to resist the gound surface.

• Journal of Ocean Engineering and Technology
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• v.9 no.2
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• pp.112-122
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• 1995

In this work, prediction of fatigue life and fatigue crack growth are studied. 4th order polynominal function is presented to describe the crack growth behaviors from artifical pit of SM45C steel. Crack growth curves obtained from 4th order polyminal growth equations are in good agreement with experimental data The crack growth behaviors at arbitrary stress levels and investigated by the concept of elastic-plastic fracture mechanics using ${\Delta}J$. Fatigue life prediction are carried out by numerical integral method. Prediction lives obtained by proposed method in this study, is in good agreement with the experimental ones. Life prediction results calculated by using of ${\Delta}J$ better than those of ${\Delta}K$.

• 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.