• Bulletin of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.495-510
• /
• 2012

Let $X_1$, $X_2$,${\ldots}$, $X_n$ be a sequence of independent and identically distributed random variables with common distribution function $F$. Convergence rates for the moments of extremes are studied by virtue of second order regularly conditions. A unified treatment is also considered under second order von Mises conditions. Some examples are given to illustrate the results.

• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.1-16
• /
• 2007

Some Kamenev-type oscillation criteria are obtained for a second order quasilinear damped differential equation with impulses. These criteria generalize and improve some well-known results for second order differential equations with land without impulses. In addition, new oscillation criteria are also obtained to generalize and improve known results. Two examples of applications are given to illustrate the theory.

• Kyungpook Mathematical Journal
• /
• v.46 no.1
• /
• pp.65-77
• /
• 2006

By using general means, some oscillation criteria for second order nonlinear elliptic differential equation with damping $$\sum_{i,j=1}^{N}D_i[a_{ij}(x)D_iy]+\sum_{i=1}^{N}b_i(x)D_iy+p(x)f(y)=0$$ are obtained. These criteria are of a high degree of generality and extend the oscillation theorems for second order linear ordinary differential equations due to Kamenev, Philos and Wong.

• Communications of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.429-437
• /
• 2019

Dilcher and Stolarsky [1] recently studied a sequence resembling the Chebyshev polynomials of the first kind. In this paper, we follow their some research directions to the Chebyshev polynomials of the second kind. More specifically, we consider a sequence resembling the Chebyshev polynomials of the second kind in two different ways, and investigate its properties including relations between this sequence and the sequence studied in [1], zero distribution and the irreducibility.

• Journal of applied mathematics & informatics
• /
• v.37 no.3_4
• /
• pp.219-234
• /
• 2019

We use the definition of Euler polynomials of the second kind with (p, q)-numbers to identify some identities and properties of these polynomials. We also investigate some relationships between (p, q)-Euler polynomials of the second kind, (p, q)-Bernoulli polynomials, and (p, q)-tangent polynomials by using the properties of (p, q)-exponential function.

• Journal of applied mathematics & informatics
• /
• v.39 no.3_4
• /
• pp.339-358
• /
• 2021

Zagreb indices and their modified versions of a molecular graph are important descriptors which can be used to characterize the structural properties of organic molecules from different aspects. In this work, we investigate some properties of the modified second multiplicative Zagreb index of graphs with given connectivity. In particular, we obtain the maximum values of the modified second multiplicative Zagreb index with fixed number of cut edges, or cut vertices, or edge connectivity, or vertex connectivity of graphs. Furthermore, we characterize the corresponding extremal graphs.

• Kyungpook Mathematical Journal
• /
• v.63 no.1
• /
• pp.79-95
• /
• 2023

In this note, we define a Berger type deformed Sasaki metric as a natural metric on the second tangent bundle of a manifold by means of a biparacomplex structure. First, we obtain the Levi-Civita connection of this metric. Secondly, we get the curvature tensor, sectional curvature, and scalar curvature. Afterwards, we obtain some formulas characterizing the geodesics with respect to the metric on the second tangent bundle. Finally, we present the harmonicity conditions for some maps.

• The Bulletin of The Korean Astronomical Society
• /
• v.46 no.1
• /
• pp.30.4-31
• /
• 2021

We will present a scenario of the presence of a second AGN in a nearby Seyfert galaxy, NGC 1068. Using VLT/MUSE IFU data, we investigated the complex kinematics of ionized gas in the central region of NGC 1068. Interestingly, at a distance of 180 pc to the northeast from the nucleus of NGC 1068, we detected a kinematical signature of the launching point of AGN gas outflows, which suggests that there would be a second AGN. We will also discuss another supporting evidence of the second AGN based on previous spectropolarimetric results.

• Journal of Applied and Pure Mathematics
• /
• v.5 no.5_6
• /
• pp.375-387
• /
• 2023

In this paper, we construct a fully modified q-poly-Euler numbers and polynomials of the second type and give some properties. Finally, we investigate the zeros of the fully modified q-poly-Euler numbers and polynomials of the second type by using computer.

• Journal of Dental Rehabilitation and Applied Science
• /
• v.16 no.2
• /
• pp.79-92
• /
• 2000

The purpose of this study was to estimate the morphology and the size of permanent maxillary molar in Korean Adult. The 100 dental college students with a normal dentition and without any dental prosthesis and severe caries were selected for this study. The subjects were taken impression to make study model. On the study model, authour three times measured those sizes and estimated morphological structures with a calipers, a Boley gauge and a protractor. The results were as follows; 1. In the maxilary first molar's clinical crown height, mesiolingual cusp height was 6.34mm, mesiobuccal cusp height was 6.05mm, distobuccal cusp height was 5.20mm. And in the maxillary second molar's clinical crown height, mesiobuccal cusp height was 5.85mm, mesiolingual cusp height was 5.71mm, distobuccal cusp height was 5.51mm, distolingual cusp height was 3.53mm. This result considered that the maxillary first molar inclined to distobuccal, and the maxillary second molar more upright than the maxillary first molar. 2. In the width of clinical crown, the maxillary first molar was 10.43mm, the maxillary second molar was 10.20mm, and the difference between the first molar's width and the second molar's width was 0.23mm. 3. The crown thickness was measured divided into mesial buccolingual half and distal buccolingual half. The mesial buccolingual half was 11.14mm, and distal buccolingual half was 10.35mm in the maxillary first molar, and in the maxilary second molar, mesial buccolingual half was 11.25mm, and distal buccolingual half was 9.72mm. This result considered that height of convergency located in mesial half of crown. 4. In the buccal groove length, total length and ratio, the maxillary first molar was 52.5%, the maxillary second molar was 50%. And the development of buccal groove in the maxillary first molar was 59% in case of the well developed buccal groove and 41% in case of the weak developed one. And frequency of buccal pit of the maxillary first molar was 12.5%. Whereas, the frequency of buccal of the well developed buccal groove in the maxillary second molar was 37% and that of the weak developed one was 63%. And frequency of buccal pit of the maxillary second molar was not seen. 5. The 3 cusp type tooth cannot be found in the maxillary first molar and the frequency of 3 cusp type tooth in the maxillary second molar was as small as 6% 6. In the case of 4 cusp type tooth, the size of distal lingual cusp molar was difference between in the maxillary first molar and in the maxillary second molar by about 1mm. 7. The intercuspal distance was similar in the maxillary first premolar and second molar. And intercuspal distanc of mesial half of the maxillary first molar and the maxillary second molar was silmillar, too. 8. The an measurement of occlusal surface in 4 cusp type tooth showed that the angle of occlusal surface between the distobuccal and mesiolingual was an obtuse angle, and the angle of occlusal surface between mesiobuccal and distolingual was an acute angle in the both cases of maxillary first and second molar. 9. The measurements of the development of Carabelli cusp showed that the frequency of the well developed one was 7% and that of the weak developed one was 56% in the maxillary first molar. And there cannot be found the well developed one and can be found 2.5% only in the case of the weak developed one in the maxillary second molar. 10. The well developed oblique ridge in the maxillary first molar showed the 100% frequency and that in the maxillary second molar showed the 85.5% frequency. The frequency of mesiomarginal ridge tubercle in the maxillary first molar was 82% and that in the maxillary second molar was 30.5%. And the frequency of distal accessory tubercle in the maxillary first molar can be seen about 19% and that in the maxillary second molar can be seen about 12%.