• Journal of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.785-795
• /
• 2018

In this paper, we give a uniqueness theorem on meromorphic solutions f of finite order of a class of differential-difference equations such that solutions f are uniquely determined by their poles and two distinct values.

• Kyungpook Mathematical Journal
• /
• v.50 no.1
• /
• pp.71-80
• /
• 2010

In this paper, we deal with the uniqueness problems of meromorphic functions that share a small function with its derivative and improve some results of Yang, Yu, Lahiri, and Zhang, also answer some questions of T. D. Zhang and W. R. L$\"{u}$.

• Journal of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.155-167
• /
• 1996

Let X be a compact Hausdorff space, C(X) denote the set of all continuous real valued functions on X and $\ell \in N$ be any natural number.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.6
• /
• pp.1511-1524
• /
• 2019

In this paper, we investigate the uniqueness of meromorphic functions of finite order concerning sharing small functions and prove that if f(z) and ${\Delta}_cf(z)$ share a(z), b(z), ${\infty}$ CM, where a(z), b(z)(${\neq}{\infty}$) are two distinct small functions of f(z), then $f(z){\equiv}{\Delta}_cf(z)$. The result improves the results due to Li et al. ([9]), Cui et al. ([1]) and $L{\ddot{u}}$ et al. ([12]).

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.3
• /
• pp.789-799
• /
• 2019

In this paper, we deal with unicity of a nonconstant zero-order meromorphic function f(z) and its shift f(qz) when they share four distinct values IM or share three distinct values with multiplicities truncated to level 4 in the extended complex plane, where $q{\in}\mathbb{C}{\setminus}\{0\}$. We also give an uniqueness result for f(z) sharing sets with its shift.

• Journal for History of Mathematics
• /
• v.21 no.3
• /
• pp.31-52
• /
• 2008

The concept of infinity, as with other scientific concepts, has a history of evolution. In the present work we intend to discuss the subject matter with regard to Bolzano since he is considered to be the first to accept the idea of actual infinity not just from a metaphysical perspective but from a mathematical one. Like modem platonists, Bolzano defended the infinite set itself regardless of the construction process; this is based on the principal of comprehension and unicity of denotation regarding all concepts. In addition, instead of considering as paradoxical the fact that a one-to-one correspondence existed between an infinite set and its parts, he regarded it in a positive way as a special characteristic. While the Greek era recognized the existence of only one infinity, Balzano acknowledged the existence of various types of infinity and formulated a logical definition for it. The question of infinity is a touchstone of constructive method which holds an increasingly important role in mathematics. The present study stops with just a brief reference to the subject matter and we will leave further in-depth investigation for later.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.19 no.1
• /
• pp.10-23
• /
• 1994

To transmit information efficiently and securely in On-line transmission, data compression, secrecy and authentication are required. In this paper, we propose LZWH4 which creates two compression strings with applying Hnageul to LZW. design HDES1 by extending S-box (S1-S16) which satsfies SAC and correlation coefficient as a partial countermeasure of Differential Cryptanalysis and implement LZWHDES1 which concatenates efficiently these for digital signature in On-line transmission. Also HDES1 is more in U.D.(Unicity Distance) than DES and HDES. We show that the proposed LZWHDES1 reduces processing times than LZWHDES which LZW is directly concatnated to DES and LZWHDES which LZWH1 is directly concatenated to HDES. LZWHDES1 can be used to digital signature system as conventional key cryptosystem.

• Journal of applied mathematics & informatics
• /
• v.33 no.5_6
• /
• pp.475-484
• /
• 2015

In this article, we deal with the uniqueness problems of meromorphic functions concerning differential polynomials and prove the following theorem. Let f and g be two nonconstant meromorphic functions, n ≥ 12 a positive integer. If fⁿ(f³ - 1)f′ and gⁿ(g³ - 1)g′ share (1, 2), f and g share ∞ IM, then f ≡ g. The results in this paper improve and generalize the results given by Meng (C. Meng, Uniqueness theorems for differential polynomials concerning fixed-point, Kyungpook Math. J. 48(2008), 25-35), I. Lahiri and R. Pal (I. Lahiri and R. Pal, Nonlinear differential polynomials sharing 1-points, Bull. Korean Math. Soc. 43(2006), 161-168), Meng (C. Meng, On unicity of meromorphic functions when two differential polynomials share one value, Hiroshima Math.J. 39(2009), 163-179).

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.205-226
• /
• 2018

In this paper, we show the Second Main Theorems for zero-order meromorphic mapping of ${\mathbb{C}}^m$ into ${\mathbb{P}}^n({\mathbb{C}})$ intersecting hyperplanes in subgeneral position without truncated multiplicity by considering the p-Casorati determinant with $p{\in}{\mathbb{C}}^m$ instead of its Wronskian determinant. As an application, we give some unicity theorems for meromorphic mapping under the growth condition "order=0". The results obtained include p-shift analogues of the Second Main Theorem of Nevanlinna theory and Picard's theorem.

• Communications for Statistical Applications and Methods
• /
• v.23 no.4
• /
• pp.321-334
• /
• 2016

In this paper, we propose power t distribution based on t distribution. We also study the properties of and inferences for power t model in order to solve the problem of real data showing both skewness and heavy tails. The comparison of skew t and power t distributions is based on density plots, skewness and kurtosis. Note that, at the given degree of freedom, the kurtosis's range of the power t model surpasses that of the skew t model at all times. We draw inferences for two parameters of the power t distribution and four parameters of the location-scale extension of power t distribution via maximum likelihood. The Fisher information matrix derived is nonsingular on the whole parametric space; in addition we obtain the profile log-likelihood functions on two parameters. The response plots for different sample sizes provide strong evidence for the estimators' existence and unicity. An application of the power t distribution suggests that the model can be very useful for real data.