• The Pure and Applied Mathematics
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• v.25 no.3
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• pp.181-191
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• 2018

In the present paper, we investigate the action of generalized derivation G associated with a derivation g in a (semi-) prime ring R satisfying $(G([x,y])-[G(x),y])^n=0$ for all x, $y{\in}I$, a nonzero ideal of R, where n is a fixed positive integer. Moreover, we also examine the above identity in Banach algebras.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.731-740
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• 2002

We derive the generalized Hermite interpolation by using the contour integral and extend the generalized Hermite interpolation to obtain the sampling expansion involving derivatives for band-limited functions f, that is, f is an entire function satisfying the following growth condition ｜f(ｚ)｜$\leq$ A exp($\sigma$｜y｜) for some A, $\sigma$ > 0 and any ｚ=$\varkappa$ + iy∈C.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.1-8
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• 2002

Let $T_{\phi}$ be a generalized Gauss transformation and $[a_1,\;a_2,\;{\cdots}]_{T_{\phi}}$ be a symbolic representation of $x{\in}[0,\;1)$ induced by $T_{\phi}$, i.e., generalized continued fraction expansion induced by $T_{\phi}$. It is shown that the distribution of relative frequency of [$k_1,\;{\cdots},\;k_n$] in $[a_1,\;a_2,\;{\cdots}]_{T_p}$ satisfies Central Limit Theorem where $k_i{\in}{\mathbb{N}}$ for $1{\leq}i{\leq}n$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1467-1480
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• 2015

Generalized Fibonacci and Lucas sequences ($U_n$) and ($V_n$) are defined by the recurrence relations $U_{n+1}=PU_n+QU_{n-1}$ and $V_{n+1}=PV_n+QV_{n-1}$, $n{\geq}1$, with initial conditions $U_0=0$, $U_1=1$ and $V_0=2$, $V_1=P$. This paper deals with Fibonacci and Lucas numbers of the form $U_n$(P, Q) and $V_n$(P, Q) with the special consideration that $P{\geq}3$ is odd and Q = -1. Under these consideration, we solve the equations $V_n=5kx^2$, $V_n=7kx^2$, $V_n=5kx^2{\pm}1$, and $V_n=7kx^2{\pm}1$ when $k{\mid}P$ with k > 1. Moreover, we solve the equations $V_n=5x^2{\pm}1$ and $V_n=7x^2{\pm}1$.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.6
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• pp.563-567
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• 2001

We generalize the widebane P0-weyl symbol (P0WS) and the widebane spreading function (WSF) using the generalized warping function . The new generalized P0WS and WSF are useful for analyzing system and communication channels producing generalized time shifts. We also investigated the relationship between the affine Wey1 symbol(AWS) and the P0WS. By using specific warping functions, we derive new P0WS and WSF as analysis tools for systems and communication channels with non-linear group delary characteristics. The new P0WS preserves specific types of changes imposed on random processes. The new WSF provides a new interpretation of output of system and communication channel as weighted superpositions of non-linear time shifts on the input. It is compared to the conventional method obtaining output of system and communication channel as a convention integration of the input with the impulse response of the system and the communication channel. The convolution integration can be interpreted as weighted superpositions of liner time shifts on the input where the weight is the impulse response of the system and the communication channel. Application examples in analysis and detection demonstrate the advantages of our new results.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.591-601
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• 2009

In the present paper, one new generalized 'useful' information generating function and two new relative 'useful' information generating functions have been defined with their particular and limiting cases. It is interesting to note that differentiations of these information generating functions at t=0 or t=1 give some known and unknown generalized measures of useful information and 'useful' relative information. The information generating functions facilitates to compute various measures and that has been illustrated by applying these information generating functions for Uniform, Geometric and Exponential probability distributions.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.601-607
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• 1996

For functions $f(z) = \sum_{n = 0}^{\infty}a_n z^n$ and $g(z) = \sum_{n = 0}^{\infty} b_n z^n$ analytic in the unit disk $\Delta = {z : $\mid$z$\mid$ < 1}$, the convolution $f * g$ is defined by $(f * g)(z) = \sum_{n = 0}^{\infty}a_n b_n z^n$. Let S denote the family of functions $f(z) = z + \cdots$ analytic and univalent in $\Delta$ and K, St, C the subfamilies that are respectively convex, starlike, and close-to-convex.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.977-994
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• 2004

A pair of quasi-definite linear functionals {u$_{0}$, u$_1$} is a generalized $\Delta$-coherent pair if monic orthogonal polynomials (equation omitted) relative to u$_{0}$ and u$_1$, respectively, satisfy a relation (equation omitted) where $\sigma$$_{n}$ and T$_{n}$ are arbitrary constants and $\Delta$p = p($\chi$＋1) - p($\chi$) is the difference operator. We show that if {u$_{0}$, u$_1$} is a generalized $\Delta$-coherent pair, then u$_{0}$ and u$_{1}$ must be discrete-semiclassical linear functionals. We also find conditions under which either u$_{0}$ or u$_1$ is discrete-classical.ete-classical.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.815-834
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• 1995

Let $\Omega$ be a rectangular domain in $R^2$ with boundary $\partial\Omega$, and T be a positive real number such that $0 < T < \infty$.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1003-1013
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• 1996

The existence of a bounded generalized solution on the real line for a nonlinear functional evolution problem of the type $$ (FDE) x'(t) + A(t,x_t)x(t) \ni 0, t \in R $$ in a general Banach spaces is considered. It is shown that (FDE) has a bounded generalized solution on the whole real line with well-known Crandall and Pazy's result and recent results of the functional differential equations involving the operator A(t).