• Journal of Advanced Navigation Technology
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• v.11 no.4
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• pp.388-393
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• 2007

In designing transform coders bit allocation is one of the important issues. In this paper we propose two optimal algorithms for integer bit allocation in transform coding. Based on high-resolution formulas for bit allocation, the most and least greedy algorithms are developed to optimally adjust non-integer bit rates of coefficient quantizers to integer values. In particular, a duality property is observed between the two greedy algorithms.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.179-192
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• 2012

We find the solution minimizing the shortfall risk by using the Lagrange-multiplier method. The conventional duality method in the expected utility maximization problem is used and we get the same results as in the paper [21].

• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.177-196
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• 2022

The Elzaki Transform method is fuzzified to fuzzy Elzaki Transform by Rehab Ali Khudair. In this article, we propose a Double fuzzy Elzaki transform (DFET) method to solving fuzzy partial differential equations (FPDEs) and we prove some properties and theorems of DFET, fundamental results of DFET for fuzzy partial derivatives of the n^th order, construct the Procedure to find the solution of FPDEs by DFET, provide duality relation of Double Fuzzy Laplace Transform (DFLT) and Double Fuzzy Sumudu Transform(DFST) with proposed Transform. Also we solve the Fuzzy Poisson's equation and fuzzy Telegraph equation to show the DFET method is a powerful mathematical tool for solving FPDEs analytically.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.387-396
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• 2005

In the setting of the half-plane of the complex plane, we introduce a modified reproducing kernel and we show that for $r>-1/2,\;B^{1,r}-cancellation$ property holds and the Bloch space is the dual space of $B^{1,r}$.

• Journal of Korean Institute of Industrial Engineers
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• v.32 no.4
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• pp.369-372
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• 2006

Suppose that a customer arrives at the GI/M/1/K queueing system when there are customers in the system, $n,m{\geq}0,\;n+m{\leq}K$. Sooner or later, the number of customers in the system will reach . In this paper, we present the Laplace transform of the remaining interarrival time upon reaching level, for the first time, since a customer arrived when there are customers in the system.

• Journal of Digital Convergence
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• v.3 no.1
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• pp.149-163
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• 2005

Researches for NN(nearest neighbor) query which is often used in LBS system, have been worked. However. Conventional NN query processing techniques are usually meaningless in moving object management system for LBS since their results may be invalidated as soon as the query and data objects move. To solve these problems, in this paper we propose a new nearest neighbor query processing technique, called CTNN, which is possible to meet continuous trajectory nearest neighbor query processing. The proposed technique consists of Approximate CTNN technique which has quick response time, and Exact CTNN technique which makes it possible to search accurately nearest neighbor objects. Experimental results using GSTD datasets shows that the Exact CTNN technique has high accuracy, but has a little low performance for response time. They also shows that the Approximate CTNN technique has low accuracy comparing with the Exact CTNN, but has high response time.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.409-445
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• 2016

The class $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ defined in the domain ${\mid}z{\mid}$ < 1 satisfying $Re\;e^{i{\phi}}\((1-{\alpha}+2{\gamma})(f/z)^{\delta}+\({\alpha}-3{\gamma}+{\gamma}\[1-1/{\delta})(zf^{\prime}/f)+1/{\delta}\(1+zf^{\prime\prime}/f^{\prime}\)\]\)(f/z)^{\delta}(zf^{\prime}/f)-{\beta}\)$ > 0, with the conditions ${\alpha}{\geq}0$, ${\beta}$ < 1, ${\gamma}{\geq}0$, ${\delta}$ > 0 and ${\phi}{\in}{\mathbb{R}}$ generalizes a particular case of the largest subclass of univalent functions, namely the class of $Bazilevi{\check{c}}$ functions. Moreover, for 0 < ${\delta}{\leq}{\frac{1}{(1-{\zeta})}}$, $0{\leq}{\zeta}$ < 1, the class $C_{\delta}({\zeta})$ be the subclass of normalized analytic functions such that $Re(1/{\delta}(1+zf^{\prime\prime}/f^{\prime})+1-1/{\delta})(zf^{\prime}/f))$ > ${\zeta}$, ${\mid}z{\mid}$<1. In the present work, the sucient conditions on ${\lambda}(t)$ are investigated, so that the non-linear integral transform $V^{\delta}_{\lambda}(f)(z)=\({\large{\int}_{0}^{1}}{\lambda}(t)(f(tz)/t)^{\delta}dt\)^{1/{\delta}}$, ${\mid}z{\mid}$ < 1, carries the fuctions from $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ into $C_{\delta}({\zeta})$. Several interesting applications are provided for special choices of ${\lambda}(t)$. These results are useful in the attempt to generalize the two most important extremal problems in this direction using duality techniques and provide scope for further research.

• The KIPS Transactions:PartB
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• v.10B no.5
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• pp.553-560
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• 2003

Since Wavelet Transform decomposes a video frame into subbands with various frequencies and resolutions, the reconstructed video qualify at a receiver fluctuates according to the location of transmission errors within frames. This deteriorates the whole visual duality of the video. Specifically, for a wavelet based video which exploits the motion estimation prediction scheme, the transmission errors of a subband not only have a bad effect on other subbands within a same frame but also propagates to the subsequent frames. In this paper, we propose BDP(Block Based Dispersive Packetization) scheme, for a wavelet based video stream, which maintains constant video quality despite packet location that a transmission error occurs. To evaluate the performance of the proposed scheme, we use MRME(Multi-Resolution Motion Estimation) scheme to compress a video in Inter coding mode and Gilbert´s error model to generate the error patterns in wireless network environment. The simulation results show that BDP is more efficient than BP (Block based Packetization) or DP (Dispersive Packetization) in both PSNR and visual quality.

• Research in Mathematical Education
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• v.14 no.3
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• pp.195-209
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• 2010

Utilizing a structure of operations known as Dissection-Motion-Operations (DMO), a set of mathematics propositions or area-formulas in school mathematics will be introduced through shape-to-shape transforms. The underlying theme for DMO is problem-solving through visual reasoning and proving manipulatively or electronically vs. rote learning and memorization. Visual reasoning is the focus here where two operations that constitute DMO are utilized. One operation is known as Dissection (or Decomposition) operation that operates on a given region in 2D or 3D and dissects it into a number of subregions. The second operation is known as Motion (or Composition) operation applied on the resultant sub-regions to form a distinct area (or volume)-equivalent region. In 2D for example, DMO can transform a given polygon into a variety of new and distinct polygons each of which is area-equivalent to the original polygon (cf [Rahim, M. H. & Sawada, D. (1986). Revitalizing school geometry through Dissection-Motion Operations. Sch. Sci. Math. 86(3), 235-246] and [Rahim, M. H. & Sawada, D. (1990). The duality of qualitative and quantitative knowing in school geometry, International Journal of Mathematical Education in Science and Technology 21(2), 303-308]).

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.9
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• pp.2120-2133
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• 2013

In this paper, we address the problem of linear minimum mean-squared error (MMSE) transmitter design for the cognitive radio (CR) multi-user multiple-input single-output (MU-MISO) broadcasting channel (BC), where the cognitive users are subject to not only a sum power constraint, but also a interference power constraint. Evidently, this multi-constraint problem renders it difficult to solve. To overcome this difficulty, we firstly transform it into its equivalent formulation with a single constraint. Then by utilizing BC-MAC duality, the problem of BC transmitter design can be solved by focusing on a dual MAC problem, which is easier to deal with due to its convexity property. Finally we propose an efficient two-level iterative algorithm to search the optimal solution. Our simulation results are provided to corroborate the effectiveness of the proposed algorithm and show that this proposed CR MMSE-based scheme achieves a suboptimal sum-rate performance compared to the optimal DPC-based algorithm with less computational complexity.