• Korean Journal of Mathematics
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• v.27 no.3
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• pp.723-734
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• 2019

We study the negative trinomial table T' of $(x^2+x+1)^{-n}$ and its t/u-slope diagonals for any t, u > 0. We investigate recurrence formula of the t/u-slope diagonal sums of T' and find interrelationships with t/u-slope diagonal sums of the trinomial table T.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.635-644
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• 2006

For a lower niltriangular matrix ring $A=NT_n(K)(n{\geq}3)$, we show that every derivation of A is a sum of certain diagonal, trivial extension and strongly nilpotent derivation. Moreover, a strongly nilpotent derivation is a sum of an inner derivation and an uaz-derivation.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.475-490
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• 2019

Let C^(q) be the q-commuting arithmetic table of (x + y)ⁿ with noncommuting variables. We study sequential properties of diagonal sums of C^(q) with various q > 0. One of our results shows that each diagonal sum plays like Fibonacci number with some minor conditions.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.131-150
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• 2007

In this paper, we will define direct producted $W^*-porobability$ spaces over their diagonal subalgebras and observe the amalgamated free-ness on them. Also, we will consider the amalgamated free stochastic calculus on such free probabilistic structure. Let ($A_{j},\;{\varphi}_{j}$) be a tracial $W^*-porobability$ spaces, for j = 1,..., N. Then we can define the corresponding direct producted $W^*-porobability$ space (A, E) over its N-th diagonal subalgebra $D_{N}\;{\equiv}\;\mathbb{C}^{{\bigoplus}N}$, where $A={\bigoplus}^{N}_{j=1}\;A_{j}\;and\;E={\bigoplus}^{N}_{j=1}\;{\varphi}_{j}$. In Chapter 1, we show that $D_{N}-valued$ cumulants are direct sum of scalar-valued cumulants. This says that, roughly speaking, the $D_{N}-freeness$ is characterized by the direct sum of scalar-valued freeness. As application, the $D_{N}-semicircularityrity$ and the $D_{N}-valued$ infinitely divisibility are characterized by the direct sum of semicircularity and the direct sum of infinitely divisibility, respectively. In Chapter 2, we will define the $D_{N}-valued$ stochastic integral of $D_{N}-valued$ simple adapted biprocesses with respect to a fixed $D_{N}-valued$ infinitely divisible element which is a $D_{N}-free$ stochastic process. We can see that the free stochastic Ito's formula is naturally extended to the $D_{N}-valued$ case.

• Journal of Korea Water Resources Association
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• v.42 no.5
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• pp.375-383
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• 2009

This study examined hydraulic characteristics on diagonal weirs with hydraulic experiment and presented a discharge coefficient equation utilizing multiple regression analysis for various design conditions. This study had a object in designing efficiently diagonal weirs utilizing this equation. Diagonal weirs maintained uniformly upstream water level than rectangular suppressed weirs. Also, as installation degrees of diagonal weirs increased, diagonal weirs increased maintenance effects of a upstream water level. Because of these characteristics, diagonal weirs were suitable to canal system. This study presented discharge coefficient equations for diagonal weirs utilizing simple regression analysis. But, these equations are some restrictions on degrees. Therefore, this study presented an equation to estimate directly discharge coefficients to various degrees utilizing multiple regression analysis. This equation was verified by making use of analyses of $R^2$, the sum of residuals, MAPE. Therefore, this equation is enable to make good use of a design in diagonal weirs.

• JSTS:Journal of Semiconductor Technology and Science
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• v.13 no.1
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• pp.8-14
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• 2013

A low density parity check (LDPC) decoder provides a most powerful error control capability for mobile communication devices and storage systems, due to its performance being close to Shannon's limit. In this paper, we introduce an efficient overlapped LDPC decoding algorithm using a upper dual-diagonal parity check matrix structure. By means of this algorithm, the LDPC decoder can concurrently execute parts of the check node update and variable node update in the sum-product algorithm. In this way, we can reduce the number of clock cycles per iteration as well as reduce the total latency. The proposed decoding structure offers a very simple control and is very flexible in terms of the variable bit length and variable code rate. The experiment results show that the proposed decoder can complete the decoding of codewords within 70% of the number of clock cycles required for a conventional non-overlapped decoder. The proposed design also reduces the power consumption by 33% when compared to the non-overlapped design.

• Steel and Composite Structures
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• v.19 no.2
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• pp.349-368
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• 2015

This paper presents a new algorithm to find the optimal distribution of steel diagonal braces (SDB) using artificial bee colony optimization technique. The four different objective functions are employed based on the transfer function amplitude of; the top displacement, the top absolute acceleration, the base shear and the base moment. The stiffness parameter of SDB at each floor level is taken into account as design variables and the sum of the stiffness parameter of the SDB is accepted as an active constraint. An optimization algorithm based on the Artificial Bee Colony (ABC) algorithm is proposed to minimize the objective functions. The proposed ABC algorithm is applied to determine the optimal SDB distribution for planar buildings in order to rehabilitate existing planar steel buildings or to design new steel buildings. Three planar building models are chosen as numerical examples to demonstrate the validity of the proposed method. The optimal SDB designs are compared with a uniform SDB design that uniformly distributes the total stiffness across the structure. The results of the analysis clearly show that each optimal SDB placement, which is determined based on different performance objectives, performs well for its own design aim.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.11
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• pp.5382-5403
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• 2018

In this paper, for a spectrum sensing purpose, we heuristically established a test statistic (TS) from a sample covariance matrix (SCM) for multiple antennas based cognitive radio. The TS is formulated as a scaled-energy which is calculated as a sum of scaled diagonal entries of a SCM; each of the diagonal entries of a SCM scaled by corresponding row's Euclidean norm. On the top of that, by combining theoretical results together with simulation observations, we have approximated a decision threshold of the TS which does not need prior knowledge of noise power and primary user signal. Furthermore, simulation results - which are obtained in a fading environment and in a spatially correlating channel model - show that the proposed method stands effect of noise power mismatch (non-uniform noise power) and has significant performance improvement compared with state-of-the-art test statistics.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.48 no.10
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• pp.1-6
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• 2011

In this paper, the sum-rate and BER performances of MU-MIMO system employing quantized differential feedback technique are analyzed over temporrally correlated channels. Several differential codebooks are assumed in the analysis such as quasi-diagonal codebook, spherical cap codebook, and differential equal gain codebook. The simulation results indicates that the system employing quantized differential feedback technique provides significant performance improvement. The performance improved 0.6bps/Hz at least in terms of sum-rate, and 4dB power gain is provided in terms of average BER.

• Honam Mathematical Journal
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• v.11 no.1
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• pp.15-19
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• 1989

A conjecture of E. T. H. Wang asserts that if every diagonal disjoint from m mutually disjoint zero diagonals of $A{\in}{\Omega}_n$ has a constant sum, then all entries off the m zero diagonals are equal to l/(n-m). E. T. H. Wang proved the conjecture for m=0, 1, n-2 and n-1. In the present paper, it is proved that the conjecture holds true for m=2.