• 대한수학회보
• /
• 제54권2호
• /
• pp.497-505
• /
• 2017

The rank over a finite field of the adjacency matrix of a directed strongly regular graph is studied, with some applications to the construction of linear codes. Three techniques are used: code orthogonality, adjacency matrix determinant, and adjacency matrix spectrum.

• 대한수학회보
• /
• 제46권6호
• /
• pp.1051-1060
• /
• 2009

In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact $T_1$-subspace. We also study the zero-divisor graph $\Gamma_I$(R) with respect to the completely semiprime ideal I of N. We show that ${\Gamma}_{\mathbb{P}}$ (R), where $\mathbb{P}$ is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph ${\Gamma}_{\mathbb{P}}$ (R).

• Kyungpook Mathematical Journal
• /
• 제59권1호
• /
• pp.175-190
• /
• 2019

In this paper, we provide results for the search number of the Cartesian product of graphs. We consider graphs on opposing ends of the spectrum: paths and cliques. Our main result determines the pathwidth of the product of cliques and provides a lower bound for the search number of the product of cliques. A consequence of this result is a bound for the search number of the product of arbitrary graphs G and H based on their respective clique numbers.

• 대한수학회보
• /
• 제56권6호
• /
• pp.1485-1495
• /
• 2019

The purpose of this paper is to compute the number of semistar operations of certain classes of finite dimensional $Pr{\ddot{u}}fer$ domains. We prove that ${\mid}SStar(R){\mid}={\mid}Star(R){\mid}+{\mid}Spec(R){\mid}+ {\mid}Idem(R){\mid}$ where Idem(R) is the set of all nonzero idempotent prime ideals of R if and only if R is a $Pr{\ddot{u}}fer$ domain with Y -graph spectrum, that is, R is a $Pr{\ddot{u}}fer$ domain with exactly two maximal ideals M and N and $Spec(R)=\{(0){\varsubsetneq}P_1{\varsubsetneq}{\cdots}{\varsubsetneq}P_{n-1}{\varsubsetneq}M,N{\mid}P_{n-1}{\varsubsetneq}N\}$. We also characterize non-local $Pr{\ddot{u}}fer$ domains R such that ${\mid}SStar(R){\mid}=7$, respectively ${\mid}SStar(R){\mid}=14$.

• Journal of Communications and Networks
• /
• 제13권6호
• /
• pp.664-677
• /
• 2011

In order to control interference and improve spectrum efficiency in the femtocell and macrocell overlaid system (FMOS), we propose a joint frequency bandwidth dynamic division, clustering and power control algorithm (JFCPA) for orthogonal-frequency-division-multiple access-based downlink FMOS. The overall system bandwidth is divided into three bands, and the macro-cellular coverage is divided into two areas according to the intensity of the interference from the macro base station to the femtocells, which are dynamically determined by using the JFCPA. A cluster is taken as the unit for frequency reuse among femtocells. We map the problem of clustering to the MAX k-CUT problem with the aim of eliminating the inter-femtocell collision interference, which is solved by a graph-based heuristic algorithm. Frequency bandwidth sharing or splitting between the femtocell tier and the macrocell tier is determined by a step-migration-algorithm-based power control. Simulations conducted to demonstrate the effectiveness of our proposed algorithm showed the frequency-reuse probability of the FMOS reuse band above 97.6% and at least 70% of the frequency bandwidth available for the macrocell tier, which means that the co-tier and the cross-tier interference were effectively controlled. Thus, high spectrum efficiency was achieved. The simulation results also clarified that the planning of frequency resource allocation in FMOS should take into account both the spatial density of femtocells and the interference suffered by them. Statistical results from our simulations also provide guidelines for actual FMOS planning.

• The Korean Journal of Ecology
• /
• 제13권2호
• /
• pp.83-92
• /
• 1990

Two-dimensional analysis provides a comprehensive description of the structure, scales of pattern and directional components in a spatial data set. In spectral analysisi, four functions are illustrated,; the autocorrelation, the periodogram, the R-spectrum and the $\theta$ -spectrum. The R-spectrum and $\theta$ -spectrum function respectively summarize the periodogram in term of scale of pattern and directional components. Sampling is measured in the Naejang National Park area where the Daphniphyllum trees grow. 320 contiguous (15$\times$15)m plots are located along the transect and density of all trees over DBH 3 cm recorded respectively. 12 species of vascular plant are recorded in this survey area. The trend surface of density of all plant are estimated using polynomial regression and are exhibited in 3-dimensional graph and density contour map. Transformation to the corresponding polar spectrum from the periodogram emphasized the directional components and the scales to pattern. R-spectrum corresponding to the scale of pattern of periodogram showed a large peak 15.47 in the interval 9$\theta$-spectrum corresponding to directional components have two peaks 8.28 and 11.05 in the interval $35^{\circ}\theta <45^{\circ}and 125^{\circ}\theta< <135^{\circ}, respectively. Programs to compute all the analyses described in this study was obtained from Dr. Ranshow and was translated to BASIC by the author.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제7권9호
• /
• pp.2101-2119
• /
• 2013

The spectrum allocation is an attractive issue for mobile cognitive radio (CR) network. However, the time-varying characteristic of the spectrum allocation is not fully investigated. Thus, this paper originally deduces the probabilities of spectrum availability and interference constrain in theory under the mobile environment. Then, we propose a prediction mechanism of the time-varying available spectrum lists and the dynamic interference topologies. By considering the node mobility and primary users' (PUs') activity, the mechanism is capable of overcoming the static shortcomings of traditional model. Based on the mechanism, two prediction-based spectrum allocation algorithms, prediction greedy algorithm (PGA) and prediction fairness algorithm (PFA), are presented to enhance the spectrum utilization and improve the fairness. Moreover, new utility functions are redefined to measure the effectiveness of different schemes in the mobile CR network. Simulation results show that PGA gets more average effective spectrums than the traditional schemes, when the mean idle time of PUs is high. And PFA could achieve good system fairness performance, especially when the speeds of cognitive nodes are high.

• 한국생산제조학회지
• /
• 제9권6호
• /
• pp.96-102
• /
• 2000

Spinning mechanism is generally used in coasting process on grass plates. Rebounding PR(Photo Resist) which leads to occur inferiority of coating process is caused by vibrational energy of whole coating system. In this study, the sensitivity analysis is performed to analyze and reduce vibrational terms in the spin coating system. The sensitivity analysis is bared on the numerical expression of this system. By the bond graph method. power flow of each system is represented by some basic bond graph elements. Any energy domain system is modeled using the unified elements. The modelled spin coater system is verified with power spectrum data measured by FFT analyzer. As the results of verifying model parameters and sensitivity analysis, principal factors causing vibration phenomenon are mentioned. A study on vibration method in the spin coating system is discussed.

• 한국통신학회논문지
• /
• 제19권9호
• /
• pp.1658-1667
• /
• 1994

셀룰라 이동통신 제어 시스템에서 고도의 스펙트럼 효과를 도출해 내기 위해 셀에서 호에 대한 채널을 할당하는 것은 한정된 주파수 대역폭내에서 중요한 문제이다. 이동통신 제어 시스템에 있어서는 스펙트럼 효과를 그래프 이론의 색채화 문제로 연관 시킬 수 있다. 본 논문에서는 셀룰라 이동통신 제어시스템의 그래프 이론을 이용하여 채널 오프셋 구조를 제안하고, 그래프 색채화 문제와 관련된 채널 오프셋 구조의 색체화 대역폭을 수식화 하였다. 수식화 된 채널할당 문제로부터 채널 구성에 따른 셀 설계와 보다 효율적인 주파수 스펙트럼의 최적 채널 오프셋을 연구하여 전체 스펙트럼 대역폭에 대한 상한치와 하한치를 부여 한다.

• ETRI Journal
• /
• 제38권2호
• /
• pp.314-325
• /
• 2016

This paper examines the resource gain that can be obtained from the creation of clusters of nodes in densely populated areas. A single node within each such cluster is designated as a "hotspot"; all other nodes then communicate with a destination node, such as a base station, through such hotspots. We propose a semi-distributed algorithm, referred to as coordinated cognitive tethering (CCT), which clusters all nodes and coordinates hotspots to tether over locally available white spaces. CCT performs the following these steps: (a) groups nodes based on a modified k-means clustering algorithm; (b) assigns white-space spectrum to each cluster based on a distributed graph-coloring approach to maximize spectrum reuse, and (c) allocates physical-layer resources to individual users based on local channel information. Unlike small cells (for example, femtocells and WiFi), this approach does not require any additions to existing infrastructure. In addition to providing parallel service to more users than conventional direct communication in cellular networks, simulation results show that CCT can increase the average battery life of devices by 30%, on average.