• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.977-988
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• 2022

The Padovan sequence is the third-order linear recurrence (𝓟_n)_n≥0 defined by 𝓟_n = 𝓟_n-2 + 𝓟_n-3 for all n ≥ 3 with initial conditions 𝓟₀ = 0 and 𝓟₁ = 𝓟₂ = 1. In this paper, we investigate a generalization of the Padovan sequence called the k-generalized Padovan sequence which is generated by a linear recurrence sequence of order k ≥ 3. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences.

• Journal of Korean Tunnelling and Underground Space Association
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• v.12 no.1
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• pp.1-14
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• 2010

Until now, the evaluation method of spalling depth using Martin et al. (1999)'s linear regression relations has long been known applicable. However, it is not likely that the proposed equation is applicable to the openings other than circular type and mostly overpredict the spalling depth in comparison with actual spalling cases. Moreover, the evaluation method to estimate the spalling width has not been presented yet; it is essential to evaluate the spalling width in addition to the spalling depth, because the shape of the spalled region influences the choice of suitable rock reinforcement. In this study, linear regression equations, in which normalized spalling depth ($d_f/W_D$) and normalized spalling width ($w_f/W_D$) are functions of three spalling evaluation indices, ${\sigma}_1/{\sigma}_c,\;D_{is}(={\sigma}_{max}/{\sigma}_c)$ and ${\sigma}_{dev}/{\sigma}_{cm}$, are established based on in-situ spalling observations and CWFS simulation results. Confidence intervals of 95% using the statistical inference theory are used in verifying the reliability of linear regression equations. Spalling depth ($d_f$) and spalling width ($w_f$) predicted from the proposed linear regression relations, which take three spalling evaluation indices into account, showed reasonable match with in-situ observations by adopting weighting factors considering the degree of variance of linear regression relations.

• Smart Structures and Systems
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• v.15 no.6
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• pp.1439-1461
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• 2015

Design criteria, modeling rules, and analysis principles of seismic isolation systems have already found place in important building codes and standards such as the Uniform Building Code and ASCE/SEI 7-05. Although real behaviors of isolation systems composed of high damping or lead rubber bearings are nonlinear, equivalent linear models can be obtained using effective stiffness and damping which makes use of linear seismic analysis methods for seismic-isolated buildings possible. However, equivalent linear modeling and analysis may lead to errors in seismic response terms of multi-story buildings and thus need to be assessed comprehensively. This study investigates the accuracy of equivalent linear modeling via numerical experiments conducted on generic five-story three dimensional seismic-isolated buildings. A wide range of nonlinear isolation systems with different characteristics and their equivalent linear counterparts are subjected to historical earthquakes and isolation system displacements, top floor accelerations, story drifts, base shears, and torsional base moments are compared. Relations between the accuracy of the estimates of peak structural responses from equivalent linear models and typical characteristics of nonlinear isolation systems including effective period, rigid-body mode period, effective viscous damping ratio, and post-yield to pre-yield stiffness ratio are established. Influence of biaxial interaction and plan eccentricity are also examined.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.96-100
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• 2003

In this paper, a DLC method is proposed for linear feedback systems to improve the tracking performance when the task of the system is repetitive. DLC can generate the desired control input directly from the previously learned control inputs corresponding to other output trajectories. It is assumed that all the desired output functions considered in this paper have some relations called proportionality and it is shown by mathematical analysis that DLC can be utilized to generate additional control efforts for the perfect tracking. To show the validity and tracking performance of the proposed method, some simulations are performed for the tracking control of a linear system with a PI controller.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.54 no.2
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• pp.76-80
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• 2005

In this paper, a Direct Learning Control (DLC) method is proposed for linear feedback systems to improve the tracking performance when the task of the control system is repetitive. DLC can generate the desired control input directly from the previously learned control inputs corresponding to other output trajectories. It is assumed that all the desired output functions given to the system have some relations called proportionality and it is shown by mathematical analysis that DLC can be utilized to genera additional control efforts for the perfect tracking. To show the validity and tracking performance of the proposed method, some simulations are performed for the tracking control of a linear system with a PI controller.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.55 no.3
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• pp.138-145
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• 2006

It is well known that the accurate calculation of the field distribution is essential for the design of electrical machines. The analytical techniques for electromagnetic field can quickly and exactly determine airgap magnetic field distribution in electrical machines. Many analytical techniques have been investigated to predict the magnetic field distribution in PM machines equipped with permanent magnets. Using the analytical technique by transfer relations, D. L. Trumper and K. R. Davey already presented the design and analysis of linear permanent-magnet machines and induction machines, respectively. Using the transfer relations (Melcher's general methodology) to describe electromagnetic phenomena, this paper deals with the analysis on the magnetic field distribution due to PM and winding current, the induced voltage and the static torque characteristics in surface-mounted slotless type permanent magnet machine. The validity of the analysis results is confirmed by finite element (FE) analysis.

• Publications of The Korean Astronomical Society
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• v.30 no.2
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• pp.261-263
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• 2015

The metallicity distribution of globular clusters (GCs) provides a crucial clue for the star formation history of their host galaxy. With the assumption that GCs are generally old, GC colors have been used as a proxy for GC metallicities. Bimodal color distributions of GCs observed in most large galaxies have, for decades, been interpreted as bimodal metallicity distributions, indicating the presence of two populations within a galaxy. However, the conventional view has been challenged by a new theory that non-linear GC color-metallicity relations can cause a bimodal color distribution even from a single-peaked metallicity distribution. Using photometric and spectroscopic data of NGC 5128 GCs in combination with stellar population simulation models, we examine the effect of non-linearity in GC color-metallicity relations on transformation of the color distributions into the metallicity distributions. Although in some colors offsets are present between observations and models for the color-metallicity relations, their overall shape agrees well for various colors. After the offsets are corrected, the observed spectroscopic metallicity distribution is well reproduced via modeled color-metallicity relations from various color distributions having different morphologies. We discuss the implications of our results.

• Fisheries and Aquatic Sciences
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• v.26 no.3
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• pp.169-180
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• 2023

Oreochromis niloticus is the most ecologically and economically important fish in tropical and sub-tropical aquatic systems. Recently, due to sever anthropogenic stressors, hydrological variations and infestations of invasive alien species in Ethiopian water bodies, fish community structure and ecosystem of Lake Tana is changing alarmingly. So far, there is paucity of information on the morphometric relations and diet composition of O. niloticus in Lake Tana, gulf of Gorgora. A total of 309 fish samples were collected and their total length (TL), standard length (SL) and total weight (TW) were measured to determine morphometric relations; and gut contents were examined to identify most important food item in the diet of the fish. Results indicated that, the relation between TL and SL was significant (p < 0.001) and linear (SL = 0.942TL-2.41) while the relation between TL and TW was curvilinear (TW = 0.014 TL^2.8) indicating allometric growth. Among the total guts scrutinized, 53 (17.3%) of them were empty and the remaining 256 (82.7%) were non-empty. Phytoplankton constituted the largest bulk and occurred in 77% of the guts examined and volumetrically accounted 44.3%. Detritus and zooplankton had an intermediate importance by occurring 60.2% and 63.3% of all guts scrutinized and constituted about 25.6% and 15.5% of the total volume respectively. Contributions of macrophytes, insects, nematodes and unidentified food items were relatively low in their importance. Ontogenetic dietary shift was observed in the diet indicating an omnivorous feeding habit of the adult fish.

• Structural Engineering and Mechanics
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• v.18 no.2
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• pp.211-229
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• 2004

The main purpose of this paper is the numerical analysis of the non-linear seismic response of a RC building mock-up. The mock-up is subjected to different synthetic horizontal seismic excitations. The numerical approach is based on a 3D-model involving multilayered shell elements. These elements are composed of several single-layer membranes with various eccentricities. Bending effects are included through these eccentricities. Basic equations are first written for a single membrane element with its own eccentricity and then generalised to the multilayered shell element by superposition. The multilayered shell is considered as a classical shell element : all information about non-linear constitutive relations are investigated at the local scale of each layer, whereas balance and kinematics are checked afterwards at global scale. The non-linear dynamic response of the building is computed with Newmark algorithm. The numerical dynamic results (blind simulations) are considered in the linear and non linear cases and compared with experimental results from shaking table tests. Multilayered shell elements are found to be a promising tool for predictive computations of RC structures behaviour under 3D seismic loadings. This study was part of the CAMUS International Benchmark.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.225-238
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• 2014

We apply modular function theory to find the relation among t-core partitions. By using the generators of function field corresponding to a certain modular group, we reprove the identities in [1] because their relations are linear for t = 3 or 5.