• Nonlinear Functional Analysis and Applications
• /
• v.28 no.4
• /
• pp.989-1004
• /
• 2023

In this paper, we are motivated to evaluate and investigate the necessary conditions for the fractional Volterra Fredholm integro-differential equation involving the ς-Hilfer fractional derivative. The given problem is converted into an equivalent fixed point problem by introducing an operator whose fixed points coincide with the solutions to the problem at hand. The existence and uniqueness results for the given problem are derived by applying Krasnoselskii and Banach fixed point theorems respectively. Furthermore, we investigate the convergence of approximated solutions to the same problem using the modified Adomian decomposition method. An example is provided to illustrate our findings.

• Journal of the Korean Mathematical Society
• /
• v.36 no.3
• /
• pp.609-619
• /
• 1999

We give a mathematically rigorous description of the recently popular latent semantic indexing (LSI) method in text information retrieval theory. Also, a related problem of finding a document ranking function in linear relevance feedback is discussed.

• Transactions of the Korean hydrogen and new energy society
• /
• v.16 no.1
• /
• pp.92-101
• /
• 2005

[ $Li_3AlH_6$ ] (5.6wt% theoretical hydrogen storage capacity) powders with and without Ti-containing dopants have been successfully synthesized by mechanochemical reaction near room temperatures from mixtures of LiH and $LiAlH_4$ powders. It has been observed that single phase $Li_3AlH_6$ could be obtained within 2-3 hours of milling, but the addition of reactive $TiCl_2\;or\;TiCl_3$ to the starting mixtures. caused partial decomposition of $LiAlH_4$ into LiCl and free Al with gaseous $H_2$. By addition of these reactive dopants to the as-synthesized $Li_3AlH_6$, this problem could be solved. The addition of 2 mol% $TiCl_2\;or\;TiCl_3\;to\;Li_3AlH_6$ decreased the decomposition start temperature up to 30-50$^{\circ}C$, while that of Ti or $TiH_2$ did not change the thermal decomposition behavior of $Li_3AIH_6$.

• Nuclear Engineering and Technology
• /
• v.48 no.3
• /
• pp.635-641
• /
• 2016

Because of prohibitive data storage requirements in large-scale simulations, the memory problem is an obstacle for Monte Carlo (MC) codes in accomplishing pin-wise three-dimensional (3D) full-core calculations, particularly for whole-core depletion analyses. Various kinds of data are evaluated and quantificational total memory requirements are analyzed based on the Reactor Monte Carlo (RMC) code, showing that tally data, material data, and isotope densities in depletion are three major parts of memory storage. The domain decomposition method is investigated as a means of saving memory, by dividing spatial geometry into domains that are simulated separately by parallel processors. For the validity of particle tracking during transport simulations, particles need to be communicated between domains. In consideration of efficiency, an asynchronous particle communication algorithm is designed and implemented. Furthermore, we couple the domain decomposition method with MC burnup process, under a strategy of utilizing consistent domain partition in both transport and depletion modules. A numerical test of 3D full-core burnup calculations is carried out, indicating that the RMC code, with the domain decomposition method, is capable of pin-wise full-core burnup calculations with millions of depletion regions.

• Korean Chemical Engineering Research
• /
• v.59 no.4
• /
• pp.481-486
• /
• 2021

In a hypersonic vehicle to solve the heat problem generated during flight, a cooling technology is being developed which uses the endothermic effect that appears during the decomposition reaction of the mounted fuel. In this study, the decomposition reaction of n-dodecane fuel was performed using HZSM-5 as a catalyst, and the catalyst was coated on metal foam to maximize the endothermic effect of the catalytic decomposition reaction and suppress coke formation. The reactor was a stainless steel flow reactor with a outer diameter of 1.27 cm, and the reaction temperature was 550 ℃, the reaction pressure was 4 MPa, and the flow rate was 12 ml per minute. As a result of the catalytic decomposition reaction using a catalyst coated with HZSM-5 on the metal foam, the heat sink was 2887 kJ/kg as a maximum, the gas phase conversion rate was 34%, and the amount of coke produced on the metal foam decreased by about 56% as the catalyst was coated compared to the uncoated catalyst.

• The Journal of the Korea Contents Association
• /
• v.22 no.7
• /
• pp.46-54
• /
• 2022

The existing methods for determining influence in social networks do not accurately determine the influence of users because they do not delete or update existing relationships before they stop in the face of an increasing number of inactive users on social networks. In this paper, we propose a user influence detremination method using the temporal k-shell decomposition technique based on the creation date of users of social networks. To solve the problem of increasing influence of old users in social networks, we apply k-shell decomposition and age-specific order centrality as attenuation coefficients due to aging in neighbors. The age-decaying k-shell decomposition and age-specific order centrality are searched for influential users at the present time by applying the attenuation coefficient and age-dependent weights. Various performance evaluations are performed to show the superiority of the proposed method.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.26 no.6
• /
• pp.842-849
• /
• 2022

With the development of deep learning technology, there are many cases of using DNNs in embedded systems such as unmanned vehicles, drones, and robotics. Typically, in the case of an autonomous driving system, it is crucial to run several DNNs which have high accuracy results and large computation amount at the same time. However, running multiple DNNs simultaneously in an embedded system with relatively low performance increases the time required for the inference. This phenomenon may cause a problem of performing an abnormal function because the operation according to the inference result is not performed in time. To solve this problem, the solution proposed in this paper first reduces the computation by applying the Tucker decomposition to DNN models with big computation amount, and then, make DNN models run in parallel as much as possible in the unit of hidden layer inside the GPU. The experimental result shows that the DNN inference time decreases by up to 75.6% compared to the case before applying the proposed technique.

• Journal of Korean Society of Transportation
• /
• v.17 no.4
• /
• pp.47-58
• /
• 1999

The Purpose of this Paper is to develop a multi-period bus scheduling model, in which a decomposition technique is applied. In general a bus scheduling requires a vast amount of calculation. Thus, a bus scheduling is a very complicated problem even with a single depot and is almost unable to obtain the optimal solution theoretically with many depots. In this paper in order to simplify the problem, the whole operating hours of a day are partitioned into several time periods. In one period, the same headways are maintained. For one period, the bus scheduling is simple and the solution applying the FIFO(First-In, First-Out) Principle is the optimal. However, connection between Periods remains as another scheduling Problem with a reduced problem size. This paper suggests how to connect bus schedules of consecutive periods efficiently, minimizing the operating cost. Through case studies for multiple routes with a single depot, this decomposition technique is proved to be effective practically.

• Structural Engineering and Mechanics
• /
• v.39 no.6
• /
• pp.813-831
• /
• 2011

This paper presents an efficient version of Hilbert-Huang transform for nonlinear non-stationary systems analyses. An ensemble empirical mode decomposition (EEMD) is introduced to alleviate the problem of mode mixing between intrinsic mode functions (IMFs) decomposed by EMD. Yet the problem has not been fully resolved when a signal of a similar scale resides in different IMF components. Instead of using a trial and error method to select the "best" outcome generated by EEMD, a hybrid algorithm based on EEMD and EMD is proposed for multi-mode signal processing. The developed approach comprises the steps from a bandpass filter design for regrouping modes of the IMFs obtained from EEMD, to the mode extraction using EMD, and to the assessment of each mode in the marginal spectrum. A simulated two-mode signal is tested to demonstrate the efficiency and robustness of the approach, showing average relative errors all equal to 1.46% for various noise levels added to the signal. The developed approach is also applied to a real bridge structure, showing more reliable results than the pure EMD. Discussions on the mode determination are offered to explain the connection between modegrouping form on the one hand, and mode-grouping performance on the other.

• Research in Mathematical Education
• /
• v.14 no.3
• /
• pp.195-209
• /
• 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]).