• Korean Journal of Mathematics
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• v.20 no.2
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• pp.161-176
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• 2012

The authors [6] introduced the concept of a complete matrix of grade $g$ > 3 to describe a structure theorem for complete intersections of grade $g$ > 3. We show that a complete matrix can be used to construct the Eagon-Northcott complex [7]. Moreover, we prove that it is the minimal free resolution $\mathbb{F}$ of a class of determinantal ideals of $n{\times}(n+2)$ matrices $X=(x_{ij})$ such that entries of each row of $X=(x_{ij})$ form a regular sequence and the second differential map of $\mathbb{F}$ is a matrix $f$ defined by the complete matrices of grade $n+2$.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2000.11a
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• pp.69-73
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• 2000

We systematically analyze the influence of fracture junction, solute transfer characteristics on transport patterns in discrete, two-dimensional fracture network models. Regular lattices and random fracture networks with power-law length distributions are considered in conjunction with particle tracking methods. Solute transfer probabilities at fracture junctions are determined from analytical considerations and from simple complete mixing and streamline routing models. For regular fracture networks, mixing conditions at fracture junctions are always dominated by either complete mixing or streamline routing end member cases. Moreover bulk transport properties such as the spreading and the dilution of solute are highly sensitive to the mixing rule. However in power-law length networks there is no significant difference in bulk transport properties, as calculated by assuming either of the two extreme mixing rules. This apparent discrepancy between the effects of mixing properties at fracture junctions in regular and random fracture networks is explained by the statistics of the coordination number and of the flow conditions at fracture intersections. We suggest that the influence of mixing rules on bulk solute transport could be important in systematic orthogonal fracture networks but insignificant in random networks.

• Proceedings of the KOR-KST Conference
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• 1996.02a
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• pp.59-86
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• 1996

Current methods for evaluating unsignalized intersections, and estimating level-of-service (LOS) is determined from efficiency-based criteria such as little or no delay to very long delays. At present, similar procedures to evaluate intersections using safety-based criteria do not exist. The improvement of sight distances at intersections is the most effective way of improving intersection safety. However, a set of procedures is necessary to account for the limitations in current methodology. Such an approach would build upon such methods, but also account for: deficiencies in the current deterministic solution for the determination of intersection sight distances; opportunity for an accident and severity of an accident; and cost-effectiveness of attaining various levels of sight distances. In this research, a model that estimates the degree of safety at two-way stop-controlled intersections is described. Only crossing maneuvers are considered in this study because accidents caused by the crossing maneuvers are the dominate type among intersection accidents. Monte Carlo methods are used to estimate the hazard at an intersection as a function of roadway features and traffic conditions. Driver`s minimum gap acceptance in the crossing vehicles and headway distribution on the major road are used in the crossing vehicles and headway distribution on the major road are used in the model to simulate the real intersectional maneuvers. Other random variables addressed in the model are: traffic speeds; preception-reaction times of both drivers in the crossing vehicles and drivers in oncoming vehicles on the major road; and vehicles on the major roads. The developed model produces the total number of conflicts per year per vehicle and total potential kinetic energy per year per vehicle dissipated during conflicts as measurements of safety at intersections. Based on the results from the developed simulation model, desirable sight distances for various speeds were determined as 350 feet, 450 feet and 550 feet for 40 mph, 50 mph and 60 mph prevailing speed on the major road, respectively. These values are seven to eight percent less than those values recommended by AASHTO. A safety based level-of-service (LOS) is also developed using the results of the simulation model. When the total number of conflicts per vehicle is less than 0.05 at an intersection, the LOS of the intersection is `A' and when the total number of conflicts per vehicle is larger than 0.25 at an intersection, the LOS is `F'. Similarly, when the total hazard per vehicle is less than 350, 000 1b-ft2/sec2, the LOS is `F'. Once evaluation of the current safety at the intersection is complete, a sensitivity analysis can be done by changing one or more input parameters. This will estimate the benefit in terms of time and budget of hazard reduction based upon improving geometric and traffic characteristics at the intersection. This method will also enable traffic engineers in local governments to generate a priority list of intersection improvement projects.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.267-298
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• 1999

A geometric construction of an exact algebraic formula for graded partition functions, of which a special one is the classical unrestricted partition function p(n), from a diophantine point of view is presented. Moreover, the involved process allows us to compute the value of a graded partition function in an inductive manner with a geometrically built-in self-error-checking ability at each step for correctness of the computed values of the partition function under consideration.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.715-736
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• 2012

Brown provided a structure theorem for a class of perfect ideals of grade 3 with type ${\lambda}$ > 0. We introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4 in a Noetherian local ring. We construct a class of perfect ideals I of grade 3 with type 2 defined by a certain skew-symmetrizable matrix. We present the Hilbert function of the standard $k$-algebras R/I, where R is the polynomial ring $R=k[v_0,v_1,{\ldots},v_m]$ over a field $k$ with indeterminates $v_i$ and deg $v_i=1$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.99-124
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• 2017

The structure theorems [3, 6, 21] for the classes of perfect ideals of grade 3 have been generalized to the structure theorems for the classes of perfect ideals linked to almost complete intersections of grade 3 by a regular sequence [15]. In this paper we obtain structure theorems for two classes of Gorenstein ideals of grade 4 expressed as the sum of a perfect ideal of grade 3 (except a Gorenstein ideal of grade 3) and an almost complete intersection of grade 3 which are geometrically linked by a regular sequence.

• International Journal of Highway Engineering
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• v.19 no.4
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• pp.61-68
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• 2017

PURPOSES : A complete signal system is not always the best solution for improving traffic operation efficiency at intersections. An alternative solution is to use a Protected Permitted Left Turn (PPLT) operation method. However, the PPLT method needs to be developed after a detailed study of driving tendencies, most notably the gap acceptance behavior, for successful implementation. In this study, the gap acceptance behavior was investigated under various variables and weather conditions, especially under rain, and the results were compared to the case of normal weather. The results of this study will be helpful in introducing the PPLT method, and are important considering the tendency of attempting unprotected left turns that is extremely common in Korean drivers. METHODS : Data was obtained by analyzing traffic footage at four intersections on a day when the precipitation was greater than 5 mm/h. The collected data was classified into seven variables for statistical analysis. Finally, we used logistic regression analysis to develop a probability distribution model. RESULTS : Gap, traffic volume, and the number of conflicting lanes were factors affecting the gap acceptance behavior of unprotected left turns under rainy conditions. CONCLUSIONS : The probability of attempting unprotected left turns is higher for larger gaps. On the other hand, the probability of attempting unprotected left turns decreases with an increase in the traffic volume. Finally, an increase in the number of conflict lanes leads to a decrease in the probability of attempting unprotected left turns.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1379-1410
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• 2017

Kang and Ko introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4. Let $R=k[w_0,\;w_1,\;w_2,\;{\ldots},\;w_m]$ be the polynomial ring over an algebraically closed field k with indetermiantes $w_l$ and deg $w_l=1$, and $I_i$ a homogeneous perfect ideal of grade 3 with type $t_i$ defined by a skew-symmetrizable matrix $G_i(1{\leq}t_i{\leq}4)$. We show that for m = 2 the Hilbert function of the zero dimensional standard k-algebra $R/I_i$ is determined by CI-sequences and a Gorenstein sequence. As an application of this result we show that for i = 1, 2, 3 and for m = 3 a Gorenstein sequence $h(R/H_i)=(1,\;4,\;h_2,\;{\ldots},\;h_s)$ is unimodal, where $H_i$ is the sum of homogeneous perfect ideals $I_i$ and $J_i$ which are geometrically linked by a homogeneous regular sequence z in $I_i{\cap}J_i$.

• Advances in nano research
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• v.14 no.5
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• pp.463-474
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• 2023

The purpose of this paper is to present the analysis of propagating and evanescent waves in functionally graded (FG) nanoplates with the consideration of nonlocal effect. The analytical integration nonlocal stress expansion Legendre polynomial method is proposed to obtain complete dispersion curves in the complex domain. Unlike the traditional Legendre polynomial method that expanded the displacement, the presented polynomial method avoids employing the relationship between local stress and nonlocal stress to construct boundary conditions. In addition, the analytical expressions of numerical integrations are presented to improve the computational efficiency. The nonlocal effect, inhomogeneity of medium and their interactions on wave propagation are studied. It is found that the nonlocal effect and inhomogeneity of medium reduce the frequency bandwidth of complex evanescent Lamb waves, and make complex evanescent Lamb waves have a higher phase velocity at low attenuation. The occurrence of intersections of propagating Lamb wave in the nonlocal homogeneous plate needs to satisfy a smaller Poisson's ratio condition than that in the classical elastic theory. In addition, the inhomogeneity of medium enhances the nonlocal effect. The conclusions obtained can be applied to the design and dynamic response evaluation of composite nanostructures.