• ETRI Journal
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• v.31 no.4
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• pp.454-456
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• 2009

The maximum likelihood linear spectral transformation (ML-LST) using a numerical iteration method has been previously proposed for robust speech recognition. The numerical iteration method is not appropriate for real-time applications due to its computational complexity. In order to reduce the computational cost, the objective function of the ML-LST is approximated and a closed-form solution is proposed in this paper. It is shown experimentally that the proposed closed-form solution for the ML-LST can provide rapid speaker and environment adaptation for robust speech recognition.

• ETRI Journal
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• v.37 no.3
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• pp.533-540
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• 2015

In wireless localization, several linear closed-form solution (LCS) methods have been investigated as a direct result of the drawbacks that plague the existing iterative methods, such as the local minimum problem and heavy computational burden. Among the known LCS methods, both the direct solution method and the difference of squared range measurements method are considered in this paper. These LCS methods do not have any of the aforementioned problems that occur in the existing iterative methods. However, each LCS method does have its own individual error property. In this paper, a hybrid LCS method is presented to reduce these errors. The hybrid LCS method integrates the two aforementioned LCS methods by using two check points that give important information on the probability of occurrence of each LCS's individual error. The results of several Monte Carlo simulations show that the proposed method has a good performance. The solutions provided by the proposed method are accurate and reliable. The solutions do not have serious errors such as those that occur in the conventional standalone LCS and iterative methods.

• Structural Engineering and Mechanics
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• v.22 no.2
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• pp.197-222
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• 2006

In this paper, the non-linear time-dependent closed-form, discrete and combined solutions for the post-elastic response of a geometrically and physically non-linear suspended cable to a uniformly distributed load considering the creep effects, are presented. The time-dependent closed-form method for the particularly straightforward determination of a vertical uniformly distributed load applied over the entire span of a cable and the accompanying deflection at time t corresponding to the elastic limit and/or to the elastic region, post-elastic and failure range of a suspended cable is described. The actual stress-strain properties of steel cables as well as creep of cables and their rheological characteristics are considered. In this solution, applying the Irvine's theory, the direct use of experimental data, such as the actual stress-strain and strain-time properties of high-strength steel cables, is implemented. The results obtained by the closed-form solution, i.e., a load corresponding to the elastic limit, post-elastic and failure range at time t, enable the direct use in the discrete non-linear time-dependent post-elastic analysis of a suspended cable. This initial value of load is necessary for the non-linear time-dependent elastic and post-elastic discrete analysis, concerning incremental and iterative solution strategies with tangent modulus concept. At each time step, the suspended cable is analyzed under the applied load and imposed deformations originated due to creep. This combined time-dependent approach, based on the closed-form solution and on the FEM, allows a prediction of the required load that occurs in the post-elastic region. The application of the described methods and derived equations is illustrated by numerical examples.

• The Journal of the Korea institute of electronic communication sciences
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• v.10 no.4
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• pp.507-512
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• 2015

In the wireless localization systems using range measurements, iteration method-based approximated solutions have been used. Also, linear closed-form solutions have been investigated in the light of local minimum problem and computational load. However, each closed-form solution has individual error factors that cause usage limit of the solutions. In this paper, a fusion method integrating two representative closed-form solutions is presented. The presented method cancels the error factors of each solution out. Weights for integrating the standalone solutions are determined using the error factors-based fuzzy method. The performance of the proposed method is verified using some simulation results.

• Wind and Structures
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• v.18 no.3
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• pp.235-252
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• 2014

An effective numerical technique to calculate the reactions of a multi-spanned transmission line conductor system, under arbitrary loads varying along the spans, is developed. Such variable loads are generated by High Intensity Wind (HIW) events in the form of tornadoes and downburst. First, a semi-closed form solution is derived to obtain the displacements and the reactions at the ends of each conductor span. The solution accounts for the nonlinearity of the system and the flexibility of the insulators. Second, a numerical scheme to solve the derived closed-form solution is proposed. Two conductor systems are analyzed under loads resulting from HIW events for validation of the proposed technique. Non-linear Finite Element Analyses (FEA) are also conducted for the same two systems. The responses resulting from the technique are shown to be in a very good agreement with those resulting from the FEA, which confirms the technique accuracy. Meanwhile, the semi-closed form technique shows superior efficiency in terms of the required computational time. The saving in computational time has a great advantage in predicting the response of the conductors under HIW events, since this requires a large number of analyses to cover different potential locations and sizes of those localized events.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.7
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• pp.144-153
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• 1997

The inverse kinematics problem of a reclaimer which excavates and transports raw materials in a raw yard is investigated. Because of the geometric feature of the equipment in which scooping buckets are attached around the rotating disk, kinematic redundancy occurs in determining joint variable. Link coordinates are introduced following the Denavit-Hartenbery representation. For a given excavation point the forward kinematics yields 3 equations, however the number of involved joint variables in the equations is four. It is shown that the rotating disk at the end of the boom provides an extra passive degree of freedom. Two approaches are investigated in obtaining inverse kinematics solutions. The first method pre-assigns the height of excavation point which can be determined through path planning. A closed form solution is obtained for the first approach. The second method exploits the orthogonality between the normal vector at the excavation point and the z axis of the end-effector coordinate system. The geometry near the reclaiming point has been approximated as a plane, and the plane equation has been obtained by the least square method considering 8 adjacent points near the point. A closed form solution is not found for the second approach, however a linear approximate solution is provided.

• Structural Engineering and Mechanics
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• v.42 no.6
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• pp.761-781
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• 2012

The collapse of structures due to snow loads on roofs occurs frequently for steel structures and rarely for reinforced concrete structures. Since the most significant difference between these structures is related to their ability to handle dead loads, dead loads are believed to play an important part in the collapse of structures by snow loads. As such, the effect of dead loads on displacements and stress couples produced by live loads is presented for plates with different edge conditions. The governing equation of plates that takes into account the effect of dead loads is formulated by means of Hamilton's principle. The existence and effect of dead loads are proven by numerical calculations based on the Galerkin method. In addition, a closed-form solution for simply supported plates is proposed by solving, in approximate terms, the governing equation that includes the effect of dead loads, and this solution is then examined. The effect of dead loads on static live loads can be explained explicitly by means of this closed-form solution. A method that reflects the effects of dead loads on live loads is presented as an example. The present study investigates an additional factor in lightweight roof structural elements, which should be considered due to their recent development.

• Korean Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.158-162
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• 1996

Algorithms to find the Bezier control points of the image of a Bezier domain curve on a Bezier surface are described. The diagonal image curve is analysed and the general linear case is transformed to the diagonal case. This proposed algorithm gives the closed form solution to find the control points of the image curve of a linear domain curve. If the domain curve is not linear, the image curve can be obtained by solving the system of linear equations.

• Journal of Advanced Research in Ocean Engineering
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• v.1 no.3
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• pp.157-167
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• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.185-196
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• 1988

We study existence of polynomial integrating factors and solutions F(x, y)=c of first order nonlinear differential equations. We characterize the homogeneous case, and give algorithms for finding existence of and a basis for polynomial solutions of linear difference and differential equations and rational solutions or linear differential equations with polynomial coefficients. We relate singularities to nature of the solution. Solution of differential equations in closed form to some degree might be called more an art than a science: The investigator can try a number of methods and for a number of classes of equations these methods always work. In particular integrating factors are tricky to find. An analogous but simpler situation exists for integrating inclosed form, where for instance there exists a criterion for when an exponential integral can be found in closed form. In this paper we make a beginning in several directions on these problems, for 2 variable ordinary differential equations. The case of exact differentials reduces immediately to quadrature. The next step is perhaps that of a polynomial integrating factor, our main study. Here we are able to provide necessary conditions based on related homogeneous equations which probably suffice to decide existence in most cases. As part of our investigations we provide complete algorithms for existence of and finding a basis for polynomial solutions of linear differential and difference equations with polynomial coefficients, also rational solutions for such differential equations. Our goal would be a method for decidability of whether any differential equation Mdx+Mdy=0 with polynomial M, N has algebraic solutions(or an undecidability proof). We reduce the question of all solutions algebraic to singularities but have not yet found a definite procedure to find their type. We begin with general results on the set of all polynomial solutions and integrating factors. Consider a differential equation Mdx+Ndy where M, N are nonreal polynomials in x, y with no common factor. When does there exist an integrating factor u which is (i) polynomial (ii) rational? In case (i) the solution F(x, y)=c will be a polynomial. We assume all functions here are complex analytic polynomial in some open set.