• 대한수학회논문집
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• 제16권3호
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• pp.371-383
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• 2001

In this survey article, we shall introduce the applications of the theory of reproducing kernels to inverse problems. At the same time, we shall present some operator versions of our fundamental general theory for linear transforms in the framework of Hilbert spaces.

• Advances in aircraft and spacecraft science
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• 제5권6호
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• pp.671-689
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• 2018

Bending, buckling and free vibration responses of functionally graded (FG) higher-order beams resting on two parameter (Winkler-Pasternak) elastic foundation are studied using a new inverse hyperbolic beam theory. The material properties of the beam are graded along the thickness direction according to the power-law distribution. In the present theory, the axial displacement accounts for an inverse hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the top and bottom surfaces of the beams. Hamilton's principle is employed to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending, bucking and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio and foundation parameter on the displacements, stresses, critical buckling loads and frequencies. Numerical results by using parabolic beam theory of Reddy and first-order beam theory of Timoshenko are specially generated for comparison of present results and found in excellent agreement with each other.

• 대한전기학회논문지:전기물성ㆍ응용부문C
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• 제55권3호
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• pp.142-148
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• 2006

The resonances that contain the information on the properties of the scattering target can be used for target reconstruction approaches. The inverse scattering theory for the resonances has been applied to the problems of the scattering for a spherical, cylindrical dielectric objects and dielectrically coated conductors, shown reasonable results. Though by using this method the thickness and the dielectric constants of the target can be obtained from a determination of the spacing and of the widths of the scattering resonances, the radius of the target should be given. In this paper, we suggest the improved inverse theory combined with the resonance scattering theory to obtain the radius in addition to the dielectric constant of the target. The applications of this method for scattering problems of electromagnetic waves from cylindrical targets were accomplished, and it shows its validity.

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.111-137
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• 2021

Higson proved that every homotopy invariant, stable and split exact functor from the category of C⁎-algebras to an additive category factors through Kasparov's KK-theory. By adapting a group equivariant generalization of this result by Thomsen, we generalize Higson's result to the inverse semigroup and locally compact, not necessarily Hausdorff groupoid equivariant setting.

• International Journal of Aerospace System Engineering
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• 제3권1호
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• pp.1-4
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• 2016

Functionally graded materials (FGMs) are becoming very popular in various industries due to their effectiveness of the utilization of their constituent elements. However, the modelling of these materials is difficult due to the complex nature of variation of material properties across the thickness. Many shear deformation theories have been developed and employed for the analysis of such functionally graded plates (FGPs). A recently developed inverse hyperbolic shear deformation theory has been successfully employed by Grover et al. [1] for the analysis of laminated composites and sandwich plates. The objective of the study is to obtain finite element solution for the structural analysis of functionally graded plates using inverse hyperbolic shear deformation theory. Finite element analysis facilitates the analysis of complex problems such as functionally graded plates with different boundary conditions and different loadings.

• 한국광학회:학술대회논문집
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• 한국광학회 1989년도 제4회 파동 및 레이저 학술발표회 4th Conference on Waves and lasers 논문집 - 한국광학회
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• pp.59-64
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• 1989

Raman vibrational Q0branch spectra of pure CO are measured by using the technique of quasicw inverse Raman spectroscopy utilizing a pulsed single-frequency laser source. This approach gives enhanced sensitivity compared to earlier work which employed CW lasers, allowing extension of that work to higher accuracy, higher J states, and higher pressure. Fitting laws with pertubation theory and modified energy gap(MEG) theory are described, and the line broadening and shifting coefficients of J=0 to 24 are determined with both fitting laws.

• Journal of electromagnetic engineering and science
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• 제6권4호
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• pp.244-252
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• 2006

A block Jacket transform and. its block inverse Jacket transformn have recently been reported in the paper 'Fast block inverse Jacket transform'. But the multiplication of the block Jacket transform and the corresponding block inverse Jacket transform is not equal to the identity transform, which does not conform to the mathematical rule. In this paper, new binary block Jacket transforms and the corresponding binary block inverse Jacket transforms of orders $N=2^k,\;3^k\;and\;5^k$ for integer values k are proposed and the mathematical proofs are also presented. With the aid of the Kronecker product of the lower order Jacket matrix and the identity matrix, the fast algorithms for realizing these transforms are obtained. Due to the simple inverse, fast algorithm and prime based $P^k$ order of proposed binary block inverse Jacket transform, it can be applied in communications such as space time block code design, signal processing, LDPC coding and information theory. Application of circular permutation matrix(CPM) binary low density quasi block Jacket matrix is also introduced in this paper which is useful in coding theory.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.155-164
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• 2003

The existence and representations of some generalized inverses, including ${A_{T,*}}^{(2)},\;{A_{T,*}}^{(1,2)},\;{A_{T,*}}^{(2,3)},\;{A_{*,S}}^{(2)},\;{A_{*,S}}^{(1,2)}\;and\;{A_{*,S}}^{(2,4)}$, are showed. As applications, the perturbation theory for the generalized inverse {A_{T,S}}^{(2)} and the perturbation bound for unique solution of the general restricted system $A_{x}$ = b(dim(AT)=dimT, $b{\in}AT$ and $x{\in}T$) are studied. Moreover, a characterization and representation of the generalized inverse ${A_{T,*}}^{(2)}$ is obtained.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제20권4호
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• pp.575-586
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• 2006

Both theory and experiment are very important parts in sciences. Especially in mathematics, theory seems to be very important, but experiment or practice doesn't. Numerical analysis of many parts in mathematics needs practice in computer. In this paper, I suggest that computer-practicing in teaching power method, inverse power method and deflation to calculate eigenvalues and eigenvectors is good in understanding the theory. It also makes students sure that mathematics is helpful.

• Advances in aircraft and spacecraft science
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• 제6권5호
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• pp.409-426
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• 2019

The aim of the present work is to study the nonlinear behavior of the laminated composite plates under transverse sinusoidal loading using a new inverse trigonometric shear deformation theory, where geometric nonlinearity in the Von-Karman sense is taken into account. In the present theory, in-plane displacements use an inverse trigonometric shape function to account the effect of transverse shear deformation. The theory satisfies the traction free boundary conditions and violates the need of shear correction factor. The governing equations of equilibrium and boundary conditions associated with present theory are obtained by using the principle of minimum potential energy. These governing equations are solved by eight nodded serendipity element having five degree of freedom per node. A square laminated composite plate is considered for the geometrically linear and nonlinear formulation. The numerical results are obtained for central deflections, in-plane stresses and transverse shear stresses. Finite element Codes are developed using MATLAB. The present results are compared with previously published results. It is concluded that the geometrically linear and nonlinear response of laminated composite plates predicted by using the present inverse trigonometric shape function is in excellent agreement with previously published results.