• Kyungpook Mathematical Journal
• /
• v.47 no.4
• /
• pp.569-578
• /
• 2007

Sufficient conditions for the existence of at least one solution of boundary value problems for higher order nonlinear difference equations are established. We allow $f$ to be at most linear, superlinear or sublinear in obtained results.

• Journal of applied mathematics & informatics
• /
• v.40 no.5_6
• /
• pp.1117-1128
• /
• 2022

We find several q-differential equations of higher order that has q-tangent polynomials as the solution and obtain its associated symmetric properties.

• Journal of the Chungcheong Mathematical Society
• /
• v.37 no.1
• /
• pp.27-40
• /
• 2024

In this paper, we consider the higher-order HartreeFock equations. The higher-order linear Schrödinger equation was introduced in [5] as the formal finite Taylor expansion of the pseudorelativistic linear Schrödinger equation. In [13], the authors established global-in-time Strichartz estimates for the linear higher-order equations which hold uniformly in the speed of light c ≥ 1 and as their applications they proved the convergence of higher-order Hartree-Fock equations to the corresponding pseudo-relativistic equation on arbitrary time interval as c goes to infinity when the Taylor expansion order is odd. To achieve this, they not only showed the existence of solutions in L² space but also proved that the solutions stay bounded uniformly in c. We address the remaining question on the convergence of higherorder Hartree-Fock equations when the Taylor expansion order is even. The distinguished feature from the odd case is that the group velocity of phase function would be vanishing when the size of frequency is comparable to c. Owing to this property, the kinetic energy of solutions is not coercive and only weaker Strichartz estimates compared to the odd case were obtained in [13]. Thus, we only manage to establish the existence of local solutions in H^s space for s > $\frac{1}{3}$ on a finite time interval [-T, T], however, the time interval does not depend on c and the solutions are bounded uniformly in c. In addition, we provide the convergence result of higher-order Hartree-Fock equations to the pseudo-relativistic equation with the same convergence rate as the odd case, which holds on [-T, T].

• Transactions of the Korean Society of Automotive Engineers
• /
• v.8 no.4
• /
• pp.85-92
• /
• 2000

The pulsating pressure waves are composed of fundamental frequency and higher order harmonics in exhaust pipe of engines. The nonlinearity in exhaust pipe is caused by their interactions. The error which is between prediction and measurement is induced by the nonlinearity. We can not explain this phenomenon using linear acoustic theory which is existing theory. So power spectrum which was used in linear theory is not useful. Bispectrum and bicoherence functions which are a higher order spectrum are applicable to explain this phenomenon. This paper proposes a nonlinear effect of pulsating pressure waves. The phenomenon proposed here is identified by using of higher order spectrum density functions.

• Journal of Mechanical Science and Technology
• /
• v.17 no.2
• /
• pp.254-268
• /
• 2003

The explicit formulation of the J-integral and the M-integral is constructed in terms of the stress intensity factor and the higher order stress coefficients for Mode II cracks under small or large scale yielding. Furthermore, the stress intensity factor and the higher order stress coefficients as well are computed with the aid of the two-state J- and the M-integral, which is found to be accurate and efficient. It is found that the contribution from the higher order singularities to the J-integral is closely related to the configuration of the plastic zone.

• Steel and Composite Structures
• /
• v.16 no.5
• /
• pp.507-519
• /
• 2014

In this paper, a higher order shear deformation beam theory is developed for static and free vibration analysis of functionally graded beams. The theory account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present higher-order shear deformation beam theory, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain frequencies. Different higher order shear deformation theories and classical beam theories were used in the analysis. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2000.06a
• /
• pp.536-542
• /
• 2000

The present paper introduces a new fixed interface component mode synthesizing technique based on the notion of higher-order field-consistency. The present technique employs higher-order residual constraint modes in addition to lower fixed interface normal modes while consistency in matching field variables at the substructure interface is maintained. The present field-consistency approach does not increase the size of the synthesized system even if higher-order residual constraint modes are included. A new field-consistent higher-order synthesis technique is first presented and a numerical example is given to verify the present method.

• Journal of the Korean Mathematical Society
• /
• v.43 no.1
• /
• pp.111-131
• /
• 2006

The goal of this paper is to define p-adic Hardy sums and p-adic q-higher-order Hardy-type sums. By using these sums and p-adic q-higher-order Dedekind sums, we construct p-adic continuous functions for an odd prime. These functions contain padic q-analogue of higher-order Hardy-type sums. By using an invariant p-adic q-integral on $\mathbb{Z}_p$, we give fundamental properties of these sums. We also establish relations between p-adic Hardy sums, Bernoulli functions, trigonometric functions and Lambert series.

• Investigative Magnetic Resonance Imaging
• /
• v.11 no.2
• /
• pp.95-102
• /
• 2007

Purpose: To acquire high-resolution spiral-scan images at higher magnetic field, high homogeneous magnetic field is needed. Field inhomogeneity mapping and in-vivo shimming are important for rapid imaging such as spiral-scan imaging. The rapid scanning sequences are very susceptible to inhomogeneity. In this paper, we proposed a higher-order shimming method to obtain homogeneous magnetic field. Materials and Methods: To reduce measurement time for field inhomogeneity mapping, simultaneous axial/ sagittal, and coronal acquisitions are done using multi-slice based Fast Spin echo sequence. Acquired field inhomogeneity map is analyzed using the spherical harmonic functions, and shim currents are obtained by the multiplication of the pseudo-inverse of the field pattern with the inhomogeneity map. Results: Since the field inhomogeneity is increasing in proportion to the magnetic field, higher order shimming to reduce the inhomogeneity becomes more important in high field imaging. The shimming technique in which axial, sagittal, and coronal section inhomogeneity maps are obtained in one scan is developed, and the shimming method based on the analysis of spherical harmonics of the imhomogenity map is applied. The proposed technique is applicable to a localized shimming as well. High resolution spiral-scan imaging was successfully obtained with the proposed higher order shimming. Conclusion: Proposed pulse sequence for rapid measurement of inhomogeneity map and higher order shimming based on the inhomogeneity map work very well at 3 Tesla MRI system. With the proposed higher order shimming and localized higher order shimming techniques, high resolution spiral-scan images are successfully obtained at 3 T MRI system.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.5 s.176
• /
• pp.1314-1322
• /
• 2000

The acoustic property of reactive type single expansion chamber can be analyzed by traditional plane wave theory. This theory can be applied in low frequency range and has good performance. But this theory can't include higher order modes, therefore another method is essential to analyze acoustic filter in high frequency range. Many researcher suggested the method that can concern higher order modes, and their methods are using mode matching technique. But there is no method that can be applied to the analysis of single expansion chamber with arbitrary inlet/outlet duct position and numbers of higher order modes of inlet/outlet duct and middle chamber. In this paper, the method which can analyze single expansion chamber with arbitrary inlet/outlet duct position and numbers of higher order modes of inlet/outlet duct and middle chamber using fundamental mode matching technique, was suggested and the predictions by this method was compared with those by the finite element method, and the influence of inlet/outlet location to acoustic performance of single expansion chamber is investigated and explained by higher order mode effects.