Introduction A near-infrared spectrum (12000 – 4000 cm-1) is composed of combination and overtone bands that are related to absorption frequencies in the mid-infrared region. These combination and overtone bands correspond to the frequencies of vibrations between the bonds of the atoms making up the material. Because each different material is a unique combination of atoms, no two compounds pro...

in hilbert space l2(rn), we prove the equivalence between the mod-ulus of smoothness and the k-functionals constructed by the sobolev space cor-responding to the fourier transform. for this purpose, using a spherical meanoperator.

s is a time-frequency transform based on the concept of short-time fourier transform and wavelet transform. the main property of this transform that separate it from the discrete short-time fourier transform is variable frequency resolution. but in this transform the change of resolution of high frequencies to low frequencies is very high. so another transform as a modified s transform is intro...

an infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. the two-dimensional coupled thermoelastodynamic pdes are specified based on equations of motion and energy equation, which are uncoupled using nowacki potential functions. the laplace integral transform and bessel-fourier series are u...

in the present work, a hybrid of fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. the fourier transform is employed with combination of homotopy perturbation method (hpm), the so called fourier transform homotopy perturbation method (fthpm) to solve the partial differential equations. the c...