Regional Seafloor Topography by Extended Kalman Filtering of Marine Gravity Data without Ship-Track Information

An iterative Extended Kalman Filter (EKF) approach is proposed to recover a regional set of topographic heights composing an undersea volcanic mount by the successive combination of large numbers of gravity measurements at sea surface using altimetry satellite-derived grids and taking the error uncertainties into account. The integration of the non-linear Newtonian operators versus the radial and angular distances (and its first derivatives) enables the estimation process to accelerate and requires only few iterations, instead of summing Legendre polynomial series or using noise-degraded 2D-FFT decomposition. To show the effectiveness of the EKF approach, we apply it to the real case of the bathymetry around the Great Meteor seamount in the Atlantic Ocean by combining only geoid height/free-air anomaly datasets and using ship-track soundings as reference for validation. Topography of the Great Meteor seamounts structures are well-reconstructed, especially when regional compensation is considered. Best solution gives a RMS equal to 400 m with respect to the single beam depth observations and it is comparable to RMS obtained for ETOPO1 of about 365 m. Larger discrepancies are located in the seamount flanks due to missing high-resolution information for gradients. This approach can improve the knowledge of seafloor topography in regions where few echo-sounder measurements are available.

The Abel – Poisson means of conjugate Fourier – Chebyshev series and their approximation properties

Herein, the approximation properties of the Abel – Poisson means of rational conjugate Fourier series on the system of the Chebyshev–Markov algebraic fractions are studied, and the approximations of conjugate functions with density | x |s , s ∈(1, 2), on the segment [–1,1] by this method are investigated. In the introduction, the results related to the study of the polynomial and rational approximations of conjugate functions are presented. The conjugate Fourier series on one system of the Chebyshev – Markov algebraic fractions is constructed. In the main part of the article, the integral representation of the approximations of conjugate functions on the segment [–1,1] by the method under study is established, the asymptotically exact upper bounds of deviations of conjugate Abel – Poisson means on classes of conjugate functions when the function satisfies the Lipschitz condition on the segment [–1,1] are found, and the approximations of the conjugate Abel – Poisson means of conjugate functions with density | x |s , s ∈(1, 2), on the segment [–1,1] are studied. Estimates of the approximations are obtained, and the asymptotic expression of the majorant of the approximations in the final part is found. The optimal value of the parameter at which the greatest rate of decreasing the majorant is provided is found. As a consequence of the obtained results, the problem of approximating the conjugate function with density | x |s , s ∈(1, 2), by the Abel – Poisson means of conjugate polynomial series on the system of Chebyshev polynomials of the first kind is studied in detail. Estimates of the approximations are established, as well as the asymptotic expression of the majorants of the approximations. This work is of both theoretical and applied nature. It can be used when reading special courses at mathematical faculties and for solving specific problems of computational mathematics.

Study on Acoustic Characteristics of a Flexible Plate Strongly Coupled with Rectangular Cavity

This paper presents a method to predict the acoustic characteristics and steady-state responses of a flexible plate strongly coupled with rectangular cavity based on energy principle theory and Legendre polynomial series. First, the displacement of the plate and the sound pressure in the cavity are constructed in the form of two-dimensional and three-dimensional Legendre polynomial series, respectively. The unknown expansion coefficients are obtained using the Rayleigh–Ritz technique based on the energy expressions for the strongly coupled plate-cavity system. The accuracy, convergence, and efficiency of the present method are verified by comparing with the results available in the FEM and literature. Finally, the effects of the structural boundary conditions, cavity depth, and structural length-width ratio on the coupling natural frequency and the steady-state responses under three excitation conditions are analyzed.

Influence of coupling effects on analytical solutions of functionally graded (FG) spherical shells of revolution

Due to the lack of commercially available finite elements packages allowing us to analyse the behaviour of porous functionally graded (FG) structures in this paper, axisymmetric deformations of coupled FG spherical shells are studied. The analytical solution is presented by using complex hypergeometric polynomial series. The results presented agree closely with the reference results for isotropic spherical shells of revolution. The influence of the effects of material properties is characterized by a multiplier characterizing an unsymmetric shell wall construction (stiffness coupling). The results can be easily adopted in design procedures. The present results can be treated as the benchmark for finite element investigations.

The NH2 scissors band of methylamine

For the first time the ν4 NH2 scissors band has been assigned in a high-resolution infrared spectrum. A rotationally resolved spectrum of methylamine was recorded using two infrared spectroscopic techniques. A White-type multi-pass cell device coupled to the Bruker IFS 125 HR Fourier transform spectrometer was implemented on the AILES beamline at the SOLEIL synchrotron facility and a room-temperature spectrum of the whole band in the region of 1540–1710 cm−1 was recorded with a resolution of 0.001 cm−1. Then, a low-temperature high-resolution spectrum in the 1622.5–1655.6 cm−1 range of Q and R branches of the ν4 band was recorded using a quantum cascade laser spectrometer. Preliminary assignment was carried out in the NH2 scissors band region, and about 2200 transitions for K from 0 to 6 have been assigned for A, B, and E1 symmetry species. The simultaneous fit of assigned lines using a group-theoretical effective Hamiltonian was not successful; instead simple polynomial series expansions were used for each symmetry and K value.

POLYNOMIAL SERIES SOLUTION OF BENJAMIN−BONA−MAHONY EQUATION VIA DIFFERENTIAL TRANSFORM METHOD

In this work, we solved the initial value problem of Benjamin−Bona−Mahony equation with generalized initial conditions by using differential transform method (DTM). We obtained the general solution in the form of a series. An example is presented for the particular initial conditions.