The determination of the true profile of XPS line by regularization method: I. Mathematical algorithm and numerical simulations

The resolution of XPS spectra is limited mainly by instrumental parameters like the spectral line width of exciting X-ray source and the finite energy resolution of the electron analyzer. A new algorithm of an inverse ill-posed problem has been proposed in which low resolution experimental XPS data can be enhanced by removing the instrumental functions. The regularization method with a special fast iteration algorithm is applied for determining the true profile line of a complex chemical compound if we know excitation and instrumental functions. This paper is structured as follows: (I) a mathematical algorithm is described and numerical simulation results are presented. (II) These algorithms have been applied to the poorly resolved C 1s spectrum of a poly-methyl methacrylate (PMMA) film studied by the conventional technique with monochromatic and polychromatic radiation. The resulting enhancement allows previously unresolved structure to be observed without any assumptions concerning number, position, shape of peaks and their ratio.     

Direct Solution of the Inverse Problem for Rough Surface Scattering

We consider the inverse scattering problem for a scalar wave field incident on a perfectly conducting one-dimensional rough surface. The Dirichlet Green function for the upper half-plane is introduced, in place of the free-space Green function, as the fundamental solution to the Helmholtz equation. Based on this half-plane Green function, two reasonable approximate operations are performed, and an integral equation is formulated to approximate the total field in the two-dimensional space, then to determine the profile of the rough surface as a minimum of the total field. Reconstructions of sinusoidal, non-sinusoidal and random rough surface are performed using numerical techniques. Good agreement of these results demonstrates that the inverse scattering method is reliable.     

Resonance States in Scattering of Slow Particles with Nonzero Orbital Angular Momentum by the Pöschl-Teller Potential

The scattering of slow particles with nonzero orbital angular momentum in the field of a finite potential is considered. The respective scattering problem is solved in the Pais approximation. The inverse problem is solved for the Pöschl-Teller equation, and a general scheme for Pais resonances and a procedure for calculating scattering cross sections for resonance particles are formulated.

     

Vibrations of an elastic strip with a rough boundary

A plane problem of steady-state forced vibrations of an elastic strip whose lower boundary contains a rough segment is considered. Using Green’s functions for a strip, the problem is reduced to a system of integral equations with integrals over the rough boundary, which is solved by the boundary-element method. The inverse problem of determining the shape of the rough boundary segment from the data on the displacement field of a certain part of the upper boundary is formulated. By the linearization procedure, the inverse problem is reduced to a Fredholm integral equation of the first kind with a smooth kernel, which is solved by Tikhonov’s regularization method.     

Threshold spectra of SBS at a finite frequency mismatch of the interacting waves

A problem of scattered radiation spectrum line width of stimulated Brillouin scattering (SBS) in plasma with two species of ions is considered. Threshold conditions, when SBS shifted frequency lines, which characterize the scattered radiation spectrum, are comparatively wide and are comparatively narrow, are defined. A possibility of existence of the scattered radiation spectrum with the frequency line width comparable to the ion-acoustic frequency is revealed.     

目标函数设置对放疗逆向计划多目标优化过程的影响

目前放疗逆向计划中常用的目标函数有两种:基于剂量分布的目标函数和基于剂量．体积直方图（DVH）的目标函数。实际系统都基于单目标优化算法进行,不考虑逆向计划的多目标性。在Pareto多目标优化理论的基础上,研究逆向计划的目标函数设置问题,比较基于剂量分布的目标函数和基于DVH的目标函数对多目标优化过程的影响,包括优化时间、收敛性和存在的问题等,为逆向计划过程中多目标优化目标函数的设置提供依据。There are two kinds of objective functions in radiotherapy inverse planning: dose distribution-based and Dose-Volume Histogram （DVH）-based functions. The treatment planning in our days is still a trial and error process because the multi-objective problem is solved by transforming it into a single objective problem using a specific set of weights for each object. This work investigates the problem of objective function setting based on Pareto multi-optimization theory, and compares the effect on multi-objective inverse planning of those two kinds of objective functions including calculation time, converge speed, etc. The basis of objective function setting on inverse planning is discussed.     

Spontaneous decay in a system of two spatially separated atoms (One-dimensional case)

The problem of the dynamics and the spectrum of spontaneous radiation is solved for a system of two atoms in one-dimensional space. In order to single out, to the maximum possible degree, phenomena associated with the influence of spatially separated atoms on each other via the radiation field, the present analysis is performed precisely for the one-dimensional case. As a result, two effects are revealed and considered in detail: (i) the existence of stable (metastable) entangled superposition states at specific distances between the atoms and (ii) a considerable distinction between the spectra of photons emitted in two opposite directions from the system where only one of the atoms is initially excited. The possibilities of observing these effects are discussed.     

Analytical solution of the inverse spectroscopic problem: Determination of electron moments of vibrational transitions of diatomic molecules by their probabilities

The inverse problem of spectroscopy of vibrational transitions of diatomic molecules was analytically solved on the basis of wave functions of the Morse oscillator. An example of the determination of the transition dipole-moment function by intensities of several lines of molecule vibrational-rotational spectra measured experimentally was considered. A similar approach based on simple expressions for matrix elements can be applied to consider optimal lasing conditions of the CO electronic transition laser.     

Statistical estimation of the spatial spectrum of secondary sources

A statistical problem of estimating the shape and maximum possible width of the spatial energy spectrum of secondary sources is formulated and solved. The secondary sources under consideration are characteristic of the class of scatterers with preset statistical mean parameters. This estimation is important for analyzing the possibility of solving inverse scattering problems, including the question of the uniqueness and stability of the solution and also the correct organization of a tomographic experiment. Results of a computer simulation are presented, and the expected statistical mean spectrum is compared with a particular realization of the spectrum. In the case of a strongly pronounced rescattering, the statistical mean width of the spectrum is mainly determined by the effective velocity contrast in the ensemble of scatterers and depends only weakly on the scale of spatial fluctuations of the scatterers’ characteristics.     

Investigation of Hg resonance 184.9 nm line profile in a low-pressure mercury-argon discharge

The line profiles of 184.9 nm Hg resonance line emitted from a Hg low-pressure high-frequency electrodeless discharge lamp, containing Hg 198 isotope, have been measured by means of a Zeeman scanning spectrometer at the mercury cold spot temperature values in the range of 0-23 °C. Two different methods were used to determine the real spectral line profile and to separate the instrument function: (i) solving the ill-posed inverse problem by means of the Tikhonov's regularization method; and (ii) the mathematical modelling by means of a non-linear multi-parameter chi-square fit. The real Hg 184.9 nm spectral line profiles, determined by both methods, are compared. Influence of instrumental function, degree of the self-absorption and temperature of the radiating atoms are obtained.     

The influence of the electrode diameter on the diffraction effects in the ultrasonic field generated by an oscillating piezoelectric disk

The problem of ultrasound radiation by a finite-size source is considered. A boundary-value problem is formulated and solved for ultrasonic waves generated by an oscillating piezoelectric disk fixed along its edge and characterized by an eigenfrequency spectrum and a corresponding oscillation amplitude distribution. The influence of the size of electrodes on the diffraction effects arising in the ultrasonic field of the piezoelectric disk is theoretically investigated.     

Inverse scattering problem for gratings with deep modulation

The similarity between one-dimensional Schrödinger and Helmholtz equations is discussed. The Helmholtz equation in optical coordinate is shown to reduce to the Schrödinger equation with an effective potential. Two examples of scattering problem are considered: sinusoidal Bragg grating with deep modulation and smooth hyperbolic secant layer. The inverse scattering problem is solved numerically for both cases. For the layer an analytical solution is presented as well. The analysis of the effective potential allows one to qualitatively predict some properties of the reflection spectrum.     

Joint power allocation and user assignment for licensed/unlicensed band users in massive MIMO cellular systems

In this paper, we study the joint user assignment and power allocation for the defined utility function (central cell throughput) maximization in massive Multiple Input-Multiple Output (MIMO) cellular system coexistence with Wireless Fidelity (WiFi) network. Firstly, the power allocation of problem is formulated as a convex optimization. Unfortunately, the formulated problem has not a closed-form solution. For solving the mentioned problem, it is converted to three sub-problem based on the number of lemmas that are expressed. Due to two of these problems remain difficult to solve, this two sub-problem are relaxed. The Ellipsoid algorithm is an iterative algorithm that used for solving of the relaxed problems. In the following, joint user assignment and power allocation will be addressed, in which two approaches are proposed for solving. In the first approach, we propose an iterative algorithm that user assignment problem and power allocation problem are solved in each iteration. In the second approach, at first, users are assigned to licensed and unlicensed bands, then for the obtained arrangement, the power allocation problem is solved. The simulation results showed that the proposed algorithms are significantly close to the benchmark methods.     

The time-delay estimation method of resolving left-right target ambiguity for twin-line array and its realization

The directivity function of twin-line array sonar can be used to identify left/right target. But the performance is limited by the distance between two lines and also exists the blind area for target identification. A method, which is based on the time-delay estimation between two line arrays, is proposed to identify left/right target. The method is robust with the variation of distance between two line array, the blind area is considerable decreased. The theoretical analysis results and realization method is described. An algorithm base on interpolation method for precisely estimating tune-delay of two line array are derived, therefore the left-right ambiguity problem is solved.     

Measurement of the amplitude and phase structures of an optical field and the transfer function for describing the effect of a medium in the form of a modulating function

The phase problem in optics is solved as applied to the detection and analysis of the amplitude and phase structures of two-dimensional optical fields forming or transmitting an image and the amplitude and phase structures of the transfer or instrumental functions of either the media containing optical inhomogeneities or the systems forming fields and involving instrumental distortions. The effect of the medium is characterized by a modulating function and described by a multiplication operation. Two variants of the optical scheme are considered. In each variant, the spatial-frequency spectrum is formed by the first optical system and the first spatial modulation is introduced in the spatial-frequency plane. The second optical system is arranged in the same plane. This system images the field under investigation into the plane located at the exit of the transmitting medium. In the first variant of the optical scheme, the second spatial modulation is introduced in the same plane. The third optical system forms a spatial-frequency spectrum in the detection plane. In the second variant of the scheme, an image of the plane positioned at the exit of the probing medium is formed in the detection plane by the third optical system. The second spatial modulation is introduced in the spatial-frequency plane of the third optical system. In both variants, four independent two-dimensional intensity distributions that make it possible to solve the problem posed are detected at the exit.     

Quantum OSP-invariant nonlinear Schrödinger equation

The generalizations of the nonlinear Schrödinger equation (NS) associated with the orthosymplectic superalgebras are formulated. The simplest osp(1/2)-NS model is solved by the quantum inverse scattering method on a finite interval under periodic boundary conditions as well as on the whole line in the case of a finite number of excitations.     

A line intensity transfer model for the rotational raman spectrum of ethylene

A new model for the spectrum of ethylene, utilizing the line-mixing concept for overlapping lines, is presented here. The Lorentzian line shape is assigned to all the lines, with the single transitions having the usual directly pressure-dependent widths, and with overlapping lines considered as a single composite feature having an inversely pressure-dependent width. This model is compared with two sets of data: interferometric data over a range of pressures, and an ad hoc model that matches experimental line spectrum data at a single pressure. Inversely pressuredependent widths are obtained for the two comparisons, and the discrepancy between the results is explained.     

Numerical evaluation of linearized image reconstruction based on finite element method for biomedical photoacoustic imaging

An image reconstruction algorithm for biomedical photoacoustic imaging is discussed. The algorithm solves the inverse problem of the photoacoustic phenomenon in biological media and images the distribution of large optical absorption coefficients, which can indicate diseased tissues such as cancers with angiogenesis and the tissues labeled by exogenous photon absorbers. The linearized forward problem, which relates the absorption coefficients to the detected photoacoustic signals, is formulated by using photon diffusion and photoacoustic wave equations. Both partial differential equations are solved by a finite element method. The inverse problem is solved by truncated singular value decomposition, which reduces the effects of the measurement noise and the errors between forward modeling and actual measurement systems. The spatial resolution and the robustness to various factors affecting the image reconstruction are evaluated by numerical experiments with 2D geometry.     

Multi-bright-dark soliton solutions to the AB system in nonlinear optics

The AB system is the basic integrable model to describe unstable baroclinic wave packets in geophysical fluids and the propagation of mesoscale gravity flows in nonlinear optics. On the basis of the spectral analysis of a Lax pair and the inverse scattering method, we establish the Riemann–Hilbert problem of the AB system. Then, the inverse problems are formulated and solved with the aid of the Riemann–Hilbert problem, from which the potentials can be reconstructed according to the asymptotic expansion of the sectional analytic function and the related symmetry relations. As an application, we obtain the multi-bright-dark soliton solutions to the AB system in the reflectionless case and discuss the dynamic behavior of elastic soliton collisions by choosing appropriate free parameters.     

A method to solve an acoustic inverse scattering problem involving smart obstacles

A time-harmonic acoustic inverse scattering problem involving smart obstacles is formulated and a method to solve it is proposed. A smart obstacle is an obstacle that, when hit by an incoming acoustic wave, tries to pursue a given goal circulating a suitable pressure current on its boundary. A pressure current is a quantity whose physical dimension is pressure divided by time. The goals pursued by the smart obstacles that we have considered are the following ones: to be undetectable or to appear with a shape and/or acoustic boundary impedance different from its actual ones eventually in a location in space different from the actual location. The following time-harmonic inverse scattering problem is considered: from the knowledge of several far fields generated by the smart obstacle when hit by known time-harmonic waves, the knowledge of the goal pursued by the smart obstacle and of its acoustic boundary impedance reconstruct the boundary of the obstacle. A method to solve this inverse problem that generalizes the so-called Herglotz function method is proposed. Some numerical experiments that validate the method proposed are presented. The website http://www.econ.univpm.it/recchioni/w13 contains some auxiliary material that helps the understanding of the current paper.