Unified Approach For Multiscale Radar Cross-Section Measurement by Synthetic Aperture Imaging

<div><div>*This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.</div></div><div><br></div>In this study, we present an improved and unified approach for image-based radar cross-section (RCS) measurement by 2-D synthetic aperture radar (SAR) imaging with an arbitrary curved antenna scanning trajectory. Because RCS is a quantity defined in the far-field distance of an object under test, direct RCS measurement of an electrically large target is often infeasible owing to the spatial limitation of the measurement facility. The method proposed in this study belongs to the class of techniques referred to as the image-based near-field to far-field transformation (NFFFT) to convert the near-field data of scattering experiment into the far-field RCS. In a previous study, we have developed an NFFFT based on 3-D SAR imaging with an arbitrary antenna scanning surface. However, the previous approach is only applicable to the surface scanning which is impossible for a certain case such as measurement using airborne SAR or vehicle-borne SAR. Therefore, one requires an alternative method that can accommodate an arbitrary scanning curve, which is the subject of this study. We derive a generalized correction factor for image-based NFFFT which is designed to ensure the integral transformation in the image reconstruction process be self-consistent for electrically small scatterers. We provide a series of numerical simulations, an indoor experiment, and an airborne SAR experiment to validate that the proposed scheme can be utilized for various situations ranging from near-field to far-field distance.

Unified Approach For Multiscale Radar Cross-Section Measurement by Synthetic Aperture Imaging

<div><div>*This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.</div></div><div><br></div>In this study, we present an improved and unified approach for image-based radar cross-section (RCS) measurement by 2-D synthetic aperture radar (SAR) imaging with an arbitrary curved antenna scanning trajectory. Because RCS is a quantity defined in the far-field distance of an object under test, direct RCS measurement of an electrically large target is often infeasible owing to the spatial limitation of the measurement facility. The method proposed in this study belongs to the class of techniques referred to as the image-based near-field to far-field transformation (NFFFT) to convert the near-field data of scattering experiment into the far-field RCS. In a previous study, we have developed an NFFFT based on 3-D SAR imaging with an arbitrary antenna scanning surface. However, the previous approach is only applicable to the surface scanning which is impossible for a certain case such as measurement using airborne SAR or vehicle-borne SAR. Therefore, one requires an alternative method that can accommodate an arbitrary scanning curve, which is the subject of this study. We derive a generalized correction factor for image-based NFFFT which is designed to ensure the integral transformation in the image reconstruction process be self-consistent for electrically small scatterers. We provide a series of numerical simulations, an indoor experiment, and an airborne SAR experiment to validate that the proposed scheme can be utilized for various situations ranging from near-field to far-field distance.

Solution Non Linear Partial Differential Equations By ZMA Decomposition Method

In this survey, viewed integral transformation (IT) combined with Adomian decomposition method (ADM) as ZMA- transform (ZMAT) coupled with (ADM) in which said ZMA decomposition method has been utilized to solve nonlinear partial differential equations (NPDE's).This work is very useful for finding the exact solution of (NPDE's) and this result is more accurate obtained with compared the exact solution obtained in the literature.

Analysis of the Fractional-Order Kaup–Kupershmidt Equation via Novel Transforms

In this article, we develop a technique to determine the analytical result of some Kaup–Kupershmidt equations with the aid of a modified technique called the new iteration transform method. This technique is a mixture of the novel integral transformation Elzaki transformation and the new iteration technique. The nonlinear term can be handled easily by a new iteration technique. The results show that the combination of the Elzaki transformation and the new iteration technique is quite capable and basically well suited for applying in such problems and that it can be implemented to other nonlinear models. This technique is viewed as an effective alternative approach to certain existing approaches for such accurate models.

Substantiating the pulse method for determining the time parameter of fire detectors with a thermoresistive sensing element

This paper substantiates the pulse method for determining the time parameter for fire detectors with a thermoresistive sensing element ‒ the time constant. The method is based on using the Joule-Lenz effect, which manifests itself when an electric current pulse passes through the thermoresistive sensing element of fire detectors. Thermal processes in such a sensing element are described by a mathematical model that belongs to the class of equations of mathematical physics. The solution to the differential equation of this class was derived using the Hankel integral transformation and is represented as a series relative to the Bessel functions. The resulting solution is used to construct a mathematical model of a thermoresistive sensing element in the form of a transfer function, which takes the form of the transfer function of the inertial link. To trigger the thermoresistive sensing element of fire detectors, a single pulse of electric current in the shape of a rectangular triangle is used. The integral Laplace transformation was applied to mathematically describe the response of a thermoresistive sensing element to the thermal effect of such a test influence. To obtain information about the time parameter of fire detectors with a thermoresistive sensing element, the ratio of its output signals is used, which are measured in the a priori defined moments. A two-parametric expression was built to determine the time parameter of fire detectors; a verbal interpretation of the pulse method to determine it was provided. The implementation of this method ensures the invariance of the time parameter of fire detectors with a thermoresistive sensing element relative to the amplitude of a single pulse of an electric current, as well as relative to the parameter that is included in its transfer coefficient.

Functional Effects of Permeability on Oldroyd-B Fluid under Magnetization: A Comparison of Slipping and Non-Slipping Solutions

In this article, the impact of Newtonian heating in addition to slip effects was critically examined on the unsteady magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid near an infinitely vertical plate. The functional effects such as the retardation and relaxation of materials can be estimated for magnetized permeability based on the relative decrease or increase during magnetization. From this perspective, a new mathematical model was formulated based on non-slippage and slippage postulates for the Oldroyd-B fluid with magnetized permeability. The heat transfer induction was also examined through a non-fractional developed mathematical model for the Oldroyd-B fluid. The exact solution expressions for non-dimensional equations of velocity and temperature were explored by employing Laplace integral transformation under slipping boundary conditions under Newtonian heating. The heat transfer rate was estimated through physical interpretation by considering the limits on the solutions induced by the Nusselt number. To comprehensively discuss the dynamics of the considered problem, the physical impacts of different parameters were studied and reverberations were graphically highlighted and deliberated. Furthermore, in order to validate the results, two limiting models, namely the Maxwell model and the second grade model, were used to compare the relevant flow characteristics. Additionally, in order to perform the parametric analysis, the graphical representation was portrayed for non-slipping and slipping solutions for velocity and temperature.

Power Law Kernel Analysis of MHD Maxwell Fluid with Ramped Boundary Conditions: Transport Phenomena Solutions Based on Special Functions

In this paper, a new approach to find exact solutions is carried out for a generalized unsteady magnetohydrodynamic transport of a rate-type fluid near an unbounded upright plate, which is analyzed for ramped-wall temperature and velocity with constant concentration. The vertical plate is suspended in a porous medium and encounters the effects of radiation. An innovative definition of the time-fractional operator in power-law-kernel form is implemented to hypothesize the constitutive mass, energy, and momentum equations. The Laplace integral transformation technique is applied on a dimensionless form of governing partial differential equations by introducing some non-dimensional suitable parameters to establish the exact expressions in terms of special functions for ramped velocity, temperature, and constant-concentration fields. In order to validate the problem, the absence of the mass Grashof parameter led to the investigated solutions obtaining good agreement in existing literature. Additionally, several system parameters were used, such as as magnetic value M, Prandtl value Pr, Maxwell parameter λ, dimensionless time τ, Schmidt number “Sc”, fractional parameter α, andMass and Thermal Grashof numbers Gm and Gr, respectively, to examine their impacts on velocity, wall temperature, and constant concentration. Results are also discussed in detail and demonstrated graphically via Mathcad-15 software. A comprehensive comparative study between fractional and non-fractional models describes that the fractional model elucidate the memory effects more efficiently.

A Riemann–von Mangoldt-Type Formula for the Distribution of Beurling Primes

In this paper we work out a Riemann–von Mangoldt type formula for the summatory function := , where is an arithmetical semigroup (a Beurling generalized system of integers) and is the corresponding von Mangoldt function attaining with a prime element and zero otherwise. On the way towards this formula, we prove explicit estimates on the Beurling zeta function , belonging to , to the number of zeroes of in various regions, in particular within the critical strip where the analytic continuation exists, and to the magnitude of the logarithmic derivative of , under the sole additional assumption that Knopfmacher’s Axiom A is satisfied. We also construct a technically useful broken line contour to which the technic of integral transformation can be well applied. The whole work serves as a first step towards a further study of the distribution of zeros of the Beurling zeta function, providing appropriate zero density and zero clustering estimates, to be presented in the continuation of this paper.

Assessing Goodness of Fit for Verifying Probabilistic Forecasts

The verification of probabilistic forecasts in hydro-climatology is integral to their development, use, and adoption. We propose here a means of utilizing goodness of fit measures for verifying the reliability of probabilistic forecasts. The difficulty in measuring the goodness of fit for a probabilistic prediction or forecast is that predicted probability distributions for a target variable are not stationary in time, meaning one observation alone exists to quantify goodness of fit for each prediction issued. Therefore, we suggest an additional dissociation that can dissociate target information from the other time variant part—the target to be verified in this study is the alignment of observations to the predicted probability distribution. For this dissociation, the probability integral transformation is used. To measure the goodness of fit for the predicted probability distributions, this study uses the root mean squared deviation metric. If the observations after the dissociation can be assumed to be independent, the mean square deviation metric becomes a chi-square test statistic, which enables statistically testing the hypothesis regarding whether the observations are from the same population as the predicted probability distributions. An illustration of our proposed rationale is provided using the multi-model ensemble prediction for El Niño–Southern Oscillation.