Image-Based Angular Distortion Metric of Map Projections by Using Surface Fitting for Noise Reduction

Measuring, analyzing, reducing, and optimizing distortions in map projections is important in cartography. In this study, we introduced a novel image-based angular distortion metric based on the previous spherical great circle arcs-based metric. Images with predefined patterns were used to generate distorted images using mapping software. The generated distorted images with known patterns were then exploited to calculate the proposed angular distortion metric. The mapping software performed the underlying transformation of map projections. Therefore, there was no direct explicit dependence on the forward equations of the map projections in our proposed metric. However, there were fairly large computation errors in the ordinary image-based approach without special correction. To reduce the error, we introduced surface-fitting-based noise reduction in our approach. We established and solved systems of linear equations based on bivariate polynomial functions in the process of noise reduction. Sufficient experiments were made to validate the proposed image-based metric and the accompanying noise reduction approach. In the experiment, the NASA G.Projector was employed as the mapping software for evaluating more than 200 map projections. Experimental results demonstrated that the proposed image-based approach and surface fitting-based noise reduction are feasible and practical for the evaluation of the angular distortion of map projections.

Computing a Group of Polynomials over a Galois Field in FPGA Architecture

For the most extensive range of tasks, such as real-time data processing in intelligent transport systems, etc., advanced computer-based techniques are required. They include field-programmable gate arrays (FPGAs). This paper proposes a method of pre-calculating the hardware complexity of computing a group of polynomial functions depending on the number of input variables of the said functions, based on the microchips of FPGAs. These assessments are reduced for a group of polynomial functions due to computing the common values of elementary polynomials. Implementation is performed using similar software IP-cores adapted to the architecture of user-programmable logic arrays. The architecture of FPGAs includes lookup tables and D flip-flops. This circumstance ensures that the pipelined data processing provides the highest operating speed of a device, which implements the group of polynomial functions defined over a Galois field, independently of the number of variables of the said functions. A group of polynomial functions is computed based on common variables. Therefore, the input/output blocks of FPGAs are not a significant limiting factor for the hardware complexity estimates. Estimates obtained in using the method proposed allow evaluating the amount of the reconfigurable resources of FPGAs, required for implementing a group of polynomial functions defined over a Galois field. This refers to both the existing FPGAs and promising ones that have not yet been implemented.

New proposed fractional-polynomial functions: new recommendation for overcome the imbalance in three-phase systems

Non-linear loads or load imbalances, etc., are the typical causes of asymmetric operation of three-phase systems. The appearance of inverse (positive) and homopolar (zero) symmetric components cause damage to the systems and electrical equipment and increase the power losses on the transmission lines. Reactive power compensation is one of the solutions that can overcome this asymmetry. The difficulty that exists in many different methods is the optimal calculation of the value of the compensator. In this paper, a new method to overcome these problems is proposed and investigagted. The proposed method is based on the fundamental electrical quantities (voltages and currents) on the controllable values of the static compensation devices and overcoming of the asymmetric operation regime in the three-phase systems.

Trajectory Determination of Chang’E-5 during Landing and Ascending

Chang’E-5 (CE-5) is China’s first lunar sample return mission. This paper focuses on the trajectory determination of the CE-5 lander and ascender during the landing and ascending phases, and the positioning of the CE-5 lander on the Moon. Based on the kinematic statistical orbit determination method using B-spline and polynomial functions, the descent and ascent trajectories of the lander and ascender are determined by using ground-based radiometric ranging, Doppler and interferometry data. The results show that a B-spline function is suitable for a trajectory with complex maneuvers. For a smooth trajectory, B-spline and polynomial functions can reach almost the same solutions. The positioning of the CE-5 lander on the Moon is also investigated here. Using the kinematic statistical positioning method, the landing site of the lander is 43.0590°N, 51.9208°W with an elevation of −2480.26 m, which is less than 200 m different from the LRO (Lunar Reconnaissance Orbiter) image data.

Semi-Hyers–Ulam–Rassias Stability of a Volterra Integro-Differential Equation of Order I with a Convolution Type Kernel via Laplace Transform

In this paper, we investigate the semi-Hyers–Ulam–Rassias stability of a Volterra integro-differential equation of order I with a convolution type kernel. To this purpose the Laplace transform is used. The results obtained show that the stability holds for problems formulated with various functions: exponential and polynomial functions. An important aspect that appears in the form of the studied equation is the symmetry of the convolution product.

A Note on a Triple Integral

A closed form expression for a triple integral not previously considered is derived, in terms of the Lerch function. Almost all Lerch functions have an asymmetrical zero-distribution. The kernel of the integral involves the product of the logarithmic, exponential, quotient radical, and polynomial functions. Special cases are derived in terms of fundamental constants; results are summarized in a table. All results in this work are new.