This manuscript proposes a novel tangent-graph-based method that provides all distinctive topology paths, as a set of trajectories that can not be transformed into each other by gradual bending and stretching without colliding with obstacles. As the global optimal trajectory (limited by dynamic constraints) may not correspond to the shortest path (almost without dynamic constraints), it is important to provide all distinctive topology paths rather than just the globally shortest one. One of the application is provide initial paths for trajectory planning methods, such as time elastic band (TEB) and dynamic window approach (DWA). Considering that a mobile platform is always working in a dynamic changing environment and that update the whole graph is time consuming, a dynamic rectify method is proposed to update tangents according to local map provided by sensor reading. Finally, results under real grid maps are presented.

Path planning in 3D environment is a fundamental research area for robots and autonomous vehicles. Based on the principle ``the shortest path consists of tangents'', RimJump* is proposed as a tangent-based path planning method suitable for finding the shortest path (both off-ground and on-ground) in 3D space (e.g., octomap and point cloud) for mobile platform to follow. RimJump* searches the tangent graph in the form of a path tree and considers the geometrical properties of the locally shortest path. Therefore, the method can provide all of the locally shortest paths that connect the starting point and the target, including the globally shortest path. And the time cost of RimJump* is insensitive to map scale increases in comparison to methods that search the whole passable space rather than the surface of the obstacle, e.g., Dijkstra and A*. In the Results, RimJump* is compared with other methods in terms of path length and time cost.

In this review paper, we present a pellucid proof of how x tanh(x/µ) approximates |x|and is better than √x² +µ  when we are concernedwith accuracy.

The development of devices for In-Situ Resource Utilization (ISRU) of the lunar surface powder (regolith) by means of microwaves needs regolith simulants with electromagnetic properties similar to the lunar regolith. This document deals with the measurement of complex permittivity and dielectric loss tangent of the aforementioned simulants at ambient temperature from 400 MHz to 20 GHz. In addition, further studies are carried out taking into account humidity of the samples and their densities. The obtained results will be applicable for comparing the measured values of EAC-1A and JSC-2A among them and with other previously measured simulants and real samples. The measurements are carried out applying two different nonresonant techniques: Open- Ended Coaxial Probe (OECP) and Transmission Line. For this purpose, the DAK and EpsiMu commercial kits were respectively used.

We present smooth approximations to $ \vert{x} \vert $ using sigmoid functions. In particular $ x\,erf(x/\mu) $ is proved to be better smooth approximation for $ \vert{x} \vert $ than $ x\,tanh(x/\mu) $ and $ \sqrt{x^2 + \mu} $ with respect to accuracy. To accomplish our goal we also provide sharp hyperbolic bounds for error function.

In this paper, we propose a methodology for analyzing the near-field coupling between two surface mount device (SMD) inductors using a 3-dimensional electromagnetic (3D-EM) model. To develop the 3D-EM model, we first extract the effective permeability of core magnetic material in the SMD using the loss tangent in the equivalent circuit model. Then the effective permeability is used in the magnetic material for the 3D-EM modeling of SMD inductor. The validity of the proposed 3D-EM model is confirmed by comparing the impedance and S-parameters obtained from both measured and EM-simulated values for the two near-field coupled SMDs. Finally, the near-field coupling effects between the two adjacent SMD inductors are visualized in terms of magnetic coupling path visualization (CPV) using the proposed 3D-EM model, which demonstrates its usefulness for near-field coupling analysis.

In this paper, an analytical form of the Unit Step Function (or Heaviside Step function) is presented. This important function constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics. In particular, Heaviside Step Function is performed in a very simple manner by the use of a finite number of standard operations, as the summation of six inverse tangent functions. The novelty of this work when compared with other analytical expressions, is that the proposed exact formula contains two arbitrary single - valued continuous functions which satisfy only one restriction. In addition, the proposed representation is not exhibited in terms of miscellaneous special functions, e.g. Bessel functions, Beta function, Logistic function. Besides, it is neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence. Hence, this formula may be much more practical, flexible and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

This study reviews methods for detecting fracture closure pressure in both unconventional and conventional reservoirs using mathematical models and fluid flow equations. It evaluates tech-niques such as the Nolte method, tangent method, and compliance method. The investigation re-lies on observing changes in fluid flow regimes from pre-closure to post-closure, using fluid flow equations to examine the post-closure flow regime effect on the G function. Reverse calculations model pressure decline across synthesized flow regimes, facilitating a detailed investigation of the closure process. The analysis reveals that the tangent method is sensitive to post-closure fluid flow, while the compliance method is less effective in reservoirs with significant tortuosity or natural fractures. The paper recommends assessing natural fractures' characteristics and perme-ability to identify the source of leak-off before selecting a technique. It proposes integrating vari-ous methods for a comprehensive understanding of subsurface formations, combining their strengths for accurate fracture closure identification and better understanding of subsurface formations. The new proposed workflow employs the Continuous Wavelet Transform (CWT) technique for fracture closure detection, avoiding physical model pre-assumptions or simplifica-tions to confirm the results. This approach offers guidance on selecting appropriate methods by integrating different techniques.

The existing segmentation-based scene text detection methods mostly need complicated post-processing, and the post-processing operation is separated from the training process, which greatly reduces the detection performance. The previous method, DBNet successfully simplified post-processing and integrated the post-processing into a segmentation network. However, the training process of the model took a long time for 1200 epochs and the sensitivity to texts of various scales was lacking, leading to some text instances being missed. Considering the above two problems, we design the text detection Network with Binarization of Hyperbolic Tangent(HTBNet). First of all, we propose Binarization of Hyperbolic Tangent (HTB), optimized along with which, the segmentation network can expedite the initial convergent speed by reducing the amount of epochs from 1200 to 600. Because features of different channels in the same scale feature map focus on the information of different regions in the image, to better represent the important features of all objects in the image, we devise the Multi-Scale Channel Attention(MSCA). Meanwhile considering that multi-scale objects in the image cannot be simultaneously detected, we propose a novel module named Fused Module with Channel and Spatial(FMCS), which can fuse the multi-scale feature maps from channel and spatial dimension. Finally we adopt cross entropy as the loss function, which measures the difference between predicted values and ground truths. The experimental results show that HTBNet compared with lightweight models has achieved competitive performance and speed on Total-Text(F-measure:86.0%, FPS:30) and MSRA-TD500 (F-measure:87.5%, FPS:30).

In this work, generalized geometry of second-order tangent groups and affine configuration complexes is proposed. Initially, geometry for higher weights n=4 and weights n=5 is presented through some interesting and suitable homomorphisms, finally, this geometry is extended and generalized for any weight n.

This article presents the theoretical study, numerical simulation and the fabrication of a phase shifter and stub resonator in microstrip ridge gap waveguide (MGCW) technology with the use of liquid crystal (LC) in its substrate as a reconfigurable material. The phase shifter and the stub resonator are filled with LC and thanks to LC's dielectric anisotropy properties, the phase shift and resonance response can be easily controlled using an external electric or magnetic bias field. The phase shifter was designed to operate in the range of 10 to 20 GHz and the resonator was designed to operate in the range of 7.8 to 8.8 GHz. The phase shifter's insertion losses, associated with both parallel and perpendicular LC's permittivity, as well as the phase response were computed and measured. Finally, the figure of merit (FoM) was extracted. The resonator's frequency response, associated with both parallel and perpendicular LC's permittivity, was computed. The resonator's frequency responses, provided different polarization voltages, were measured and compared to the simulation results. The technological issues were discussed. The good agreement between simulation and measurement results establishes this technology as a viable approach to the development of RF reconfigurable devices.

The paper presents a new method of path planning for an industrial robot manipulator performing thermal plasma spraying of coatings. Path planning and automatic generation of the manipulator motion program are performed using preliminary 3D surface scanning data from a laser trian-gulation distance sensor installed on the same robot arm. The new path planning algorithm is based on constructing a function of the geodesic distance from the starting curve. A new method for constructing a geodesic distance function on a surface is proposed based on the application of discrete exterior calculus methods characterized by high computational efficiency. The developed algorithms and their software implementation were experimentally tested through robotic mi-croplasma spraying of a protective coating on the surface of a jaw crusher plate, which was then successfully operated for crushing mineral raw materials.

With the rapid advancements in remote sensing technology, the spectral information from hyperspectral remote sensing images has become increasingly rich, facilitating detailed spectral analysis of the Earth's surface objects. However, this abundance of spectral data poses significant challenges in data processing, such as the curse of dimensionality leading to the “Hughes” phenomenon, "strong correlation" due to high resolution, and "non-linear characteristics" caused by varied surface reflectance rates. Therefore, dimensionality reduction of hyperspectral data has become a crucial task. This paper, grounded in manifold theory and manifold learning techniques, and considering the non-linear structures and features in hyperspectral remote sensing data, elucidates the principles and processes of dimensionality reduction in hyperspectral remote sensing images using manifold learning, with a formalized expression of the process. This article introduces spectral information divergence (SID) into the nearest neighbor graph computation of manifold learning algorithms. The principles and computational processes of nearest neighbor graph algorithms based on Euclidean distance (ED), spectral angle mapping (SAM), and SID are studied, and a comparative analysis of the dimensionality reduction effects under these three metrics in hyperspectral data is conducted. Experiments on feature extraction under different metrics were performed using the publicly available Indian Pines hyperspectral dataset. The intrinsic features obtained post-dimensionality reduction were used as inputs for classification algorithms in ground objects classification experiments, with algorithm runtime, overall accuracy, and Kappa coefficient as evaluation metrics for dimensionality reduction quality. The results demonstrate that nearest neighbor graph computation based on SAM and SID outperforms traditional ED methods; SAM-based computation has the lowest time complexity, while SID-based manifold learning yields the highest accuracy in ground objects classification. Thus, manifold learning based on SAM and SID metrics proves to be an effective method for feature extraction in hyperspectral remote sensing data, underscoring the potential of manifold learning techniques in the dimensionality reduction of hyperspectral remote sensing images.

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

A facile and environmentally benign method for a single-phase barium titanate synthesis in water vapor medium was studied to reveal the mechanism of phase transformation of the initial simple oxides mixture and estimate the capability of the product to be used as a raw material for low-frequency dielectric ceramics. The composition and structure of the reaction mixture treated in vapor at 130…150 °C as well as 230 °C for various time were investigated by means of XRD, SEM, HRTEM, EDX, and FTIR methods. The kinetics of the occurring phase transformation was described by Johnson-Mehl-Avrami-Erofeev equation. The reaction between the initial oxides was considered as a topochemical process with an apparent activation energy of 74…80 kJ mol^-1. A crucial role in this process belonged to the water vapor medium, which facilitated the generation of the reaction zone and its spreading inward the solid particles. The synthesized tetragonal barium titanate powder (mean particle size of 135 ± 24 nm) was sintered by a conventional technique at 1250 °C to obtain ceramics with grains of about 2 μm. Capacitance measurements performed a dielectric constant and loss tangent of ceramics, which reached 3879 and 6.7 10^-3, respectively, at 1 kHz and room temperature.

This work is a physical review, with elements of additions and thinning, on the methods of theoretical studies of nonlinear electrophysical phenomena in crystals with ion-molecular chemical bonds (CIMB). Crystals of this class include ionic dielectrics (characterized by high ionic conductivity), layered crystals, a special case of which are hydrogen-bonded crystals (HBC), defined as proton semiconductors and dielectrics (PSD).A scientific review (comparative analysis and justification of various approximations) was carried out on the methods of constructing and solving a generalized quasi-classical kinetic equation describing the mechanism of nonlinear relaxation polarization and conductivity processes in dielectric materials with ion-molecular chemical bonds (a special case is hydrogen-bonded crystals (HBC)) in a wide temperature range (1-1550 K) and polarizing field strengths (0.1-1000 V/m) at alternating field frequencies of the order of 1 kHz - 1000 MHz. The most important variant of the equations of the kinetic theory of dielectric relaxation in this work is the generalized non-linear by polarizing field quasi-classical kinetic equation of ionic (in HBC, proton) relaxation, based on the particle number balance equation (conductivity ions) in potential wells and having (in these models) the meaning of the ion current continuity equation (in HBC, protons), solved by the method of successive approximations by decomposition into infinite power series by degrees of a small dimensionless comparison parameter. It was found that in the area of ​ ​ weak fields (0.1-1 MW/m) at temperatures T = 50 - 550 K, for a number of ionic dielectrics (including HBC and similar dielectric properties and lattice structure) the generalized quasi-classical kinetic equation transforms to the linearized Fokker – Planck equation and, in the region of low (50-100K) and higher temperatures (250-550 K) begin to manifest non-linear polarization effects due to respectively proton tunneling (in the case of HBC) and volume charge relaxation (in the case of the HBC and for a wider class of ionic dielectrics). At ultra-low (1-10 K) temperatures in the region of weak fields (0.1-1 MW/m) and ultra-high temperatures (550-1550 K) in the region of strong fields (10-1000 MW/m), the contribution of this kind of effects to polarization is significantly enhanced. The effect of nonlinearities on relaxation times for microscopic acts of proton transitions across a potential barrier (assumed to be parabolic) is investigated. Nonlinear effects at volume-charge polarization in the hydrogen-bonded crystals (HBC) in alternating electric field, in radio frequency range are investigated. From the solution of the system of nonlinear Fokker-Planck equations (macroscopic kinetic equation) and Poisson, with blocking electrodes, using Fourier series, a recurrent (convenient for use in any approximation of perturbation theory) expression is constructed for complex amplitudes of relaxation modes of volumetric charge. Complex dielectric permittivity (CDP) is calculated as a series decomposition over even frequency harmonics of a variable field. The effect of quantum proton transitions and polarizing field parameters (strength, frequency) on the nonlinear properties of proton semiconductors and dielectrics has been established.