The extra precession of Mercury - 42.9 seconds of arc per century - explained by General Relativity (GR), is the result of a secular addition of 5.02 × 10⁻⁷ rad. at the end of every orbit around the Sun. We will analyze, the instantaneous precession and its addition along one orbit, determine the magnitude and oscillations around the mean value, comparing key theoretical proposals. This angular precession, should be the result reaction of Mercury to the gravitoelectric action produced by the geometric curve space-time at each single point of the elliptic orbit. The better we should know about this instantaneous precession, the better we will determine the external action and its quantum core nature, if that is the case. The Doppler tracking of the MESSENGER spacecraft, produces only 1 m error, enough precision to deduce the complete geodesic orbit of Mercury as an open free-fall path, isolated from other planets gravitational interference. The aim of this article is also to encourage JPL, IMCCE. and other scientific teams to do so because, as far as I know, it has not been entirely measured yet, by accurately tracking that motion.

High precision angular actuators are used for high demanding applications such as laser steering for photolithography. Piezo technology allows developing actuators with such a high resolution that the characterization of the same is out of the capabilities of commercially available instruments. At INRIM we have designed and built a device to the purpose of characterizing precision 2D angular actuators with a resolution surpassing the best devices on the market. The device is based on a multi reflection scheme that allows multiplying the deflection angle by a factor of 70. The ultimate resolution of the device is 2 prad/√Hz over a measurement range of 36 µrad with a measurement band > 10 kHz. The working principle, the practical realization and the case study on a top-level commercial angular actuator (Nano-MTA2 produced by MadCityLabs) are described.

The goal of this study was to analyze the instability during stepping of young and older adults at fast and spontaneous speed. To this aim, the anteroposterior and the mediolateral distances between the body center of mass (COM) and the minimum moment axis (MMA) were computed. A total of 15 young adults (25y.o. [19-29]) and 15 older adults 68.7y.o. [63-77] volunteered for this study. For the computation of the distances, a complete biomechanical protocol combining two force platforms and a 3D motion capture analysis system was setup. The subjects were equipped with 47 reflective markers and were modeled as a frictionless multibody with 19 segments, 18 joints and 42 degrees of freedom and were asked to perform a stepping at both speeds. The stepping was divided in 5 phases with successive swing and double stance phases. The greater instability was observed during the swing phases. The distances indicate a significant higher instability at fast speed for both groups (p < 0.001) for all the phases. The anteroposterior distance also increases significantly for older adults highlighting greater instability while no differences were observed for the mediolateral distance all along the 5 phases suggesting higher risks of backward of forward falls during stepping.

We emphasize the point that, standard model of cosmology is basically a model of classical general relativity and it seems inevitable to have a revision with reference to quantum model of cosmology. Utmost important point to be noted is that, ‘Spin’ is a basic property of quantum mechanics and ‘rotation’ is a very common experience. In this context, we propose five assumptions in line with Planck mass as the baby universe. We appeal that, 1) Universe can be modeled as a time-reversed black hole (a white hole) with rotation and light speed expansion, and 2) ‘Light speed expanding cosmic space’ can be called as ‘Flat space’. With reference to light speed expansion, if one is willing to re-define cosmic red shift as [z/(1+z)], without considering Lambda cosmology model of matter density fractions, light travel distances can be reproduced with a marginal error of +8.6% at z =1.2, (i.e. traditional light travel distance is 8.6% higher than our estimate), 0% at z = 11.5 and -5.5% at z = 1200.( i.e. traditional light travel distance is 5.5% lower than our estimate). Advantages of our model are, 1) A quantum model of cosmology can be developed with unification of general theory of relativity and quantum mechanics. 2) Tension in estimating the current Hubble parameter can be eliminated via scaled Hawking’s black hole temperature formula with great confidence. 3) Galactic dark matter and visible matter can be studied in a unified manner. 4) Galactic light travel distances can be estimated very easily without matter density fractions. 5) Big Bang and Inflation like non-general relativistic concepts can be relinquished with further study.

This paper proposes an enhanced Quantum Key Distribution (QKD) protocol by incorporating a Three-Dimensional Angular Momentum Representation (3D AMR) to address vulnerabilities inherent in traditional two-dimensional polarization states-based systems. The 3D AMR method expands the state space, potentially increasing security against sophisticated quantum attacks. We present a theoretical and computational framework that transitions from the conventional two-dimensional polarization to a three-dimensional angular momentum space, which inherently increases the complexity and security of the quantum states used in QKD.

A picture is a powerful and convenient medium for inducing the illusion that one perceives a real three-dimensional scene. The relative invariance of picture perception across viewing positions has aroused the interest of painters, photographers and visual scientists. Many studies have been devoted to perceptual invariance when pictures are viewed from oblique directions. Invariance across viewing distances has received less attention. This study presents a computational analysis of pictures of perspective scenes taken from different distances between camera and physical objects. Distances and directions of pictorial objects were computed as function of viewing distance to the picture and compared with distances and directions of the physical objects as function of camera position. The computations show that pictorial distance and direction are determined by angular size of the depicted objects. Pictorial distance and direction are independent of camera position, focal length of the lens, and picture size. Ratios of pictorial distances, directions and sizes are constant as function of viewing distance. The constant ratios are proposed as the reason for invariance of picture perception over a range of viewing distances. Reanalysis of distance judgments obtained from the literature shows that perspective space, previously proposed as the model for visual space, is also a good model for pictorial space. The geometry of pictorial space contradicts some conceptions about picture perception.

The flywheel is a widespread mechanical component used for the storage of kinetic energy and angular momentum. It typically consists of a cylindrical inertia rotating about its axis on rolling bearings, which involves undesired friction, lubrication, and wear. This paper presents an alternative mechanism that is functionally equivalent to a classical flywheel while relying exclusively on limited-stroke flexure-joints. This novel 1-degrees-of-freedom zero-stiffness mechanism has no wear and requires no lubrication: it is thus compatible with extreme environments, such as vacuum, cryogenics, or ionizing radiation. The mechanism is composed of two coupled pivoting rigid bodies whose individual angular momenta vary during motion but whose sum is constant at all times when the pivoting rate is constant. The quantitative comparison of the flexure-based flywheel to classical ones based on a hollow cylinder as inertia shows that the former stores typically 6 times less angular momentum and kinetic energy for the same mass while occupying typically 10 times more volume. The freedom of design of the shape of the rigid bodies offers the possibility of modifying the ratio of the kinetic energy stored versus angular momentum, which is not possible with classical flywheels. For example, a flexure-based flywheel with rigid pivoting bodies in the shape of thin discs stores 100 times more kinetic energy than a classical flywheel with the same angular momentum. A proof-of-concept prototype was successfully built and characterized in terms of reaction moment generation, which validates the presented analytical model.

The angular diameter is the angle subtended by a generic object – an apple or a star – to the eye of an observer, and it describes how large the object appears from a given viewpoint. The angular diameter represents a powerful tool for distance calculations starting from a directly measurable information and it finds application in several contexts varying from cosmography to architecture. In this article, the author proposes a novel equation to calculate the apparent diameter of whatever object. This equation defines the relationship between the object’s apparent diameter with respect to the travelled distance starting from the initial distance R₀ at which the observed object is located. Based on the preliminary tests conducted, the model seems to faithfully portray this relation with respect to measured values, also at the astronomical scale, thus considering the Earth-Moon distance, where, the absolute error detected is about 0.56%. Tests highlight also a dependency between the results accuracy and the measurement conditions suggesting a high level of sensibility linked to the initial magnification effect produced by the retina or the artificial lens employed.

The variation of photonic orbital angular momentum at Compton scattering is characterized. We determine scattering matrix of a twisted light based on the fundamental conservation of orbital angular momenta. Numerical values for two different twisted light modes: Laguerre Gaussian and Bessel Gaussian, are generated and illustrated. Our analysis indicate that states of photonic orbital angular momentum are highly changeable at wide angle scattering but more consistent at small angle scattering.

Gold nanohole arrays are periodic metastructures gathering huge interest for biosensing applica-tions. The grating-like structure defines their plasmonic mode features and their angular disper-sion can be used to highlight efficiently their interaction with the fluorescence emission of a properly tuned fluorophore. Resorting to a properly tuned/engineered/optimised plasmonic na-nohole array and a commercial organic dye, we performed an accurate resolved angle-resolved optical characterization. The plasmonic fingerprints was consequently identified as a modification of the dye photoluminescence signal in terms of both spectral redistribution and enhancement. Interestingly, by analyzing the results, an advantageous measurement configuration can be iden-tified to better engineer a suitable platform for efficiency maximization in plasmon-enhanced flu-orescence-based applications. Therefore, the coupling mechanism with the plasmonic modes, and nanostructure properties can be carefully co-optimized.

Micro-gyroscopes based on the Coriolis principle are widely employed in inertial navigation, motion control, and vibration analysis applications. This paper presents our main contributions which include a novel dual-frame optomechanical gyroscope, a unique photonic crystal cavity design, and advanced numerical simulation and optimization methods. The proposed design utilizes an optical cavity formed between dual oscillating frames, whereby input rotation induces a measurable phase shift via optomechanical coupling. Actuation of the frames is achieved electrostatically via an interdigitated comb-drive design. Through theoretical modeling based on cavity optomechanics and finite element simulation, the operating principle and performance parameters are evaluated in detail. Results indicate an expected angular rate sensitivity of 22.8 mV/°/s and angle random walk of 7.1×10-5 °/h1/2, representing superior precision than to existing micro-electromechanical systems gyroscopes of comparable scale. Detailed analysis of the optomechanical transduction mechanism suggests this dual-frame approach could enable angular vibration detection with resolution exceeding state-of-the-art solutions.

We review recent progress in high-speed orbital angular momentum (OAM) multiplexed free-space optical communication systems. The outdoor atmospheric turbulence is emulated by an indoor turbulence emulator, which is based on split-step beam propagation method. Adaptive optics, channel coding, Huffman coding combined with LDPC coding, and spatial offset are used for turbulence mitigation; while OAM multiplexing and wavelength-division multiplexing (WDM) are applied to boost aggregate capacity.

The application of non-uniform spiral gratings to control structure, topological parameters and propagation of orbital angular momentum (OAM) beams was studied experimentally with coherent near-infrared light. Adapted digital spiral grating structures were programmed into the phase map of a high-resolution liquid-crystal-on-silicon spatial light modulator (LCoS-SLM). It is shown that characteristic spatio-spectral anomalies related to Gouy phase shift can be used as pointers to quantify rotational beam properties. Depending on sign and gradient of spatially variable periods of chirped spiral gratings (CSG), variations of rotation angle and angular velocity as a function of propagation distance were measured. Propagation-dependent self-torque is introduced in analogy to known local self-torque phenomena of OAM beams as obtained by the superposition of temporally chirped or phase modulated wavepackets.

We show that analyzing archived and future multibeam backscatter and bathymetry data, in tandem with regional environmental parameters, can help identify polymetallic nodule fields in the world’s oceans. Extensive archived multibeam transit data through remote areas of the world’s oceans are available for data mining. New multibeam data will be made available through the Seabed 2030 Project. Uniformity of along and across track backscatter, backscatter intensity, angular response, water depth, nearby ground-truth data, and local slope, sedimentation rate, and seafloor age provide thresholds for discriminating areas permissive for nodule presence. A case study of this methodology is presented using archived multibeam data from a remote section of the South Pacific along the Foundation Seamounts between the Selkirk paleomicroplate and East Pacific Rise that were collected in 1997 during the Hotline cruise. The 12 kHz Simrad EM12 DUAL multibeam and the forementioned data strongly suggest a previously unknown nodule occurrence exists. Methods include comparing analyses using three different backscatter products to further determine if scanned backscatter products, rather than primary digital multibeam files can be used for analysis, and comparing results from using digitized 8-bit images, or 8-bit and decibel-value surfaces derived from the MB-SystemTM software. We show this expeditious analysis of broad areas of multibeam data could characterize benthic habitat types efficiently in remote deep ocean areas prior to more time consuming and expensive video and sample acquisition surveys. Additionally, utilizing software other than specialty sonar processing programs during this research explores how multibeam data products could be interrogated by a broader range of scientists and data users. Future mapping, video, and sampling cruises in this area would test our prediction and investigate how far it might extend to the north and south.

in this article, an ultra-wideband traveling wave antenna with antipodal topology is proposed. The proposed design is realized on an economical substrate with minimum thickness. The proposed design offers an ultra-wide bandwidth of 26 to 40 GHz, translating to 42%. The dimensions of the antenna are 20mm x10mm x 0.5mm indicating an electrically compact structure. The proposed antenna offers high front to back ratio of at least 10dB across the bandwidth of operation. The forward gain of the antenna varies from 4 to 7dBi in the afore-mentioned band. The pattern integrity is maintained throughout the band. The antenna is fabricated using the commercial photolithography process. A mutli-step topology of the antennas is also proposed for wide angular coverage. The coverage is greater than 150º with mutual coupling less than 25dB. These performance metrics is achieved with a very small footprint. Simulated and experimental results are presented in this paper.

Tunable circular devices made of liquid crystals or other materials, like lenses, axicons or phase plates are often constrained by limitations in size, tunability, power and other parameters. These constrains restrict their use and limit their applicability. In this review, a thorough study of the use of light orbital angular momentum in LC devices manufacturing is presented. Twisted light amazingly fosters the simultaneous optimization of most critical parameters. Experimental demonstrations of unmatched performance of tunable LC lenses, axicons and other elements, in magnitudes such as lens diameter (> 1”), power and tunability (> ±6 diopters), fill factor (> 98%) and time response have been achieved by reversible vortex generation created by azimuthal phase delay. This phase delay can be eventually removed within the optical system, so that the lens performance is not affected.

The suspended test masses of gravitational-wave (GW) detectors require precise alignment to be able to operate the detector stably and with high sensitivity. This includes the continuous counter-acting of seismic disturbances, which, below a few Hertz, are not sufficiently reduced by the seismic isolation system. The residual angular motion of suspended test masses is further suppressed by the Angular Sensing and Control (ASC) system. However, in doing so, the angular motion can be enhanced by the ASC at higher frequencies where the seismic isolation system is very effective. This has led to sensitivity limitations between about 10 Hz and 25 Hz of the LIGO detectors in past observation runs. The observed ASC noise was larger than simple models predict, which means that more accurate detector models and new simulation tools are required. We present Lightsaber, a new time-domain simulator of the ASC in LIGO. The simulation is a nonlinear simulation of the optomechanical system consisting of the high-power cavity laser beam and the last two stages of suspension in LIGO including the ASC. The main noise inputs are power fluctuations of the laser beam at the input of the arm cavities, read-out noise of sensors used for the ASC, displacement noise from the suspension platforms, and noise introduced by the suspension damping loops. While the plant simulation uses local degrees of freedom of individual suspension systems, the control is applied on a global angular basis, which requires a conversion between the local and global bases for sensing and actuation. Some of the studies that can be done with this simulation concern mis-centering of the beam-spot (BS) position on the test masses, the role of laser power fluctuations for angular dynamics, and the role of the various nonlinear dynamics.

We will outline the relationship between luminosity distance and cosmological redshifts, demonstrating that it is consistent with a new cosmological model recently proposed by Haug and Tatum [1], which appears to resolve the Hubble tension within the Rh = ct cosmology.

Conical emission is a typical nonlinear phenomenon that occurs when the femtosecond laser pulses interact with transparent media. In this work, the conical emission induced by two kinds of typical vortex beams (i.e., Laguerre-Gaussian (LG) and Bessel-Gaussian (BG) beams) in water is experimentally studied. By recording the light spots of different wavelengths on the screen, the characteristics of the conical emission induced by femtosecond vortex beams are studied. It is found that the spots of the supercontinuum induced by the two kinds of vortex beams differ greatly from each other: The spots of the supercontinuum induced by the BG beam are a set of concentric rings like a rainbow with a white center, while the whit light spot in the case of the LG beam are a circular white disk, which is different from the commonly observed white light spots. By measuring the maximum divergence angle, it is observed that the divergence angle increases with the decrease of the wavelength, while the TC merely affects the divergence angle, which is explained from the formation mechanism of conical emission in terms of self-phase modulation. We hope this work can be helpful to the understanding of interaction between the intense laser pulses and matters.

Abstract: Embodied pedagogy maintains that teaching and learning abstract concepts can benefit significantly from integrating bodily movements in the process. Here we explored the involvement of eye movements in the process of collective embodied learning of a concept in physics - angular velocity. Embodied learning was accomplished by the subjects forming a line that rotated around a central object, in this case, a bottle. We tracked the gaze resulting from eye and head movements in 12 subjects, who both actively participated in the collective embodied exercise and passively watched it. The tracking data of 7 of these 12 subjects passed our tracking reliability criteria in all trials and are reported here. During active learning, the learners tended to look ahead of the rotating line (by 35.18±14.82 degrees). In contrast, while passively watching others performing the task, the learners tended to look directly at the line. Interestingly, while the learners were performing the collective exercise they were unaware of looking ahead of the rotating line. We discuss possible differences between active and passive embodied learning that might be indicated by the observed differences in gaze control.

Cell-free massive multiple input multiple output (MIMO) has the potential of providing joint services including joint initial access, efficient clustering of access points (APs) and pilot allocation to user equipments (UEs) over large coverage area with reduced interference. In cell-free massive MIMO, large coverage area corresponds to provision and maintenance of scalable quality of service requirements for infinitely large number of UEs. The research in cell free massive MIMO is mostly focused on time division duplex mode due to availability of channel reciprocity which aids in avoiding feedback overhead. However, frequency division duplex (FDD) protocol still dominates the current wireless standards and the provision of angle reciprocity aids in reducing this overhead. The challenge of providing a scalable cell-free massive MIMO system in FDD setting is also prevalent, since computational complexity regarding signal processing tasks such as channel estimation, precoding/combining and power allocation, becomes prohibitively high with increase in number of UEs. In this work, we consider an FDD based scalable cell-free network with angular reciprocity and dynamic cooperation clustering approach. We have proposed scalability for our FDD cell-free and perform comparative analysis with reference to channel estimation, power allocation and precoding/combining techniques. We present expressions for scalable spectral efficiency, angle based precoding/combining schemes and provide comparison of overhead between conventional and scalable angle based estimation as well as combining schemes. Simulations confirm that the proposed scalable cell-free network based on FDD scheme outperforms the conventional matched filtering scheme based on non-scalable precoding/combiming schemes. The angle based LP-MMSE in FDD cell-free network provides 14.3% improvement in spectral efficiency and 11.11% improvement in energy efficiency compared to non-scalable MF scheme.

State transition in the multiple-levels system has the great potential applications in the quantum technology. In this article we employ a deterministic approach in complex space to analyze the dynamics of the 1s-2p electron transition in the hydrogen atom. The electron’s spin motion is embodied in the framework of quantum Hamilton mechanics that allows us to examine the transition dynamics more precisely. The transition is driven by an oscillating electric field in the z-direction. The electron’s transition process can be visualized by monitoring its motion in the complex space. The quantum potential and the total energy proposed in this paper provide new indices to observe the dynamic changes of electrons in the transition process.

The purpose of this work is to optimize angular extrusion for sever plastic deformation of tubular specimens. A finite element model (FEM) was built in Deform-3D^® for three extrusion dies and analyzed. The dies were ECAP (135°), TCAP with external groove of 90° (denoted as TCAP-e) and TCAP with internal groove of 90° (denoted as TCAP-i). The analysis for process parameters (such as coefficient of friction-μ, die angles-ѱ and φ, temperature - T, and radius ratio-R) showed that TCAP-i was the optimal die in processing Al6063 tubes based on strain and load distribution of the model. The TCAP-i die model was further optimized for different parameters namely die angles, coefficient of friction, deformation ratio and temperature. The results showed that at constant process temperature of 25 °C, the optimal TCAP-i has the following parameters: φ₂=80⁰, Ѱ₁=30⁰, Ѱ₂=80⁰, Ѱ₃=30⁰, μ =0.4 and R =1.5.

One of the keys to understanding the universe is the proper measurement of the relation between the luminosity distance dL and the angular diameter distance dA. In 1933, Etherington deduced from general relativity the reciprocity equation dL=dA(1+z)γ, with γ=1 for a local, i.e. non-expanding, universe. This equation was adapted to an expanding universe –through the comoving distance concept– with the value γ=2. On the other hand, the feasibility of an expanding universe rest on the Friedmann-Lemaître-Robertson-Walker (FLRW) metric that meets the Einstein’s Field Equations for an homogeneous and isotropic universe. The FLRW metric includes a time dependent factor a(t) – unlike the Einstein’s static universe– that accounts for the cosmological redshift. In this work, we show that the radial coordinate (r) of FLRW metric admits two different interpretations driving to an expanding and non-expanding universes. When r is considered has a radial comoving coordinate, the integration on r produces the comoving distance, and hence the metric drives to an expanding universe. Nevertheless, when r is considered simply has a radial coordinate, the integration on r produces the luminosity distance, and hence the metric drives to a non-expanding universe. Thus, weeding out the comoving concept, a non-expanding nature of FLRW model emerges, where a(t) accounts for the cosmological redshift in the form of a time downscaling or as a magnetic permeability growth with cosmic time, rather than as space scaling. Even more, the presence of the time varying factor a(t) drives to the same Friedmann equations, which guarantees the stability of the non-expanding universe, unlike the Einstein’s static universe.

To win a taekwondo competition, more points must be scored, and the key to scoring points is to improve the motor performance of the kick. The wing kick is an offensive and defensive maneuver. Core stability appears to be important for improving athletic performance, but the specific relationship and effect of core stability on athletic performance in the aerial phase of taekwondo is unclear. The aim of this study was to investigate the relationship between core stability and athletic performance in taekwondo in order to provide appropriate theoretical support for training and to help coaches and athletes to improve athletic performance. A total of 16 subjects (height: 167.34±9.2 cm; weight: 61±8.96 kg; age: 24.7±3.25 years) were studied. Data were captured using 13 infrared cameras at 120Hz, kinematic and kinetic data were captured using a motivated motion capture system, and the data were exported to Visual3D in order to calculate the execution time of the aerial phase, the angular momentum of the left lower extremity, and MVC analysis of the EMG using EMG works. The core stability level of the subjects were measured using the Sahrmann Core Stability Test (SCST) to correlate with the other data, and then the subjects were grouped according to their core stability levels and the data from both groups were analyzed with t-tests. Results During the double fly lifting of aerial segments, SCST levels showed a very strong negative correlation with execution time (r= -0.739) and there was a statistically significant difference in execution time between high and low SCST levels (p < 0.001), and the desired negative correlation was also seen in lower limb angular momentum X-axis (thigh r= -0.6294, shank r= -0.536, foot r= -0.6175), especially in the X-axis. The left rectus femoris (LRF) data had greater activation in the low SCST group(p=0.0019*). Through this experiment, we found that athletes with high core stability had faster execution times, lower angular momentum, and higher core muscle activation. Therefore, we conclude that incorporating core stability training into taekwondo training has the potential to improve kicking performance.

We study the influence of high-order twisting phases on polarization states and optical angular momentum of a vector light field with locally linear polarization and a hybrid state of polarization (SoP). The initial SoP of a twisted vector optical field (TVOF) modulated by the high-order twisting phase possesses various symmetric distributions. The propagating properties of a high-order TVOF with locally linear polarization and hybrid SoP are explored, including the intensity compression, expansion, and conversion between the linear and circular polarization components. In particular, orbital angular momentum (OAM) appears in a high-order TVOF during propagation where no OAM exists in the initial field. The variation of OAM distribution in cross-section becomes more frequent with the increase of the twisting phase order. In addition, a non-symmetric OAM distribution appears in an anisotropic TVOF, leading to the rotation of the beam around the propagation axis during propagation. These results provide a new approach for optical field manipulation in a high-order TVOF.

In particle physics, spin is an intrinsic form of angular momentum carried by the elementary particles. It is believed that spin is a solely quantum-mechanical phenomenon, which does not have a counterpart in classical mechanics. We have derived the simplest equations of spin and magnetic moment of a charged elementary particle. These formulas enable us to understand the physical nature of the spin and the structure of elementary particles. It is shown that the electron and muon are in the shape of a thin ring with a circular cross section (torus), and the proton is in the form of a ring with a non-circular cross section (toroid). The connection between the photon’s spin of and the propagation of electromagnetic waves is considered.

Utilization of Bidirectional Reflectance Distribution Function (BRDF) model parameters obtained from the multi-angular remote sensing is one of the approaches for the retrieval of vegetation structural information. In this research, the potential of multi-angular vegetation indices, formulated by the combination of multi-spectral reflectance from different view angles, for the retrieval of forest above ground biomass was assessed. This research was implemented in the New England region with the availability of a high quality forest inventory database. The multi-angular vegetation indices were generated by the simulation of the Moderate Resolution Imaging Spectroradiometer (MODIS) BRDF/Albedo Model Parameters Product (MCD43A1 Version 6) based BRDF parameters. The effects of seasonal (spring, summer, autumn, and winter) composites of the multi-angular vegetation indices on above ground biomass, angular relationship of the spectral reflectance with above ground biomass, and the interrelationships between the multi-angular vegetation indices were analyzed. Among the existing multi-angular vegetation indices, only the Nadir BRDF-adjusted NDVI ( and Hot-spot incorporated NDVI ( showed significant relationship (more than 50%) with the above ground biomass. This research proposed two more sensitive vegetation structural indices, Fore-scattering Back-scattering NDVI and Vegetation Structure Index (VSI). The Fore-scattering Back-scattering NDVI showed higher sensitivity (R² = 0.62, RMSE = 52.46) towards the above ground biomass than existing multi-angular vegetation indices. Furthermore, the VSI performed in the most efficient way explaining 64% variation of the above ground biomass, suggesting that the right choice of the spectral channel and observation geometry should be considered for improving the estimates of the above ground biomass. In addition, the right choice of seasonal data (summer) was found to be important for estimating the forest biomass while other seasonal data were either insensitive or pointless. The promising results shown by the VSI suggest that it could be an appropriate candidate for monitoring vegetation structure from the multi-angular satellite remote sensing.

Unification point of view, quantum cosmology must be given a priority and one should make a note that, Spin is a basic property of quantum physics and rotation is a very common experience. In this context, we have developed a quantum model of cosmology associated with Machian universe having Planck scale origin, total dark matter, light speed rotation and equality of gravitational self energy density and thermal energy density. We would like to appeal that, observed cosmic radius and age seem to be shortened by 146.3 times their actual magnitudes.

Originally developed to image the shadow region of the central black hole in Sagittarius A* and in the nearby galaxy M87, the Event Horizon Telescope (EHT) provides deep, very high angular resolution data on other AGN sources too. The challenges of working with EHT data have spurred the development of new image reconstruction algorithms. This work briefly reviews the status of the EHT and its utility for observing AGN sources, with emphasis on novel imaging techniques that offer the promise of better reconstructions at 1.3 mm and other wavelengths.

(1) Background: The significant progress observed over last two decades in coherent beam combining (CBC) technology has mainly focused on its applications in high-energy physics and laser weapons. This work provides insight into the basic principles of CBC and the search for an alternative, namely optical angular momentum (OAM) generation using CBC; (2) Methods: The semi-analytical model based on the paraxial wave equation explored generating OAM-CBC beams by manipulating the tilts and phases of CBC (T&P-CBC) of hexagonal architecture; (3) Results: The specially arranged T&P-CBC shows typical properties of OAM, such as annular profiles for the zero diffraction order and 1-st order replicas in the far field and correlation coefficients of 1% between different OAM-CBC fields; (4) Conclusions: The differences between classical OAM beams and OAM-CBC are substantial due to hexagonal lattice properties. Moreover, applications in free space optical communications are feasible as T&P CBC fulfills the main conditions and requirements for OAM generation.

The success of near-infrared spectroscopy (NIRS) analysis hinges on the precision and robustness of the calibration model. Shallow learning (SL) algorithms like partial least squares discriminant analysis (PLS-DA) often fall short in capturing interrelationships between adjacent spectral variables, and the analysis results are easily affected by spectral noise, which dramatically limits the breadth and depth application of NIRS. Deep learning (DL) methods, with their capacity to discern intricate features from limited samples, are progressively integrated into NIRS. In this paper, two discriminant analysis problems including wheat kernels and Yali pears were used as examples, and several representative calibration models to research the robustness and effectiveness of the model. Additionally, this article proposed a near-infrared calibration model, which is based on gramian angular difference field and coordinate attention convolutional neural networks (G-CACNN). The research results show that, compared with SL, spectral preprocessing has a smaller impact on the analysis accuracy of consensus learning (CL) and DL, and the latter has the highest analysis accuracy in the modeling results of using the original spectrum. The accuracy of G-CACNN in two discrimination tasks is 98.48% and 99.39%, respectively. Finally, This research compared the performance of various models under noise to evaluate the robustness and noise resistance of the proposed method.

Femtosecond laser-induced fluorescence (FLIF) and femtosecond laser-induced optical breakdown spectroscopy (FIBS) are important tools for remote diagnostics of atmospheric aerosols using LiDAR techniques. They are based on light emission excitation in disperse medium via the multiphoton nonlinear processes in aerosol particles induced by high-power optical pulses. To date, the main challenge restraining the large-scale application of the FLIF and FIBS in atmospheric studies is the lack of valued theory of the stimulated light emission in liquid microparticles with sufficiently broad range of sizes. In this paper, we fill this gap and present the theoretical model of dye water droplets emission under high-intense laser exposure that adequately simulates the processes of multiphoton excited fluorescence and optical breakdown plasma emission in microparticles and gives quantitative estimates of the angular and power characteristics of the nonlinear emission. The model is based on the numerical solution to the inhomogeneous Helmholtz equations for the stimulating (primary) and nonlinear (secondary) waves provided by the random nature of molecule emission in particles. We show that droplet fluorescence stimulated by the multiphoton absorption generally becomes more intensive with increasing particle size. Moreover, far-field plasma emission from liquid particles demonstrates larger angular diversity when changing droplet radius in comparison with the multiphoton excited fluorescence, which is mainly due to the excitation of the internal optical field resonances in spherical particles.

The relativistic effects of the dynamical properties of light at angular incidence were analyzed from the perspectives of Bohr indeterminacy and Heisenberg uncertainties and statistical dispersion. It was found that these effects report minimal uncertainties that agree with one or the other according to the angular range of incidence and that decrease with increasing refringence of the medium, constituting a specific relativistic uncertainty at angular incidence. An anomaly is indicated for the uncertainty principle in the Quantum Theory (QT) setting for small angles of incidence, where the accuracy of the angular position does not imply an increase in the uncertainty of the linear momentum. The anomalies arise because TQ does not predict the alternation between the classical and relativistic regimes of photon inertia at angular incidence. Specific relativistic uncertainty particularizes the uncertainty principle in the transmission of light between media pairs at angular incidence for the relativistic scenario, considering an observer that registers the relativistic effects of measurements that interfere with the observed system, in another inertial referential.

The article analyzes existing materials and structures with quadratic-nonlinear optical properties that can be used to generate a difference frequency in the terahertz and sub-terahertz frequency ranges. The principle of constructing a nonlinear optical-radio converter, based on an optical focon (a focusing cone), is proposed. Based on the assumption that this focon can be implemented from the metal-organic framework (MOF), we propose a technique for modeling its parameters. The mathematical model of the process of propagation and nonlinear interaction of waves inside the focon is based on a simplification of the nonlinear wave equation. Within the framework of the developed model, the following parameters are approximately determined: the 3D gradient of the linear refractive index and the function determining the geometric profile of the focon, which provide a few-mode-based generation of the difference frequency.

Recently it was found from Cassini data that the mean recession speed of Titan from Saturn is v = 11.3 ± 2.0 cm/yr which corresponds to a tidal quality factor of Saturn Q ≈ 100 while the standard estimate yields Q ≥ 6 · 10⁴ . It was assumed that such a large speed v is due to a resonance locking mechanism of five inner mid-sized moons of Saturn. In this paper, we show that an essential part of v may come from a local Hubble expansion, where the Hubble-Lemaˆıtre constant H0 recalculated to the Saturn-Titan distance D is 8.15 cm/(yrD). Our hypothesis is based on many other observations showing a slight expansion of the Solar system and also of our Galaxy at a rate comparable with H0. We demonstrate that the large disproportion in estimating the Q factor can be just caused by the local expansion effect. [Accepted for publication in "Gravitation and Cosmology". The paper is to appear in Vol. 28, Issue 2 (2022) of the journal Gravitation and Cosmology.]

Equal-Channel Angular Pressing (ECAP) is a method used to introduce severe plastic deformation into a metallic billet without changing its geometry. In special cases strain localization occurs and a pattern consisting of regions with high and low deformation (so-called shear and matrix bands) can emerge. This paper studies this phenomenon numerically adopting two-dimensional finite element simulations of one ECAP pass. The mechanical behavior of aluminum is modeled using phenomenological plasticity theory with isotropic or kinematic hardening. The effects of the two different strain hardening types are investigated numerically by systematic parameter studies: While isotropic hardening only causes minor fluctuations in the plastic strain fields, a material with high initial hardening rate and sufficient strain hardening capacity can exhibit pronounced localized deformation after ECAP. The corresponding finite element simulation results show a regular pattern of shear and matrix bands. This result is confirmed experimentally by ECAP-processing of AA6060 material in a severely cold worked condition, where microstructural analysis also reveals the formation of shear and matrix bands. Excellent agreement is found between the experimental and numerical results in terms of shear and matrix band width and length scale. The simulations provide additional insights regarding the evolution of the strain and stress states in shear and matrix bands.

We propose the Ramsey approach for the analysis of behavior of isolated mechanical systems containing interacting particles. The total momentum of the system in the frame of the center of masses is zero. The mechanical system is described by the Ramsey, bi-colored, complete graph. Vectors of momenta of the particles pi serve as the vertices of the graph. We start from the graph representing the system in the frame of the center of masses, the momenta of the particles in this system are pcmi. If (pcmi(t)∙pcmj(t))≥0 is true, vectors of momenta of the particles numbered i and j are connected with the red link; if (pcmi(t)∙pcmj(t))<0 takes place, the vectors of momenta are connected with the green link. Thus, the complete, bi-colored graph emerges. Consider the isolated system built of six interacting particles. According to the Ramsey Theorem, the graph inevitably comprises at least one monochromatic triangle. The coloring procedure is invariant relatively rotations/translations of frames; thus, the graph representing the system contains at least one monochromatic triangle in any of frames emerging by rotation/translation of the original frame. This gives rise to the novel kind of a mechanical invariant. Similar coloring is introduced for the angular momenta of the particles. However, the coloring procedure is sensitive to Galilean/Lorenz transformations. Extensions of the suggested approach are discussed.

The majority of current methods for measuring the angular deflection of a laser beam enable measurement only in one selected plane. However, there are tasks in which measurements of laser beam deflections in 3D are required. In this paper, we present a way of enabling two-axial measurements of the deflection of a beam based on a single-axis sensor. The key idea is to direct a laser beam alternately into one of two arms of a measurement system. In the first arm, the beam is transmitted directly to the angular sensor, while in the second, the beam is directed to the sensor via a special optical element that rotates the plane of the beam deflection; in other words, this element changes the deflection in the horizontal plane into a deflection in the vertical plane, and vice versa. To alternate the path of the beam, a variable phase retarder and a polarising beamsplitter are used. The proposed technique is experimentally verified, and the results confirm its effectiveness.

Universal gravitation is investigated with principles of foundational classical (Newtonian) physics. The results reveal gravitation an atomic field action; hence, Newton’s law, although absolutely valid, unavoidably misleads in creating the impression of matter rather than waveform action. Six force constants fully define gravitation: (i) a waveform torque field ; (ii) an expansion force field ; (iii) a centripetal force field ; (iv) a matter-wave torque field (the force fields , and constitute gravitational inertial rest frame); (v) a Galilean acceleration field and (vi) nuclear inverse mass-squared centripetal force constant The inertial rest frame force constants sum up to give observational G = 2.266 + 2.61 + 2.61cos46^o) x 10^-11 = 6.689 x 10^-11 m³ kg^-1 s^-2. Notably, the procedure is able to account also for observational inclination of galaxies and their aligned conjunctions. An attempt is made to account for angular momentum quantization and rectilinear, parabolic or elliptic profile of objects in gravitational acceleration. Same quantitative expression, , defines the photon and gravitation thus uniquely unifying gravitation, electricity and magnetism; furthermore, the expression reveals the photon packed with tremendous energy amounting to some . It is argued that: (i) neither mass nor gravitation curves spacetime; (ii) the principles that sustain cosmic time-scale dynamic equilibrium, scale invariance and inertia are incompatible with quantum gravitation; and (iii) the cosmic vacuum field comprises gravitational (photonic) waves, hence the interferometer likely measures shock waves.

In this paper, we revisit a modified version of the classical Whitehead's theory of gravity in which all possible bilinear forms are considered to define the corresponding metric. Although, this is a linear theory that fails to give accurate results for the most sophisticated predictions of general relativity, such as gravity waves, it can still provide a convenient framework to analyze some new phenomena in the Solar System. In particular, recent development in the accurate tracking of spacecraft and the ephemerides of planetary positions have revealed certain anomalies in relation with our standard paradigm for celestial mechanics. Among them the so-called flyby anomaly and the anomalous increase of the astronomical unit play a prominent role. In the first case the total energy of the spacecraft changes during the flyby and a secular variation of the semi-major axis of the planetary orbits is found in the second anomaly. For this to happen it seems that a net energy and angular momentum transfer is taken place among the orbiting and the central body. We evaluate the total transfer per revolution for a planet orbiting the Sun in order to predict the astronomical unit anomaly in the context of Whitehead's theory. This could lead to a more deeply founded hypothesis for an extended gravity model.

Study design: Retrospective observational study. Objectives: To evaluate the change in adjacent segment disease (ASD) after hybrid dynamic stabilization with Dynesys-Transition-Optima (DTO). Methods: In 2012–2020, 115 lumbar spinal stenosis patients with spondylolisthesis re-fractory to nonsurgical management received hybrid dynamic stabilization with DTO system in a single medical center from a single neurosurgeon. After excluding those who did not receive L3–L4 dynamic stabilization and L4–L5 transforaminal lumbar interbody fusion fixation and those with incomplete postoperative data (n = 84), the 31 patients studied received follow-up vis-its at 6, 12 and 24 months postoperatively. Radiological assessment applied at the L2–L3, L3–L4 and L5–S1 segments separately included disc height, listhesis distance and angular change while in motion. Implant failure and screw loosening sign were both documented. Results: In the L3–L4 segment, the listhesis distance appeared 1 year after the operation; however, alterations in other segments showed at 6 months. At 2 years, the L3–L4 segment showed significantly less increase in listhesis distance and relatively less disc height reduction than other segments. In motion an-gular change, only the L3–L4 segment had a significant decrease at 2 years. Only the L3–L4 seg-ment maintained negative growth over 2 years in time-dependent assessment of motion angular change. Conclusions: In our study, disc height decreased, listhesis distance increased less and ASD changed later at the index level than the L2–L3 and L5–S1 levels. Angular change was re-duced at the index level while in motion. Although ASD was not significantly prevented, index level degeneration was both minor

With reference to Planck scale, increasing support for large scale cosmic anisotropy and preferred directions and by considering an increasing ratio of Hubble parameter to angular velocity, right from the beginning of Planck scale, we make an attempt to estimate ordinary matter density ratio, dark matter density ratio, mass, radius, temperature, age and expansion velocity (from and about the baby universe in all directions). We would like suggest that, from the beginning of Planck scale, 1) Dark matter can be considered as a kind of cosmic foam responsible for formation of galaxies. 2) Cosmic angular velocity decreases with square of the decreasing cosmic temperature. 3) Increasing ratio of Hubble parameter to angular velocity plays a crucial role in estimating increasing cosmic expansion velocity and decreasing density ratios of dark matter and ordinary matter. 4) There is no need to consider dark energy for understanding cosmic acceleration.

Since general relativity (GR) has already established that matter can simultaneously have two different values of mass depending on its context, we argue that the missing mass attributed to non-baryonic dark matter (DM) actually obtains because there are two different values of mass for the baryonic matter involved. The globally obtained "dynamical mass'' of baryonic matter can be understood as a small perturbation to a background spacetime metric even though it's much larger than the locally obtained "proper mass". Having successfully fit the SCP Union2.1 SN Ia data without accelerating expansion or a cosmological constant, we employ the same ansatz to compute dynamical mass from proper mass and explain galactic rotation curves (THINGS data), the mass profiles of X-ray clusters (ROSAT and ASCA data) and the angular power spectrum of the cosmic microwave background (Planck 2015 data) without DM. We compare our fits to modified Newtonian dynamics (MOND), metric skew-tensor gravity (MSTG) and scalar-tensor-vector gravity (STVG) for each data set, respectively, since these modified gravity programs are known to generate good fits to these data. Overall, we find our fits to be comparable to those of MOND, MSTG and STVG. While this favorable comparison does not establish the validity of our proposition, it does provide confidence in using the fits to pursue an underlying action. Indeed, the functional form of our ansatz reveals an interesting structure in these fits.

An analysis of the consistency of the Abraham and Minkowski momenta in the determination of the photon trajectory was carried out considering a new principle of conservation of the photon's mechanical energy, in which the photon conserves translational energy in orbital angular momentum when transiting between two media, introducing the relativistic energy wave (REW). The confrontation between REW and the recent theory of space-time waves (ST) was considered, pondering your differences. Throughout this study it was possible to verify that the Abraham momentum appears a relativistic photon ignition device in the transition between two media, acting as the hidden momentum of the Minkowski’s relativistic momentum. The wavy behavior in the matter is relativistic, and the relativistic trajectory appears with delays and advances, with points of synchronization between source-observer. The classical or relativistic trajectories are determined as a function of the angle of incidence and the relative refractive index, by one of two distinct non-additive torques, the classic by Abraham or the relativistic by Minkowski. It was found that the same analysis conducted under the principle of conservation of the mechanical energy of the photon can be treated by an new Doppler, Relativistic Apparent, that can be confused with other Dopplers in the treatment of redshift from distant sources. It was found that the conservation of energy in Orbital Angular Momentum (OAM), in the interaction with matter, explains that the synchronization instants are found in the inversion of the OAM, where the advances and delays of REW occur under negligible variations of the OAM, however, opposites.

Atomic state preparation can benefit from a compact and uniform magnetic field source. Simulations and experimental measurements have been used to design, build, and test such a source as shown by optical pumping of atomic Helium. This source is a 9.5 mm (3/8") OD x 6.7 mm (1/4") ID x 9.5 mm (3/8") long, NdFeB-N42 assembly of 1.6 mm (1/16") thick customized annular magnets. It has octopole decay with a residual dipole far field from imperfect dipole cancelations. It has greater than 50% clear aperture with uniform and collimated magnetic field consistent with the prediction of several models. Octopole roll-off localizes the field minimizing the need for shielding in applications. The device is applied to a high precision 3,4He laser spectroscopy experiment using σ+ or σ- optical pumping currently resulting in a measured 99.3% preparation efficiency and in accordance with a rate-equation model.

The critical period (CP) phenomenon in language development ranks among the 125 conundrums facing scientists in the 21st century, according to Science. While the phenomenon itself has been noncontroversial in first language acquisition, it still warrants an adequate explanation. Predicated on language acquisition as a complex process, questions among the first to be raised include: How do children accomplish this remarkable feat in such a short amount of time? And how do nature and nurture come together to influence language learning? In second language acquisition, however, both the notion of CP, albeit popular, and its empirical evidence have remained contested to this date - among the questions, whether the observed evidence counts as CP-specific and/or whether or not it warrants an isomorphic attribution to maturational constraints. Entwined in this debate are two well-established facets of inter-learner differential attainment. The first is that there exists a stark difference in ultimate attainment between younger and older learners. A second facet is the vast differences in ultimate attainment among older learners. In this article, adopting a social physics approach, we mathematically establish both the relationship between nature and nurture contributions and the presence of a critical period, and, at once, tender a parsimonious and probable theory for the twin phenomena of inter-learner differential attainment.

With reference to Planck scale, Mach’s relation, increasing support for large scale cosmic anisotropy and preferred directions and by introducing two new parameters Gamma and Beta, right from the beginning of Planck scale, we make an attempt to estimate ordinary matter density ratio, dark matter density ratio, mass, radius, temperature, age and expansion velocity (from and about the baby universe in all directions). We would like suggest that, from the beginning of Planck scale, 1) Dark matter can be considered as a kind of cosmic foam responsible for formation of galaxies. 2) Cosmic angular velocity is directly proportional to squared cosmic temperature. 3) Ratio of critical temperature to actual temperature plays a heuristic role in understanding ordinary and dark matter density ratios. 4) Cosmic expansion velocity increases with decreasing total matter density ratio. 5) There is no need to consider dark energy for understanding cosmic acceleration.

Anthracnose (ANT) and angular leaf spot (ALS) are significant diseases in common bean, leading to considerable yield losses under specific environmental conditions. The California Dark Red Kidney (CDRK) bean cultivar is known for its resistance to multiple races of both pathogens. Previous studies have identified the CoPv01CDRK/PhgPv01CDRK resistance loci on chromosome Pv01. Here, we evaluated the expression levels of ten candidate genes near the CoPv01CDRK/PhgPv01CDRK loci and plant defense genes using quantitative real-time PCR in CDRK cultivar inoculated with races 73 of Colletotrichum lindemuthianum and 63-39 of Pseudocercospora griseola. Gene expression analysis revealed that the Phvul.001G246300 gene exhibited the most elevated levels, showing remarkable 7.8-fold and 8.5-fold increases for ANT and ALS, respectively. The Phvul.001G246300 gene encodes an abscisic acid (ABA) receptor pyrabactin resistance - PYR1-like (PYL) protein, which plays a central role in crosstalk between ABA and jasmonic acid responses. Interestingly, our results also showed that the other defense genes were initially activated. These findings provide critical insights into the molecular mechanisms underlying plant defense against these diseases and could contribute to the development of more effective disease management strategies in the future.

This paper aims the automatic ball balancers (ABBs) used in passive balancing devices for suppressing vibration of the eccentric rotor. The system model describes which equipped with a skew-mounted ABB with angular deviation. The dynamic equilibrium equations of the system are deduced from the perspective of three-dimensional (3D) dynamics. The results obtained are consistent with those derived from the Euler-Lagrange equations. It is exciting that the spatial dynamics method reveals the spatial geometric characteristic of dynamic balance positioning of the balls when the system is balanced with vibration suppression. The spatial property emerges the perpendicular line from each ball to the rotating spindle of the system must pass through the central axis of the orbit perpendicular to the ABB plane. This characteristic is a general rule that can be used to explain the phenomenon of the stable equilibrium positions of the balls in all previously studied cases.

This paper presents a new method for parameterizing the Lorentz group based on coupled parameters. From the Euler–Hamilton equations, an additional angular rapidity and perpendicular rapidity are obtained, and the Hamiltonian and Lagrangian of a relativistic particle are expanded into rapidity spectra. A so-called passage to the limit is introduced that makes it possible to decompose physical quantities into spectra in terms of elementary functions when explicit decomposition is difficult. New rapidity-dependent Lorentz-invariant coordinates are obtained, and the descriptions of particle motion using the old and new Lorentz-invariant forms as applied to plane waves are compared. Based on a classical model of particle motion in the field of a plane monochromatic electromagnetic wave and in that of a plane laser pulse, the rapidity-dependent spectral decompositions into elementary functions are presented, and the Euler–Hamilton equations are derived as rapidity functions in 3+1 dimensions.

Pure titanium is limited to be used in biomedical applications due to its lower mechanical strength compared to its alloy counterpart. To enhance its properties and improve medical implants feasibility, advancements in titanium processing technologies are necessary. One such technique is equal channel angular pressing (ECAP) for its severe plastic deformation (SPD). This study aimed to surface modify commercially pure titanium using micro arc oxidation (MAO) technology and mineral solutions containing Ca and P. The composition and shape of the changed surface were characterized using X-ray diffraction (XRD) and scanning electron microscope (SEM), respectively. The weight % of Ca and P in the coating was determined using Energy Dispersive Spectroscopy (EDS), and the corrosion resistance was evaluated through potentiodynamic measurement. The behavior of human dental pulp cell and periodontal cell behavior was also studied through a biomedical experiment over a period of 1-, 3-, and 7-days using trypsin as the culture medium and ELISA as the observation method. This study showed that the mechanical grain refinement method and surface modification significantly improved the biomechanical properties of commercially pure (CP) Titanium. Although the results showed variations in the absorbance values of cells cultured on different surfaces, this study provides valuable insights into pulp cell behavior and advances the field of biomedical research.

A diffusion welding of coarse-grained and ultrafine-grained (UFG) specimens of titanium near-α alloy Ti-5Al-2V used in nuclear power engineering was made by Spark Plasma Sintering. The failure of the welded specimens in the conditions of hot salt corrosion and of electrochemical corrosion were shown to have preferentially intercrystalline character. In the case of presence of macrodefects, crevice corrosion of the welded joints was observed. The resistance of the alloys against the intercrystalline corrosion was found to be determined by the concentration of vanadium at the titanium grain boundaries, by the size and volume fraction of the β-phase particles and by the presence of micro- and macropores in the welded joints. The specimens of the welded joints of the UFG alloy have higher hardness, hot salt corrosion resistance and the electrochemical corrosion.

This study describes the properties of high-T_c cuprates by introducing rotating holes that are created by angular momentum conservations on a 2D CuO₂ surface, and which have a different mass from that of a normal hole because of the magnetic field energy induced by the rotation. This new particle called a macroscopic Boson describes the doping dependences of pseudo-gap temperature and the transition temperature at which an anomaly metal phase appears and describes the origin of the pseudo-gap. Furthermore, this study introduces a new model to handle many-body interactions, which results in a new statistic equation. This statistic equation describing many-body interactions accurately explains why high-T_c cuprates have significantly high critical temperatures. Moreover, a partition function of macroscopic Bosons describes the properties of anomaly metal phase, which sufficiently agree with experiments. Note that, the calculations were conducted, using the result from our previous study that analytically describes the doping dependence of T_c. By introducing a macroscopic Boson and the new statistical model for many-body interactions, this study uncovered the mystery of high- T_c cuprates, which have been a challenge for many researchers. An important point is that, in this study, pure analytical calculations are consistently conducted, which agree with experimental data well (i.e., they do not use numerical calculations or fitting methods but use many actual physical constants).

The aim of this work is to propose an angular positioning solution for the round cutting insert of an indexable insert torus milling cutter, dedicated to the multi-axis milling process under HSM conditions. The solution was based on the development of a wear model using a nonlinear estimation method with an eigenfunction, the development of a tool life model taking into account parameter of the cutter blade working angle and the method of reference marking and insert mounting, as well as the measurement methodology. The own function adopted to approximate the wear of the tool over its useful life is adequate and provides a prediction accuracy of 90%. The developed procedure for angular positioning and measurement enables the entire cutting edge of the cutting blade to be fully used, so that the total lifespan of the tool as an indexable insert tool is significantly extended. In addition, the measured largest defect values between the worn cutting edge and the nominal outline of the insert indicate the location of “notching” type wear.

In our previous papers [1,3], using only the concepts of the zero-point energy and quantized space–times, all the fields including gravity were explained. However, the previous papers had the following limitations: First, the concept of the quantized space-time must be experimentally confirmed. Second, we should clarify the meaning of the quantized Einstein’s gravity equation, which is derived in [1]. Moreover, in another paper [2], we succeeded in describing the neutrinos’ self-energy and their oscillations. However, this paper assumes the rest energy of 3-leptons in advance, which is why we needed to uncover the reason why leptons have 3-generations. As mentioned, using the concepts of the zero-point energy and quantized space–times, we derived the quantized Einstein’s gravity equation in our previous paper [1]. The paper provides an analytical solution of this equalized Einstein’s equation, which implies the conservation of angular momentum in terms of quantized space–times. Employing this solution and without the standard big bang model, a unique form of acceleration equation for the acceleration-expansion universe is derived. Moreover, the temperature of the cosmic microwave background (CMB) emission is also obtained. Further, this solution results in an analytical (not numerical) derivation of the gravity wave. Moreover, based on the configuration of quantized space–times in terms of both electric and magnetic fields, we analytically attempted to calculate every equation in terms of electromagnetic and gravity fields, using the solution of the quantized Einstein’s gravity equation. As a result of this theory, first the calculated acceleration and temperature of CMB emission agree with the measurements. Furthermore, the analytical solution of the quantized Einstein’s gravity equation resulted in all the laws of electromagnetic and gravity fields in addition to the analytically derived gravity wave, which agrees well with the recent measurements. Moreover, the calculations of the energies in the basic configuration of the quantized space–times resulted in all 3-leptons’ rest energies. Considering this basic configuration is uniformly distributed everywhere in the universe, we can conclude that τ-particles or static magnetic field energy derived from the basic configuration of the quantized space–times is the identity of dark energy, which also distributes uniformly in the universe.

Leaky-wave antennas (LWAs) represent a recent class of radiating systems, first appeared in the second half of the past century. Initially treated with a certain dose of skepticism due to the apparent non-physical nature of supported wave solutions, LWAs have so far deeply evolved from the original configuration of slotted metallic lossy waveguide and adapted to a huge number of practical application fields, from microwave to millimeter waves and even up to the terahertz frequency range. Due to physics of relevant working principle, LWAs are often found in planar and low-profile configurations, being critically required in many cutting-edge applications, where device miniaturization, scaling and integration are required. Here we propose a review of some of the most recent and perspective array-fed 2-D LWAs, selecting two of most widespread categories in applications, Fabry–Perot Cavity Antennas (FPCAs) and Bull’s-Eye Antennas (BEAs), discussing and illustrating some advanced features recently proposed.

Large values and gradients of stresses and deformations, triggering concentrations of stresses and deformations, arise in the corner areas of a structure. The action of forced deformations, leading to the finite rupture of the contact between the elements of a structure, also triggers the concentration of stresses, while the rupture reaches an irregular point, a line on the area boundary. The theoretical analysis of the stress-strain state (SSS) of areas with angular cutouts in the boundary under the action of discontinuous forced deformations is reduced to the study of singular solutions to the homogeneous problem of the elasticity theory that has power-related features. The calculation of stress concentration coefficients in the domain of a singular solution to the elastic problem makes no sense. It is experimentally proven that the zone, that is close to the vertex of the angular cutout in the area boundary, has substantial deformations, rotations, and it corresponds to rising values of the first and second derivatives of displacements along the radius in cases of sufficiently small radii in the neighbourhood of the irregular point of the boundary. For such areas, it is necessary to consider the plane problem of the elasticity theory, taking into account the geometric nonlinearity under the action of forced deformations. This will allow analyzing the effect of relations between orders of values of deformations, rotations, and forced deformations on the form of the equation of equilibrium. The purpose of this work is to analyze the effect of relations of deformation orders, rotations, forced deformations on the form of the equilibrium equation in the polar coordinate system for a V-shaped area under the action of forced temperature-induced deformations with regard for the geometrical non-linearity and physical linearity.

We point out an inconsistency in Newton's equations of celestial mechanics. A set of differential equations implied by Newton's equations are shown to be free of this inconsistency. We then investigate the integrals of motion associated with this relative difference system.

The transport and entanglement of photons is becoming prominent in optics applied to information and quantum computing, where the angular momentum of light stands out in the exchange and inversion of quantized states, with prospects for several technological applications, such as the transport and storage of quantum information. In order to contribute to the understanding of quantized states in photon-matter interaction, we describe a quantized state equation in multidimensional Hilbert space for the diagnosis of OAM states, where probabilities arise in a relativistic setting. It was found that the classical-relativistic variability of the probabilities constitutes a resultant capable of describing the quantized states of light, where the state variable is the variation of the angular momentum of the photon, capable of estimating the orbital angular momentum inversion points at angular incidence. It was found that the chances of finding the quantized states of light at angular incidence can be treated by purely relativistic probabilities, explaining that when both states have equal chances of being found and the angular momentum variation is zero, the source-observer synchronizations occur at the step of increasing relativistic regime of the photon dynamics. We found that the relativistic effect from the perspective of the source referential is able to alter the chances of an event occurring, dilating and contracting the probabilities of finding a quantized state of light at angular incidence.

The Hyper-Torus Universe Model (HTUM) proposes a novel framework to unify quantum mechanics, cosmology, and consciousness. This paper introduces HTUM's core concept: a higher-dimensional hyper-torus encompassing all possible states of existence. HTUM suggests that the universe functions as a quantum system where all outcomes are inherently connected, with consciousness playing a significant role in actualizing reality. The model introduces several key innovations, including the universe's 4-dimensional toroidal structure (4DTS), providing a new geometric interpretation of spacetime. HTUM presents dark matter and dark energy as nonlinear probabilistic phenomena within this toroidal framework, offering a unique perspective on their nature and interactions. The model proposes a mechanism for wave function collapse through universal self-observation, bridging quantum mechanics and gravity. It introduces a Topological Vacuum Energy Modulator (TVEM) function, offering a potential resolution to the cosmological constant problem. Furthermore, HTUM integrates consciousness as a fundamental aspect of the universe, influencing quantum state actualization and potentially resolving the hard problem of consciousness. The model explores the implications of a timeless singularity and the emergence of time as a product of causal relationships within the toroidal structure. This framework addresses critical challenges in modern physics, including the nature of quantum entanglement, the origin and fate of the universe, and the relationship between mind and matter. The paper discusses the mathematical formulation of HTUM, its implications for quantum mechanics and cosmology, and its potential to bridge the gap between science and philosophy. We present detailed predictions for the cosmic microwave background (CMB) power spectrum, gravitational wave signatures, and large-scale structure formation, demonstrating how HTUM differs from the standard ΛCDM model. Our analysis reveals distinctive oscillatory patterns in the relative difference between HTUM and ΛCDM predictions, with deviations reaching up to ±20% at certain scales. The paper also explores the unification of fundamental forces within the HTUM framework, proposing novel approaches to particle physics and quantum field theory. It introduces the concept of unified mathematical operations, suggesting a more holistic approach to mathematical thinking that aligns with the model's interconnected view of the universe. Additional testable predictions and proposed experimental approaches are discussed, including advanced space-based tests and laboratory experiments probing quantum gravity effects. These specific, quantifiable predictions offer multiple avenues for empirical validation, highlighting HTUM's potential to be distinguished from ΛCDM and other alternative cosmological models. HTUM represents a significant new perspective in our understanding of the universe, inviting further research and exploration into the nature of reality, consciousness, and the fundamental structure of the cosmos. By providing a comprehensive framework that unifies various aspects of physics, cosmology, and consciousness studies, HTUM offers a promising path toward a more complete understanding of our universe.