In the present paper, we efficiently solve the two-body problem for extreme cases such as those with high eccentricities. The use of numerical methods, with the usual variables, cannot maintain the perihelion passage accurately. In previous articles, we have verified that this problem is treated more adequately through temporal reparametrizations related to the mean anomaly through the partition function. The biparametric family of anomalies, with an appropriate partition function, allows a systematic study of these transformations. In the present work, we consider the elliptical orbit as a meridian section of the ellipsoid of revolution, and the partition function depends on two variables raised to specific parameters. One of the variables is the mean radius of the ellipsoid at the secondary, and the other is the distance to the primary. One parameter regulates the concentration of points in the apoapsis region, and the other produces a symmetrical displacement between the polar and equatorial regions. The three most used geodesy latitude variables are also studied, resulting in one not belonging to the biparametric family. However, it is in the one introduced now, which implies an extension of the biparametric method. The results obtained by the method presented here now allow a causal interpretation of the operation of numerous reparametrizations used in the study of orbital motion.

Transportation tasks in nursing are common and shorten the time for direct patient care in times of nursing shortage and an aging society. There is a lack of research on transportation needs, with most studies focusing on overall nursing task analysis without a deeper analysis of transportation tasks. In July and September 2023, we conducted weekly observations of nurses to assess clinical transportation needs. We aim to understand the economic impact and the methods nurses use for transportation tasks. We conducted a participant observation using a standardized app-based form over a seven-day observation period in two rural clinics. N=1,830 transports were made by nurses and examined by descriptive analysis. Non-medical supplies account for 27.05 % (n=495) of all transports, followed by medical supplies at 17.32 % (n=317), pharmacotherapy at 14.10 % (n=258) and other other categories like meals or drinks contributing 12.68 % (n=232). Most transports had a factual transport time of under a minute, with patient transport and lab samples displaying more variability. In total, 77.15 % of all transports were made by hand. Requirements to collect items or connect transports with patient care were included in 5 % of all transports. Our economic evaluation spotlighted meals as the most costly transport, with 9,596.16€ p.a. in the observed clinics. Budget-friendly robots would amortize over one year by transporting meals. We support understanding nurses’ transportation needs via further research on assistive robots to validate our findings and determine the feasibility of transport robots.

Human motion analysis using inertial measurement units (IMUs) has recently been shown to provide accuracy similar to the gold standard, marker-based optical motion capture, but at much lower costs and while being less restrictive and time-consuming. However, IMU-based motion analysis requires precise knowledge of the orientation in which the sensor is attached to the body segments. This knowledge is commonly obtained via an anatomical calibration procedure based on precisely defined poses or motions, which is time-consuming and error-prone. In the present work, we propose a self-calibrating approach for magnetometer-free joint angle tracking that is suitable for joints with two degrees of freedom (DoF), such as the elbow, ankle, and metacarpophalangeal finger joints. The proposed methods exploit kinematic constraints to simultaneously identify the joint axes and the heading offset. The experimental evaluation shows that the proposed methods are able to estimate plausible and consistent joint axes from just ten seconds of arbitrary elbow joint motion. Comparison with optical motion capture shows that the proposed methods yield joint angles with similar accuracy as a conventional IMU-based method while being much less restrictive. Therefore, the proposed methods improve the practical usability of IMU-based motion tracking in many clinical and biomedical applications.

According to the Cosmological Principle the Universe is isotropic and no preferred direction would be seen by an observer that might be stationary with respect to the expanding cosmic fluid. However, because of observer’s partaking in the solar system peculiar motion, there would appear in some of the observed properties of the Cosmos a dipole anisotropy, which could in turn be exploited to determine the peculiar motion of the solar system. The dipole anisotropy in the Cosmic Microwave Background Radiation (CMBR) has given a peculiar velocity vector 370 km s−1 along l=264∘,b=48∘. However, some other dipoles, for instance, from the number counts, sky brightness or redshift distributions in large samples of distant Active Galactic Nuclei (AGNs), have yielded values of the peculiar velocity many times larger than that from the CMBR, though surprisingly, in all cases the directions agreed with the CMBR dipole. Here we determine our peculiar motion from a sample of 0.28 million AGNs, selected from the Mid Infra Red Active Galactic Nuclei (MIRAGN) sample comprising more than a million sources. From this, we find a peculiar velocity, which is more than four times the CMBR value, although the direction seems to be within ∼2σ of the CMBR dipole. A genuine value of the solar peculiar velocity should be the same irrespective of the data or the technique employed to estimate it. Therefore, such discordant dipole amplitudes, might mean that the explanation for these dipoles, including that of the CMBR, might in fact be something else. But, the observed fact that the direction in all cases, is the same, though obtained from completely independent surveys using different instruments and techniques, by different sets of people employing different computing routines, might nonetheless indicate that these dipoles are not merely due to some systematics, otherwise why would they all be pointing along the same direction. It might instead suggest a preferred direction in the Universe, implying a genuine anisotropy, which would violate the Cosmological Principle, the core of the modern cosmology.

We discuss the dynamics of a roller coaster cart driven by a constant force along the suspended track of a winding roller coaster. The track is assumed arbitrarily long and specially shaped. It is made by semicircular track portions, in the form of valleys and hills, standing perfectly vertical in the same plane. This is a mechanical analog of a Josephson junction electrodynamics. To demonstrate the explanatory potential of the analogy, we focus particularly on the conditions of de-trapping of the cart from one of the valleys of the track. This mechanical process has its analog in a non-noise-generated premature switching to the finite voltage state of a Josephson junction.

Traditional painting artefacts study and documentation face the limitations of well-known recording tools and methods, such as handwritten or digital descriptions, scaled 2D drawings in situ, measurements with calipers, rulers or tape measures, sketches, tracings, as well as conventional or technical photographs. This paper advocates Close-Range Photogrammetry (SfM-MVS) and Reflectance Transformation Imaging (RTI) for recording vital morphological and 2.5D geometric features of painted surfaces with high accuracy. These digital tools, widely accessible due to increased computing power, enhance art observation, material study and conservation assessment. Despite specialized alternatives like 3D laser scanners, the focus here is on the cost-effective SfM-MVS and RTI, which offer advanced pixel colour accuracy. The ability to reproduce photorealistic textures proves essential for accurate documentation of painted artefacts. The paper showcases promising results from applying these methods to a mural from the Palace of Tiryns, justifying their fundamental role in an integrated scientific art study methodology.

Human violence recognition is an area of great interest in the scientific community, given its broad spectrum of applications, especially in video surveillance systems, since detecting violence in real-time could prevent criminal acts and save lives. Despite the number of existing proposals and research, most focus on the precision of results, leaving aside efficiency and its practical implementation. Thus, this work proposes a model that is effective and efficient in recognizing human violence in real-time. The proposed model consists of three modules: a first module called Spatial Motion Extractor (SME), in charge of extracting regions of interest from a frame; a second module called Short Temporal Extractor (STC), whose function is to extract temporal characteristics of rapid movements, finally the Global Temporal Extractor (GET) module, responsible for identifying long-lasting temporal features and fine-tuning the model. The proposal was evaluated regarding efficiency, effectiveness, and ability to operate in real-time. The results obtained on Hockey, Movies, and RWF-2000 datasets demonstrated that this approach is highly efficient compared to other alternatives. A VioPeru dataset was created to validate real-time applicability with violent and non-violent videos captured by real video surveillance cameras in Peru. The effectiveness results in this dataset outperformed the best existing proposal. Therefore, our proposal has contributions in efficiency, effectiveness, and real-time.

The mechanisms of natural oscillations and resonance are described, considering the peculiarities of the transformation of elastic and kinetic energy in the implementation of the law of conservation of energy in local and integral volumes of the body, using the concept of mechanics based on the concepts of space, time and energy. When describing the motion in the Lagrange form, the elastic deformation energy of the particles is determined by the quadratic invariant of the tensor, whose components are the partial derivatives of Euler variables with respect to Lagrange variables. The increment of the invariant due to elastic deformation is represented as the sum of two scalars, one of which depends on the average value of the relative lengths of the edges of the particles in the form of an infinitesimal parallelepiped, the second is equal to the standard deviation of these lengths from the average value. It is shown that each of the scalars can be represented in the form of two dimensionless kinematic parameters of elastic energy, which participate in different ways in the implementation of the law of conservation of energy. One part of the elastic energy passes into kinetic energy and participates in the implementation of the law of conservation of energy for the body as a whole, considering external forces. The second part is not converted into kinetic energy but changes the deformed state of the particles in accordance with the equations of motion while maintaining the same level of the part of the elastic energy of the particles used for this. The kinematic parameters differ from the volume density of the corresponding types of energy by a factor equal to the elastic modulus, which is directly proportional to the density and heat capacity of the material and inversely proportional to the volume compression coefficient. Transverse, torsional, and longitudinal vibrations are considered free and under resonance conditions. The mechanisms of transformation of forced vibrations into their own after the termination of external influences and resonance at the superposition of free and forced vibrations with the same or similar frequency are considered. The formation of a new free wave at each cycle with an increase in the amplitude, which occurs mainly due to internal energy sources, and not external forces, is justified.

The construction of molecular robotic-like objects that imitate living things is an important challenge for current chemists. Such molecular devices are expected to perform their duties robustly to carry out mechanical motion, process information, and make independent decisions. Dissipative self-organization plays an essential role in meeting these purposes. To produce a micro-robot that can perform the above tasks autonomously as a single entity, a function generator is required. Although many elegant review articles featuring chemical devices that mimic biological mechanical functions have been published recently, the dissipative structure, which is the minimum requirement, has not been sufficiently discussed. This article aims to show clearly that dissipative self-organization is a phenomenon involving autonomy, robustness, mechanical functions, and energy transformation. Moreover, the author details the recent experimental results of an autonomous light-driven molecular device that achieves all of these features. In addition, a chemical model of cell-amplification is also discussed to focus on the generation of hierarchical movement by dissipative self-organization. By reviewing this research, it may be perceived that mainstream approaches to synthetic chemistry have not always been appropriate. In summary, the author proposes that the integration of catalytic functions is a key issue for the creation of autonomous microarchitecture.

Neural or mental simulation of actions is a powerful tool for allowing cognitive agents to develop Prospection Capabilities that are crucial for learning and memorizing key aspects for challenging skills. In previous studies we developed an approach based on the animation of the redundant human Body Schema based on the Passive Motion Paradigm (PMP). In this paper we show that this approach can be easily extended to hyper-redundant serpentine robots as well as to hybrid configurations where the serpentine robot is functionally integrated with a traditional skeletal infrastructure. A simulation model is analyzed in detail showing that it incorporates spatio-temporal features discovered in the biomechanical studies of biological hydrostats like the elephant trunk or the octopus tentacles. It is proposed that such generative internal model can be the basis for a cognitive architecture appropriate for serpentine robots, independent of the underlying design and control technologies. Although robotic hydrostats have received a lot of attention in the last decades, the great majority of research activities have been focused on the actuation/sensorial/material technologies that can support the design of hyperredundant soft robots as well as the related control methodologies. The cognitive level of analysis has been limited to motion planning, without addressing synergy formation and metal time travel. This is where the contribution of the paper is focused on.

It is important to understand the statistical-physical structure of the rain in the vertical so that observations aloft can be translated meaningfully into what will occur at the surface. In order to achieve this understanding, it is necessary to gather high temporal and spatial resolution observations of rain in the vertical. This can only be accomplished using radars. It can be achieved by translating radar Doppler spectra into drop size distributions which can then be integrated to calculate variables such as the rain fall rate. A long-standing difficulty in using such measurements, however, is the problem of vertical air motion which can shift the Doppler spectra, and, therefore, significantly alter the deduced drop size distributions and integrated variables. In this work, we illustrate the improvement in measured rain structures using a new approach for removing the effect of mean vertical air motion. It is demonstrated that the new approach proposed here not only produces what appear to be better estimates of the rainfall rates, but, also as a consequence, provides estimates of the temporal and spatial regionally coherent updraft and downdrafts occurring in the precipitation. Furthermore, the technique is readily applicable to other radars especially those operating at non-attenuating frequencies.

Jumping side volley has created breathtaking moments and cherished memories for us. Regrettably, a scientific study on the skill has not been found in literature. Relying on talent of athletes to improvise on the fly can hardly be considered a viable learning strategy. This study targets to fill the gap by quantifying factors contributing to develop its coaching method. Using 3D motion capture (12-cameras, 200Hz) and full-body biomechanical modeling, our study aimed to identify elements that govern entrainment of the skill by examining jumping, kicking and falling phases of its execution. Given the rarity of players who have acquired this skill, we found five subjects for the study. Twenty-three trials were captured and quantified. The results unveil the following key elements: 1) the control of trunk rotation during the jumping, 2) the angle between thighs upon take-off, 3) the whip-like control of the kicking leg during airborne, 4) timing between ball motion and limbs’ coordination, and 5) damping mechanism during falling. An accurate kick can only be achieved through repetitive training. This underlines the need for athletes to master a safe landing technique that minimizes risk of injury during practice. Therefore, training should begin with learning a safe falling technique.

With the rapid development of renewable energy, accurately forecasting wind power is crucial for the stable operation of power systems and effective energy management. This paper proposes a short-term wind power forecasting method based on the Orthogonalized Maximal Information Coefficient (OMNIC) combined with an Adaptive Fractional Generalized Pareto Motion (fGPm) model. The method quantifies the influence of meteorological factors on wind power prediction and identifies the optimal set and number of influencing factors. The model accounts for long-range dependence (LRD) in time series data and constructs an uncertainty model using the properties and parameters of the fractional generalized Pareto distribution (GPD), significantly improving prediction accuracy under nonlinear conditions. The proposed approach was validated using a real dataset from a wind farm in northwest China and compared with other models such as Convolutional Neural Network-Long Short-Term Memory (CNN-LSTM) and Convolutional Neural Network-Gated Recurrent Unit (CNN-GRU). Results demonstrate that the adaptive fGPm model significantly reduces wind power forecasting errors, offering high accuracy and robustness. This method provides practical value in alleviating peak voltage and frequency regulation challenges in power systems and in promoting the integration of wind power into the grid.

Characterized in biomedical terms, stretching exercises have been defined as movements applied by external and/or internal forces – to increase muscle and joint flexibility, decrease muscle stiffness, to elevate joint range of motion (ROM), to increase the length of the morpho-functional unit “muscle-tendon”, to improve joint, muscle and tendon movements, contraction and relaxa-tion. The present review examines and summarizes the initial and recent literature data related to the biomechanical, physiological and therapeutic effects of static stretching (SS) on flexibility and other physiological characteristics of the main structural and functional unit “joint-ligaments-tendon-muscle”. The healing and therapeutic effects of SS, soon combined with other rehabilitation techniques (massage, foam rolling – with and without vibrations; hot/cold therapy, etc.) are discussed in relationship to creation of individual (patient-specific) or group programs for treatment and prevention of joint injuries as well as for improving performance in sports. From a theoretical point of view, the role of SS as positively affecting the composition of the connective tissue matrix is pointed out: type I-III collagen synthesis, hyaluronic acid and glucosaminoglycans (GAGs) turnover – under influence of the transforming growth factor beta-1 (TGF-β-1). Different variables as collagen type, biochemistry, elongation and elasticity are used as molecular biomarkers. Recent studies evaluated that the static progressive stretching therapy could prevent/reduce the development of arthrogenic contractures, joint capsule fibrosis, muscle stiffness and need new clinical applications. Combined stretch techniques are proposed and ap-plied in medicine and sports, depending on their long- and short-term effects on variables such as ROM, EMG activity, muscle stiffness, etc. The results obtained are of theoretical and practical interest for development of new experimental, mathematical and computational models and creation of efficient therapeutic programs. The healing SS effects on the main structural and functional unit – “joint-ligament-tendon-muscle” need further investigations, which could clarify and evaluate benefits of SS in prophylaxis and treatment of joint injuries - in healthy and ill in-dividuals, in older adults, as compared to young, active and well-trained persons, as well as to professional athletes.

Debris-covered glaciers are a notable feature in the greater Himalaya, and their ongoing mass loss under changing climate will affect the water resources of over a billion people. The current knowledge of the mass balance of Himalayan glaciers is restricted by the paucity of in-situ measurements of glaciers in both space and time, as well as the resolution of satellite remote sensing imageries. Recently, the use of Unmanned Aerial System (UAS) imagery has shown the potential to bridge this gap by enabling very detailed monitoring of inaccessible glacial areas. UAS imagery-based monitoring of Himalayan glaciers has so far been limited to a single glacier in the entire Himalaya, providing a limited understanding of spatial variability in glacier mass balance and driving factors. In the first UAS based glacial mass change estimation in the trans-Himalaya, we conducted two Unmanned Aerial System (UAS) surveys (May and November 2019) over the debris-covered Annapurna III glacier in the Himalaya. We performed Structure-from-Motion (SfM) analysis and utilized differential GPS field observations to derive geometrically accurate point clouds, ortho-mosaics and digital surface models (DSMs). The glacial volumetric loss was estimated from DSM differencing, and the magnitude and spatial variability of glacier surface change was derived from 3-D differencing of point clouds. Results revealed a heterogeneous glacial melt pattern, with an average elevation loss of 0.89 m during the monitored time period. The majority of the glacial tongue exhibited surface lowering except the area above and around the glacial snout that surprisingly exhibited significant elevation gain. Both the highest magnitude of mass loss and the highest spatial variability in mass change was observed in areas with exposed ice-cliffs and supraglacial ponds. Glacial surface velocity derived from manual feature tracking showed velocity ranging from 0-4.1 m. A detailed evaluation of specific areas allowed an improved understanding of the complex interplay of factors leading to observed surface change. Our findings expand the extent of UAS based monitoring of debris-covered glaciers in the Himalaya and conclude that UAS derived 3D topographic products will become increasingly important for monitoring of thinning debris-covered glaciers.

(1) Background: Glenohumeral internal and external rotational range of movement (GIRD and GERD) has been considered one of the primary outcomes to determine risk of injury in overhead athletes, as tennis players. Nevertheless, current testing position doesn’t consider than most tennis actions are repeated at 45of abduction, and actively. The aim of this study is establishing normative values of pathological GIRD and GERD in tennis players, to estimate the passive and active range of motion of the glenohumeral joint at 90° and 45º of abduction.; (2) Methods: 43 tennis players voluntarily participated in the study (19.1±2.75 years). Dominant and non-dominant shoulder range of motion (ROM), external rotation (ER), internal rotation (IR) at 90 and 45 in active and passive conditions were evaluated. GIRD and GERD were calculated in both positions and conditions; (3) Results: There were significant differences for all passive measurements between 45 and 90 testing position. ER and TROM at 90 and 45 showed significant differences in both passive and active conditions and in the dominant and non-dominant side. There were no significant differences in IR and TROM actively in both the dominant and the non-dominant at 90 or 45; (4) Conclusions: It is necessary to evaluate the ER under the same conditions at 90 or 45. Practitioners should consider assessing ER at the angle at which most actions are repeated in tennis (45°) as a method to monitor GERD. Evaluating GERD in asymptomatic tennis players could help avoid future biomechanical and GIRD problems. Both GIRD and GERD should be considered as a percentage of the athlete's own deficit in IR or ER, instead of having as a reference specific degree that have been observed in baseball pitchers.

Trunk-like robots have attracted a lot of attention in the community of researchers interested in the general field of bio-inspired soft robotics, because trunk-like soft arms may exhibit high dexterity and adaptability very similar to the elephants and potentially quite superior to traditional articulated manipulators. In view of practical applications, the integration of a soft hydrostatic segment with a hard-articulated segment, i.e. a hybrid kinematic structure similar to the elephant’s body, is probably the best design framework. It is proposed that this integration should occur at the conceptual/cognitive level before being implemented in specific soft technologies, including the related control paradigms. The proposed modeling approach is based on the Passive Motion Paradigm (PMP), originally conceived for addressing the degrees of freedom problem of highly-redundant, articulated structures. It is shown that this approach can be naturally extended from highly-redundant to hyper-redundant structures, including hybrid structures that include a hard and a soft component. The PMP model is force-based, not motion-based and is characterized by two main computational modules: the Jacobian matrix of the hybrid kinematic chain and a Compliance matrix that maps generalized force fields into coordinated gestures of the whole body-model. It is shown how the modulation of the compliance matrix can be used for the synergy formation process, that coordinates the hyper-redundant nature of the hybrid body-model and, at the same time, for the preparation of the trunk-tip in view of a stable physical interaction of the body with the environment, in agreement with the general impedance-control concept.

Multivariate Time Series Classification (MTSC) is one of most important tasks in time series analysis, aiding in activities such as human motion recognition and medical diagnostics. Existing methods for MTSC do not explicitly model temporal differences and generalize the idea of temporal difference into a efficient temporal module. Additionally, existing methods are not yet able to capture cross-variable relationships well during network training. As a result, they are unable to achieve convincing feature representation, leading to suboptimal classification accuracy. In this paper, we propose a novel MTSC model called Temporal Difference and Cross-variate Fusion Network (TDCFN), which integrates a two-stream differential LSTM network and a cross-variate feature extraction network to enhance feature representation. TDCFN achieves superior classification accuracy by capturing dynamic temporal evolution and inter-variable relationships. The experimental results show that TDCFN can achieve competitive performance with state-of-the-art multivariate time series classification approaches.

This paper revisits the analytical theory of fractional vibrations with the highlights in five aspects. First, we address the cases of structures with frequency dependent mass or damping or stiffness in Sections 2-4. Second, we introduce the theory based on the general second-order vibration motion equation with frequency dependent elements (mass, damping, stiffness) in Sections 5-7. Third, we present the analytical theory of seven specific classes of second-order vibration systems with frequency dependent mass or damping or stiffness in Sections 8 and 9. Fourth, we bring forward the analytical theory of seven classes of fractional vibration systems in Sections 10-12. Finally, as an application, we give the closed form expression of the forced response to multi-fractional Euler-Bernoulli beam in Section 13. The explanation of the nonlinearity of fractional vibrations is given in Section 14.

Powered ankle prostheses have been proven to improve the walking economy of people with transtibial amputation. All commercial powered ankle prostheses that are currently available can only perform one-degree-of-freedom motion in a limited range. However, studies have shown that the frontal plane motion during ambulation is associated with balancing. In addition, as more advanced neural interfaces have become available for people with amputation, it is possible to fully recover ankle function by combining neural signals and a robotic ankle. Accordingly, there is a need for a powered ankle prosthesis that can have active control on not only plantarflexion and dorsiflexion but also eversion and inversion. We designed, built, and evaluated a two-degree-of-freedom (2-DoF) powered ankle-foot prosthesis that is untethered and can support level-ground walking. Benchtop tests were conducted to characterize the dynamics of the system. Walking trials were performed with a 77 kg subject that has unilateral transtibial amputation to evaluate system performance under realistic conditions. Benchtop tests demonstrated a step response rise time of less than 50 milliseconds for a torque of 40 N·m on each actuator. The closed-loop torque bandwidth of the actuator is 9.74 Hz. Walking trials demonstrated torque tracking errors (root mean square) of less than 7 N·m. These results suggested that the device can perform adequate torque control and support level-ground walking. This prosthesis can serve as a platform for studying biomechanics related to balance and has the possibility of further recovering the biological function of the ankle-subtalar-foot complex beyond the existing powered ankles.

As most of the current dynamic positioning systems are based on model ships, they cannot accu-rately reflect the motion state, position changes, and mutual influence of each part of the dynamic positioning system of actual ships in complex environments. Other actual ships such as cargo ships cannot add various sensors and auxiliary equipment to verify and analyze the positioning system. This article takes the intelligent research and training dual-use ship of Dalian Maritime University, which integrates scientific research and training, as the object of study. This ship will not be affected by the voyage period and route and can choose a suitable sea area for research. Therefore, in order to improve the accuracy and reliability of the dynamic positioning system, research on the ship’s dynamic positioning system was carried out. Firstly, an accurate mathematical model of ship motion was established, and the hydrodynamic derivatives of ship model motion were obtained by nu-merical calculation, and applied to the three-degree-of-freedom model of the intelligent research and training dual-use ship. Then, the model was used as part of the closed-loop simulation model of the ship’s dynamic positioning system, and the terminal sliding mode controller was used for sim-ulation and emulation, thereby obtaining ideal simulation test results. This research helps to im-prove the accuracy and reliability of the dynamic positioning system and provides new ideas and methods for ship motion control.

This study aims to identify the model that best approximates the credit spread that should be fixed on debt instruments issued by both public and private companies, considering the particularities of the Mexican market. Five models were analyzed: Merton's [1], those proposed by Denzler et al., the one presented in this paper, which includes the conformable derivatives, taking as a reference the change of variable made by Morales-Bañuelos et al., and the Corporate Default Risk Model (DRSK) for Publics Firms of Bloomberg [4]. The required financial information was obtained from the Bloomberg platform, from which the probabilities of default, credit spreads, and credit ratings for each company in the sample under the model (DRSK) were extracted directly. Likewise, the program developed by Moody's K.M.V. was used to obtain the EDF (Expected Default Frequencies). It was concluded that the Modified Merton model approximates to a greater extent the credit spreads that fix on a prime rate on the loans granted to the Mexican non-financial companies.

This study introduces a remote sensing application using satellite imagery to survey a network-scale aggregate stockpile inventory. First, a real scale aggregate quarry site was surveyed using a small Unmanned Aerial Vehicle (sUAV) to produce digital terrain models that enabled analysis of aggregate pile geometry. Second, a lab experiment was designed and performed to validate the applicability of close-range Structure from Motion (SfM) photogrammetry for measuring aggregate piles' physical properties such as volume and density. The other part of the lab experiment delved into direct measurement of aggregate density under varying compaction efforts. These experimental results, in conjunction with some simplifying assumptions, enabled the calculation of aggregate stockpile volumes and estimated weights from satellite imagery. We estimated that an inventory of 4.4 and 1.1 million metric tons of crushed aggregates and Reclaimed Asphalt Pavement (RAP), respectively, stockpiled in Washington State for asphalt production in 2017. The merit of producing such database was further showcased in an example on the economic and environmental impacts of material transportation. We approximated that hauling aggregates from quarry plants to construction sites within Washington State incurs a cost of about $50 thousand to over $4 million, consumes about 0.25 to 20 TJ of energy, and emits 20 to over 1,500 tons of CO₂-eq per asphalt plant annually.

The present article addresses the long-standing problem of the polymer brush bilayers under stationary shear flow at non-linear response regime where the system gets a non-Newtonian fluid. The main idea behind this research would be the fact that the immense lubricity of the polymer brush bilayers originates from a global restructuring that takes place at large shear rates. It is shown here that physical quantities like, stress tensor, viscosity tensor, the friction coefficient and the chain extensions could become dependent on the shear rate at non-Newtonian regime. Apparently, the sub-linear scaling of the physical quantities at large shear rates is solely due to the fact that the chains stretch in the shear direction.

Dams are a critical infrastructure system for many communities, but they are also one of the most challenging to inspect. Dams are typically very large and complex structures, and the result is that inspections are often time-intensive and require expensive, specialized equipment and training to provide inspectors with comprehensive access to the structure. The scale and nature of dam inspections also introduces additional safety risks to the inspectors. Unmanned aerial vehicles (UAV) have the potential to address many of these challenges, particularly when used as a data acquisition platform for photogrammetric three-dimensional (3D) reconstruction and analysis, though the nature of both UAV and modern photogrammetric methods necessitates careful planning and coordination for integration. This paper presents a case study on one such integration at the Brighton Dam, a large-scale concrete gravity dam in Maryland, USA. A combination of multiple UAV platforms and multi-scale photogrammetry was used to create two comprehensive and high-resolution 3D point clouds of the dam and surrounding environment at intervals. These models were then assessed for their overall quality, as well as their ability to resolve flaws and defects that were artificially applied to the structure between inspection intervals. The results indicate that the integrated process is capable of generating models that accurately render a variety of defect types with sub-millimeter accuracy. Recommendations for mission planning and imaging specifications are provided as well.

Background. The markerless motion capture system (MLS) is a new technology that uses deep learning to detect body segments from digital images. This study tested the agreement between the MLS and a force-plate based system (FPS, “gold standard”) to quantify stability control and motor performance (MP) during gait initiation (GI). Methods. Healthy adults (young and elderly) and patients with Parkinson’s disease (PD) performed GI series at spontaneous and maximal velocity on an FPS while being filmed by an MLS. Signals from both systems were used to compute the peak of forward center-of-mass velocity (indicator of MP) and the braking index (BI, indicator of stability control). Results. Descriptive statistics indicated that both systems detected between-groups differences and velocity effects similarly, while a Bland-Altman (BA) plot anal-ysis showed that BI and MP mean biases were virtually zero in all groups and conditions. Bayes factor 01 indicated strong (for BI) and moderate (for MP) evidence that both systems provided equivalent values. However, trial-by-trial analysis of BA plots revealed the possibility of differ-ences > 10% between the two systems. Conclusion. Although non-negligible differences do occur, MLS appears to be as efficient as FPS in detecting PD and velocity condition effects on BI and MP

Today electricity is distributed to the individual users via physical Copper connections. From the power stations, the energy is transported through transmission lines where the electricity, sinusoidally modulated at a fixed frequency of about 50 Hz, is raised up to a voltage in a range approximately variating between 30, and 110 kV. When electrons, aligned at this voltage, pass through the transmission lines, they cause coherent vibrations, sometimes even audible in the acoustic frequencies. In the spectrum of movements to which electric cables are subjected, there are also unexpected and sporadic movements caused by winds and rain. The problem of carrying out persistent, precise and spatially distributed monitoring of transmission line health is to use a large number of sensors physically distributed everywhere and somehow transmit the results to a control station. The use of synthetic aperture radar (SAR) data could be a viable solution of persistent and wide-area high-voltage vibration monitoring. In this paper we produce a comprehensive survey on how to monitor both movements in terms of vibrational displacement, due to weathering, and those due to electricity transmission, normally fixed at about 50 Hz. The results demonstrate the technical feasibility of an operational use of SAR for these purposes in the very short term. This would allow the possibility of monitoring malfunctions such as black-outs or other frequency anomalies.

Rapid post-earthquake damage diagnosis of bridges can guide decision-making for emergency response management and recovery. This can be facilitated using digital technologies to remove the barriers of manual post-event inspections. Prior mechanics-based Finite Element (FE) models can be used for post-event response simulation using the measured ground motions at nearby stations; however, the damage assessment outcomes would suffer from uncertainties in structural and soil material properties, input excitations, etc. For instrumented bridges, these uncertainties can be reduced by integrating sensory data with prior models through a model updating approach. This study presents a sequential Bayesian model updating technique, through which a linear/nonlinear FE model, including soil-structure interaction effects, and the foundation input motions are jointly identified from measured acceleration responses. The efficacy of the presented model updating technique is first examined through a numerical verification study. Then, seismic data recorded from the San Rogue Canyon Bridge in California are used for a real-world case study. Comparison between the free-field and the foundation input motions reveals valuable information regarding the soil-structure interaction effects at the bridge site. Moreover, the reasonable agreement between the recorded and estimated bridge responses shows the potentials of the presented model updating technique for real-world applications. The updated FE model is considered as the digital twin of the bridge and can be used to analyze the bridge and monitor the structural response at element, section, and fiber levels to diagnose the location and severity of any potential damage mechanism.

Height assignment is an important problem for satellite measurements of Atmospheric Motion Vectors (AMVs) that are interpreted as winds by forecast and assimilation systems. Stereo methods assign heights to AMVs from the parallax observed between observations from different vantage points in orbit while tracking cloud or moisture features. In this paper, we fully develop the stereo method to jointly retrieve wind vectors with their geometric heights from geostationary satellite pairs. Synchronization of observations between observing systems is not required. NASA and NOAA stereo-winds codes have implemented this method and we have processed large datasets from GOES-16, -17, and Himawari-8. Our retrievals are validated against rawinsonde observations and demonstrate the potential to improve forecast skill. Stereo winds also offer an important mitigation for the loop heat pipe anomaly on GOES-17 during times when warm focal plane temperatures cause infra-red channels that are needed for operational height assignments to fail. We also examine several application areas, including deep convection in tropical cyclones, planetary boundary layer dynamics, and fire smoke plumes, where stereo methods provide insights into atmospheric processes. The stereo method is broadly applicable across the geostationary ring where systems offering similar Image Navigation and Registration (INR) performance as GOES-R are deployed.

Technological advances in game-mediated robotics provide an opportunity to engage children with cerebral palsy (CP) and other neuromotor disabilities in more frequent and intensive therapy by making personalized, programmed interventions available 24/7 in children’s homes. Though shown to be clinically effective and feasible to produce, little is known of the subjective factors impacting acceptance of what we term assistive/rehabilitative (A/R) gamebots by their target populations. This research describes the conceptualization phase of an effort to develop a valid and reliable instrument to guide the design of A/R gamebots. We conducted in-depth interviews with 8 children with CP and their families who had trialed an exemplar A/R gamebot, PedBotHome, for 28 days in their homes. The goal was to understand how existing theories and instruments were either appropriate or inappropriate for measuring the subjective experience of A/R gamebots. Key findings were the importance of differentiating the use case of therapy from that of assistance in rehabilitative technology assessment, the need to incorporate the differing perspectives of children with CP and those of their parents into A/R gamebot evaluation, and the potential conflict between the goals of preserving the quality of the experience of game play for the child while also optimizing the intensity and duration of therapy provided during play.

Motivated by a common Mathematical Finance topic, this paper surveys several results concerning windings of 2-dimensional processes, including planar Brownian motion, complex-valued Ornstein-Uhlenbeck processes and planar stable processes. In particular, we present Spitzer's asymptotic Theorem for each case. We also relate this study to the pricing of Asian options.

We study whether the center of relativistic energy (CRE) is always constant in an isolated frame of reference (IFR). First, we assume that two objects in a moving isolated frame of reference (MIFR) move parallel to and very close to a coordinate axis from opposite directions and with equal speed. Here each length in the direction of travel of the objects is much longer than that perpendicular to the direction of travel of them, and moreover the latter is negligibly extremely short. Hence, the location of the CRE (LCRE) of the objects is very close to the coordinate axis in initial condition. When they become perfectly symmetric with respect to the coordinate axis, the forces perpendicular to the direction of travel of the objects are applied to each CRE and thereby a perfectly inelastic collision between them occurs on the coordinate axis. The combined object (CO) resulting from the perfectly inelastic collision begins to rotate because each momentum of the objects before the combination between them acts like the moment of force on the CO. For simplicity, we examine the energy distribution of the CO when it becomes perpendicular to the coordinate axis due rotation. The magnitude of velocity of each minute portion (MP) symmetrical with respect to the coordinate axis are different depending on whether the direction of each rotational velocity is the same or opposite to the direction of travel of the MIFR. Then the energy of each MP is not the same. As a result, the LCRE of the CO moves to the direction perpendicular to the coordinate axis, and its LCRE becomes far from the coordinate axis since the length in such direction is long enough. Therefore, we conclude that the LCRE in the MIFR is not necessarily invariant. Second, we suppose a process in which a force causes a negative acceleration on a moving object (MO) and thereafter the MO eventually comes to rest. What is considered here is the LCRE when the MO comes to rest. We pay attention to the position of the force applied to the MO because the transmission time of force (TTF) inside the MO may vary depending on the position of the MO where the force is applied. As a result, we find that the position at which the MO comes to rest differs depending on the TTF inside the MO. Therefore, we conclude that the LCRE in an IFR differs depending on the position of the MO where the force is applied, in other words, it in an IFR is not necessarily uniquely determined.

This comprehensive treatise is written for the special occasion of the author’s 70th birthday. It presents his lifelong endeavors and reflections with original reasoning and re-interpretations of the most critical and misleading issues in thermodynamics; since now, we have the advantage to look at the historical developments more comprehensively and objectively than the pioneers. Starting from Carnot (grand-father of thermodynamics-to-be) to Kelvin and Clausius (fathers of thermodynamics), and other followers, the most relevant issues are critically examined and put in historical and contemporary perspective. From original reasoning of energy forcing and displacement to logical-proofs of the fundamental laws, to ubiquity of thermal motion and heat, and indestructibility of entropy, including new concept of “thermal roughness” and inevitability of dissipative irreversibility, to “dissecting Carnot true reversible-equivalency” and critical concept of “Carnot-Clausius heat-work equivalency (CCHWE)” regarding interchangeability of heat and work, and to demonstrating “no hope” for the “challengers” of the Second Law of thermodynamics, among others, are offered. It is hoped that the novel contributions presented will enhance comprehension and resolve some of the fundamental issues, as well as promote collaboration and future progress.

This article provides exact analytical formulae for various kinds of rainbow step barrier options. These are highly flexible and sophisticated multi-asset barrier options based on the following principle : the option life is divided into several time intervals on which different barriers are monitored w.r.t. different underlying assets. From a mathematical point of view, new formulae are provided for the first passage time of a multidimensional geometric Brownian motion to a boundary defined as a step function. The article shows how to implement the obtained valuation formulae in a simple and very efficient manner. Numerical results highlight a strong sensitivity of rainbow step barrier options to the correlations between the underlying assets.

In this paper, we review a new treatment of classical radiation damping, which resolves a well-known contradiction in the Abraham-Lorentz equation that has long been a concern. This radiation damping problem has already been solved in quantum mechanics by the method introduced by Friedrichs. Based on Friedrichs’ treatment, we solved this long-standing problem by classicizing quantum mechanics by replacing the canonical commutation relation in quantum mechanics with the Poisson bracket relation in classical mechanics. As an application of our new approach, we will analyze the anomalous damping experienced by electrons undergoing cyclotron motion inside a waveguide near the cut-off frequency. This anomalous damping cannot be described using the existing Abraham-Lorentz equation.

A method for generating fluoroscopic (time-varying) volumetric images using patient-specific motion models derived from 4-dimensional cone-beam CT (4D-CBCT) images is developed. 4D-CBCT images acquired immediately prior to treatment have the potential to accurately represent patient anatomy and respiration during treatment. Fluoroscopic 3D image estimation is done in two steps: 1) deriving motion models and 2) optimization. To derive motion models, every phase in a 4D-CBCT set is registered to a reference phase chosen from the same set using deformable image registration (DIR). Principal components analysis (PCA) is used to reduce the dimensionality of the displacement vector fields (DVFs) resulting from DIR into a few vectors representing organ motion found in the DVFs. The PCA motion models are optimized iteratively by comparing a cone-beam CT (CBCT) projection to a simulated projection computed from both the motion model and a reference 4D-CBCT phase, resulting in a sequence of fluoroscopic 3D images. Patient datasets were used to evaluate the method by estimating the tumor location in the generated images compared to manually defined ground truth positions. Experimental results showed that the average tumor mean absolute error (MAE) along the superior-inferior (SI) direction and the 95th percentile in two patient datasets were (2.29 mm and 5.79 mm) for patient 1 and (1.89 mm and 4.82 mm) for patient 2. This study has demonstrated the feasibility of deriving 4D-CBCT-based PCA motion models that have the potential to account for the 3D non-rigid patient motion and localize tumors and other patient anatomical structures on the day of treatment.

We study the effect of the generation of the mechanical transverse wave (MTW)　travelling in the opposite direction (OD) to a moving medium (MM) on the relativistic energy conservation law (RECL). From the viewpoint of the relativity of simultaneity (RS), the time on the coordinate coinciding with the advance end of the wave (AEW) travelling toward the rear of the MM passes faster than that on the coordinate coinciding with the wave source (WS). Then the AEW in the MM travels forward compared to that in the rest frame of reference (RFR) which is stationary relative to the medium when the time on the coordinate coinciding with the WS is same for each inertial frame of reference (IFR). Hence, the coordinate interval (CI) between the AEW and WS in the MM is observed to be larger than that between them in the RFR. We show that this difference holds true for the CI of any portion having transverse velocities mutually converted by the Lorentz transformation (LT). This difference in the CI leads to that in the rest mass (RM). We demonstrate that the RM included in wave motion (WM) in the MM is larger than one included in WM in the RFR when comparing the portions having transverse velocities mutually converted by the LT. This relation holds true for all portions in WM. Therefore, the total coordinate interval of the portion (CIP) and total RM (TRM) included in WM in the MM (WMMM) are large compared to them included in WM in the RFR. Furthermore, we compare the relativistic kinetic energy (RKE) of the MTW travelling in the OD to the MM (ODMM) with that of the MTW propagating in the direction vertical to the moving direction of the medium. We prove that the CIP and RM included in the former MTW are larger than them included in the latter MTW when comparing each portion with the same transverse velocity (TV). Moreover, the total CIP and TRM included in the former MTW are also large compared to them included in the latter MTW. The reason for these is that the latter CIP and RM are equal to them in the RFR when comparing the portions having transverse velocities mutually converted by the LT. On the other hand, the energy supplied to generate each MTW is the same. From these, we demonstrate that the RKE of the MTW travelling in the ODMM can be larger than the total relativistic energy (TRE) of the MTW propagating in the direction vertical to the moving direction of the medium. Consequently, we propose a violation of the RECL and Einstein’s principle of relativity (EPR) because the TRE is not necessarily conserved in the IFR in which the medium is moving.

Rapid developments in the field of underwater photogrammetry have given scientists1the ability to produce accurate 3-dimensional (3D) models which are now increasingly used in the representation and study of local areas of interest. This paper addresses the lack of systematic analysis of 3D reconstruction and navigation fusion strategies, as well as associated error evaluation of models produced at larger scales in GPS-denied environments using a monocular camera (often in deep-sea scenarios). Based on our prior work on automatic scale estimation of Structure from Motion (SfM)-based 3D models using laser scalers, an automatic scale accuracy framework is presented. The confidence level for each of the scale error estimates is independently assessed through the propagation of the uncertainties associated with image features and laser spot detections using a Monte Carlo simulation. The number of iterations used in the simulation was validated through the analysis of the final estimate behaviour. To facilitate the detection and uncertainty estimation of even greatly attenuated laser beams, an automatic laser spot detection method, mitigating the effects of scene texture, was developed, with the main novelty of estimating the uncertainties based on the recovered characteristic shapes of laser spots with radially decreasing1 intensities. The effects of four different reconstruction strategies resulting from the combinations of Incremental/GlobalSfM, and thea priori/a posterioriuse of navigation data were analyzed using two distinct survey scenarios captured during the SUBSAINTES 2017 cruise (doi: 10.17600/17001000). The study demonstrates that surveys with multiple overlaps of non-sequential images result in a nearly identical solution regardless of the strategy (SfM or navigation fusion), while surveys with weakly connected sequentially acquired images are prone to produce broad-scale deformation (doming effect) when navigation is not included in the optimization. Thus the scenarios with complex survey patterns substantially benefit from using multi-objective BA navigation fusion. In all cases, the errors in the models are inferior to 5%, with errors often being around 1%. The effects of combining data from multiple surveys were also evaluated. The introduction of additional vectors in the optimization of multi-survey problems successfully accounted for offset changes present in the underwater USBL-based navigation data and thus minimize the effect of contradicting navigation priors. Our results also illustrate the importance of collecting a multitude of evaluation data at different locations and moments during the survey.

This research aims to estimate the micro-motion (m-m) of ships. The problem of motion and m-m detection of targets is usually solved using synthetic aperture radar (SAR) along-track interferometry (ATI) which is observed employing two radars spatially distanced by a baseline extended in the azimuth direction. This paper is proposing a new approach where the m-m estimation of ships, occupying thousands of pixels, is measured processing the information given by sub-pixel tracking generated during the coregistration process of several re-synthesized time-domain and overlapped sub-apertures. The SAR products are generated splitting the raw data, according to a small-temporal baseline strategy, observed by one single wide-band staring spotlight (ST) SAR image. The predominant vibrational modes of different ships are estimated and results are promising to extend this application in performing surveillance also of land-based industries activities. Experiments are performed processing one ST SAR image observed by the COSMO-SkyMed satellite system.

Sea level rise due to global warming is a continuing and, disappointingly, accelerating process, which has already affected and will further impact coastal lowlands and the social and economic activities in these areas. Delos Island, situated in the middle of the Cyclades in the Aegean Sea, was considered the most sacred of all islands in ancient Greek culture and a trading hub for the entire eastern Mediterranean. Uninhabited since the 7th century AD, and consistently the focus of research and touristic attention, the island is designated as an archaeological site and inscribed on the Unesco World Heritage List. Previous studies on the relative sea level (rsl) changes suggest a steadily rsl rise during the last 6,300 years, starting from a sea level at -4.80±0.20m in the Late Neolithic. The seafront of the ancient city of Delos is subject to the effects of the rsl rise, which have caused significant coastline retreat and exposure to the northerly winds and waves, whereas parts of the coastal lowland where the remains of the ancient city lie are inundated, forming extended wetlands. The future impacts of rsl rise on the seafront of ancient Delos are illustrated on very high-resolution digital surface models, evaluating both the flooding risk under different climatic projections, as provided by the IPCC AR6 report, and the ongoing land subsidence, as recorded by GNSS data. An rsl rise ranging from 87cm (SSP1-2.6 scenario) to 148cm (SSP5-8.5 scenario) is anticipated by 2150, requiring both resilience strategies and adaptation solutions as well as mitigation policies to cope with the effects of climate change.

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long–range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long–range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations and agent–based models. Reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first–passage time distributions. Research has lead us to question whether the observed long–range memory is a result of actual long–range memory process or just a consequence of non–linearity of Markov processes. As our most recent result we discuss the long–range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the ARFIMA sample series. Our newly obtained results seem indicate that new estimators of self–similarity and long–range memory for analyzing systems with non–Gaussian distributions have to be developed.

The current study characterizes the transient M/M/1 queue manifold info-geometrically, through devising Fisher Information matrix(FIM) and its inverse(IFIM). Additionally, the impact of stability on the existence of IFIM and explore the geodesic equations of motion has been revealed. More potentially, the paper discusses the relationship between stability and the Gaussian curvature, as well as the connections between queueing theory, information geometry, , Riemannian geometry, and the Theory of Relativity.

Robots in space are necessarily extremely light and lack structural stiffness resulting in natural frequencies of resonance so low as to reside inside the attitude controller’s bandwidth. A variety of input trajectories can be used to drive a controller’s attempt to ameliorate the control-structural interactions where feedback is provided by low-quality, noisy sensors. Traditionally, step functions are used as the ideal input trajectory. However, step functions are not ideal in many applications, as they are discontinuous. Alternative input trajectories are explored in this manuscript and applied to an example system that includes a flexible appendage attached to a rigid main body. The main body is controlled by a reaction wheel. The equations of motion of the flexible appendage, rigid body, and reaction wheel are derived. A feedback controller is developed to account for the rigid body modes. Additional filters are added to compensate for the system’s flexible modes. Sinusoidal trajectories are autonomously generated to feed the controller. Whiplash compensation is additionally implemented for comparison. The control method without random errors with the smallest error is the sinusoidal trajectory method, which showed a 97.39% improvement when compared to the baseline response when step trajectories were commanded, while the sinusoidal method was inferior to traditional step trajectories when sensor noise and random errors were present.

Gyroscopes are fascinating instruments with a history of about 200 years. When J.G.F. Bohnenberger presented his machine to his students in 1810 at the University of Tuebingen, Germany, nobody could have foreseen that this fascinating development would be used for complex orientation and positioning. At the University of Stuttgart, Germany, a collection of 160 exhibits is available and in transition for a sustainable future. Here, the systems are digitized in 2D, 2.5D and 3D and are made available for a world-wide community using OpenAccess platforms. The technologies being used are Computed Tomography, Computer Vision, Endoscopy and Photogrammetry. The workflows for combining voxel representations and colored point clouds are described, to create Digital Twins of the tangible assets. Advantages and disadvantages are discussed und work for near future is outlined in this new and challenging field of Tech Heritage digitization.

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.

Research for a theory of quantum gravity has recently led to the use of presheaf topos. Quantum uncertainty is linked to the truth values of intuitionistic logic. This paper proposes transposing this model into a classic probability context, that of conditional mathematical expectations. A simulation of Brownian motion is offered for illustrative purposes.

The current study characterizes the transient M/M/1 queue manifold info-geometrically, through devising Fisher Information matrix(FIM) and its inverse(IFIM). Additionally, the impact of stability on the existence of IFIM and explore the geodesic equations of motion has been revealed. More potentially, the paper discusses some info-geometric applications to Machine Learning are highlighted. Closing remarks with some challenging open problems combined with the next phase of research are given.

A particular challenge in the conceptual design of direct-from orbit delivery systems is the seemingly well-known kinematics retain fallacies whose efficacies are reduced over great distances. Rotation about the local wing of an aerospace vehicle is almost never the pitch angle, yet modern application of kinematics often assumes such (with accompanying angular error). The same assertion is usually true about the nature of roll and yaw angles. Expressing motion in coordinates of rotating reference frames necessitates transformation between reference frames, and one such transformation is embodied in the Direction Cosine Matrices (DCM) formed by a sequence of three successive frame rotations. One of two ubiquitous sequences of three rotations used to construct the DCM involves first a rotation around the inertial z-axis, then intermediate y-axis, then finally about the body’s x-axis; a sequence commonly called the “aerospace sequence” or the a “3-2-1 rotation sequence”. The second ubiquitous sequence is the so-called “orbital sequence” or “3-1-3 rotation sequence” with rotations about the inertial z axis first, then about the intermediate x-axis, then finally about the body z-axis. This manuscript evaluates which sequence is the most advantageous for an object starting in space and then travels through the atmosphere to a target on the Earth’s surface. Six degrees of freedom of vehicle motion were simulated starting in orbit with a given thrust and commanded maneuver. The simulation performs all twelve possible rotation sequences (transforming inertial coordinates to body coordinates) with comparison by computational burden and error representing rotations about body axes (roll, pitch, and yaw respectively). Simulation precision is validated using the quaternion normalization condition indicating near machine precision (0.9\times{10}^{-15}) and reveals the so-called 132 rotation is the most accurate with an average error of 0.14° and a computational time of 0.013 seconds: resulting in a 97.95% increase in accuracy over the so-called 321 rotation and a 99.84% increase over the so-called 313 rotation.

From a differential geometric perspective, information geometry (IG) aims to characterise the structure of statistical geodesic models. The research done for this paper offers a novel method for modelling the information geometry of a queuing system. From the perspective of IG, the manifold of the transient M/M/infinity queue is described in this context. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of transient M/M/infinity QM are devised. In addition to that, new results that uncovered the significant impact of stability of QM on the existence of (IFIM) are obtained. Moreover, the Geodesic equations of motion of the coordinates of the underlying transient are obtained. Also, it is revealed that stable QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of transient M/M/iInfinity queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability(instability) phases of M/M/Infinity QM. Furthermore, a new discovery that presents the significant impact of stability of queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. Also, it is shown that stability of the devised (IME) enforces the instability of M/M/ Infinity QM. More interestingly, novel relativistic info-geometric queueing theoretic links are revealed .

This paper delves into the intricate nature of the different essence interactions that shape our perceived reality, leveraging a blend of existing empirical data and original experiments. Through a multidisciplinary approach encompassing quantum mechanics, general physics, metaphysics, philosophy, and spiritualism, it seeks to elucidate the fundamental interplays governing phenomena such as gravity, mass, electromagnetism, force, motion, and quantum mechanics. This exploration promises a reexamination and unification of these principles, offering novel perspectives on the extraordinary phenomena that underpin our reality. By comprehending and manipulating these interactions, the potential arises to orchestrate reality towards desired ends. This study not only unveils compelling avenues for scientific advancement but also proposes transformative technologies and concepts, including light-speed transportation, remote viewing, communication with the deceased, alchemy, and the realization of what is commonly perceived as magic. These visionary notions not only push the boundaries of current understanding but also provide a captivating glimpse into the future possibilities that may await humanity.

We delve into nonrelativistic quantum electrodynamics within a background magnetic field, ensuring gauge invariance via a vector potential. Our exploration extends to the Lagrangian, which incorporates electron self-interactions and electromagnetic field interactions. Through the path integral formalism, we elucidate the effective action, with a specific focus on the photon propagator and screening effects. Examining density and current components reveals Laurent expansions in the hydrodynamic limit. The equations of motion in real space are derived, leading to discussions on phenomena such as Poiseuille-like flow and the Navier-Stokes equation. To ground our theoretical framework at practical contexts, we consider applications such as the fluid dynamics at binary star systems. Depending on the velocity of the expelled fluid, our analysis allows for both nonrelativistic and relativistic treatments, providing a versatile tool for understanding the intricacies of fluid behavior at astrophysical scenarios. Additionally, we recognize that at the presence of a magnetic field, magnetohydrodynamics becomes crucial. While our current focus is at nonrelativistic quantum electrodynamics, the insights gained here contribute to a broader understanding, offering a comprehensive foundation for quantum electrodynamics analysis at diverse physical systems.

This paper delves into the intricate nature of the different essence interactions that shape our perceived reality, leveraging a blend of existing empirical data and original experiments. Through a multidisciplinary approach encompassing quantum mechanics, general physics, metaphysics, philosophy, and spiritualism, it seeks to elucidate the fundamental interplays governing phenomena such as gravity, mass, electromagnetism, force, motion, and quantum mechanics. This exploration promises a reexamination and unification of these principles, offering novel perspectives on the extraordinary phenomena that underpin our reality. By comprehending and manipulating these interactions, the potential arises to orchestrate reality towards desired ends. This study not only unveils compelling avenues for scientific advancement but also proposes transformative technologies and concepts, including light-speed transportation, remote viewing, communication with the deceased, alchemy, and the realization of what is commonly perceived as magic. These visionary notions not only push the boundaries of current understanding but also provide a captivating glimpse into the future possibilities that may await humanity.