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In this research, linear programming is the chosen method for optimizing aircraft center of gravity. The method was tested on the Airbus A320 and Boeing 757 aircraft. In order to successfully accommodate the special company requests, certain modifications are applied. Formulation of the proposed method enables the use of real data for the passenger and cabin baggage weight, instead of statistical values which are commonly used. The proposed method is simple to use, modify, upgrade or apply in existing systems.

This paper addresses the center of gravity doctrine; this doctrine is applicable to some wars, at some moments, but not to all of them. Clausewitz predictedthis and stated that “in war the result is never final”. We argue that attacking one party’s center of gravity results in its defeat only when both adversaries apply the same strategy, namely the classic war. Today, finding the center of gravity is an integral part of the planning process.

This paper presents examination of a proposed method for center of gravity (COG) velocity estimation during walking using information obtained from lower limb motion measurements. Lower limb joints and muscles around these joints are used during walking. Gait velocity changes according to lower limb muscle activity. Some earlier reports of relevant studies have suggested that lower limb muscle weakness reduces the walking rate, which increases the probability of falling. Therefore, the relation between the COG velocity and lower limb motion during walking must be clarified. For this study, we constructed gait COG velocity models that represent the relation between the COG velocity and lower limb joint power for each gait phase. For this experiment, gait was measured using a 3D motion analysis system and floor reaction force gauges. We estimated the gait COG velocity models’ parameters by applying Kalman filtering using measurement information. The results of analyses using gait COG velocity models indicate a quantitative relation between the COG velocity and the lower limb joint power during walking. Furthermore, results demonstrated that the lower limb joint power that influences the COG movement differs in each gait phase. This analytical method is anticipated for use in the evaluation of healthy feet and ill feet and for evaluating the balance of left and right feet.

Background:  It has already been demonstrated by previous studies that Baduanjin training can improve the body's balance. However, its biomechanical mechanism remains unknown. Center of gravity (COG) trajectory analysis is an essential biomechanical test to explore the balance ability of the human body. Previous studies have not used the COG trajectory analysis technique to research Baduanjin training. The study utilizes COG trajectory analysis to analyze the trajectory of COG during Baduanjin training and compare it with that of walking, which is a common exercise for improving balance and aerobic ability, to determine if Baduanjin exercises affect the COG more than walking., Materials and Methods:  Eight healthy female college students performed the walking and the eight forms of Baduanjin, a total of nine motions. The lower body kinematics were captured by the Vicon Motion Capture and Analysis System, while the kinetic data were acquired by the Kistler 3D Force Platform. The data were imported into Visual 3D to process the trajectory of the COG displacement amplitude, velocity, and acceleration of each motion. The COG horizontal envelope areas were calculated by Origin 9.0 Software (Origin Lab, Northampton, Massachusetts, USA) ., Results: Specific motions of Baduanjin provided significantly higher COG displacement amplitude, velocities, and acceleration training than walking. The F2 and F5 motions could provide a larger COG horizontal envelope area than walking. On the x-axis, F2 provided a greater COG displacement amplitude than walking, F1, F2, and F5 provided greater velocities, while all the motions provided greater accelerations. On the y-axis, all the motions except F2 provided greater COG displacement velocities and accelerations than walking. On the z-axis, F1-7 provided a greater COG displacement amplitude than walking, all the motions provided greater velocities, while all the motions except F2 provided greater accelerations., Conclusion: Baduanjin training provides a more intense COG perturbation than walking, which may be a more challenging balance training than walking., Competing Interests: The authors have declared that no competing interests exist., (Copyright © 2024, Jiang et al.)

Background: Myopia, a condition affecting approximately one-quarter of the world' s population, has been projected to double in prevalence by the year 2050. It can have an impact on postural control during walking and can increase the risk of falls and injuries., Objective: (1) To examine the abnormal performance of postural control during walking in male college students who used convex lenses for myopia intervention from a kinematic perspective; (2) to establish theoretical foundation for preventing falls and injuries in the myopic population., Methods: A total of 22 male college students participated in this study. The center of gravity (COG), the percentage of gait cycle (PGC) and the joint angle(JT) were collected as indications of postural control during walking. A quantitative analysis was conducted using a One-Way Repeated Measures ANOVA to examine the variations among the three groups., Results: During myopic interventions, (1) the range of vertical COG changes is significant to be greater compared with normal vision ( P < 0.05). (2) there was an significant increase in the PGC in single-legged support, accompanied by a decrease in the PGC in double-legged support, compared with normal vision ( P < 0.05). (3) The myopic intervention leads to increased variability in JT of the hip and the knee during the single-leg support and swing, as compared to individuals with normal vision ( P < 0.05). Severe myopic interventions result in more changes in JT of ankle., Conclusion: Myopia has been found to have a negative impact on postural control during walking, leading to changes in balance, increased instability, and an elevated risk of injury., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Xue, Zeng, Wang, Han and Pang.)

We construct the world's centres of gravity for human population, GDP and CO2 emissions by taking the best out of five recognised data sources covering the last two centuries. On the basis of a novel distortion‐free representation of these centres of gravity, we find a radical Western shift of GDP and CO2 emission centres in the nineteenth century, in sharp contrast with the stability of the demographic centre of gravity. Both GDP and emissions trends are reversed in the first half of the twentieth century, after World War I for CO2 emissions, after World War II for GDP. Since then, both centres are moving eastward at an accelerating speed. These patterns are perfectly consistent with the lead of Western countries starting the industrial revolution, the gradual replacement of coal by oil and gas as alternative sources of energy and the progressive catch‐up of Asian countries in the recent past. [ABSTRACT FROM AUTHOR]

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Measuring the mass and Center of Gravity (CG) of rigid bodies with a multi-point weighing method is widely used nowadays. Traditional methods usually include two parts with a certain location, i.e., a fixed platform and a mobile platform. In this paper, a novel structure is proposed to adjust the mobile platform for eliminating side forces which may load on the load cells. In addition, closed-form equations are formulated to evaluate the performance of the structure, and transformation matrices are used to estimate the characteristics of the structure. Simulation results demonstrate that repeatability of the proposed structure is higher than the traditional one and there are no side forces. Moreover, the measurement results show that the relative error of mass was within 0.05%, and the error of CG was within ±0.3 mm. The structure presented in this paper provides a foundation for practical applications. [ABSTRACT FROM AUTHOR]

In this paper, we examine the concept of center of gravity and its relationship to the concept of possibilistic mean. We propose new transformations between the center of gravity and the possibilistic mean for triangular and trapezoidal fuzzy numbers. [ABSTRACT FROM AUTHOR]

Abstract Diffusion MRI-based probabilistic tractography is a powerful tool for non-invasively investigating normal brain architecture and alterations in structural connectivity associated with disease states. Both voxelwise and region-of-interest methods of analysis are capable of integrating population differences in tract amplitude (streamline count or density), given proper alignment of the tracts of interest. However, quantification of tract differences (between groups, or longitudinally within individuals) has been hampered by two related features of white matter. First, it is unknown to what extent healthy individuals differ in the precise location of white matter tracts, and to what extent experimental factors influence perceived tract location. Second, white matter lacks the gross neuroanatomical features (e.g., gyri, histological subtyping) that make parcellation of grey matter plausible – determining where tracts "should" lie within larger white matter structures is difficult. Accurately quantifying tractographic connectivity between individuals is thus inherently linked to the difficulty of identifying and aligning precise tract location. Tractography is often utilized to study neurological diseases in which the precise structural and connectivity abnormalities are unknown, underscoring the importance of accounting for individual differences in tract location when evaluating the strength of structural connectivity. We set out to quantify spatial variance in tracts aligned through a standard, whole-brain registration method, and to assess the impact of location mismatch on groupwise assessments of tract amplitude. We then developed a method for tract alignment that enhances the existing standard whole brain registration, and then tested whether this method improved the reliability of groupwise contrasts. Specifically, we conducted seed-based probabilistic diffusion tractography from primary motor, supplementary motor, and visual cortices, projecting through the corpus callosum. Streamline counts decreased rapidly with movement from the tract center (−35% per millimeter); tract misalignment of a few millimeters caused substantial compromise of amplitude comparisons. Alignment of tracts "peak-to-peak" is essential for accurate amplitude comparisons. However, for all transcallosal tracts registered through the whole-brain method, the mean separation distance between an individual subject's tract and the average tract (3.2 mm) precluded accurate comparison: at this separation, tract amplitudes were reduced by 74% from peak value. In contrast, alignment of subcortical tracts (thalamo-putaminal, pallido-rubral) was substantially better than alignment for cortical tracts; whole-brain registration was sufficient for these subcortical tracts. We demonstrated that location mismatches in cortical tractography were sufficient to produce false positive and false negative amplitude estimates in both groupwise and longitudinal comparisons. We then showed that our new tract alignment method substantially reduced location mismatch and improved both reliability and statistical power of subsequent quantitative comparisons. Highlights • Both location and amplitude are key when quantifying probabilistic tractography. • In callosal tracts, location mismatch reduces streamline density by up to 8.9-fold. • Mismatches in tract location compromise both voxelwise and groupwise comparisons. • Tract-to-tract registration reduces both false positive and false negative results. • Between-subjects variability in tract location explained 55% of tract mismatch. [ABSTRACT FROM AUTHOR]

Highlights • Using markerless motion capture system, the COG during sit-to-stand motion was measured. • The COG was compared with the measured value of marker-based motion capture system. • There were significant differences in COG displacement between system. • However, there was no difference in velocity and acceleration in the anteroposterior direction. Abstract Purpose In order to evaluate the movement strategy in sit-to-stand (STS) motion, it is necessary to measure the center of gravity (COG). However, there is no established method for enabling this using convenience device in the clinical setting. The purpose of this study was to validate the measurement of the COG during the STS motion using an inexpensive, portable and markerless motion capture system (MLS). Method Eighteen healthy adults participated in our study. The coordinates of the joint centers during the STS motion were collected using the Microsoft Kinect system (as a MLS) and the Vicon system (as a marker-based motion capture system [MBS]). The center of mass of each segment—which was calculated based on the segmental mass and length—were synthesized to calculate the COG. The displacement, velocity, acceleration of the COG during the STS motion were calculated from the data obtained using each system and compared between systems. Results The two systems showed significant difference in their measurements of displacement in both the vertical and anteroposterior directions. However, in the anteroposterior direction, there was no significant difference in the measurements of either velocity or acceleration. Conclusion Our results suggested the validity of the COG in the anteroposterior direction during the STS motion measured using the MLS. The method developed in the present study enables the evaluation of a patient's movement strategy. [ABSTRACT FROM AUTHOR]

We propose a horizontal-pendulum type thrust stand in which two-point acceleration measurement is applied to the null-balance method. The conventional displacement method was been applied to thrust measurement; thrust is determined by pendulum displacement which is caused by thrust. The null-balance method is also applied to the thrust measurement; a controller adjusts actuator force on the basis of pendulum displacement so as to null the pendulum displacement, and thrust is determined from actuator-driving current or voltage. However, both measurement methods can evaluate thrust variation up to one-third of the natural frequency that is determined by the configuration of the controller and pendulum. Hence, we proposed to apply acceleration measurement to the null-balance method, and showed that thrust variation could be measured up to 80 Hz. However, the proposed methods showed errors beyond 80 Hz; the error was caused by the translational flexibility of the torsional hinges. Then, we propose a new method that uses two-point acceleration measurement and adjustment of the center of gravity position to evaluate thrust variation beyond 80 Hz. The prototype evaluated thrust variation accurately beyond 200 Hz, although at 20-160 Hz, underestimating the amplitudes of reference thrust by 50 %. [ABSTRACT FROM AUTHOR]

Abstract Dirty industries tend to relocate to regions with looser environmental regulations, thus turning those regions into pollution havens. Numerous studies have tested the pollution haven effect of inter-country industrial relocation. However, little attention has been paid to the effect that is hidden in domestic industry relocation. Considering that domestic investment is about 10-fold that of foreign investment, it is vital to examine this issue to ensure the achievability of China's international pledge of mitigating carbon emissions. This research integrated multiregional input-output analysis and a center of gravity model to visualize the dislocation between carbon emissions, value added, and outputs at a sectoral level from 2007 to 2012 in China. Carbon emissions were also decomposed to three segments of final demand. We also investigated the movement of the center of gravity of these segments, and their dislocation with the outputs. Our analysis found that more carbon emissions had relocated from east to west with domestic industry relocation, yet the opposite was found for value added. Specifically, carbon intensive sectors showed clear tendencies of shifting west. Capital formation was the major cause of the pollution haven effects for the economy as a whole. Thus, our results suggest that pollution haven effects exist in the relocation processes of most sectors. In turn, our findings support the idea that mitigation policies should differ by region and by industry. Our recommendations include a negative list for regions in the west, a mitigation policy for industries with high pollution, and differentiated supply chain management for final demands. Graphical abstract Image Highlights • MRIO and center of gravity are used to visualize the pollution haven effect. • Center of gravity is decomposed by final demand categories. • Most industries moving to the north and the west have pollution haven effect. • Capital formation is the major cause of pollution haven effect. [ABSTRACT FROM AUTHOR]

Abstract In this paper we show that for a Berger metric g ˆ on S 3 , the non-positively curved conformally compact Einstein metric on the 4-ball B 1 (0) with (S 3 , [ g ˆ ]) as its conformal infinity is unique up to isometries and it is the metric constructed by Pedersen [21]. In particular, since in [18] , we proved that if the Yamabe constant of the conformal infinity Y (S 3 , [ g ˆ ]) is close to that of the round sphere then any conformally compact Einstein manifold filled in must be negatively curved and simply connected, therefore if g ˆ is a Berger metric on S 3 with Y (S 3 , [ g ˆ ]) close to that of the round metric, the conformally compact Einstein metric filled in is unique up to isometries. [ABSTRACT FROM AUTHOR]

Abstract This paper presents the CoG-FPOM, an adaptation of the Fuzzy Pay-Off Method (FPOM). The FPOM is a scenario-based real option valuation method that uses fuzzy numbers as possibility distributions. The paper shows that there are situations in which the original FPOM calculates the real option value to be negative, what is theoretically incorrect. The cause is related to the method used for obtaining a single representative value out of a fuzzy number. Instead of the possibilistic expected value operation used in the original FPOM, the CoG-FPOM uses the center of gravity (CoG) to accomplish the task – a proof of its general validity is presented. An application to calculate the abandonment real option for petroleum producing fields shows that the proposal can be easily used for project valuation under uncertainty. [ABSTRACT FROM AUTHOR]

Tropical cyclones (TC) prediction and intensity detection is one of the most emerging fields of research. Starting from Dvorak technique many approaches are used by meteorologist towards the TC intensity prediction and estimation. In this paper we have proposed an image processing based approach to categorise the cyclone intensity by using feature vector. The feature vector of a TC constructed using mean, variance, density and decentricity. Further, this vector converges to a distinct weight value by random weight genetic algorithm. Finally weight values under each intensity scale are used to find the intensity of a test image. This approach can be used in cyclone intensity detection technique. This paper focuses on estimate the intensity of tropical cyclones from satellite images over the Bay of Bengal. [ABSTRACT FROM AUTHOR]

Objective: The main objective of the tests conducted was to analyze the position variability of the human body’s center of gravity during propelling the wheelchair, and to demonstrate the properties enabling the description of this variability by means of plane figures with a symmetry axis. A secondary objective was to show the impact of the used manual propulsion type and the wheelchair inclination angle in relation to the plane on the dimensions of the position variability areas of the center of gravity. Method and materials: Three patients participated in the research representing 50 centiles of anthropometric dimensions. Each patient carried out fifteen measurement tests on three wheelchairs for three inclination angles of the wheelchair frame in relation to the level. Each measurement test consisted of five propulsion cycles for which the positions of the center of gravity were determined with the sampling frequency of 100 Hz. The measured positions of the center of gravity were approximated with ellipses containing 95.4% of the measurements conducted, assuming their dimension scaling basis in the form of the double value of standard deviation defined based on the registered results. Results: Based on the measurements conducted, the average values of five ellipses parameters were determined for nine cases in which a variable was the type of wheelchair propulsion and its inclination angle in relation to the level. The area of the highest variability of the position of the center of gravity was measured for the wheelchair with a multispeed transmission. The average dimensions of the ellipse semi-axis amounted to 108.53 mm for the semi-axis a and 29.75 for the semi-axis b, the average position of the ellipse center amounted to x = 114.51 mm and y = −10.53 mm, and the average inclination angle of the ellipse α amounted to −6.92°. The area of the lowest variability of the position of the center of gravity was measured for the wheelchair with a hybrid transmission. In this case, the average dimensions of the ellipse semi-axis amounted to 64.07 mm for the semi-axis a and 33.85 for the semi-axis b; whereas, the average position of the ellipse center amounted to x = 245.13 mm and y = −28.24 mm, and the average inclination angle of the ellipse α amounted to −0.56°.

• Power system dynamic equivalents play an important role in studying system-wide phenomena in large, interconnected power systems. • Equivalent model representations may result in a fast and efficient simulation of system behavior. • Data-driven approaches based on measured data, in which variability of sources is inherently considered, provide complementary information to model-based simulations are introduced. • This paper investigates the ability of the COG-based equivalent model to assess both, small- and large-signal frequency behavior. In this paper, a unified framework to study small- and large-signal frequency response based on the notion of center-of-gravity (COG)-based dynamic equivalents is presented. The method combines the ability of COG equivalents to capture short-term system response with that of unsupervised probabilistic learning techniques to extract the (slow) dominant oscillation patterns associated with observational data. First, a reduced-order representation is obtained in which the overall system dynamics is represented by the interaction of geographical or coherent areas with a virtual COG at which the total system power equations are at balance. Then, a small-signal representation is derived from which key linear relationships between the frequency of the local centers of inertia (COIs) and the COG are determined. Next, the physical properties of the model are studied, and alternative procedures to compute COG equivalents are explored. Finally, the effectiveness of the developed models is demonstrated through applications to two sample systems, thereby verifying their accuracy. [ABSTRACT FROM AUTHOR]

• The feasibility of weight and center-of-gravity estimation based on the aircraft trim data is qualitatively analyzed, and the trim data calculation method for the aircraft with variable center of mass is introduced. • On the basis of the aircraft trim data, a novel estimation method for aircraft weight and the longitudinal center-of-gravity position via inverse interpolation is presented. • An improved moving average filter is introduced to eliminate the adverse effect on estimation results caused by the high-frequency noise of airborne sensors. • Some simulations are operated, and the impact of the weight estimation error and the elevator deflection measurement error on the estimation result of center-of-gravity is discussed. Aircraft weight and center-of-gravity are significant parameters that affect flight stability and controllability, and unreasonable CG position may cause serious flight accidents. However, there is no airborne sensor can directly measure aircraft weight and center-of-gravity. In view of this, a novel estimation method for weight and center-of-gravity via the aircraft trim data is introduced. Specifically, the trim data calculation process for the aircraft with variable center of mass is given. Then, an inverse interpolation approach based on the binary search algorithm is presented to estimate the aircraft weight and center-of-gravity, and an improved moving average filter is introduced to eliminate the adverse effect on estimation results caused by the high-frequency noise of airborne sensors. Some simulations are given to demonstrate the validity of the proposed estimation method, and it can be drawn from the result that the aircraft longitudinal CG position estimation error is within 0.05 %MAC. [ABSTRACT FROM AUTHOR]

This article presents a study of measures of center of gravity (COG) in phrase-final fricative epithesis (PFFE) produced by L1 and L2 speakers of Continental French (CF). Participants completed a reading task targeting 98 tokens of /i,y,u/ in phrase-final position. COG measures were taken at the 25%, 50% and 75% marks, normalized and submitted to a mixed linear regression. Results revealed that L2 speakers showed higher COG values than L1 speakers in low PFFE-to-vowel ratios at the 25%, 50%, and 75% marks. COG measures were then categorized into six profile types on the basis of their frequencies at each timepoint: flat–low, flat–high, rising, falling, rising–falling, and falling–rising. Counts of COG profile were then submitted to multinomial logistic regression. Results revealed that although L1 speakers produced predominantly flat–low profile types at lower percent devoicings, L2 speakers preferred multiple strategies involving higher levels of articulatory energy (rising, falling, rise–fall). These results suggest that while L1 speakers realize PFFE differently with respect to phonological context, L2 speakers rely on its most common allophone, strong frication, in most contexts. As such, the findings of this study argue for an additional phonetic dimension in the construct of L2 sociophonetic competence.

The center of mass of a given system is referred to as a position that is the average of all of its components. I am given two cases in which I need to find the center of mass for the problem of flipping over an incline. To solve the problem given, I utilize many equations that are derived to find the center of mass of both cases and then test each system when it is encountered with three different inclines increasing by fifteen degrees increments. The tests prove that the probability that a system will flip on an incline is due to many factors, the main of them being the height of the system, the area of support, as well as the weight of the system. This method of solving is not the most time-efficient one to find the center of mass and flipping probability; however, it does work and gives a viable solution.

The article discusses a case study at a company that works on Fast Moving Consumer Goods (FMCG) section using B2B distribution system, and is conducting a market test for its new alternative tobacco products using B2C distribution system. The purpose of this study is to determine both number and location of warehouses that provides a minimum total logistics costs for the B2C process, where the company is currently still using company-owned B2B warehouses. Determination of the number and location of these warehouses is performed using Agglomerative Hierarchical Clustering where grouping is based on the shortest distance and is done using Evolutionary Solver. Centre of Gravity is also used to determine the location of the warehouses. Iteration will be carried out to obtain the number of warehouses that provide minimal total cost. The result of the modelling shows that the optimal number of warehouses is six and each warehouse will have their own market division.

Due to the growing elderly population in many developed countries like Japan, assistive devices are increasingly needed to overcome the difficulties of their activities of daily living (ADL). The motion of standing up places a particular burden on the ankle and knee joints and connects static motions (e.g., sitting and lying) and kinetic motions (e.g., walking and climbing up/down the stairs). In our previous research, two types of standing-up assistance apparatuses were introduced according to the suitable standing-up motions. However, these devices are bulky and cannot be widely used in practical settings such as bus terminals. Regarding the suitable standing-up motions of the elderly in the previous literature, a standing-up apparatus with a pantograph mechanism is introduced to diminish the size of the mechanism based on three design principles: (1) the trajectory of the user's COG is an arc; (2) the trajectory of the user's hip joint while standing up is a straight line at an angle of 45 [deg] from the horizon; and (3) the user is supported until the knee angle reaches 60 [deg]. Simulations showed that the load on knee and ankle joint is decreased, and user may stand up easily with our proposed apparatus. A prototype of the apparatus that may be installed on various chairs in public was fabricated. Considering that the apparatus may be used in places without electric power supply, the apparatus is made simply with links and a gas spring instead of electric actuators. Experimental measurements of the trajectories of the center of gravity (COG) and hip joints show that the proposed apparatus may help users to stand in a way that minimizes stress on their lower-body joints.